@noble/curves - npm Package Compare versions

Comparing version 1.9.5 to 1.9.6

abstract/bls.d.ts

@@ -29,5 +29,5 @@ /**
     toBytes(point: WeierstrassPoint<Fp>): Uint8Array;
+    toHex(point: WeierstrassPoint<Fp>): string;
     /** @deprecated use `toBytes` */
     toRawBytes(point: WeierstrassPoint<Fp>): Uint8Array;
-    toHex(point: WeierstrassPoint<Fp>): string;
 };
@@ -38,5 +38,5 @@ export type SignatureCoder<Fp> = {
     toBytes(point: WeierstrassPoint<Fp>): Uint8Array;
+    toHex(point: WeierstrassPoint<Fp>): string;
     /** @deprecated use `toBytes` */
     toRawBytes(point: WeierstrassPoint<Fp>): Uint8Array;
-    toHex(point: WeierstrassPoint<Fp>): string;
 };
@@ -43,0 +43,0 @@ export type BlsFields = {

abstract/bls.d.ts.map

@@ -1,1 +0,1 @@
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+{"version":3,"file":"bls.d.ts","sourceRoot":"","sources":["../src/abstract/bls.ts"],"names":[],"mappings":"AAAA;;;;;;;;;;;;;;;IAeI;AACJ,sEAAsE;AACtE,OAAO,EAKL,KAAK,KAAK,EACV,KAAK,GAAG,EACR,KAAK,OAAO,EACb,MAAM,aAAa,CAAC;AAErB,OAAO,EAEL,KAAK,SAAS,EACd,KAAK,WAAW,EAChB,KAAK,OAAO,EAEZ,KAAK,YAAY,EACjB,KAAK,UAAU,EAChB,MAAM,oBAAoB,CAAC;AAC5B,OAAO,EAAoC,KAAK,MAAM,EAAE,MAAM,cAAc,CAAC;AAC7E,OAAO,KAAK,EAAE,IAAI,EAAE,OAAO,EAAE,GAAG,EAAE,MAAM,EAAE,MAAM,EAAE,MAAM,YAAY,CAAC;AACrE,OAAO,EAGL,KAAK,cAAc,EACnB,KAAK,eAAe,EACpB,KAAK,gBAAgB,EACrB,KAAK,oBAAoB,EAC1B,MAAM,kBAAkB,CAAC;AAE1B,KAAK,EAAE,GAAG,MAAM,CAAC;AAKjB,MAAM,MAAM,SAAS,GAAG,gBAAgB,GAAG,UAAU,CAAC;AAEtD,MAAM,MAAM,mBAAmB,CAAC,EAAE,IAAI;IACpC,SAAS,CAAC,KAAK,EAAE,UAAU,GAAG,gBAAgB,CAAC,EAAE,CAAC,CAAC;IACnD,OAAO,CAAC,GAAG,EAAE,GAAG,GAAG,gBAAgB,CAAC,EAAE,CAAC,CAAC;IACxC,OAAO,CAAC,KAAK,EAAE,gBAAgB,CAAC,EAAE,CAAC,GAAG,UAAU,CAAC;IACjD,KAAK,CAAC,KAAK,EAAE,gBAAgB,CAAC,EAAE,CAAC,GAAG,MAAM,CAAC;IAC3C,gCAAgC;IAChC,UAAU,CAAC,KAAK,EAAE,gBAAgB,CAAC,EAAE,CAAC,GAAG,UAAU,CAAC;CACrD,CAAC;AAEF,MAAM,MAAM,cAAc,CAAC,EAAE,IAAI;IAC/B,SAAS,CAAC,KAAK,EAAE,UAAU,GAAG,gBAAgB,CAAC,EAAE,CAAC,CAAC;IACnD,OAAO,CAAC,GAAG,EAAE,GAAG,GAAG,gBAAgB,CAAC,EAAE,CAAC,CAAC;IACxC,OAAO,CAAC,KAAK,EAAE,gBAAgB,CAAC,EAAE,CAAC,GAAG,UAAU,CAAC;IACjD,KAAK,CAAC,KAAK,EAAE,gBAAgB,CAAC,EAAE,CAAC,GAAG,MAAM,CAAC;IAC3C,gCAAgC;IAChC,UAAU,CAAC,KAAK,EAAE,gBAAgB,CAAC,EAAE,CAAC,GAAG,UAAU,CAAC;CACrD,CAAC;AAEF,MAAM,MAAM,SAAS,GAAG;IACtB,EAAE,EAAE,MAAM,CAAC,EAAE,CAAC,CAAC;IACf,EAAE,EAAE,MAAM,CAAC,MAAM,CAAC,CAAC;IACnB,GAAG,EAAE,MAAM,CAAC;IACZ,GAAG,EAAE,MAAM,CAAC;IACZ,IAAI,EAAE,OAAO,CAAC;CACf,CAAC;AAEF,MAAM,MAAM,wBAAwB,GAAG,CACrC,EAAE,EAAE,GAAG,EACP,EAAE,EAAE,GAAG,EACP,EAAE,EAAE,GAAG,EACP,EAAE,EAAE,GAAG,EACP,EAAE,EAAE,GAAG,KACJ;IAAE,EAAE,EAAE,GAAG,CAAC;IAAC,EAAE,EAAE,GAAG,CAAC;IAAC,EAAE,EAAE,GAAG,CAAA;CAAE,CAAC;AACnC,MAAM,MAAM,gBAAgB,GAAG,CAC7B,EAAE,EAAE,GAAG,EACP,EAAE,EAAE,GAAG,EACP,EAAE,EAAE,GAAG,EACP,EAAE,EAAE,GAAG,EACP,EAAE,EAAE,GAAG,EACP,QAAQ,EAAE,wBAAwB,KAC/B,IAAI,CAAC;AACV,MAAM,MAAM,UAAU,GAAG;IACvB,IAAI,EAAE,OAAO,CAAC;IACd,sBAAsB,EAAE,CAAC,CAAC,EAAE,gBAAgB,CAAC,GAAG,CAAC,KAAK,UAAU,CAAC;IACjE,eAAe,EAAE,CAAC,KAAK,EAAE,CAAC,UAAU,EAAE,EAAE,EAAE,EAAE,CAAC,EAAE,KAAK,IAAI,CAAC;IACzD,OAAO,EAAE,CAAC,CAAC,EAAE,gBAAgB,CAAC,EAAE,CAAC,EAAE,CAAC,EAAE,gBAAgB,CAAC,GAAG,CAAC,EAAE,iBAAiB,CAAC,EAAE,OAAO,KAAK,IAAI,CAAC;IAClG,YAAY,EAAE,CACZ,KAAK,EAAE;QAAE,EAAE,EAAE,gBAAgB,CAAC,EAAE,CAAC,CAAC;QAAC,EAAE,EAAE,gBAAgB,CAAC,GAAG,CAAC,CAAA;KAAE,EAAE,EAChE,iBAAiB,CAAC,EAAE,OAAO,KACxB,IAAI,CAAC;CACX,CAAC;AAEF,MAAM,MAAM,gBAAgB,GAAG;IAI7B,WAAW,EAAE,MAAM,CAAC;IACpB,SAAS,EAAE,OAAO,CAAC;IACnB,SAAS,EAAE,SAAS,CAAC;IAErB,cAAc,CAAC,EAAE,gBAAgB,CAAC;CACnC,CAAC;AACF,MAAM,MAAM,SAAS,GAAG;IACtB,EAAE,EAAE,eAAe,CAAC,EAAE,CAAC,GAAG;QACxB,cAAc,EAAE,cAAc,CAAC,EAAE,CAAC,CAAC;QACnC,UAAU,EAAE,UAAU,CAAC,EAAE,CAAC,CAAC;QAC3B,WAAW,EAAE,OAAO,CAAC;KACtB,CAAC;IACF,EAAE,EAAE,eAAe,CAAC,GAAG,CAAC,GAAG;QACzB,SAAS,EAAE,cAAc,CAAC,GAAG,CAAC,CAAC;QAC/B,UAAU,EAAE,UAAU,CAAC,GAAG,CAAC,CAAC;QAC5B,WAAW,EAAE,OAAO,CAAC;KACtB,CAAC;IACF,MAAM,EAAE,SAAS,CAAC;IAClB,MAAM,EAAE;QAIN,WAAW,EAAE,gBAAgB,CAAC,aAAa,CAAC,CAAC;QAC7C,SAAS,EAAE,gBAAgB,CAAC,WAAW,CAAC,CAAC;QACzC,CAAC,EAAE,MAAM,CAAC;QACV,SAAS,EAAE,gBAAgB,CAAC,WAAW,CAAC,CAAC;KAC1C,CAAC;IACF,WAAW,EAAE,OAAO,CAAC;IACrB,IAAI,EAAE,KAAK,CAAC;IACZ,WAAW,CAAC,EAAE,CAAC,WAAW,CAAC,EAAE,MAAM,KAAK,UAAU,CAAC;IAEnD,cAAc,CAAC,EAAE,gBAAgB,CAAC;CACnC,CAAC;AAEF,KAAK,gBAAgB,GAAG,CAAC,GAAG,EAAE,GAAG,EAAE,GAAG,CAAC,EAAE,CAAC;AAC1C,KAAK,UAAU,GAAG,gBAAgB,EAAE,CAAC;AAErC;;;;GAIG;AACH,MAAM,WAAW,YAAY;IAC3B,cAAc,EAAE,OAAO,CAAC,MAAM,EAAE,GAAG,CAAC,CAAC;IACrC,eAAe,EAAE,OAAO,CAAC,GAAG,EAAE,MAAM,CAAC,CAAC;IACtC,eAAe,EAAE,UAAU,CAAC,iBAAiB,CAAC,CAAC;IAC/C,OAAO,EAAE,UAAU,CAAC,SAAS,CAAC,CAAC;IAC/B,YAAY,EAAE,UAAU,CAAC,cAAc,CAAC,CAAC;IACzC,EAAE,EAAE;QAAE,KAAK,EAAE,oBAAoB,CAAC,MAAM,CAAC,CAAA;KAAE,GAAG,SAAS,CAAC,EAAE,CAAC,CAAC;IAC5D,EAAE,EAAE;QAAE,KAAK,EAAE,oBAAoB,CAAC,GAAG,CAAC,CAAA;KAAE,GAAG,SAAS,CAAC,GAAG,CAAC,CAAC;IAC1D,MAAM,EAAE;QACN,EAAE,EAAE,MAAM,CAAC,EAAE,CAAC,CAAC;QACf,GAAG,EAAE,MAAM,CAAC;QACZ,GAAG,EAAE,MAAM,CAAC;QACZ,IAAI,EAAE,OAAO,CAAC;QACd,EAAE,EAAE,MAAM,CAAC,MAAM,CAAC,CAAC;KACpB,CAAC;IACF,KAAK,EAAE;QACL,eAAe,EAAE,MAAM,UAAU,CAAC;QAClC,sCAAsC;QACtC,gBAAgB,EAAE,MAAM,UAAU,CAAC;QACnC,sBAAsB,EAAE,UAAU,CAAC,wBAAwB,CAAC,CAAC;KAC9D,CAAC;CACH;AAED,MAAM,MAAM,OAAO,GAAG,YAAY,GAAG;IACnC,oDAAoD;IACpD,YAAY,EAAE,CAAC,SAAS,EAAE,OAAO,KAAK,UAAU,CAAC;IACjD,qDAAqD;IACrD,8BAA8B,EAAE,CAAC,SAAS,EAAE,OAAO,KAAK,UAAU,CAAC;IACnE,4CAA4C;IAC5C,IAAI,EAAE;QACJ,CAAC,OAAO,EAAE,GAAG,EAAE,SAAS,EAAE,OAAO,EAAE,OAAO,CAAC,EAAE,YAAY,GAAG,UAAU,CAAC;QACvE,CACE,OAAO,EAAE,gBAAgB,CAAC,GAAG,CAAC,EAC9B,SAAS,EAAE,OAAO,EAClB,OAAO,CAAC,EAAE,YAAY,GACrB,gBAAgB,CAAC,GAAG,CAAC,CAAC;KAC1B,CAAC;IACF,6CAA6C;IAC7C,kBAAkB,EAAE;QAClB,CAAC,OAAO,EAAE,GAAG,EAAE,SAAS,EAAE,OAAO,EAAE,OAAO,CAAC,EAAE,YAAY,GAAG,UAAU,CAAC;QACvE,CACE,OAAO,EAAE,gBAAgB,CAAC,EAAE,CAAC,EAC7B,SAAS,EAAE,OAAO,EAClB,OAAO,CAAC,EAAE,YAAY,GACrB,gBAAgB,CAAC,EAAE,CAAC,CAAC;KACzB,CAAC;IACF,8CAA8C;IAC9C,MAAM,EAAE,CACN,SAAS,EAAE,GAAG,GAAG,gBAAgB,CAAC,GAAG,CAAC,EACtC,OAAO,EAAE,GAAG,GAAG,gBAAgB,C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abstract/curve.d.ts

@@ -68,5 +68,5 @@ import { type IField } from './modular.ts';
 export interface CurveLengths {
-    secret?: number;
-    public?: number;
-    publicUncompressed?: number;
+    secretKey?: number;
+    publicKey?: number;
+    publicKeyUncompressed?: number;
     publicKeyHasPrefix?: boolean;
@@ -73,0 +73,0 @@ signature?: number;

abstract/curve.d.ts.map

@@ -1,1 +0,1 @@
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abstract/edwards.d.ts

@@ -129,2 +129,8 @@ /**
          * Converts ed public key to x public key.
+         *
+         * There is NO `fromMontgomery`:
+         * - There are 2 valid ed25519 points for every x25519, with flipped coordinate
+         * - Sometimes there are 0 valid ed25519 points, because x25519 *additionally*
+         *   accepts inputs on the quadratic twist, which can't be moved to ed25519
+         *
          * @example
@@ -184,4 +190,2 @@ * ```js
     toAffine(invertedZ?: bigint): AffinePoint<bigint>;
-    /** @deprecated use `toBytes` */
-    toRawBytes(): Uint8Array;
     toHex(): string;
@@ -201,2 +205,4 @@ toString(): string;
     protected abstract init(ep: EdwardsPoint): T;
+    /** @deprecated use `toBytes` */
+    toRawBytes(): Uint8Array;
 }
@@ -203,0 +209,0 @@ /**

abstract/edwards.d.ts.map

@@ -1,1 +0,1 @@
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abstract/edwards.js

@@ -31,3 +31,3 @@ "use strict";
     let CURVE = validated.CURVE;
-    const { h: cofactor, n: CURVE_ORDER } = CURVE;
+    const { h: cofactor } = CURVE;
     (0, utils_ts_1._validateObject)(extraOpts, {}, { uvRatio: 'function' });
@@ -142,3 +142,3 @@ // Important:
             const max = zip215 ? MASK : Fp.ORDER;
-            (0, utils_ts_1.aInRange)('pointHex.y', y, _0n, max);
+            (0, utils_ts_1.aInRange)('point.y', y, _0n, max);
             // Ed25519: x² = (y²-1)/(dy²+1) mod p. Ed448: x² = (y²-1)/(dy²-1) mod p. Generic case:
@@ -151,3 +151,3 @@ // ax²+y²=1+dx²y² => y²-1=dx²y²-ax² => y²-1=x²(dy²-a) => x²=(y²-1)/(dy²-a)
             if (!isValid)
-                throw new Error('Point.fromHex: invalid y coordinate');
+                throw new Error('bad point: invalid y coordinate');
             const isXOdd = (x & _1n) === _1n; // There are 2 square roots. Use x_0 bit to select proper
@@ -157,3 +157,3 @@ const isLastByteOdd = (lastByte & 0x80) !== 0; // x_0, last bit
                 // if x=0 and x_0 = 1, fail
-                throw new Error('Point.fromHex: x=0 and x_0=1');
+                throw new Error('bad point: x=0 and x_0=1');
             if (isLastByteOdd !== isXOdd)
@@ -248,5 +248,6 @@ x = modP(-x); // if x_0 != x mod 2, set x = p-x
         multiply(scalar) {
-            const n = scalar;
-            (0, utils_ts_1.aInRange)('scalar', n, _1n, CURVE_ORDER); // 1 <= scalar < L
-            const { p, f } = wnaf.cached(this, n, (p) => (0, curve_ts_1.normalizeZ)(Point, p));
+            // 1 <= scalar < L
+            if (!Fn.isValidNot0(scalar))
+                throw new Error('invalid scalar: expected 1 <= sc < curve.n');
+            const { p, f } = wnaf.cached(this, scalar, (p) => (0, curve_ts_1.normalizeZ)(Point, p));
             return (0, curve_ts_1.normalizeZ)(Point, [p, f])[0];
@@ -260,9 +261,10 @@ }
         multiplyUnsafe(scalar, acc = Point.ZERO) {
-            const n = scalar;
-            (0, utils_ts_1.aInRange)('scalar', n, _0n, CURVE_ORDER); // 0 <= scalar < L
-            if (n === _0n)
+            // 0 <= scalar < L
+            if (!Fn.isValid(scalar))
+                throw new Error('invalid scalar: expected 0 <= sc < curve.n');
+            if (scalar === _0n)
                 return Point.ZERO;
-            if (this.is0() || n === _1n)
+            if (this.is0() || scalar === _1n)
                 return this;
-            return wnaf.unsafe(this, n, (p) => (0, curve_ts_1.normalizeZ)(Point, p), acc);
+            return wnaf.unsafe(this, scalar, (p) => (0, curve_ts_1.normalizeZ)(Point, p), acc);
         }
@@ -279,3 +281,3 @@ // Checks if point is of small order.
         isTorsionFree() {
-            return wnaf.unsafe(this, CURVE_ORDER).is0();
+            return wnaf.unsafe(this, CURVE.n).is0();
         }
@@ -294,10 +296,9 @@ // Converts Extended point to default (x, y) coordinates.
             const { x, y } = this.toAffine();
-            const bytes = (0, utils_ts_1.numberToBytesLE)(y, Fp.BYTES); // each y has 2 x values (x, -y)
-            bytes[bytes.length - 1] |= x & _1n ? 0x80 : 0; // when compressing, it's enough to store y
-            return bytes; // and use the last byte to encode sign of x
+            // Fp.toBytes() allows non-canonical encoding of y (>= p).
+            const bytes = Fp.toBytes(y);
+            // Each y has 2 valid points: (x, y), (x,-y).
+            // When compressing, it's enough to store y and use the last byte to encode sign of x
+            bytes[bytes.length - 1] |= x & _1n ? 0x80 : 0;
+            return bytes;
         }
-        /** @deprecated use `toBytes` */
-        toRawBytes() {
-            return this.toBytes();
-        }
         toHex() {
@@ -331,2 +332,5 @@ return (0, utils_ts_1.bytesToHex)(this.toBytes());
         }
+        toRawBytes() {
+            return this.toBytes();
+        }
     }
@@ -341,3 +345,4 @@ // base / generator point
     Point.Fn = Fn;
-    const wnaf = new curve_ts_1.wNAF(Point, Fn.BYTES * 8); // Fn.BITS?
+    const wnaf = new curve_ts_1.wNAF(Point, Fn.BITS);
+    Point.BASE.precompute(8); // Enable precomputes. Slows down first publicKey computation by 20ms.
     return Point;
@@ -378,6 +383,2 @@ }
     }
-    /** @deprecated use `toBytes` */
-    toRawBytes() {
-        return this.toBytes();
-    }
     toHex() {
@@ -418,2 +419,6 @@ return (0, utils_ts_1.bytesToHex)(this.toBytes());
     }
+    /** @deprecated use `toBytes` */
+    toRawBytes() {
+        return this.toBytes();
+    }
 }
@@ -435,6 +440,5 @@ exports.PrimeEdwardsPoint = PrimeEdwardsPoint;
     const { prehash } = eddsaOpts;
-    const { BASE: G, Fp, Fn } = Point;
-    const CURVE_ORDER = Fn.ORDER;
-    const randomBytes_ = eddsaOpts.randomBytes || utils_ts_1.randomBytes;
-    const adjustScalarBytes = eddsaOpts.adjustScalarBytes || ((bytes) => bytes); // NOOP
+    const { BASE, Fp, Fn } = Point;
+    const randomBytes = eddsaOpts.randomBytes || utils_ts_1.randomBytes;
+    const adjustScalarBytes = eddsaOpts.adjustScalarBytes || ((bytes) => bytes);
     const domain = eddsaOpts.domain ||
@@ -447,13 +451,9 @@ ((data, ctx, phflag) => {
         }); // NOOP
-    function modN(a) {
-        return Fn.create(a);
-    }
     // Little-endian SHA512 with modulo n
     function modN_LE(hash) {
-        // Not using Fn.fromBytes: hash can be 2*Fn.BYTES
-        return modN((0, utils_ts_1.bytesToNumberLE)(hash));
+        return Fn.create((0, utils_ts_1.bytesToNumberLE)(hash)); // Not Fn.fromBytes: it has length limit
     }
     // Get the hashed private scalar per RFC8032 5.1.5
     function getPrivateScalar(key) {
-        const len = lengths.secret;
+        const len = lengths.secretKey;
         key = (0, utils_ts_1.ensureBytes)('private key', key, len);
@@ -471,3 +471,3 @@ // Hash private key with curve's hash function to produce uniformingly random input
         const { head, prefix, scalar } = getPrivateScalar(secretKey);
-        const point = G.multiply(scalar); // Point on Edwards curve aka public key
+        const point = BASE.multiply(scalar); // Point on Edwards curve aka public key
         const pointBytes = point.toBytes();
@@ -492,9 +492,9 @@ return { head, prefix, scalar, point, pointBytes };
         const r = hashDomainToScalar(options.context, prefix, msg); // r = dom2(F, C) || prefix || PH(M)
-        const R = G.multiply(r).toBytes(); // R = rG
+        const R = BASE.multiply(r).toBytes(); // R = rG
         const k = hashDomainToScalar(options.context, R, pointBytes, msg); // R || A || PH(M)
-        const s = modN(r + k * scalar); // S = (r + k * s) mod L
-        (0, utils_ts_1.aInRange)('signature.s', s, _0n, CURVE_ORDER); // 0 <= s < l
-        const L = Fp.BYTES;
-        const res = (0, utils_ts_1.concatBytes)(R, (0, utils_ts_1.numberToBytesLE)(s, L));
-        return (0, utils_ts_1.ensureBytes)('result', res, L * 2); // 64-byte signature
+        const s = Fn.create(r + k * scalar); // S = (r + k * s) mod L
+        if (!Fn.isValid(s))
+            throw new Error('sign failed: invalid s'); // 0 <= s < L
+        const rs = (0, utils_ts_1.concatBytes)(R, Fn.toBytes(s));
+        return (0, utils_ts_1._abytes2)(rs, lengths.signature, 'result');
     }
@@ -509,6 +509,6 @@ // verification rule is either zip215 or rfc8032 / nist186-5. Consult fromHex:
         const { context, zip215 } = options;
-        const len = lengths.signature; // Verifies EdDSA signature against message and public key. RFC8032 5.1.7.
-        sig = (0, utils_ts_1.ensureBytes)('signature', sig, len); // An extended group equation is checked.
+        const len = lengths.signature;
+        sig = (0, utils_ts_1.ensureBytes)('signature', sig, len);
         msg = (0, utils_ts_1.ensureBytes)('message', msg);
-        publicKey = (0, utils_ts_1.ensureBytes)('publicKey', publicKey, lengths.public);
+        publicKey = (0, utils_ts_1.ensureBytes)('publicKey', publicKey, lengths.publicKey);
         if (zip215 !== undefined)
@@ -528,3 +528,3 @@ (0, utils_ts_1._abool2)(zip215, 'zip215');
             R = Point.fromBytes(r, zip215);
-            SB = G.multiplyUnsafe(s); // 0 <= s < l is done inside
+            SB = BASE.multiplyUnsafe(s); // 0 <= s < l is done inside
         }
@@ -535,3 +535,3 @@ catch (error) {
         if (!zip215 && A.isSmallOrder())
-            return false;
+            return false; // zip215 allows public keys of small order
         const k = hashDomainToScalar(context, R.toBytes(), A.toBytes(), msg);
@@ -543,11 +543,10 @@ const RkA = R.add(A.multiplyUnsafe(k));
     }
-    G.precompute(8); // Enable precomputes. Slows down first publicKey computation by 20ms.
-    const _size = Fp.BYTES;
+    const _size = Fp.BYTES; // 32 for ed25519, 57 for ed448
     const lengths = {
-        secret: _size,
-        public: _size,
+        secretKey: _size,
+        publicKey: _size,
         signature: 2 * _size,
         seed: _size,
     };
-    function randomSecretKey(seed = randomBytes_(lengths.seed)) {
+    function randomSecretKey(seed = randomBytes(lengths.seed)) {
         return (0, utils_ts_1._abytes2)(seed, lengths.seed, 'seed');
@@ -560,8 +559,3 @@ }
     function isValidSecretKey(key) {
-        try {
-            return !!Fn.fromBytes(key, false);
-        }
-        catch (error) {
-            return false;
-        }
+        return (0, utils_ts_1.isBytes)(key) && key.length === Fn.BYTES;
     }
@@ -589,11 +583,6 @@ function isValidPublicKey(key, zip215) {
          *   - `(x, y) = (sqrt(156324)*u/v, (1+u)/(1-u))`
-         *
-         * There is NO `fromMontgomery`:
-         * - There are 2 valid ed25519 points for every x25519, with flipped coordinate
-         * - Sometimes there are 0 valid ed25519 points, because x25519 *additionally*
-         *   accepts inputs on the quadratic twist, which can't be moved to ed25519
          */
         toMontgomery(publicKey) {
             const { y } = Point.fromBytes(publicKey);
-            const size = lengths.public;
+            const size = lengths.publicKey;
             const is25519 = size === 32;
@@ -606,3 +595,3 @@ if (!is25519 && size !== 57)
         toMontgomeryPriv(secretKey) {
-            const size = lengths.secret;
+            const size = lengths.secretKey;
             (0, utils_ts_1._abytes2)(secretKey, size);
@@ -652,3 +641,9 @@ const hashed = cHash(secretKey.subarray(0, size));
 function _eddsa_new_output_to_legacy(c, eddsa) {
-    const legacy = Object.assign({}, eddsa, { ExtendedPoint: eddsa.Point, CURVE: c });
+    const Point = eddsa.Point;
+    const legacy = Object.assign({}, eddsa, {
+        ExtendedPoint: Point,
+        CURVE: c,
+        nBitLength: Point.Fn.BITS,
+        nByteLength: Point.Fn.BYTES,
+    });
     return legacy;
@@ -655,0 +650,0 @@ }

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abstract/montgomery.js

@@ -133,4 +133,4 @@ "use strict";
     const lengths = {
-        secret: fieldLen,
-        public: fieldLen,
+        secretKey: fieldLen,
+        publicKey: fieldLen,
         seed: fieldLen,
@@ -137,0 +137,0 @@ };

abstract/montgomery.js.map

@@ -1,1 +0,1 @@
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+{"version":3,"file":"montgomery.js","sourceRoot":"","sources":["../src/abstract/montgomery.ts"],"names":[],"mappings":";;AAwDA,gCAyIC;AAjMD;;;;;GAKG;AACH,sEAAsE;AACtE,0CAQqB;AAErB,6CAAmC;AAEnC,MAAM,GAAG,GAAG,MAAM,CAAC,CAAC,CAAC,CAAC;AACtB,MAAM,GAAG,GAAG,MAAM,CAAC,CAAC,CAAC,CAAC;AACtB,MAAM,GAAG,GAAG,MAAM,CAAC,CAAC,CAAC,CAAC;AA2BtB,SAAS,YAAY,CAAC,KAAgB;IACpC,IAAA,0BAAe,EAAC,KAAK,EAAE;QACrB,iBAAiB,EAAE,UAAU;QAC7B,UAAU,EAAE,UAAU;KACvB,CAAC,CAAC;IACH,OAAO,MAAM,CAAC,MAAM,CAAC,EAAE,GAAG,KAAK,EAAW,CAAC,CAAC;AAC9C,CAAC;AAED,SAAgB,UAAU,CAAC,QAAmB;IAC5C,MAAM,KAAK,GAAG,YAAY,CAAC,QAAQ,CAAC,CAAC;IACrC,MAAM,EAAE,CAAC,EAAE,IAAI,EAAE,iBAAiB,EAAE,UAAU,EAAE,WAAW,EAAE,IAAI,EAAE,GAAG,KAAK,CAAC;IAC5E,MAAM,OAAO,GAAG,IAAI,KAAK,QAAQ,CAAC;IAClC,IAAI,CAAC,OAAO,IAAI,IAAI,KAAK,MAAM;QAAE,MAAM,IAAI,KAAK,CAAC,cAAc,CAAC,CAAC;IACjE,MAAM,YAAY,GAAG,IAAI,IAAI,sBAAW,CAAC;IAEzC,MAAM,cAAc,GAAG,OAAO,CAAC,CAAC,CAAC,GAAG,CAAC,CAAC,CAAC,GAAG,CAAC;IAC3C,MAAM,QAAQ,GAAG,OAAO,CAAC,CAAC,CAAC,EAAE,CAAC,CAAC,CAAC,EAAE,CAAC;IACnC,MAAM,EAAE,GAAG,OAAO,CAAC,CAAC,CAAC,MAAM,CAAC,CAAC,CAAC,CAAC,CAAC,CAAC,MAAM,CAAC,CAAC,CAAC,CAAC;IAC3C,eAAe;IACf,0EAA0E;IAC1E,6CAA6C;IAC7C,yCAAyC;IACzC,MAAM,GAAG,GAAG,OAAO,CAAC,CAAC,CAAC,MAAM,CAAC,MAAM,CAAC,CAAC,CAAC,CAAC,MAAM,CAAC,KAAK,CAAC,CAAC;IACrD,+DAA+D;IAC/D,2DAA2D;IAC3D,4EAA4E;IAC5E,MAAM,SAAS,GAAG,OAAO,CAAC,CAAC,CAAC,GAAG,IAAI,MAAM,CAAC,GAAG,CAAC,CAAC,CAAC,CAAC,GAAG,IAAI,MAAM,CAAC,GAAG,CAAC,CAAC;IACpE,MAAM,QAAQ,GAAG,OAAO;QACtB,CAAC,CAAC,MAAM,CAAC,CAAC,CAAC,GAAG,GAAG,IAAI,MAAM,CAAC,GAAG,CAAC,GAAG,GAAG;QACtC,CAAC,CAAC,MAAM,CAAC,CAAC,CAAC,GAAG,GAAG,IAAI,MAAM,CAAC,GAAG,CAAC,GAAG,GAAG,CAAC;IACzC,MAAM,SAAS,GAAG,SAAS,GAAG,QAAQ,GAAG,GAAG,CAAC,CAAC,cAAc;IAC5D,MAAM,IAAI,GAAG,CAAC,CAAS,EAAE,EAAE,CAAC,IAAA,gBAAG,EAAC,CAAC,EAAE,CAAC,CAAC,CAAC;IACtC,MAAM,OAAO,GAAG,OAAO,CAAC,EAAE,CAAC,CAAC;IAC5B,SAAS,OAAO,CAAC,CAAS;QACxB,OAAO,IAAA,0BAAe,EAAC,IAAI,CAAC,CAAC,CAAC,EAAE,QAAQ,CAAC,CAAC;IAC5C,CAAC;IACD,SAAS,OAAO,CAAC,CAAM;QACrB,MAAM,EAAE,GAAG,IAAA,sBAAW,EAAC,cAAc,EAAE,CAAC,EAAE,QAAQ,CAAC,CAAC;QACpD,+DAA+D;QAC/D,uEAAuE;QACvE,IAAI,OAAO;YAAE,EAAE,CAAC,EAAE,CAAC,IAAI,GAAG,CAAC,CAAC,cAAc;QAC1C,4EAA4E;QAC5E,sEAAsE;QACtE,uEAAuE;QACvE,kCAAkC;QAClC,OAAO,IAAI,CAAC,IAAA,0BAAe,EAAC,EAAE,CAAC,CAAC,CAAC;IACnC,CAAC;IACD,SAAS,YAAY,CAAC,MAAW;QAC/B,OAAO,IAAA,0BAAe,EAAC,iBAAiB,CAAC,IAAA,sBAAW,EAAC,QAAQ,EAAE,MAAM,EAAE,QAAQ,CAAC,CAAC,CAAC,CAAC;IACrF,CAAC;IACD,SAAS,UAAU,CAAC,MAAW,EAAE,CAAM;QACrC,MAAM,EAAE,GAAG,gBAAgB,CAAC,OAAO,CAAC,CAAC,CAAC,EAAE,YAAY,CAAC,MAAM,CAAC,CAAC,CAAC;QAC9D,yEAAyE;QACzE,sDAAsD;QACtD,sCAAsC;QACtC,IAAI,EAAE,KAAK,GAAG;YAAE,MAAM,IAAI,KAAK,CAAC,wCAAwC,CAAC,CAAC;QAC1E,OAAO,OAAO,CAAC,EAAE,CAAC,CAAC;IACrB,CAAC;IACD,kFAAkF;IAClF,SAAS,cAAc,CAAC,MAAW;QACjC,OAAO,UAAU,CAAC,MAAM,EAAE,OAAO,CAAC,CAAC;IACrC,CAAC;IAED,oCAAoC;IACpC,SAAS,KAAK,CAAC,IAAY,EAAE,GAAW,EAAE,GAAW;QACnD,uCAAuC;QACvC,wEAAwE;QACxE,qDAAqD;QACrD,MAAM,KAAK,GAAG,IAAI,CAAC,IAAI,GAAG,CAAC,GAAG,GAAG,GAAG,CAAC,CAAC,CAAC;QACvC,GAAG,GAAG,IAAI,CAAC,GAAG,GAAG,KAAK,CAAC,CAAC,CAAC,sBAAsB;QAC/C,GAAG,GAAG,IAAI,CAAC,GAAG,GAAG,KAAK,CAAC,CAAC,CAAC,sBAAsB;QAC/C,OAAO,EAAE,GAAG,EAAE,GAAG,EAAE,CAAC;IACtB,CAAC;IAED;;;;;OAKG;IACH,SAAS,gBAAgB,CAAC,CAAS,EAAE,MAAc;QACjD,IAAA,mBAAQ,EAAC,GAAG,EAAE,CAAC,EAAE,GAAG,EAAE,CAAC,CAAC,CAAC;QACzB,IAAA,mBAAQ,EAAC,QAAQ,EAAE,MAAM,EAAE,SAAS,EAAE,SAAS,CAAC,CAAC;QACjD,MAAM,CAAC,GAAG,MAAM,CAAC;QACjB,MAAM,GAAG,GAAG,CAAC,CAAC;QACd,IAAI,GAAG,GAAG,GAAG,CAAC;QACd,IAAI,GAAG,GAAG,GAAG,CAAC;QACd,IAAI,GAAG,GAAG,CAAC,CAAC;QACZ,IAAI,GAAG,GAAG,GAAG,CAAC;QACd,IAAI,IAAI,GAAG,GAAG,CAAC;QACf,KAAK,IAAI,CAAC,GAAG,MAAM,CAAC,cAAc,GAAG,CAAC,CAAC,EAAE,CAAC,IAAI,GAAG,EAAE,CAAC,EAAE,EAAE,CAAC;YACvD,MAAM,GAAG,GAAG,CAAC,CAAC,IAAI,CAAC,CAAC,GAAG,GAAG,CAAC;YAC3B,IAAI,IAAI,GAAG,CAAC;YACZ,CAAC,EAAE,GAAG,EAAE,GAAG,EAAE,GAAG,KAAK,CAAC,IAAI,EAAE,GAAG,EAAE,GAAG,CAAC,CAAC,CAAC;YACvC,CAAC,EAAE,GAAG,EAAE,GAAG,EAAE,GAAG,EAAE,GAAG,EAAE,GAAG,KAAK,CAAC,IAAI,EAAE,GAAG,EAAE,GAAG,CAAC,CAAC,CAAC;YACjD,IAAI,GAAG,GAAG,CAAC;YAEX,MAAM,CAAC,GAAG,GAAG,GAAG,GAAG,CAAC;YACpB,MAAM,EAAE,GAAG,IAAI,CAAC,CAAC,GAAG,CAAC,CAAC,CAAC;YACvB,MAAM,CAAC,GAAG,GAAG,GAAG,GAAG,CAAC;YACpB,MAAM,EAAE,GAAG,IAAI,CAAC,CAAC,GAAG,CAAC,CAAC,CAAC;YACvB,MAAM,CAAC,GAAG,EAAE,GAAG,EAAE,CAAC;YAClB,MAAM,CAAC,GAAG,GAAG,GAAG,GAAG,CAAC;YACpB,MAAM,CAAC,GAAG,GAAG,GAAG,GAAG,CAAC;YACpB,MAAM,EAAE,GAAG,IAAI,CAAC,CAAC,GAAG,CAAC,CAAC,CAAC;YACvB,MAAM,EAAE,GAAG,IAAI,CAAC,CAAC,GAAG,CAAC,CAAC,CAAC;YACvB,MAAM,IAAI,GAAG,EAAE,GAAG,EAAE,CAAC;YACrB,MAAM,KAAK,GAAG,EAAE,GAAG,EAAE,CAAC;YACtB,GAAG,GAAG,IAAI,CAAC,IAAI,GAAG,IAAI,CAAC,CAAC;YACxB,GAAG,GAAG,IAAI,CAAC,GAAG,GAAG,IAAI,CAAC,KAAK,GAAG,KAAK,CAAC,CAAC,CAAC;YACtC,GAAG,GAAG,IAAI,CAAC,EAAE,GAAG,EAAE,CAAC,CAAC;YACpB,GAAG,GAAG,IAAI,CAAC,CAAC,GAAG,CAAC,EAAE,GAAG,IAAI,CAAC,GAAG,GAAG,CAAC,CAAC,CAAC,CAAC,CAAC;QACvC,CAAC;QACD,CAAC,EAAE,GAAG,EAAE,GAAG,EAAE,GAAG,KAAK,CAAC,IAAI,EAAE,GAAG,EAAE,GAAG,CAAC,CAAC,CAAC;QACvC,CAAC,EAAE,GAAG,EAAE,GAAG,EAAE,GAAG,EAAE,GAAG,EAAE,GAAG,KAAK,CAAC,IAAI,EAAE,GAAG,EAAE,GAAG,CAAC,CAAC,CAAC;QACjD,MAAM,EAAE,GAAG,UAAU,CAAC,GAAG,CAAC,CAAC,CAAC,iDAAiD;QAC7E,OAAO,IAAI,CAAC,GAAG,GAAG,EAAE,CAAC,CAAC,CAAC,6BAA6B;IACtD,CAAC;IACD,MA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abstract/tower.d.ts

@@ -34,4 +34,5 @@ import * as mod from './modular.ts';
 export type Fp2Bls = mod.IField<Fp2> & {
+    Fp: mod.IField<Fp>;
     frobeniusMap(num: Fp2, power: number): Fp2;
-    fromBigTuple(num: [bigint, bigint]): Fp2;
+    fromBigTuple(num: BigintTuple): Fp2;
     mulByB: (num: Fp2) => Fp2;
@@ -43,5 +44,10 @@ mulByNonresidue: (num: Fp2) => Fp2;
     };
+    Fp4Square: (a: Fp2, b: Fp2) => {
+        first: Fp2;
+        second: Fp2;
+    };
     NONRESIDUE: Fp2;
 };
 export type Fp6Bls = mod.IField<Fp6> & {
+    Fp2: Fp2Bls;
     frobeniusMap(num: Fp6, power: number): Fp6;
@@ -55,2 +61,3 @@ fromBigSix: (tuple: BigintSix) => Fp6;
 export type Fp12Bls = mod.IField<Fp12> & {
+    Fp6: Fp6Bls;
     frobeniusMap(num: Fp12, power: number): Fp12;
@@ -78,2 +85,3 @@ fromBigTwelve: (t: BigintTwelve) => Fp12;
     ORDER: bigint;
+    X_LEN: number;
     NONRESIDUE?: Fp;
@@ -83,4 +91,2 @@ FP2_NONRESIDUE: BigintTuple;
     Fp2mulByB: (num: Fp2) => Fp2;
-    Fp12cyclotomicSquare: (num: Fp12) => Fp12;
-    Fp12cyclotomicExp: (num: Fp12, n: bigint) => Fp12;
     Fp12finalExponentiate: (num: Fp12) => Fp12;
@@ -93,7 +99,3 @@ };
     Fp12: Fp12Bls;
-    Fp4Square: (a: Fp2, b: Fp2) => {
-        first: Fp2;
-        second: Fp2;
-    };
 };
 //# sourceMappingURL=tower.d.ts.map

abstract/tower.d.ts.map

@@ -1,1 +0,1 @@
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abstract/tower.js

@@ -69,19 +69,75 @@ "use strict";
 }
-function tower12(opts) {
-    const { ORDER } = opts;
-    // Fp
-    const Fp = mod.Field(ORDER);
-    const FpNONRESIDUE = Fp.create(opts.NONRESIDUE || BigInt(-1));
-    const Fpdiv2 = Fp.div(Fp.ONE, _2n); // 1/2
-    // Fp2
-    const FP2_FROBENIUS_COEFFICIENTS = calcFrobeniusCoefficients(Fp, FpNONRESIDUE, Fp.ORDER, 2)[0];
-    const Fp2Add = ({ c0, c1 }, { c0: r0, c1: r1 }) => ({
-        c0: Fp.add(c0, r0),
-        c1: Fp.add(c1, r1),
-    });
-    const Fp2Subtract = ({ c0, c1 }, { c0: r0, c1: r1 }) => ({
-        c0: Fp.sub(c0, r0),
-        c1: Fp.sub(c1, r1),
-    });
-    const Fp2Multiply = ({ c0, c1 }, rhs) => {
+const Fp2fromBigTuple = (Fp, tuple) => {
+    if (tuple.length !== 2)
+        throw new Error('invalid tuple');
+    const fps = tuple.map((n) => Fp.create(n));
+    return { c0: fps[0], c1: fps[1] };
+};
+class _Field2 {
+    constructor(Fp, opts = {}) {
+        this.MASK = _1n;
+        const ORDER = Fp.ORDER;
+        const FP2_ORDER = ORDER * ORDER;
+        this.Fp = Fp;
+        this.ORDER = FP2_ORDER;
+        this.BITS = (0, utils_ts_1.bitLen)(FP2_ORDER);
+        this.BYTES = Math.ceil((0, utils_ts_1.bitLen)(FP2_ORDER) / 8);
+        this.isLE = Fp.isLE;
+        this.ZERO = { c0: Fp.ZERO, c1: Fp.ZERO };
+        this.ONE = { c0: Fp.ONE, c1: Fp.ZERO };
+        this.Fp_NONRESIDUE = Fp.create(opts.NONRESIDUE || BigInt(-1));
+        this.Fp_div2 = Fp.div(Fp.ONE, _2n); // 1/2
+        this.NONRESIDUE = Fp2fromBigTuple(Fp, opts.FP2_NONRESIDUE);
+        // const Fp2Nonresidue = Fp2fromBigTuple(opts.FP2_NONRESIDUE);
+        this.FROBENIUS_COEFFICIENTS = calcFrobeniusCoefficients(Fp, this.Fp_NONRESIDUE, Fp.ORDER, 2)[0];
+        this.mulByB = opts.Fp2mulByB;
+        Object.seal(this);
+    }
+    fromBigTuple(tuple) {
+        return Fp2fromBigTuple(this.Fp, tuple);
+    }
+    create(num) {
+        return num;
+    }
+    isValid({ c0, c1 }) {
+        function isValidC(num, ORDER) {
+            return typeof num === 'bigint' && _0n <= num && num < ORDER;
+        }
+        return isValidC(c0, this.ORDER) && isValidC(c1, this.ORDER);
+    }
+    is0({ c0, c1 }) {
+        return this.Fp.is0(c0) && this.Fp.is0(c1);
+    }
+    isValidNot0(num) {
+        return !this.is0(num) && this.isValid(num);
+    }
+    eql({ c0, c1 }, { c0: r0, c1: r1 }) {
+        return this.Fp.eql(c0, r0) && this.Fp.eql(c1, r1);
+    }
+    neg({ c0, c1 }) {
+        return { c0: this.Fp.neg(c0), c1: this.Fp.neg(c1) };
+    }
+    pow(num, power) {
+        return mod.FpPow(this, num, power);
+    }
+    invertBatch(nums) {
+        return mod.FpInvertBatch(this, nums);
+    }
+    // Normalized
+    add(f1, f2) {
+        const { c0, c1 } = f1;
+        const { c0: r0, c1: r1 } = f2;
+        return {
+            c0: this.Fp.add(c0, r0),
+            c1: this.Fp.add(c1, r1),
+        };
+    }
+    sub({ c0, c1 }, { c0: r0, c1: r1 }) {
+        return {
+            c0: this.Fp.sub(c0, r0),
+            c1: this.Fp.sub(c1, r1),
+        };
+    }
+    mul({ c0, c1 }, rhs) {
+        const { Fp } = this;
         if (typeof rhs === 'bigint')
@@ -97,4 +153,5 @@ return { c0: Fp.mul(c0, rhs), c1: Fp.mul(c1, rhs) };
         return { c0: o0, c1: o1 };
-    };
-    const Fp2Square = ({ c0, c1 }) => {
+    }
+    sqr({ c0, c1 }) {
+        const { Fp } = this;
         const a = Fp.add(c0, c1);
@@ -104,132 +161,152 @@ const b = Fp.sub(c0, c1);
         return { c0: Fp.mul(a, b), c1: Fp.mul(c, c1) };
-    };
-    const Fp2fromBigTuple = (tuple) => {
-        if (tuple.length !== 2)
-            throw new Error('invalid tuple');
-        const fps = tuple.map((n) => Fp.create(n));
-        return { c0: fps[0], c1: fps[1] };
-    };
-    function isValidC(num, ORDER) {
-        return typeof num === 'bigint' && _0n <= num && num < ORDER;
     }
-    const FP2_ORDER = ORDER * ORDER;
-    const Fp2Nonresidue = Fp2fromBigTuple(opts.FP2_NONRESIDUE);
-    const Fp2 = {
-        ORDER: FP2_ORDER,
-        isLE: Fp.isLE,
-        NONRESIDUE: Fp2Nonresidue,
-        BITS: (0, utils_ts_1.bitLen)(FP2_ORDER),
-        BYTES: Math.ceil((0, utils_ts_1.bitLen)(FP2_ORDER) / 8),
-        MASK: (0, utils_ts_1.bitMask)((0, utils_ts_1.bitLen)(FP2_ORDER)),
-        ZERO: { c0: Fp.ZERO, c1: Fp.ZERO },
-        ONE: { c0: Fp.ONE, c1: Fp.ZERO },
-        create: (num) => num,
-        isValid: ({ c0, c1 }) => isValidC(c0, FP2_ORDER) && isValidC(c1, FP2_ORDER),
-        is0: ({ c0, c1 }) => Fp.is0(c0) && Fp.is0(c1),
-        isValidNot0: (num) => !Fp2.is0(num) && Fp2.isValid(num),
-        eql: ({ c0, c1 }, { c0: r0, c1: r1 }) => Fp.eql(c0, r0) && Fp.eql(c1, r1),
-        neg: ({ c0, c1 }) => ({ c0: Fp.neg(c0), c1: Fp.neg(c1) }),
-        pow: (num, power) => mod.FpPow(Fp2, num, power),
-        invertBatch: (nums) => mod.FpInvertBatch(Fp2, nums),
-        // Normalized
-        add: Fp2Add,
-        sub: Fp2Subtract,
-        mul: Fp2Multiply,
-        sqr: Fp2Square,
-        // NonNormalized stuff
-        addN: Fp2Add,
-        subN: Fp2Subtract,
-        mulN: Fp2Multiply,
-        sqrN: Fp2Square,
-        // Why inversion for bigint inside Fp instead of Fp2? it is even used in that context?
-        div: (lhs, rhs) => Fp2.mul(lhs, typeof rhs === 'bigint' ? Fp.inv(Fp.create(rhs)) : Fp2.inv(rhs)),
-        inv: ({ c0: a, c1: b }) => {
-            // We wish to find the multiplicative inverse of a nonzero
-            // element a + bu in Fp2. We leverage an identity
-            //
-            // (a + bu)(a - bu) = a² + b²
-            //
-            // which holds because u² = -1. This can be rewritten as
-            //
-            // (a + bu)(a - bu)/(a² + b²) = 1
-            //
-            // because a² + b² = 0 has no nonzero solutions for (a, b).
-            // This gives that (a - bu)/(a² + b²) is the inverse
-            // of (a + bu). Importantly, this can be computing using
-            // only a single inversion in Fp.
-            const factor = Fp.inv(Fp.create(a * a + b * b));
-            return { c0: Fp.mul(factor, Fp.create(a)), c1: Fp.mul(factor, Fp.create(-b)) };
-        },
-        sqrt: (num) => {
-            if (opts.Fp2sqrt)
-                return opts.Fp2sqrt(num);
-            // This is generic for all quadratic extensions (Fp2)
-            const { c0, c1 } = num;
-            if (Fp.is0(c1)) {
-                // if c0 is quadratic residue
-                if (mod.FpLegendre(Fp, c0) === 1)
-                    return Fp2.create({ c0: Fp.sqrt(c0), c1: Fp.ZERO });
-                else
-                    return Fp2.create({ c0: Fp.ZERO, c1: Fp.sqrt(Fp.div(c0, FpNONRESIDUE)) });
-            }
-            const a = Fp.sqrt(Fp.sub(Fp.sqr(c0), Fp.mul(Fp.sqr(c1), FpNONRESIDUE)));
-            let d = Fp.mul(Fp.add(a, c0), Fpdiv2);
-            const legendre = mod.FpLegendre(Fp, d);
-            // -1, Quadratic non residue
-            if (legendre === -1)
-                d = Fp.sub(d, a);
-            const a0 = Fp.sqrt(d);
-            const candidateSqrt = Fp2.create({ c0: a0, c1: Fp.div(Fp.mul(c1, Fpdiv2), a0) });
-            if (!Fp2.eql(Fp2.sqr(candidateSqrt), num))
-                throw new Error('Cannot find square root');
-            // Normalize root: at this point candidateSqrt ** 2 = num, but also -candidateSqrt ** 2 = num
-            const x1 = candidateSqrt;
-            const x2 = Fp2.neg(x1);
-            const { re: re1, im: im1 } = Fp2.reim(x1);
-            const { re: re2, im: im2 } = Fp2.reim(x2);
-            if (im1 > im2 || (im1 === im2 && re1 > re2))
-                return x1;
-            return x2;
-        },
-        // Same as sgn0_m_eq_2 in RFC 9380
-        isOdd: (x) => {
-            const { re: x0, im: x1 } = Fp2.reim(x);
-            const sign_0 = x0 % _2n;
-            const zero_0 = x0 === _0n;
-            const sign_1 = x1 % _2n;
-            return BigInt(sign_0 || (zero_0 && sign_1)) == _1n;
-        },
-        // Bytes util
-        fromBytes(b) {
-            if (b.length !== Fp2.BYTES)
-                throw new Error('fromBytes invalid length=' + b.length);
-            return { c0: Fp.fromBytes(b.subarray(0, Fp.BYTES)), c1: Fp.fromBytes(b.subarray(Fp.BYTES)) };
-        },
-        toBytes: ({ c0, c1 }) => (0, utils_ts_1.concatBytes)(Fp.toBytes(c0), Fp.toBytes(c1)),
-        cmov: ({ c0, c1 }, { c0: r0, c1: r1 }, c) => ({
-            c0: Fp.cmov(c0, r0, c),
-            c1: Fp.cmov(c1, r1, c),
-        }),
-        reim: ({ c0, c1 }) => ({ re: c0, im: c1 }),
-        // multiply by u + 1
-        mulByNonresidue: ({ c0, c1 }) => Fp2.mul({ c0, c1 }, Fp2Nonresidue),
-        mulByB: opts.Fp2mulByB,
-        fromBigTuple: Fp2fromBigTuple,
-        frobeniusMap: ({ c0, c1 }, power) => ({
+    // NonNormalized stuff
+    addN(a, b) {
+        return this.add(a, b);
+    }
+    subN(a, b) {
+        return this.sub(a, b);
+    }
+    mulN(a, b) {
+        return this.mul(a, b);
+    }
+    sqrN(a) {
+        return this.sqr(a);
+    }
+    // Why inversion for bigint inside Fp instead of Fp2? it is even used in that context?
+    div(lhs, rhs) {
+        const { Fp } = this;
+        // @ts-ignore
+        return this.mul(lhs, typeof rhs === 'bigint' ? Fp.inv(Fp.create(rhs)) : this.inv(rhs));
+    }
+    inv({ c0: a, c1: b }) {
+        // We wish to find the multiplicative inverse of a nonzero
+        // element a + bu in Fp2. We leverage an identity
+        //
+        // (a + bu)(a - bu) = a² + b²
+        //
+        // which holds because u² = -1. This can be rewritten as
+        //
+        // (a + bu)(a - bu)/(a² + b²) = 1
+        //
+        // because a² + b² = 0 has no nonzero solutions for (a, b).
+        // This gives that (a - bu)/(a² + b²) is the inverse
+        // of (a + bu). Importantly, this can be computing using
+        // only a single inversion in Fp.
+        const { Fp } = this;
+        const factor = Fp.inv(Fp.create(a * a + b * b));
+        return { c0: Fp.mul(factor, Fp.create(a)), c1: Fp.mul(factor, Fp.create(-b)) };
+    }
+    sqrt(num) {
+        // This is generic for all quadratic extensions (Fp2)
+        const { Fp } = this;
+        const Fp2 = this;
+        const { c0, c1 } = num;
+        if (Fp.is0(c1)) {
+            // if c0 is quadratic residue
+            if (mod.FpLegendre(Fp, c0) === 1)
+                return Fp2.create({ c0: Fp.sqrt(c0), c1: Fp.ZERO });
+            else
+                return Fp2.create({ c0: Fp.ZERO, c1: Fp.sqrt(Fp.div(c0, this.Fp_NONRESIDUE)) });
+        }
+        const a = Fp.sqrt(Fp.sub(Fp.sqr(c0), Fp.mul(Fp.sqr(c1), this.Fp_NONRESIDUE)));
+        let d = Fp.mul(Fp.add(a, c0), this.Fp_div2);
+        const legendre = mod.FpLegendre(Fp, d);
+        // -1, Quadratic non residue
+        if (legendre === -1)
+            d = Fp.sub(d, a);
+        const a0 = Fp.sqrt(d);
+        const candidateSqrt = Fp2.create({ c0: a0, c1: Fp.div(Fp.mul(c1, this.Fp_div2), a0) });
+        if (!Fp2.eql(Fp2.sqr(candidateSqrt), num))
+            throw new Error('Cannot find square root');
+        // Normalize root: at this point candidateSqrt ** 2 = num, but also -candidateSqrt ** 2 = num
+        const x1 = candidateSqrt;
+        const x2 = Fp2.neg(x1);
+        const { re: re1, im: im1 } = Fp2.reim(x1);
+        const { re: re2, im: im2 } = Fp2.reim(x2);
+        if (im1 > im2 || (im1 === im2 && re1 > re2))
+            return x1;
+        return x2;
+    }
+    // Same as sgn0_m_eq_2 in RFC 9380
+    isOdd(x) {
+        const { re: x0, im: x1 } = this.reim(x);
+        const sign_0 = x0 % _2n;
+        const zero_0 = x0 === _0n;
+        const sign_1 = x1 % _2n;
+        return BigInt(sign_0 || (zero_0 && sign_1)) == _1n;
+    }
+    // Bytes util
+    fromBytes(b) {
+        const { Fp } = this;
+        if (b.length !== this.BYTES)
+            throw new Error('fromBytes invalid length=' + b.length);
+        return { c0: Fp.fromBytes(b.subarray(0, Fp.BYTES)), c1: Fp.fromBytes(b.subarray(Fp.BYTES)) };
+    }
+    toBytes({ c0, c1 }) {
+        return (0, utils_ts_1.concatBytes)(this.Fp.toBytes(c0), this.Fp.toBytes(c1));
+    }
+    cmov({ c0, c1 }, { c0: r0, c1: r1 }, c) {
+        return {
+            c0: this.Fp.cmov(c0, r0, c),
+            c1: this.Fp.cmov(c1, r1, c),
+        };
+    }
+    reim({ c0, c1 }) {
+        return { re: c0, im: c1 };
+    }
+    Fp4Square(a, b) {
+        const Fp2 = this;
+        const a2 = Fp2.sqr(a);
+        const b2 = Fp2.sqr(b);
+        return {
+            first: Fp2.add(Fp2.mulByNonresidue(b2), a2), // b² * Nonresidue + a²
+            second: Fp2.sub(Fp2.sub(Fp2.sqr(Fp2.add(a, b)), a2), b2), // (a + b)² - a² - b²
+        };
+    }
+    // multiply by u + 1
+    mulByNonresidue({ c0, c1 }) {
+        return this.mul({ c0, c1 }, this.NONRESIDUE);
+    }
+    frobeniusMap({ c0, c1 }, power) {
+        return {
             c0,
-            c1: Fp.mul(c1, FP2_FROBENIUS_COEFFICIENTS[power % 2]),
-        }),
-    };
-    // Fp6
-    const Fp6Add = ({ c0, c1, c2 }, { c0: r0, c1: r1, c2: r2 }) => ({
-        c0: Fp2.add(c0, r0),
-        c1: Fp2.add(c1, r1),
-        c2: Fp2.add(c2, r2),
-    });
-    const Fp6Subtract = ({ c0, c1, c2 }, { c0: r0, c1: r1, c2: r2 }) => ({
-        c0: Fp2.sub(c0, r0),
-        c1: Fp2.sub(c1, r1),
-        c2: Fp2.sub(c2, r2),
-    });
-    const Fp6Multiply = ({ c0, c1, c2 }, rhs) => {
+            c1: this.Fp.mul(c1, this.FROBENIUS_COEFFICIENTS[power % 2]),
+        };
+    }
+}
+class _Field6 {
+    constructor(Fp2) {
+        this.MASK = _1n;
+        this.Fp2 = Fp2;
+        this.ORDER = Fp2.ORDER; // TODO: unused, but need to verify
+        this.BITS = 3 * Fp2.BITS;
+        this.BYTES = 3 * Fp2.BYTES;
+        this.isLE = Fp2.isLE;
+        this.ZERO = { c0: Fp2.ZERO, c1: Fp2.ZERO, c2: Fp2.ZERO };
+        this.ONE = { c0: Fp2.ONE, c1: Fp2.ZERO, c2: Fp2.ZERO };
+        const { Fp } = Fp2;
+        const frob = calcFrobeniusCoefficients(Fp2, Fp2.NONRESIDUE, Fp.ORDER, 6, 2, 3);
+        this.FROBENIUS_COEFFICIENTS_1 = frob[0];
+        this.FROBENIUS_COEFFICIENTS_2 = frob[1];
+        Object.seal(this);
+    }
+    add({ c0, c1, c2 }, { c0: r0, c1: r1, c2: r2 }) {
+        const { Fp2 } = this;
+        return {
+            c0: Fp2.add(c0, r0),
+            c1: Fp2.add(c1, r1),
+            c2: Fp2.add(c2, r2),
+        };
+    }
+    sub({ c0, c1, c2 }, { c0: r0, c1: r1, c2: r2 }) {
+        const { Fp2 } = this;
+        return {
+            c0: Fp2.sub(c0, r0),
+            c1: Fp2.sub(c1, r1),
+            c2: Fp2.sub(c2, r2),
+        };
+    }
+    mul({ c0, c1, c2 }, rhs) {
+        const { Fp2 } = this;
         if (typeof rhs === 'bigint') {
@@ -254,4 +331,5 @@ return {
         };
-    };
-    const Fp6Square = ({ c0, c1, c2 }) => {
+    }
+    sqr({ c0, c1, c2 }) {
+        const { Fp2 } = this;
         let t0 = Fp2.sqr(c0); // c0²
@@ -267,108 +345,214 @@ let t1 = Fp2.mul(Fp2.mul(c0, c1), _2n); // 2 * c0 * c1
         };
-    };
-    const [FP6_FROBENIUS_COEFFICIENTS_1, FP6_FROBENIUS_COEFFICIENTS_2] = calcFrobeniusCoefficients(Fp2, Fp2Nonresidue, Fp.ORDER, 6, 2, 3);
-    const Fp6 = {
-        ORDER: Fp2.ORDER, // TODO: unused, but need to verify
-        isLE: Fp2.isLE,
-        BITS: 3 * Fp2.BITS,
-        BYTES: 3 * Fp2.BYTES,
-        MASK: (0, utils_ts_1.bitMask)(3 * Fp2.BITS),
-        ZERO: { c0: Fp2.ZERO, c1: Fp2.ZERO, c2: Fp2.ZERO },
-        ONE: { c0: Fp2.ONE, c1: Fp2.ZERO, c2: Fp2.ZERO },
-        create: (num) => num,
-        isValid: ({ c0, c1, c2 }) => Fp2.isValid(c0) && Fp2.isValid(c1) && Fp2.isValid(c2),
-        is0: ({ c0, c1, c2 }) => Fp2.is0(c0) && Fp2.is0(c1) && Fp2.is0(c2),
-        isValidNot0: (num) => !Fp6.is0(num) && Fp6.isValid(num),
-        neg: ({ c0, c1, c2 }) => ({ c0: Fp2.neg(c0), c1: Fp2.neg(c1), c2: Fp2.neg(c2) }),
-        eql: ({ c0, c1, c2 }, { c0: r0, c1: r1, c2: r2 }) => Fp2.eql(c0, r0) && Fp2.eql(c1, r1) && Fp2.eql(c2, r2),
-        sqrt: utils_ts_1.notImplemented,
-        // Do we need division by bigint at all? Should be done via order:
-        div: (lhs, rhs) => Fp6.mul(lhs, typeof rhs === 'bigint' ? Fp.inv(Fp.create(rhs)) : Fp6.inv(rhs)),
-        pow: (num, power) => mod.FpPow(Fp6, num, power),
-        invertBatch: (nums) => mod.FpInvertBatch(Fp6, nums),
-        // Normalized
-        add: Fp6Add,
-        sub: Fp6Subtract,
-        mul: Fp6Multiply,
-        sqr: Fp6Square,
-        // NonNormalized stuff
-        addN: Fp6Add,
-        subN: Fp6Subtract,
-        mulN: Fp6Multiply,
-        sqrN: Fp6Square,
-        inv: ({ c0, c1, c2 }) => {
-            let t0 = Fp2.sub(Fp2.sqr(c0), Fp2.mulByNonresidue(Fp2.mul(c2, c1))); // c0² - c2 * c1 * (u + 1)
-            let t1 = Fp2.sub(Fp2.mulByNonresidue(Fp2.sqr(c2)), Fp2.mul(c0, c1)); // c2² * (u + 1) - c0 * c1
-            let t2 = Fp2.sub(Fp2.sqr(c1), Fp2.mul(c0, c2)); // c1² - c0 * c2
-            // 1/(((c2 * T1 + c1 * T2) * v) + c0 * T0)
-            let t4 = Fp2.inv(Fp2.add(Fp2.mulByNonresidue(Fp2.add(Fp2.mul(c2, t1), Fp2.mul(c1, t2))), Fp2.mul(c0, t0)));
-            return { c0: Fp2.mul(t4, t0), c1: Fp2.mul(t4, t1), c2: Fp2.mul(t4, t2) };
-        },
-        // Bytes utils
-        fromBytes: (b) => {
-            if (b.length !== Fp6.BYTES)
-                throw new Error('fromBytes invalid length=' + b.length);
-            return {
-                c0: Fp2.fromBytes(b.subarray(0, Fp2.BYTES)),
-                c1: Fp2.fromBytes(b.subarray(Fp2.BYTES, 2 * Fp2.BYTES)),
-                c2: Fp2.fromBytes(b.subarray(2 * Fp2.BYTES)),
-            };
-        },
-        toBytes: ({ c0, c1, c2 }) => (0, utils_ts_1.concatBytes)(Fp2.toBytes(c0), Fp2.toBytes(c1), Fp2.toBytes(c2)),
-        cmov: ({ c0, c1, c2 }, { c0: r0, c1: r1, c2: r2 }, c) => ({
+    }
+    addN(a, b) {
+        return this.add(a, b);
+    }
+    subN(a, b) {
+        return this.sub(a, b);
+    }
+    mulN(a, b) {
+        return this.mul(a, b);
+    }
+    sqrN(a) {
+        return this.sqr(a);
+    }
+    create(num) {
+        return num;
+    }
+    isValid({ c0, c1, c2 }) {
+        const { Fp2 } = this;
+        return Fp2.isValid(c0) && Fp2.isValid(c1) && Fp2.isValid(c2);
+    }
+    is0({ c0, c1, c2 }) {
+        const { Fp2 } = this;
+        return Fp2.is0(c0) && Fp2.is0(c1) && Fp2.is0(c2);
+    }
+    isValidNot0(num) {
+        return !this.is0(num) && this.isValid(num);
+    }
+    neg({ c0, c1, c2 }) {
+        const { Fp2 } = this;
+        return { c0: Fp2.neg(c0), c1: Fp2.neg(c1), c2: Fp2.neg(c2) };
+    }
+    eql({ c0, c1, c2 }, { c0: r0, c1: r1, c2: r2 }) {
+        const { Fp2 } = this;
+        return Fp2.eql(c0, r0) && Fp2.eql(c1, r1) && Fp2.eql(c2, r2);
+    }
+    sqrt(_) {
+        return (0, utils_ts_1.notImplemented)();
+    }
+    // Do we need division by bigint at all? Should be done via order:
+    div(lhs, rhs) {
+        const { Fp2 } = this;
+        const { Fp } = Fp2;
+        return this.mul(lhs, typeof rhs === 'bigint' ? Fp.inv(Fp.create(rhs)) : this.inv(rhs));
+    }
+    pow(num, power) {
+        return mod.FpPow(this, num, power);
+    }
+    invertBatch(nums) {
+        return mod.FpInvertBatch(this, nums);
+    }
+    inv({ c0, c1, c2 }) {
+        const { Fp2 } = this;
+        let t0 = Fp2.sub(Fp2.sqr(c0), Fp2.mulByNonresidue(Fp2.mul(c2, c1))); // c0² - c2 * c1 * (u + 1)
+        let t1 = Fp2.sub(Fp2.mulByNonresidue(Fp2.sqr(c2)), Fp2.mul(c0, c1)); // c2² * (u + 1) - c0 * c1
+        let t2 = Fp2.sub(Fp2.sqr(c1), Fp2.mul(c0, c2)); // c1² - c0 * c2
+        // 1/(((c2 * T1 + c1 * T2) * v) + c0 * T0)
+        let t4 = Fp2.inv(Fp2.add(Fp2.mulByNonresidue(Fp2.add(Fp2.mul(c2, t1), Fp2.mul(c1, t2))), Fp2.mul(c0, t0)));
+        return { c0: Fp2.mul(t4, t0), c1: Fp2.mul(t4, t1), c2: Fp2.mul(t4, t2) };
+    }
+    // Bytes utils
+    fromBytes(b) {
+        const { Fp2 } = this;
+        if (b.length !== this.BYTES)
+            throw new Error('fromBytes invalid length=' + b.length);
+        const B2 = Fp2.BYTES;
+        return {
+            c0: Fp2.fromBytes(b.subarray(0, B2)),
+            c1: Fp2.fromBytes(b.subarray(B2, B2 * 2)),
+            c2: Fp2.fromBytes(b.subarray(2 * B2)),
+        };
+    }
+    toBytes({ c0, c1, c2 }) {
+        const { Fp2 } = this;
+        return (0, utils_ts_1.concatBytes)(Fp2.toBytes(c0), Fp2.toBytes(c1), Fp2.toBytes(c2));
+    }
+    cmov({ c0, c1, c2 }, { c0: r0, c1: r1, c2: r2 }, c) {
+        const { Fp2 } = this;
+        return {
             c0: Fp2.cmov(c0, r0, c),
             c1: Fp2.cmov(c1, r1, c),
             c2: Fp2.cmov(c2, r2, c),
-        }),
-        fromBigSix: (t) => {
-            if (!Array.isArray(t) || t.length !== 6)
-                throw new Error('invalid Fp6 usage');
-            return {
-                c0: Fp2.fromBigTuple(t.slice(0, 2)),
-                c1: Fp2.fromBigTuple(t.slice(2, 4)),
-                c2: Fp2.fromBigTuple(t.slice(4, 6)),
-            };
-        },
-        frobeniusMap: ({ c0, c1, c2 }, power) => ({
+        };
+    }
+    fromBigSix(t) {
+        const { Fp2 } = this;
+        if (!Array.isArray(t) || t.length !== 6)
+            throw new Error('invalid Fp6 usage');
+        return {
+            c0: Fp2.fromBigTuple(t.slice(0, 2)),
+            c1: Fp2.fromBigTuple(t.slice(2, 4)),
+            c2: Fp2.fromBigTuple(t.slice(4, 6)),
+        };
+    }
+    frobeniusMap({ c0, c1, c2 }, power) {
+        const { Fp2 } = this;
+        return {
             c0: Fp2.frobeniusMap(c0, power),
-            c1: Fp2.mul(Fp2.frobeniusMap(c1, power), FP6_FROBENIUS_COEFFICIENTS_1[power % 6]),
-            c2: Fp2.mul(Fp2.frobeniusMap(c2, power), FP6_FROBENIUS_COEFFICIENTS_2[power % 6]),
-        }),
-        mulByFp2: ({ c0, c1, c2 }, rhs) => ({
+            c1: Fp2.mul(Fp2.frobeniusMap(c1, power), this.FROBENIUS_COEFFICIENTS_1[power % 6]),
+            c2: Fp2.mul(Fp2.frobeniusMap(c2, power), this.FROBENIUS_COEFFICIENTS_2[power % 6]),
+        };
+    }
+    mulByFp2({ c0, c1, c2 }, rhs) {
+        const { Fp2 } = this;
+        return {
             c0: Fp2.mul(c0, rhs),
             c1: Fp2.mul(c1, rhs),
             c2: Fp2.mul(c2, rhs),
-        }),
-        mulByNonresidue: ({ c0, c1, c2 }) => ({ c0: Fp2.mulByNonresidue(c2), c1: c0, c2: c1 }),
-        // Sparse multiplication
-        mul1: ({ c0, c1, c2 }, b1) => ({
+        };
+    }
+    mulByNonresidue({ c0, c1, c2 }) {
+        const { Fp2 } = this;
+        return { c0: Fp2.mulByNonresidue(c2), c1: c0, c2: c1 };
+    }
+    // Sparse multiplication
+    mul1({ c0, c1, c2 }, b1) {
+        const { Fp2 } = this;
+        return {
             c0: Fp2.mulByNonresidue(Fp2.mul(c2, b1)),
             c1: Fp2.mul(c0, b1),
             c2: Fp2.mul(c1, b1),
-        }),
-        // Sparse multiplication
-        mul01({ c0, c1, c2 }, b0, b1) {
-            let t0 = Fp2.mul(c0, b0); // c0 * b0
-            let t1 = Fp2.mul(c1, b1); // c1 * b1
-            return {
-                // ((c1 + c2) * b1 - T1) * (u + 1) + T0
-                c0: Fp2.add(Fp2.mulByNonresidue(Fp2.sub(Fp2.mul(Fp2.add(c1, c2), b1), t1)), t0),
-                // (b0 + b1) * (c0 + c1) - T0 - T1
-                c1: Fp2.sub(Fp2.sub(Fp2.mul(Fp2.add(b0, b1), Fp2.add(c0, c1)), t0), t1),
-                // (c0 + c2) * b0 - T0 + T1
-                c2: Fp2.add(Fp2.sub(Fp2.mul(Fp2.add(c0, c2), b0), t0), t1),
-            };
-        },
-    };
-    // Fp12
-    const FP12_FROBENIUS_COEFFICIENTS = calcFrobeniusCoefficients(Fp2, Fp2Nonresidue, Fp.ORDER, 12, 1, 6)[0];
-    const Fp12Add = ({ c0, c1 }, { c0: r0, c1: r1 }) => ({
-        c0: Fp6.add(c0, r0),
-        c1: Fp6.add(c1, r1),
-    });
-    const Fp12Subtract = ({ c0, c1 }, { c0: r0, c1: r1 }) => ({
-        c0: Fp6.sub(c0, r0),
-        c1: Fp6.sub(c1, r1),
-    });
-    const Fp12Multiply = ({ c0, c1 }, rhs) => {
+        };
+    }
+    // Sparse multiplication
+    mul01({ c0, c1, c2 }, b0, b1) {
+        const { Fp2 } = this;
+        let t0 = Fp2.mul(c0, b0); // c0 * b0
+        let t1 = Fp2.mul(c1, b1); // c1 * b1
+        return {
+            // ((c1 + c2) * b1 - T1) * (u + 1) + T0
+            c0: Fp2.add(Fp2.mulByNonresidue(Fp2.sub(Fp2.mul(Fp2.add(c1, c2), b1), t1)), t0),
+            // (b0 + b1) * (c0 + c1) - T0 - T1
+            c1: Fp2.sub(Fp2.sub(Fp2.mul(Fp2.add(b0, b1), Fp2.add(c0, c1)), t0), t1),
+            // (c0 + c2) * b0 - T0 + T1
+            c2: Fp2.add(Fp2.sub(Fp2.mul(Fp2.add(c0, c2), b0), t0), t1),
+        };
+    }
+}
+class _Field12 {
+    constructor(Fp6, opts) {
+        this.MASK = _1n;
+        const { Fp2 } = Fp6;
+        const { Fp } = Fp2;
+        this.Fp6 = Fp6;
+        this.ORDER = Fp2.ORDER; // TODO: verify if it's unuesd
+        this.BITS = 2 * Fp6.BITS;
+        this.BYTES = 2 * Fp6.BYTES;
+        this.isLE = Fp6.isLE;
+        this.ZERO = { c0: Fp6.ZERO, c1: Fp6.ZERO };
+        this.ONE = { c0: Fp6.ONE, c1: Fp6.ZERO };
+        this.FROBENIUS_COEFFICIENTS = calcFrobeniusCoefficients(Fp2, Fp2.NONRESIDUE, Fp.ORDER, 12, 1, 6)[0];
+        this.X_LEN = opts.X_LEN;
+        this.finalExponentiate = opts.Fp12finalExponentiate;
+    }
+    create(num) {
+        return num;
+    }
+    isValid({ c0, c1 }) {
+        const { Fp6 } = this;
+        return Fp6.isValid(c0) && Fp6.isValid(c1);
+    }
+    is0({ c0, c1 }) {
+        const { Fp6 } = this;
+        return Fp6.is0(c0) && Fp6.is0(c1);
+    }
+    isValidNot0(num) {
+        return !this.is0(num) && this.isValid(num);
+    }
+    neg({ c0, c1 }) {
+        const { Fp6 } = this;
+        return { c0: Fp6.neg(c0), c1: Fp6.neg(c1) };
+    }
+    eql({ c0, c1 }, { c0: r0, c1: r1 }) {
+        const { Fp6 } = this;
+        return Fp6.eql(c0, r0) && Fp6.eql(c1, r1);
+    }
+    sqrt(_) {
+        (0, utils_ts_1.notImplemented)();
+    }
+    inv({ c0, c1 }) {
+        const { Fp6 } = this;
+        let t = Fp6.inv(Fp6.sub(Fp6.sqr(c0), Fp6.mulByNonresidue(Fp6.sqr(c1)))); // 1 / (c0² - c1² * v)
+        return { c0: Fp6.mul(c0, t), c1: Fp6.neg(Fp6.mul(c1, t)) }; // ((C0 * T) * T) + (-C1 * T) * w
+    }
+    div(lhs, rhs) {
+        const { Fp6 } = this;
+        const { Fp2 } = Fp6;
+        const { Fp } = Fp2;
+        return this.mul(lhs, typeof rhs === 'bigint' ? Fp.inv(Fp.create(rhs)) : this.inv(rhs));
+    }
+    pow(num, power) {
+        return mod.FpPow(this, num, power);
+    }
+    invertBatch(nums) {
+        return mod.FpInvertBatch(this, nums);
+    }
+    // Normalized
+    add({ c0, c1 }, { c0: r0, c1: r1 }) {
+        const { Fp6 } = this;
+        return {
+            c0: Fp6.add(c0, r0),
+            c1: Fp6.add(c1, r1),
+        };
+    }
+    sub({ c0, c1 }, { c0: r0, c1: r1 }) {
+        const { Fp6 } = this;
+        return {
+            c0: Fp6.sub(c0, r0),
+            c1: Fp6.sub(c1, r1),
+        };
+    }
+    mul({ c0, c1 }, rhs) {
+        const { Fp6 } = this;
         if (typeof rhs === 'bigint')
@@ -384,4 +568,5 @@ return { c0: Fp6.mul(c0, rhs), c1: Fp6.mul(c1, rhs) };
         };
-    };
-    const Fp12Square = ({ c0, c1 }) => {
+    }
+    sqr({ c0, c1 }) {
+        const { Fp6 } = this;
         let ab = Fp6.mul(c0, c1); // c0 * c1
@@ -393,121 +578,148 @@ return {
         }; // AB + AB
-    };
-    function Fp4Square(a, b) {
-        const a2 = Fp2.sqr(a);
-        const b2 = Fp2.sqr(b);
+    }
+    // NonNormalized stuff
+    addN(a, b) {
+        return this.add(a, b);
+    }
+    subN(a, b) {
+        return this.sub(a, b);
+    }
+    mulN(a, b) {
+        return this.mul(a, b);
+    }
+    sqrN(a) {
+        return this.sqr(a);
+    }
+    // Bytes utils
+    fromBytes(b) {
+        const { Fp6 } = this;
+        if (b.length !== this.BYTES)
+            throw new Error('fromBytes invalid length=' + b.length);
         return {
-            first: Fp2.add(Fp2.mulByNonresidue(b2), a2), // b² * Nonresidue + a²
-            second: Fp2.sub(Fp2.sub(Fp2.sqr(Fp2.add(a, b)), a2), b2), // (a + b)² - a² - b²
+            c0: Fp6.fromBytes(b.subarray(0, Fp6.BYTES)),
+            c1: Fp6.fromBytes(b.subarray(Fp6.BYTES)),
         };
     }
-    const Fp12 = {
-        ORDER: Fp2.ORDER, // TODO: unused, but need to verify
-        isLE: Fp6.isLE,
-        BITS: 2 * Fp6.BITS,
-        BYTES: 2 * Fp6.BYTES,
-        MASK: (0, utils_ts_1.bitMask)(2 * Fp6.BITS),
-        ZERO: { c0: Fp6.ZERO, c1: Fp6.ZERO },
-        ONE: { c0: Fp6.ONE, c1: Fp6.ZERO },
-        create: (num) => num,
-        isValid: ({ c0, c1 }) => Fp6.isValid(c0) && Fp6.isValid(c1),
-        is0: ({ c0, c1 }) => Fp6.is0(c0) && Fp6.is0(c1),
-        isValidNot0: (num) => !Fp12.is0(num) && Fp12.isValid(num),
-        neg: ({ c0, c1 }) => ({ c0: Fp6.neg(c0), c1: Fp6.neg(c1) }),
-        eql: ({ c0, c1 }, { c0: r0, c1: r1 }) => Fp6.eql(c0, r0) && Fp6.eql(c1, r1),
-        sqrt: utils_ts_1.notImplemented,
-        inv: ({ c0, c1 }) => {
-            let t = Fp6.inv(Fp6.sub(Fp6.sqr(c0), Fp6.mulByNonresidue(Fp6.sqr(c1)))); // 1 / (c0² - c1² * v)
-            return { c0: Fp6.mul(c0, t), c1: Fp6.neg(Fp6.mul(c1, t)) }; // ((C0 * T) * T) + (-C1 * T) * w
-        },
-        div: (lhs, rhs) => Fp12.mul(lhs, typeof rhs === 'bigint' ? Fp.inv(Fp.create(rhs)) : Fp12.inv(rhs)),
-        pow: (num, power) => mod.FpPow(Fp12, num, power),
-        invertBatch: (nums) => mod.FpInvertBatch(Fp12, nums),
-        // Normalized
-        add: Fp12Add,
-        sub: Fp12Subtract,
-        mul: Fp12Multiply,
-        sqr: Fp12Square,
-        // NonNormalized stuff
-        addN: Fp12Add,
-        subN: Fp12Subtract,
-        mulN: Fp12Multiply,
-        sqrN: Fp12Square,
-        // Bytes utils
-        fromBytes: (b) => {
-            if (b.length !== Fp12.BYTES)
-                throw new Error('fromBytes invalid length=' + b.length);
-            return {
-                c0: Fp6.fromBytes(b.subarray(0, Fp6.BYTES)),
-                c1: Fp6.fromBytes(b.subarray(Fp6.BYTES)),
-            };
-        },
-        toBytes: ({ c0, c1 }) => (0, utils_ts_1.concatBytes)(Fp6.toBytes(c0), Fp6.toBytes(c1)),
-        cmov: ({ c0, c1 }, { c0: r0, c1: r1 }, c) => ({
+    toBytes({ c0, c1 }) {
+        const { Fp6 } = this;
+        return (0, utils_ts_1.concatBytes)(Fp6.toBytes(c0), Fp6.toBytes(c1));
+    }
+    cmov({ c0, c1 }, { c0: r0, c1: r1 }, c) {
+        const { Fp6 } = this;
+        return {
             c0: Fp6.cmov(c0, r0, c),
             c1: Fp6.cmov(c1, r1, c),
-        }),
-        // Utils
-        // toString() {
-        //   return '' + 'Fp12(' + this.c0 + this.c1 + '* w');
-        // },
-        // fromTuple(c: [Fp6, Fp6]) {
-        //   return new Fp12(...c);
-        // }
-        fromBigTwelve: (t) => ({
+        };
+    }
+    // Utils
+    // toString() {
+    //   return '' + 'Fp12(' + this.c0 + this.c1 + '* w');
+    // },
+    // fromTuple(c: [Fp6, Fp6]) {
+    //   return new Fp12(...c);
+    // }
+    fromBigTwelve(t) {
+        const { Fp6 } = this;
+        return {
             c0: Fp6.fromBigSix(t.slice(0, 6)),
             c1: Fp6.fromBigSix(t.slice(6, 12)),
-        }),
-        // Raises to q**i -th power
-        frobeniusMap(lhs, power) {
-            const { c0, c1, c2 } = Fp6.frobeniusMap(lhs.c1, power);
-            const coeff = FP12_FROBENIUS_COEFFICIENTS[power % 12];
-            return {
-                c0: Fp6.frobeniusMap(lhs.c0, power),
-                c1: Fp6.create({
-                    c0: Fp2.mul(c0, coeff),
-                    c1: Fp2.mul(c1, coeff),
-                    c2: Fp2.mul(c2, coeff),
-                }),
-            };
-        },
-        mulByFp2: ({ c0, c1 }, rhs) => ({
+        };
+    }
+    // Raises to q**i -th power
+    frobeniusMap(lhs, power) {
+        const { Fp6 } = this;
+        const { Fp2 } = Fp6;
+        const { c0, c1, c2 } = Fp6.frobeniusMap(lhs.c1, power);
+        const coeff = this.FROBENIUS_COEFFICIENTS[power % 12];
+        return {
+            c0: Fp6.frobeniusMap(lhs.c0, power),
+            c1: Fp6.create({
+                c0: Fp2.mul(c0, coeff),
+                c1: Fp2.mul(c1, coeff),
+                c2: Fp2.mul(c2, coeff),
+            }),
+        };
+    }
+    mulByFp2({ c0, c1 }, rhs) {
+        const { Fp6 } = this;
+        return {
             c0: Fp6.mulByFp2(c0, rhs),
             c1: Fp6.mulByFp2(c1, rhs),
-        }),
-        conjugate: ({ c0, c1 }) => ({ c0, c1: Fp6.neg(c1) }),
-        // Sparse multiplication
-        mul014: ({ c0, c1 }, o0, o1, o4) => {
-            let t0 = Fp6.mul01(c0, o0, o1);
-            let t1 = Fp6.mul1(c1, o4);
-            return {
-                c0: Fp6.add(Fp6.mulByNonresidue(t1), t0), // T1 * v + T0
-                // (c1 + c0) * [o0, o1+o4] - T0 - T1
-                c1: Fp6.sub(Fp6.sub(Fp6.mul01(Fp6.add(c1, c0), o0, Fp2.add(o1, o4)), t0), t1),
-            };
-        },
-        mul034: ({ c0, c1 }, o0, o3, o4) => {
-            const a = Fp6.create({
-                c0: Fp2.mul(c0.c0, o0),
-                c1: Fp2.mul(c0.c1, o0),
-                c2: Fp2.mul(c0.c2, o0),
-            });
-            const b = Fp6.mul01(c1, o3, o4);
-            const e = Fp6.mul01(Fp6.add(c0, c1), Fp2.add(o0, o3), o4);
-            return {
-                c0: Fp6.add(Fp6.mulByNonresidue(b), a),
-                c1: Fp6.sub(e, Fp6.add(a, b)),
-            };
-        },
-        // A cyclotomic group is a subgroup of Fp^n defined by
-        //   GΦₙ(p) = {α ∈ Fpⁿ : α^Φₙ(p) = 1}
-        // The result of any pairing is in a cyclotomic subgroup
-        // https://eprint.iacr.org/2009/565.pdf
-        _cyclotomicSquare: opts.Fp12cyclotomicSquare,
-        _cyclotomicExp: opts.Fp12cyclotomicExp,
-        // https://eprint.iacr.org/2010/354.pdf
-        // https://eprint.iacr.org/2009/565.pdf
-        finalExponentiate: opts.Fp12finalExponentiate,
-    };
-    return { Fp, Fp2, Fp6, Fp12, Fp4Square };
+        };
+    }
+    conjugate({ c0, c1 }) {
+        return { c0, c1: this.Fp6.neg(c1) };
+    }
+    // Sparse multiplication
+    mul014({ c0, c1 }, o0, o1, o4) {
+        const { Fp6 } = this;
+        const { Fp2 } = Fp6;
+        let t0 = Fp6.mul01(c0, o0, o1);
+        let t1 = Fp6.mul1(c1, o4);
+        return {
+            c0: Fp6.add(Fp6.mulByNonresidue(t1), t0), // T1 * v + T0
+            // (c1 + c0) * [o0, o1+o4] - T0 - T1
+            c1: Fp6.sub(Fp6.sub(Fp6.mul01(Fp6.add(c1, c0), o0, Fp2.add(o1, o4)), t0), t1),
+        };
+    }
+    mul034({ c0, c1 }, o0, o3, o4) {
+        const { Fp6 } = this;
+        const { Fp2 } = Fp6;
+        const a = Fp6.create({
+            c0: Fp2.mul(c0.c0, o0),
+            c1: Fp2.mul(c0.c1, o0),
+            c2: Fp2.mul(c0.c2, o0),
+        });
+        const b = Fp6.mul01(c1, o3, o4);
+        const e = Fp6.mul01(Fp6.add(c0, c1), Fp2.add(o0, o3), o4);
+        return {
+            c0: Fp6.add(Fp6.mulByNonresidue(b), a),
+            c1: Fp6.sub(e, Fp6.add(a, b)),
+        };
+    }
+    // A cyclotomic group is a subgroup of Fp^n defined by
+    //   GΦₙ(p) = {α ∈ Fpⁿ : α^Φₙ(p) = 1}
+    // The result of any pairing is in a cyclotomic subgroup
+    // https://eprint.iacr.org/2009/565.pdf
+    // https://eprint.iacr.org/2010/354.pdf
+    _cyclotomicSquare({ c0, c1 }) {
+        const { Fp6 } = this;
+        const { Fp2 } = Fp6;
+        const { c0: c0c0, c1: c0c1, c2: c0c2 } = c0;
+        const { c0: c1c0, c1: c1c1, c2: c1c2 } = c1;
+        const { first: t3, second: t4 } = Fp2.Fp4Square(c0c0, c1c1);
+        const { first: t5, second: t6 } = Fp2.Fp4Square(c1c0, c0c2);
+        const { first: t7, second: t8 } = Fp2.Fp4Square(c0c1, c1c2);
+        const t9 = Fp2.mulByNonresidue(t8); // T8 * (u + 1)
+        return {
+            c0: Fp6.create({
+                c0: Fp2.add(Fp2.mul(Fp2.sub(t3, c0c0), _2n), t3), // 2 * (T3 - c0c0)  + T3
+                c1: Fp2.add(Fp2.mul(Fp2.sub(t5, c0c1), _2n), t5), // 2 * (T5 - c0c1)  + T5
+                c2: Fp2.add(Fp2.mul(Fp2.sub(t7, c0c2), _2n), t7),
+            }), // 2 * (T7 - c0c2)  + T7
+            c1: Fp6.create({
+                c0: Fp2.add(Fp2.mul(Fp2.add(t9, c1c0), _2n), t9), // 2 * (T9 + c1c0) + T9
+                c1: Fp2.add(Fp2.mul(Fp2.add(t4, c1c1), _2n), t4), // 2 * (T4 + c1c1) + T4
+                c2: Fp2.add(Fp2.mul(Fp2.add(t6, c1c2), _2n), t6),
+            }),
+        }; // 2 * (T6 + c1c2) + T6
+    }
+    // https://eprint.iacr.org/2009/565.pdf
+    _cyclotomicExp(num, n) {
+        let z = this.ONE;
+        for (let i = this.X_LEN - 1; i >= 0; i--) {
+            z = this._cyclotomicSquare(z);
+            if ((0, utils_ts_1.bitGet)(n, i))
+                z = this.mul(z, num);
+        }
+        return z;
+    }
 }
+function tower12(opts) {
+    const Fp = mod.Field(opts.ORDER);
+    const Fp2 = new _Field2(Fp, opts);
+    const Fp6 = new _Field6(Fp2);
+    const Fp12 = new _Field12(Fp6, opts);
+    return { Fp, Fp2, Fp6, Fp12 };
+}
 //# sourceMappingURL=tower.js.map

abstract/tower.js.map

@@ -1,1 +0,1 @@
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abstract/weierstrass.d.ts

@@ -323,2 +323,3 @@ import { type CHash, type Hex, type PrivKey } from '../utils.ts';
  * const p256_sha224 = ecdsa(p256_Point, sha224);
+ * const p256_sha224_r = ecdsa(p256_Point, sha224, { randomBytes: (length) => { ... } });
  * ```
@@ -325,0 +326,0 @@ */

abstract/weierstrass.d.ts.map

@@ -1,1 +0,1 @@
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abstract/weierstrass.js

@@ -291,3 +291,3 @@ "use strict";
         (0, utils_ts_1._abytes2)(bytes, undefined, 'Point');
-        const { public: comp, publicUncompressed: uncomp } = lengths; // e.g. for 32-byte: 33, 65
+        const { publicKey: comp, publicKeyUncompressed: uncomp } = lengths; // e.g. for 32-byte: 33, 65
         const length = bytes.length;
@@ -736,2 +736,3 @@ const head = bytes[0];
     const wnaf = new curve_ts_1.wNAF(Point, extraOpts.endo ? Math.ceil(bits / 2) : bits);
+    Point.BASE.precompute(8); // Enable precomputes. Slows down first publicKey computation by 20ms.
     return Point;
@@ -869,5 +870,5 @@ }
     return {
-        secret: Fn.BYTES,
-        public: 1 + Fp.BYTES,
-        publicUncompressed: 1 + 2 * Fp.BYTES,
+        secretKey: Fn.BYTES,
+        publicKey: 1 + Fp.BYTES,
+        publicKeyUncompressed: 1 + 2 * Fp.BYTES,
         publicKeyHasPrefix: true,
@@ -894,3 +895,3 @@ signature: 2 * Fn.BYTES,
     function isValidPublicKey(publicKey, isCompressed) {
-        const { public: comp, publicUncompressed } = lengths;
+        const { publicKey: comp, publicKeyUncompressed } = lengths;
         try {
@@ -900,3 +901,3 @@ const l = publicKey.length;
                 return false;
-            if (isCompressed === false && l !== publicUncompressed)
+            if (isCompressed === false && l !== publicKeyUncompressed)
                 return false;
@@ -936,6 +937,7 @@ return !!Point.fromBytes(publicKey);
             return true;
-        if (Fn.allowedLengths || lengths.secret === lengths.public)
+        const { secretKey, publicKey, publicKeyUncompressed } = lengths;
+        if (Fn.allowedLengths || secretKey === publicKey)
             return undefined;
         const l = (0, utils_ts_1.ensureBytes)('key', item).length;
-        return l === lengths.public || l === lengths.publicUncompressed;
+        return l === publicKey || l === publicKeyUncompressed;
     }
@@ -986,2 +988,3 @@ /**
  * const p256_sha224 = ecdsa(p256_Point, sha224);
+ * const p256_sha224_r = ecdsa(p256_Point, sha224, { randomBytes: (length) => { ... } });
  * ```
@@ -998,4 +1001,4 @@ */
     });
-    const randomBytes_ = ecdsaOpts.randomBytes || utils_ts_1.randomBytes;
-    const hmac_ = ecdsaOpts.hmac ||
+    const randomBytes = ecdsaOpts.randomBytes || utils_ts_1.randomBytes;
+    const hmac = ecdsaOpts.hmac ||
         ((key, ...msgs) => (0, hmac_js_1.hmac)(hash, key, (0, utils_ts_1.concatBytes)(...msgs)));
@@ -1016,5 +1019,2 @@ const { Fp, Fn } = Point;
     }
-    function normalizeS(s) {
-        return isBiggerThanHalfOrder(s) ? Fn.neg(s) : s;
-    }
     function validateRS(title, num) {
@@ -1025,2 +1025,8 @@ if (!Fn.isValidNot0(num))
     }
+    function validateSigLength(bytes, format) {
+        validateSigFormat(format);
+        const size = lengths.signature;
+        const sizer = format === 'compact' ? size : format === 'recovered' ? size + 1 : undefined;
+        return (0, utils_ts_1._abytes2)(bytes, sizer, `${format} signature`);
+    }
     /**
@@ -1038,4 +1044,3 @@ * ECDSA signature with its (r, s) properties. Supports compact, recovered & DER representations.
         static fromBytes(bytes, format = defaultSigOpts_format) {
-            validateSigFormat(format);
-            const size = lengths.signature;
+            validateSigLength(bytes, format);
             let recid;
@@ -1047,3 +1052,2 @@ if (format === 'der') {
             if (format === 'recovered') {
-                (0, utils_ts_1._abytes2)(bytes, size + 1);
                 recid = bytes[0];
@@ -1053,4 +1057,3 @@ format = 'compact';
             }
-            (0, utils_ts_1._abytes2)(bytes, size);
-            const L = size / 2;
+            const L = Fn.BYTES;
             const r = bytes.subarray(0, L);
@@ -1066,3 +1069,3 @@ const s = bytes.subarray(L, L * 2);
         }
-        recoverPublicKey(msgHash) {
+        recoverPublicKey(messageHash) {
             const FIELD_ORDER = Fp.ORDER;
@@ -1089,3 +1092,3 @@ const { r, s, recovery: rec } = this;
             const ir = Fn.inv(radj); // r^-1
-            const h = bits2int_modN((0, utils_ts_1.ensureBytes)('msgHash', msgHash)); // Truncate hash
+            const h = bits2int_modN((0, utils_ts_1.ensureBytes)('msgHash', messageHash)); // Truncate hash
             const u1 = Fn.create(-h * ir); // -hr^-1
@@ -1149,3 +1152,3 @@ const u2 = Fn.create(s * ir); // sr^-1
     const bits2int = ecdsaOpts.bits2int ||
-        function (bytes) {
+        function bits2int_def(bytes) {
             // Our custom check "just in case", for protection against DoS
@@ -1161,10 +1164,8 @@ if (bytes.length > 8192)
     const bits2int_modN = ecdsaOpts.bits2int_modN ||
-        function (bytes) {
+        function bits2int_modN_def(bytes) {
             return Fn.create(bits2int(bytes)); // can't use bytesToNumberBE here
         };
-    // NOTE: pads output with zero as per spec
+    // Pads output with zero as per spec
     const ORDER_MASK = (0, utils_ts_1.bitMask)(fnBits);
-    /**
-     * Converts to bytes. Checks if num in `[0..ORDER_MASK-1]` e.g.: `[0..2^256-1]`.
-     */
+    /** Converts to bytes. Checks if num in `[0..ORDER_MASK-1]` e.g.: `[0..2^256-1]`. */
     function int2octets(num) {
@@ -1175,2 +1176,6 @@ // IMPORTANT: the check ensures working for case `Fn.BYTES != Fn.BITS * 8`
     }
+    function validateMsgAndHash(message, prehash) {
+        (0, utils_ts_1._abytes2)(message, undefined, 'message');
+        return prehash ? (0, utils_ts_1._abytes2)(hash(message), undefined, 'prehashed message') : message;
+    }
     /**
@@ -1188,6 +1193,3 @@ * Steps A, D of RFC6979 3.2.
         const { lowS, prehash, extraEntropy } = validateSigOpts(opts, defaultSigOpts);
-        // RFC6979 3.2: we skip step A, because we already provide hash
-        message = (0, utils_ts_1._abytes2)(message, undefined, 'message');
-        if (prehash)
-            message = (0, utils_ts_1._abytes2)(hash(message), undefined, 'prehashed message');
+        message = validateMsgAndHash(message, prehash); // RFC6979 3.2 A: h1 = H(m)
         // We can't later call bits2octets, since nested bits2int is broken for curves
@@ -1203,3 +1205,3 @@ // with fnBits % 8 !== 0. Because of that, we unwrap it here as int2octets call.
             // gen random bytes OR pass as-is
-            const e = extraEntropy === true ? randomBytes_(lengths.secret) : extraEntropy;
+            const e = extraEntropy === true ? randomBytes(lengths.secretKey) : extraEntropy;
             seedArgs.push((0, utils_ts_1.ensureBytes)('extraEntropy', e)); // check for being bytes
@@ -1234,3 +1236,3 @@ }
             if (lowS && isBiggerThanHalfOrder(s)) {
-                normS = normalizeS(s); // if lowS was passed, ensure s is always
+                normS = Fn.neg(s); // if lowS was passed, ensure s is always
                 recovery ^= 1; // // in the bottom half of N
@@ -1256,8 +1258,41 @@ }
         const { seed, k2sig } = prepSig(message, secretKey, opts); // Steps A, D of RFC6979 3.2.
-        const drbg = (0, utils_ts_1.createHmacDrbg)(hash.outputLen, Fn.BYTES, hmac_);
+        const drbg = (0, utils_ts_1.createHmacDrbg)(hash.outputLen, Fn.BYTES, hmac);
         const sig = drbg(seed, k2sig); // Steps B, C, D, E, F, G
         return sig;
     }
-    // Enable precomputes. Slows down first publicKey computation by 20ms.
-    Point.BASE.precompute(8);
+    function tryParsingSig(sg) {
+        // Try to deduce format
+        let sig = undefined;
+        const isHex = typeof sg === 'string' || (0, utils_ts_1.isBytes)(sg);
+        const isObj = !isHex &&
+            sg !== null &&
+            typeof sg === 'object' &&
+            typeof sg.r === 'bigint' &&
+            typeof sg.s === 'bigint';
+        if (!isHex && !isObj)
+            throw new Error('invalid signature, expected Uint8Array, hex string or Signature instance');
+        if (isObj) {
+            sig = new Signature(sg.r, sg.s);
+        }
+        else if (isHex) {
+            try {
+                sig = Signature.fromBytes((0, utils_ts_1.ensureBytes)('sig', sg), 'der');
+            }
+            catch (derError) {
+                if (!(derError instanceof exports.DER.Err))
+                    throw derError;
+            }
+            if (!sig) {
+                try {
+                    sig = Signature.fromBytes((0, utils_ts_1.ensureBytes)('sig', sg), 'compact');
+                }
+                catch (error) {
+                    return false;
+                }
+            }
+        }
+        if (!sig)
+            return false;
+        return sig;
+    }
     /**
@@ -1277,64 +1312,17 @@ * Verifies a signature against message and public key.
     function verify(signature, message, publicKey, opts = {}) {
-        const sg = signature;
-        message = (0, utils_ts_1.ensureBytes)('msgHash', message);
+        const { lowS, prehash, format } = validateSigOpts(opts, defaultSigOpts);
         publicKey = (0, utils_ts_1.ensureBytes)('publicKey', publicKey);
-        const { lowS, prehash, format } = validateSigOpts(opts, defaultSigOpts);
-        let _sig = undefined;
-        let P;
+        message = validateMsgAndHash((0, utils_ts_1.ensureBytes)('message', message), prehash);
         if ('strict' in opts)
             throw new Error('options.strict was renamed to lowS');
-        if (format === undefined) {
-            // Try to deduce format
-            const isHex = typeof sg === 'string' || (0, utils_ts_1.isBytes)(sg);
-            const isObj = !isHex &&
-                sg !== null &&
-                typeof sg === 'object' &&
-                typeof sg.r === 'bigint' &&
-                typeof sg.s === 'bigint';
-            if (!isHex && !isObj)
-                throw new Error('invalid signature, expected Uint8Array, hex string or Signature instance');
-            if (isObj) {
-                _sig = new Signature(sg.r, sg.s);
-            }
-            else if (isHex) {
-                // TODO: remove this malleable check
-                // Signature can be represented in 2 ways: compact (2*Fn.BYTES) & DER (variable-length).
-                // Since DER can also be 2*Fn.BYTES bytes, we check for it first.
-                try {
-                    _sig = Signature.fromDER(sg);
-                }
-                catch (derError) {
-                    if (!(derError instanceof exports.DER.Err))
-                        throw derError;
-                }
-                if (!_sig) {
-                    try {
-                        _sig = Signature.fromCompact(sg);
-                    }
-                    catch (error) {
-                        return false;
-                    }
-                }
-            }
-        }
-        else {
-            if (format === 'compact' || format === 'der') {
-                if (typeof sg !== 'string' && !(0, utils_ts_1.isBytes)(sg))
-                    throw new Error('"der" / "compact" format expects Uint8Array signature');
-                _sig = Signature.fromBytes((0, utils_ts_1.ensureBytes)('sig', sg), format);
-            }
-            else {
-                throw new Error('format must be "compact", "der" or "js"');
-            }
-        }
-        if (!_sig)
+        const sig = format === undefined
+            ? tryParsingSig(signature)
+            : Signature.fromBytes((0, utils_ts_1.ensureBytes)('sig', signature), format);
+        if (sig === false)
             return false;
         try {
-            P = Point.fromHex(publicKey);
-            if (lowS && _sig.hasHighS())
+            const P = Point.fromBytes(publicKey);
+            if (lowS && sig.hasHighS())
                 return false;
-            // todo: optional.hash => hash
-            if (prehash)
-                message = hash(message);
-            const { r, s } = _sig;
+            const { r, s } = sig;
             const h = bits2int_modN(message); // mod n, not mod p
@@ -1355,7 +1343,4 @@ const is = Fn.inv(s); // s^-1 mod n
     function recoverPublicKey(signature, message, opts = {}) {
-        const prehash = opts.prehash !== undefined ? opts.prehash : defaultSigOpts.prehash;
-        (0, utils_ts_1._abool2)(prehash, 'prehash');
-        message = (0, utils_ts_1._abytes2)(message, undefined, 'message');
-        if (prehash)
-            message = (0, utils_ts_1._abytes2)(hash(message), undefined, 'prehashed message');
+        const { prehash } = validateSigOpts(opts, defaultSigOpts);
+        message = validateMsgAndHash(message, prehash);
         return Signature.fromBytes(signature, 'recovered').recoverPublicKey(message).toBytes();
@@ -1362,0 +1347,0 @@ }

abstract/weierstrass.js.map

@@ -1,1 +0,1 @@
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bls12-381.d.ts.map

@@ -1,1 +0,1 @@
-{"version":3,"file":"bls12-381.d.ts","sourceRoot":"","sources":["src/bls12-381.ts"],"names":[],"mappings":"AAgFA,OAAO,EAAO,KAAK,OAAO,EAAE,MAAM,mBAAmB,CAAC;AACtD,OAAO,EAAS,KAAK,MAAM,EAAE,MAAM,uBAAuB,CAAC;AAoE3D,eAAO,MAAM,YAAY,EAAE,MAAM,CAAC,MAAM,CAAuD,CAAC;AA0VhG;;;;;;;;;;GAUG;AACH,eAAO,MAAM,SAAS,EAAE,OA8HtB,CAAC"}
+{"version":3,"file":"bls12-381.d.ts","sourceRoot":"","sources":["src/bls12-381.ts"],"names":[],"mappings":"AAgFA,OAAO,EAAO,KAAK,OAAO,EAAE,MAAM,mBAAmB,CAAC;AACtD,OAAO,EAAS,KAAK,MAAM,EAAE,MAAM,uBAAuB,CAAC;AAmE3D,eAAO,MAAM,YAAY,EAAE,MAAM,CAAC,MAAM,CAGtC,CAAC;AAuTH;;;;;;;;;;GAUG;AACH,eAAO,MAAM,SAAS,EAAE,OA8HtB,CAAC"}

bls12-381.js

@@ -124,6 +124,9 @@ "use strict";
 // CURVE FIELDS
-exports.bls12_381_Fr = (0, modular_ts_1.Field)(bls12_381_CURVE_G1.n, { modFromBytes: true });
-const { Fp, Fp2, Fp6, Fp4Square, Fp12 } = (0, tower_ts_1.tower12)({
-    // Order of Fp
+exports.bls12_381_Fr = (0, modular_ts_1.Field)(bls12_381_CURVE_G1.n, {
+    modFromBytes: true,
+    isLE: true,
+});
+const { Fp, Fp2, Fp6, Fp12 } = (0, tower_ts_1.tower12)({
     ORDER: bls12_381_CURVE_G1.p,
+    X_LEN: BLS_X_LEN,
     // Finite extension field over irreducible polynominal.
@@ -138,38 +141,2 @@ // Fp(u) / (u² - β) where β = -1
     },
-    // Fp12
-    // A cyclotomic group is a subgroup of Fp^n defined by
-    //   GΦₙ(p) = {α ∈ Fpⁿ : α^Φₙ(p) = 1}
-    // The result of any pairing is in a cyclotomic subgroup
-    // https://eprint.iacr.org/2009/565.pdf
-    Fp12cyclotomicSquare: ({ c0, c1 }) => {
-        const { c0: c0c0, c1: c0c1, c2: c0c2 } = c0;
-        const { c0: c1c0, c1: c1c1, c2: c1c2 } = c1;
-        const { first: t3, second: t4 } = Fp4Square(c0c0, c1c1);
-        const { first: t5, second: t6 } = Fp4Square(c1c0, c0c2);
-        const { first: t7, second: t8 } = Fp4Square(c0c1, c1c2);
-        const t9 = Fp2.mulByNonresidue(t8); // T8 * (u + 1)
-        return {
-            c0: Fp6.create({
-                c0: Fp2.add(Fp2.mul(Fp2.sub(t3, c0c0), _2n), t3), // 2 * (T3 - c0c0)  + T3
-                c1: Fp2.add(Fp2.mul(Fp2.sub(t5, c0c1), _2n), t5), // 2 * (T5 - c0c1)  + T5
-                c2: Fp2.add(Fp2.mul(Fp2.sub(t7, c0c2), _2n), t7),
-            }), // 2 * (T7 - c0c2)  + T7
-            c1: Fp6.create({
-                c0: Fp2.add(Fp2.mul(Fp2.add(t9, c1c0), _2n), t9), // 2 * (T9 + c1c0) + T9
-                c1: Fp2.add(Fp2.mul(Fp2.add(t4, c1c1), _2n), t4), // 2 * (T4 + c1c1) + T4
-                c2: Fp2.add(Fp2.mul(Fp2.add(t6, c1c2), _2n), t6),
-            }),
-        }; // 2 * (T6 + c1c2) + T6
-    },
-    Fp12cyclotomicExp(num, n) {
-        let z = Fp12.ONE;
-        for (let i = BLS_X_LEN - 1; i >= 0; i--) {
-            z = Fp12._cyclotomicSquare(z);
-            if ((0, utils_ts_1.bitGet)(n, i))
-                z = Fp12.mul(z, num);
-        }
-        return z;
-    },
-    // https://eprint.iacr.org/2010/354.pdf
-    // https://eprint.iacr.org/2009/565.pdf
     Fp12finalExponentiate: (num) => {
@@ -176,0 +143,0 @@ const x = BLS_X;

bls12-381.js.map

@@ -1,1 +0,1 @@
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bn254.d.ts.map

@@ -1,1 +0,1 @@
-{"version":3,"file":"bn254.d.ts","sourceRoot":"","sources":["src/bn254.ts"],"names":[],"mappings":"AAyDA,OAAO,EAEL,KAAK,OAAO,IAAI,UAAU,EAC1B,KAAK,gBAAgB,EAEtB,MAAM,mBAAmB,CAAC;AAC3B,OAAO,EAAS,KAAK,MAAM,EAAE,MAAM,uBAAuB,CAAC;AAG3D,OAAO,EAAE,KAAK,OAAO,EAAqC,MAAM,2BAA2B,CAAC;AAsB5F,eAAO,MAAM,QAAQ,EAAE,MAAM,CAAC,MAAM,CAA2B,CAAC;AAqFhE,eAAO,MAAM,eAAe,EAAE,gBAY7B,CAAC;AAmBF;;;GAGG;AACH,eAAO,MAAM,KAAK,EAAE,UAgDlB,CAAC;AAEH;;;;;GAKG;AACH,eAAO,MAAM,iBAAiB,EAAE,OAS9B,CAAC"}
+{"version":3,"file":"bn254.d.ts","sourceRoot":"","sources":["src/bn254.ts"],"names":[],"mappings":"AAyDA,OAAO,EAEL,KAAK,OAAO,IAAI,UAAU,EAC1B,KAAK,gBAAgB,EAEtB,MAAM,mBAAmB,CAAC;AAC3B,OAAO,EAAS,KAAK,MAAM,EAAE,MAAM,uBAAuB,CAAC;AAG3D,OAAO,EAAE,KAAK,OAAO,EAAqC,MAAM,2BAA2B,CAAC;AAsB5F,eAAO,MAAM,QAAQ,EAAE,MAAM,CAAC,MAAM,CAA2B,CAAC;AAsDhE,eAAO,MAAM,eAAe,EAAE,gBAY7B,CAAC;AAmBF;;;GAGG;AACH,eAAO,MAAM,KAAK,EAAE,UAgDlB,CAAC;AAEH;;;;;GAKG;AACH,eAAO,MAAM,iBAAiB,EAAE,OAS9B,CAAC"}

bn254.js

@@ -89,39 +89,7 @@ "use strict";
 };
-const { Fp, Fp2, Fp6, Fp4Square, Fp12 } = (0, tower_ts_1.tower12)({
+const { Fp, Fp2, Fp6, Fp12 } = (0, tower_ts_1.tower12)({
     ORDER: bn254_G1_CURVE.p,
+    X_LEN: BN_X_LEN,
     FP2_NONRESIDUE: [BigInt(9), _1n],
     Fp2mulByB: (num) => Fp2.mul(num, Fp2B),
-    // The result of any pairing is in a cyclotomic subgroup
-    // https://eprint.iacr.org/2009/565.pdf
-    Fp12cyclotomicSquare: ({ c0, c1 }) => {
-        const { c0: c0c0, c1: c0c1, c2: c0c2 } = c0;
-        const { c0: c1c0, c1: c1c1, c2: c1c2 } = c1;
-        const { first: t3, second: t4 } = Fp4Square(c0c0, c1c1);
-        const { first: t5, second: t6 } = Fp4Square(c1c0, c0c2);
-        const { first: t7, second: t8 } = Fp4Square(c0c1, c1c2);
-        let t9 = Fp2.mulByNonresidue(t8); // T8 * (u + 1)
-        return {
-            c0: Fp6.create({
-                c0: Fp2.add(Fp2.mul(Fp2.sub(t3, c0c0), _2n), t3), // 2 * (T3 - c0c0)  + T3
-                c1: Fp2.add(Fp2.mul(Fp2.sub(t5, c0c1), _2n), t5), // 2 * (T5 - c0c1)  + T5
-                c2: Fp2.add(Fp2.mul(Fp2.sub(t7, c0c2), _2n), t7),
-            }), // 2 * (T7 - c0c2)  + T7
-            c1: Fp6.create({
-                c0: Fp2.add(Fp2.mul(Fp2.add(t9, c1c0), _2n), t9), // 2 * (T9 + c1c0) + T9
-                c1: Fp2.add(Fp2.mul(Fp2.add(t4, c1c1), _2n), t4), // 2 * (T4 + c1c1) + T4
-                c2: Fp2.add(Fp2.mul(Fp2.add(t6, c1c2), _2n), t6),
-            }),
-        }; // 2 * (T6 + c1c2) + T6
-    },
-    Fp12cyclotomicExp(num, n) {
-        let z = Fp12.ONE;
-        for (let i = BN_X_LEN - 1; i >= 0; i--) {
-            z = Fp12._cyclotomicSquare(z);
-            if ((0, utils_ts_1.bitGet)(n, i))
-                z = Fp12.mul(z, num);
-        }
-        return z;
-    },
-    // https://eprint.iacr.org/2010/354.pdf
-    // https://eprint.iacr.org/2009/565.pdf
     Fp12finalExponentiate: (num) => {
@@ -128,0 +96,0 @@ const powMinusX = (num) => Fp12.conjugate(Fp12._cyclotomicExp(num, BN_X));

bn254.js.map

@@ -1,1 +0,1 @@
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ed25519.js

@@ -23,12 +23,11 @@ "use strict";
 // prettier-ignore
-const _0n = BigInt(0), _1n = BigInt(1), _2n = BigInt(2), _3n = BigInt(3);
+const _0n = /* @__PURE__ */ BigInt(0), _1n = BigInt(1), _2n = BigInt(2), _3n = BigInt(3);
 // prettier-ignore
 const _5n = BigInt(5), _8n = BigInt(8);
-// 2n**255n-19n
+// P = 2n**255n-19n
 const ed25519_CURVE_p = BigInt('0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffed');
-// P = 2n**255n - 19n
 // N = 2n**252n + 27742317777372353535851937790883648493n
 // a = Fp.create(BigInt(-1))
 // d = -121665/121666 a.k.a. Fp.neg(121665 * Fp.inv(121666))
-const ed25519_CURVE = {
+const ed25519_CURVE = /* @__PURE__ */ (() => ({
     p: ed25519_CURVE_p,
@@ -41,3 +40,3 @@ n: BigInt('0x1000000000000000000000000000000014def9dea2f79cd65812631a5cf5d3ed'),
     Gy: BigInt('0x6666666666666666666666666666666666666666666666666666666666666658'),
-};
+}))();
 function ed25519_pow_2_252_3(x) {
@@ -146,3 +145,3 @@ // prettier-ignore
 exports.x25519 = (() => {
-    const P = exports.ed25519.CURVE.Fp.ORDER;
+    const P = Fp.ORDER;
     return (0, montgomery_ts_1.montgomery)({
@@ -162,3 +161,3 @@ P,
 // SageMath returns different root first and everything falls apart
-const ELL2_C1 = /* @__PURE__ */ (() => (Fp.ORDER + _3n) / _8n)(); // 1. c1 = (q + 3) / 8       # Integer arithmetic
+const ELL2_C1 = /* @__PURE__ */ (() => (ed25519_CURVE_p + _3n) / _8n)(); // 1. c1 = (q + 3) / 8       # Integer arithmetic
 const ELL2_C2 = /* @__PURE__ */ (() => Fp.pow(_2n, ELL2_C1))(); // 2. c2 = 2^c1
@@ -168,3 +167,3 @@ const ELL2_C3 = /* @__PURE__ */ (() => Fp.sqrt(Fp.neg(Fp.ONE)))(); // 3. c3 = sqrt(-1)
 function map_to_curve_elligator2_curve25519(u) {
-    const ELL2_C4 = (Fp.ORDER - _5n) / _8n; // 4. c4 = (q - 5) / 8       # Integer arithmetic
+    const ELL2_C4 = (ed25519_CURVE_p - _5n) / _8n; // 4. c4 = (q - 5) / 8       # Integer arithmetic
     const ELL2_J = BigInt(486662);
@@ -233,3 +232,3 @@ let tv1 = Fp.sqr(u); //  1.  tv1 = u^2
     encodeDST: 'edwards25519_XMD:SHA-512_ELL2_NU_',
-    p: Fp.ORDER,
+    p: ed25519_CURVE_p,
     m: 1,
@@ -261,3 +260,3 @@ k: 128,
     const { d } = ed25519_CURVE;
-    const P = Fp.ORDER;
+    const P = ed25519_CURVE_p;
     const mod = (n) => Fp.create(n);
@@ -327,3 +326,3 @@ const r = mod(SQRT_M1 * r0 * r0); // 1
         // 3. Check that s is non-negative, or else abort
-        if (!(0, utils_ts_1.equalBytes)((0, utils_ts_1.numberToBytesLE)(s, 32), bytes) || (0, modular_ts_1.isNegativeLE)(s, P))
+        if (!(0, utils_ts_1.equalBytes)(Fp.toBytes(s), bytes) || (0, modular_ts_1.isNegativeLE)(s, P))
             throw new Error('invalid ristretto255 encoding 1');
@@ -391,3 +390,3 @@ const s2 = mod(s * s);
             s = mod(-s);
-        return (0, utils_ts_1.numberToBytesLE)(s, 32); // 11
+        return Fp.toBytes(s); // 11
     }
@@ -431,7 +430,8 @@ /**
         const DST = options?.DST || 'ristretto255_XMD:SHA-512_R255MAP_RO_';
-        return ristretto255_map((0, hash_to_curve_ts_1.expand_message_xmd)(msg, DST, 64, sha2_js_1.sha512));
+        const xmd = (0, hash_to_curve_ts_1.expand_message_xmd)(msg, DST, 64, sha2_js_1.sha512);
+        return ristretto255_map(xmd);
     },
     hashToScalar(msg, options = { DST: hash_to_curve_ts_1._DST_scalar }) {
         const xmd = (0, hash_to_curve_ts_1.expand_message_xmd)(msg, options.DST, 64, sha2_js_1.sha512);
-        return exports.ristretto255.Point.Fn.create((0, utils_ts_1.bytesToNumberLE)(xmd));
+        return Fn.create((0, utils_ts_1.bytesToNumberLE)(xmd));
     },
@@ -438,0 +438,0 @@ };

ed25519.js.map

@@ -1,1 +0,1 @@
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ed448.d.ts

@@ -33,7 +33,6 @@ import type { AffinePoint } from './abstract/curve.ts';
 export declare const ed448_hasher: H2CHasher<bigint>;
-type ExtendedPoint = EdwardsPoint;
 /**
- * Each ed448/ExtendedPoint has 4 different equivalent points. This can be
+ * Each ed448/EdwardsPoint has 4 different equivalent points. This can be
  * a source of bugs for protocols like ring signatures. Decaf was created to solve this.
- * Decaf point operates in X:Y:Z:T extended coordinates like ExtendedPoint,
+ * Decaf point operates in X:Y:Z:T extended coordinates like EdwardsPoint,
  * but it should work in its own namespace: do not combine those two.
@@ -47,3 +46,3 @@ * See [RFC9496](https://www.rfc-editor.org/rfc/rfc9496).
     static Fn: IField<bigint>;
-    constructor(ep: ExtendedPoint);
+    constructor(ep: EdwardsPoint);
     static fromAffine(ap: AffinePoint<bigint>): _DecafPoint;
@@ -50,0 +49,0 @@ protected assertSame(other: _DecafPoint): void;

ed448.d.ts.map

@@ -1,1 +0,1 @@
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ed448.js

@@ -101,6 +101,10 @@ "use strict";
 // Finite field 2n**448n - 2n**224n - 1n
+// The value fits in 448 bits, but we use 456-bit (57-byte) elements because of bitflags.
+// - ed25519 fits in 255 bits, allowing using last 1 byte for specifying bit flag of point negation.
+// - ed448 fits in 448 bits. We can't use last 1 byte: we can only use a bit 224 in the middle.
 const Fp = /* @__PURE__ */ (() => (0, modular_ts_1.Field)(ed448_CURVE.p, { BITS: 456, isLE: true }))();
-// RFC 7748 has 56-byte keys, RFC 8032 has 57-byte keys
-const Fn = /* @__PURE__ */ (() => (0, modular_ts_1.Field)(ed448_CURVE.n, { BITS: 448, isLE: true }))();
-// Fn456 has BITS: 456
+const Fn = /* @__PURE__ */ (() => (0, modular_ts_1.Field)(ed448_CURVE.n, { BITS: 456, isLE: true }))();
+// decaf448 uses 448-bit (56-byte) keys
+const Fp448 = /* @__PURE__ */ (() => (0, modular_ts_1.Field)(ed448_CURVE.p, { BITS: 448, isLE: true }))();
+const Fn448 = /* @__PURE__ */ (() => (0, modular_ts_1.Field)(ed448_CURVE.n, { BITS: 448, isLE: true }))();
 // SHAKE256(dom4(phflag,context)||x, 114)
@@ -110,3 +114,3 @@ function dom4(data, ctx, phflag) {
         throw new Error('context must be smaller than 255, got: ' + ctx.length);
-    return (0, utils_js_1.concatBytes)((0, utils_js_1.utf8ToBytes)('SigEd448'), new Uint8Array([phflag ? 1 : 0, ctx.length]), ctx, data);
+    return (0, utils_js_1.concatBytes)((0, utils_ts_1.asciiToBytes)('SigEd448'), new Uint8Array([phflag ? 1 : 0, ctx.length]), ctx, data);
 }
@@ -119,2 +123,3 @@ // const ed448_eddsa_opts = { adjustScalarBytes, domain: dom4 };
     Fn,
+    nBitLength: Fn.BITS,
     hash: shake256_114,
@@ -258,4 +263,2 @@ adjustScalarBytes,
 const invertSqrt = (number) => uvRatio(_1n, number);
-const MAX_448B = /* @__PURE__ */ BigInt('0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff');
-const bytes448ToNumberLE = (bytes) => Fp.create((0, utils_ts_1.bytesToNumberLE)(bytes) & MAX_448B);
 /**
@@ -293,5 +296,9 @@ * Elligator map for hash-to-curve of decaf448.
     (0, utils_js_1.abytes)(bytes, 112);
-    const r1 = bytes448ToNumberLE(bytes.slice(0, 56));
+    const skipValidation = true;
+    // Note: Similar to the field element decoding described in
+    // [RFC7748], and unlike the field element decoding described in
+    // Section 5.3.1, non-canonical values are accepted.
+    const r1 = Fp448.create(Fp448.fromBytes(bytes.subarray(0, 56), skipValidation));
     const R1 = calcElligatorDecafMap(r1);
-    const r2 = bytes448ToNumberLE(bytes.slice(56, 112));
+    const r2 = Fp448.create(Fp448.fromBytes(bytes.subarray(56, 112), skipValidation));
     const R2 = calcElligatorDecafMap(r2);
@@ -301,5 +308,5 @@ return new _DecafPoint(R1.add(R2));
 /**
- * Each ed448/ExtendedPoint has 4 different equivalent points. This can be
+ * Each ed448/EdwardsPoint has 4 different equivalent points. This can be
  * a source of bugs for protocols like ring signatures. Decaf was created to solve this.
- * Decaf point operates in X:Y:Z:T extended coordinates like ExtendedPoint,
+ * Decaf point operates in X:Y:Z:T extended coordinates like EdwardsPoint,
  * but it should work in its own namespace: do not combine those two.
@@ -330,7 +337,7 @@ * See [RFC9496](https://www.rfc-editor.org/rfc/rfc9496).
         const P = Fp.ORDER;
-        const mod = (n) => Fp.create(n);
-        const s = bytes448ToNumberLE(bytes);
+        const mod = (n) => Fp448.create(n);
+        const s = Fp448.fromBytes(bytes);
         // 1. Check that s_bytes is the canonical encoding of a field element, or else abort.
         // 2. Check that s is non-negative, or else abort
-        if (!(0, utils_ts_1.equalBytes)((0, utils_ts_1.numberToBytesLE)(s, 56), bytes) || (0, modular_ts_1.isNegativeLE)(s, P))
+        if (!(0, utils_ts_1.equalBytes)(Fn448.toBytes(s), bytes) || (0, modular_ts_1.isNegativeLE)(s, P))
             throw new Error('invalid decaf448 encoding 1');
@@ -382,3 +389,3 @@ const s2 = mod(s * s); // 1
             s = mod(-s);
-        return (0, utils_ts_1.numberToBytesLE)(s, 56);
+        return Fn448.toBytes(s);
     }
@@ -393,5 +400,4 @@ /**
         const { X: X2, Y: Y2 } = other.ep;
-        const mod = (n) => Fp.create(n);
         // (x1 * y2 == y1 * x2)
-        return mod(X1 * Y2) === mod(Y1 * X2);
+        return Fp.create(X1 * Y2) === Fp.create(Y1 * X2);
     }
@@ -411,6 +417,6 @@ is0() {
 _DecafPoint.Fp = 
-/* @__PURE__ */ (() => Fp)();
+/* @__PURE__ */ (() => Fp448)();
 // prettier-ignore
 _DecafPoint.Fn = 
-/* @__PURE__ */ (() => Fn)();
+/* @__PURE__ */ (() => Fn448)();
 exports.decaf448 = { Point: _DecafPoint };
@@ -423,4 +429,9 @@ /** Hashing to decaf448 points / field. RFC 9380 methods. */
     },
+    // Warning: has big modulo bias of 2^-64.
+    // RFC is invalid. RFC says "use 64-byte xof", while for 2^-112 bias
+    // it must use 84-byte xof (56+56/2), not 64.
     hashToScalar(msg, options = { DST: hash_to_curve_ts_1._DST_scalar }) {
-        return Fn.create((0, utils_ts_1.bytesToNumberLE)((0, hash_to_curve_ts_1.expand_message_xof)(msg, options.DST, 64, 256, sha3_js_1.shake256)));
+        // Can't use `Fn448.fromBytes()`. 64-byte input => 56-byte field element
+        const xof = (0, hash_to_curve_ts_1.expand_message_xof)(msg, options.DST, 64, 256, sha3_js_1.shake256);
+        return Fn448.create((0, utils_ts_1.bytesToNumberLE)(xof));
     },
@@ -427,0 +438,0 @@ };

ed448.js.map

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esm/abstract/bls.d.ts

@@ -29,5 +29,5 @@ /**
     toBytes(point: WeierstrassPoint<Fp>): Uint8Array;
+    toHex(point: WeierstrassPoint<Fp>): string;
     /** @deprecated use `toBytes` */
     toRawBytes(point: WeierstrassPoint<Fp>): Uint8Array;
-    toHex(point: WeierstrassPoint<Fp>): string;
 };
@@ -38,5 +38,5 @@ export type SignatureCoder<Fp> = {
     toBytes(point: WeierstrassPoint<Fp>): Uint8Array;
+    toHex(point: WeierstrassPoint<Fp>): string;
     /** @deprecated use `toBytes` */
     toRawBytes(point: WeierstrassPoint<Fp>): Uint8Array;
-    toHex(point: WeierstrassPoint<Fp>): string;
 };
@@ -43,0 +43,0 @@ export type BlsFields = {

esm/abstract/bls.d.ts.map

@@ -1,1 +0,1 @@
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+{"version":3,"file":"bls.d.ts","sourceRoot":"","sources":["../../src/abstract/bls.ts"],"names":[],"mappings":"AAAA;;;;;;;;;;;;;;;IAeI;AACJ,sEAAsE;AACtE,OAAO,EAKL,KAAK,KAAK,EACV,KAAK,GAAG,EACR,KAAK,OAAO,EACb,MAAM,aAAa,CAAC;AAErB,OAAO,EAEL,KAAK,SAAS,EACd,KAAK,WAAW,EAChB,KAAK,OAAO,EAEZ,KAAK,YAAY,EACjB,KAAK,UAAU,EAChB,MAAM,oBAAoB,CAAC;AAC5B,OAAO,EAAoC,KAAK,MAAM,EAAE,MAAM,cAAc,CAAC;AAC7E,OAAO,KAAK,EAAE,IAAI,EAAE,OAAO,EAAE,GAAG,EAAE,MAAM,EAAE,MAAM,EAAE,MAAM,YAAY,CAAC;AACrE,OAAO,EAGL,KAAK,cAAc,EACnB,KAAK,eAAe,EACpB,KAAK,gBAAgB,EACrB,KAAK,oBAAoB,EAC1B,MAAM,kBAAkB,CAAC;AAE1B,KAAK,EAAE,GAAG,MAAM,CAAC;AAKjB,MAAM,MAAM,SAAS,GAAG,gBAAgB,GAAG,UAAU,CAAC;AAEtD,MAAM,MAAM,mBAAmB,CAAC,EAAE,IAAI;IACpC,SAAS,CAAC,KAAK,EAAE,UAAU,GAAG,gBAAgB,CAAC,EAAE,CAAC,CAAC;IACnD,OAAO,CAAC,GAAG,EAAE,GAAG,GAAG,gBAAgB,CAAC,EAAE,CAAC,CAAC;IACxC,OAAO,CAAC,KAAK,EAAE,gBAAgB,CAAC,EAAE,CAAC,GAAG,UAAU,CAAC;IACjD,KAAK,CAAC,KAAK,EAAE,gBAAgB,CAAC,EAAE,CAAC,GAAG,MAAM,CAAC;IAC3C,gCAAgC;IAChC,UAAU,CAAC,KAAK,EAAE,gBAAgB,CAAC,EAAE,CAAC,GAAG,UAAU,CAAC;CACrD,CAAC;AAEF,MAAM,MAAM,cAAc,CAAC,EAAE,IAAI;IAC/B,SAAS,CAAC,KAAK,EAAE,UAAU,GAAG,gBAAgB,CAAC,EAAE,CAAC,CAAC;IACnD,OAAO,CAAC,GAAG,EAAE,GAAG,GAAG,gBAAgB,CAAC,EAAE,CAAC,CAAC;IACxC,OAAO,CAAC,KAAK,EAAE,gBAAgB,CAAC,EAAE,CAAC,GAAG,UAAU,CAAC;IACjD,KAAK,CAAC,KAAK,EAAE,gBAAgB,CAAC,EAAE,CAAC,GAAG,MAAM,CAAC;IAC3C,gCAAgC;IAChC,UAAU,CAAC,KAAK,EAAE,gBAAgB,CAAC,EAAE,CAAC,GAAG,UAAU,CAAC;CACrD,CAAC;AAEF,MAAM,MAAM,SAAS,GAAG;IACtB,EAAE,EAAE,MAAM,CAAC,EAAE,CAAC,CAAC;IACf,EAAE,EAAE,MAAM,CAAC,MAAM,CAAC,CAAC;IACnB,GAAG,EAAE,MAAM,CAAC;IACZ,GAAG,EAAE,MAAM,CAAC;IACZ,IAAI,EAAE,OAAO,CAAC;CACf,CAAC;AAEF,MAAM,MAAM,wBAAwB,GAAG,CACrC,EAAE,EAAE,GAAG,EACP,EAAE,EAAE,GAAG,EACP,EAAE,EAAE,GAAG,EACP,EAAE,EAAE,GAAG,EACP,EAAE,EAAE,GAAG,KACJ;IAAE,EAAE,EAAE,GAAG,CAAC;IAAC,EAAE,EAAE,GAAG,CAAC;IAAC,EAAE,EAAE,GAAG,CAAA;CAAE,CAAC;AACnC,MAAM,MAAM,gBAAgB,GAAG,CAC7B,EAAE,EAAE,GAAG,EACP,EAAE,EAAE,GAAG,EACP,EAAE,EAAE,GAAG,EACP,EAAE,EAAE,GAAG,EACP,EAAE,EAAE,GAAG,EACP,QAAQ,EAAE,wBAAwB,KAC/B,IAAI,CAAC;AACV,MAAM,MAAM,UAAU,GAAG;IACvB,IAAI,EAAE,OAAO,CAAC;IACd,sBAAsB,EAAE,CAAC,CAAC,EAAE,gBAAgB,CAAC,GAAG,CAAC,KAAK,UAAU,CAAC;IACjE,eAAe,EAAE,CAAC,KAAK,EAAE,CAAC,UAAU,EAAE,EAAE,EAAE,EAAE,CAAC,EAAE,KAAK,IAAI,CAAC;IACzD,OAAO,EAAE,CAAC,CAAC,EAAE,gBAAgB,CAAC,EAAE,CAAC,EAAE,CAAC,EAAE,gBAAgB,CAAC,GAAG,CAAC,EAAE,iBAAiB,CAAC,EAAE,OAAO,KAAK,IAAI,CAAC;IAClG,YAAY,EAAE,CACZ,KAAK,EAAE;QAAE,EAAE,EAAE,gBAAgB,CAAC,EAAE,CAAC,CAAC;QAAC,EAAE,EAAE,gBAAgB,CAAC,GAAG,CAAC,CAAA;KAAE,EAAE,EAChE,iBAAiB,CAAC,EAAE,OAAO,KACxB,IAAI,CAAC;CACX,CAAC;AAEF,MAAM,MAAM,gBAAgB,GAAG;IAI7B,WAAW,EAAE,MAAM,CAAC;IACpB,SAAS,EAAE,OAAO,CAAC;IACnB,SAAS,EAAE,SAAS,CAAC;IAErB,cAAc,CAAC,EAAE,gBAAgB,CAAC;CACnC,CAAC;AACF,MAAM,MAAM,SAAS,GAAG;IACtB,EAAE,EAAE,eAAe,CAAC,EAAE,CAAC,GAAG;QACxB,cAAc,EAAE,cAAc,CAAC,EAAE,CAAC,CAAC;QACnC,UAAU,EAAE,UAAU,CAAC,EAAE,CAAC,CAAC;QAC3B,WAAW,EAAE,OAAO,CAAC;KACtB,CAAC;IACF,EAAE,EAAE,eAAe,CAAC,GAAG,CAAC,GAAG;QACzB,SAAS,EAAE,cAAc,CAAC,GAAG,CAAC,CAAC;QAC/B,UAAU,EAAE,UAAU,CAAC,GAAG,CAAC,CAAC;QAC5B,WAAW,EAAE,OAAO,CAAC;KACtB,CAAC;IACF,MAAM,EAAE,SAAS,CAAC;IAClB,MAAM,EAAE;QAIN,WAAW,EAAE,gBAAgB,CAAC,aAAa,CAAC,CAAC;QAC7C,SAAS,EAAE,gBAAgB,CAAC,WAAW,CAAC,CAAC;QACzC,CAAC,EAAE,MAAM,CAAC;QACV,SAAS,EAAE,gBAAgB,CAAC,WAAW,CAAC,CAAC;KAC1C,CAAC;IACF,WAAW,EAAE,OAAO,CAAC;IACrB,IAAI,EAAE,KAAK,CAAC;IACZ,WAAW,CAAC,EAAE,CAAC,WAAW,CAAC,EAAE,MAAM,KAAK,UAAU,CAAC;IAEnD,cAAc,CAAC,EAAE,gBAAgB,CAAC;CACnC,CAAC;AAEF,KAAK,gBAAgB,GAAG,CAAC,GAAG,EAAE,GAAG,EAAE,GAAG,CAAC,EAAE,CAAC;AAC1C,KAAK,UAAU,GAAG,gBAAgB,EAAE,CAAC;AAErC;;;;GAIG;AACH,MAAM,WAAW,YAAY;IAC3B,cAAc,EAAE,OAAO,CAAC,MAAM,EAAE,GAAG,CAAC,CAAC;IACrC,eAAe,EAAE,OAAO,CAAC,GAAG,EAAE,MAAM,CAAC,CAAC;IACtC,eAAe,EAAE,UAAU,CAAC,iBAAiB,CAAC,CAAC;IAC/C,OAAO,EAAE,UAAU,CAAC,SAAS,CAAC,CAAC;IAC/B,YAAY,EAAE,UAAU,CAAC,cAAc,CAAC,CAAC;IACzC,EAAE,EAAE;QAAE,KAAK,EAAE,oBAAoB,CAAC,MAAM,CAAC,CAAA;KAAE,GAAG,SAAS,CAAC,EAAE,CAAC,CAAC;IAC5D,EAAE,EAAE;QAAE,KAAK,EAAE,oBAAoB,CAAC,GAAG,CAAC,CAAA;KAAE,GAAG,SAAS,CAAC,GAAG,CAAC,CAAC;IAC1D,MAAM,EAAE;QACN,EAAE,EAAE,MAAM,CAAC,EAAE,CAAC,CAAC;QACf,GAAG,EAAE,MAAM,CAAC;QACZ,GAAG,EAAE,MAAM,CAAC;QACZ,IAAI,EAAE,OAAO,CAAC;QACd,EAAE,EAAE,MAAM,CAAC,MAAM,CAAC,CAAC;KACpB,CAAC;IACF,KAAK,EAAE;QACL,eAAe,EAAE,MAAM,UAAU,CAAC;QAClC,sCAAsC;QACtC,gBAAgB,EAAE,MAAM,UAAU,CAAC;QACnC,sBAAsB,EAAE,UAAU,CAAC,wBAAwB,CAAC,CAAC;KAC9D,CAAC;CACH;AAED,MAAM,MAAM,OAAO,GAAG,YAAY,GAAG;IACnC,oDAAoD;IACpD,YAAY,EAAE,CAAC,SAAS,EAAE,OAAO,KAAK,UAAU,CAAC;IACjD,qDAAqD;IACrD,8BAA8B,EAAE,CAAC,SAAS,EAAE,OAAO,KAAK,UAAU,CAAC;IACnE,4CAA4C;IAC5C,IAAI,EAAE;QACJ,CAAC,OAAO,EAAE,GAAG,EAAE,SAAS,EAAE,OAAO,EAAE,OAAO,CAAC,EAAE,YAAY,GAAG,UAAU,CAAC;QACvE,CACE,OAAO,EAAE,gBAAgB,CAAC,GAAG,CAAC,EAC9B,SAAS,EAAE,OAAO,EAClB,OAAO,CAAC,EAAE,YAAY,GACrB,gBAAgB,CAAC,GAAG,CAAC,CAAC;KAC1B,CAAC;IACF,6CAA6C;IAC7C,kBAAkB,EAAE;QAClB,CAAC,OAAO,EAAE,GAAG,EAAE,SAAS,EAAE,OAAO,EAAE,OAAO,CAAC,EAAE,YAAY,GAAG,UAAU,CAAC;QACvE,CACE,OAAO,EAAE,gBAAgB,CAAC,EAAE,CAAC,EAC7B,SAAS,EAAE,OAAO,EAClB,OAAO,CAAC,EAAE,YAAY,GACrB,gBAAgB,CAAC,EAAE,CAAC,CAAC;KACzB,CAAC;IACF,8CAA8C;IAC9C,MAAM,EAAE,CACN,SAAS,EAAE,GAAG,GAAG,gBAAgB,CAAC,GAAG,CAAC,EACtC,OAAO,EAAE,GAAG,GAAG,gBAAg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esm/abstract/curve.d.ts

@@ -68,5 +68,5 @@ import { type IField } from './modular.ts';
 export interface CurveLengths {
-    secret?: number;
-    public?: number;
-    publicUncompressed?: number;
+    secretKey?: number;
+    publicKey?: number;
+    publicKeyUncompressed?: number;
     publicKeyHasPrefix?: boolean;
@@ -73,0 +73,0 @@ signature?: number;

esm/abstract/curve.d.ts.map

@@ -1,1 +0,1 @@
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esm/abstract/edwards.d.ts

@@ -129,2 +129,8 @@ /**
          * Converts ed public key to x public key.
+         *
+         * There is NO `fromMontgomery`:
+         * - There are 2 valid ed25519 points for every x25519, with flipped coordinate
+         * - Sometimes there are 0 valid ed25519 points, because x25519 *additionally*
+         *   accepts inputs on the quadratic twist, which can't be moved to ed25519
+         *
          * @example
@@ -184,4 +190,2 @@ * ```js
     toAffine(invertedZ?: bigint): AffinePoint<bigint>;
-    /** @deprecated use `toBytes` */
-    toRawBytes(): Uint8Array;
     toHex(): string;
@@ -201,2 +205,4 @@ toString(): string;
     protected abstract init(ep: EdwardsPoint): T;
+    /** @deprecated use `toBytes` */
+    toRawBytes(): Uint8Array;
 }
@@ -203,0 +209,0 @@ /**

esm/abstract/edwards.d.ts.map

@@ -1,1 +0,1 @@
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esm/abstract/edwards.js

@@ -8,3 +8,3 @@ /**
 /*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
-import { _validateObject, _abool2 as abool, _abytes2 as abytes, aInRange, bytesToHex, bytesToNumberLE, concatBytes, copyBytes, ensureBytes, memoized, notImplemented, numberToBytesLE, randomBytes, } from "../utils.js";
+import { _validateObject, _abool2 as abool, _abytes2 as abytes, aInRange, bytesToHex, bytesToNumberLE, concatBytes, copyBytes, ensureBytes, isBytes, memoized, notImplemented, randomBytes as randomBytesWeb, } from "../utils.js";
 import { _createCurveFields, normalizeZ, pippenger, wNAF, } from "./curve.js";
@@ -26,3 +26,3 @@ import { Field } from "./modular.js";
     let CURVE = validated.CURVE;
-    const { h: cofactor, n: CURVE_ORDER } = CURVE;
+    const { h: cofactor } = CURVE;
     _validateObject(extraOpts, {}, { uvRatio: 'function' });
@@ -137,3 +137,3 @@ // Important:
             const max = zip215 ? MASK : Fp.ORDER;
-            aInRange('pointHex.y', y, _0n, max);
+            aInRange('point.y', y, _0n, max);
             // Ed25519: x² = (y²-1)/(dy²+1) mod p. Ed448: x² = (y²-1)/(dy²-1) mod p. Generic case:
@@ -146,3 +146,3 @@ // ax²+y²=1+dx²y² => y²-1=dx²y²-ax² => y²-1=x²(dy²-a) => x²=(y²-1)/(dy²-a)
             if (!isValid)
-                throw new Error('Point.fromHex: invalid y coordinate');
+                throw new Error('bad point: invalid y coordinate');
             const isXOdd = (x & _1n) === _1n; // There are 2 square roots. Use x_0 bit to select proper
@@ -152,3 +152,3 @@ const isLastByteOdd = (lastByte & 0x80) !== 0; // x_0, last bit
                 // if x=0 and x_0 = 1, fail
-                throw new Error('Point.fromHex: x=0 and x_0=1');
+                throw new Error('bad point: x=0 and x_0=1');
             if (isLastByteOdd !== isXOdd)
@@ -243,5 +243,6 @@ x = modP(-x); // if x_0 != x mod 2, set x = p-x
         multiply(scalar) {
-            const n = scalar;
-            aInRange('scalar', n, _1n, CURVE_ORDER); // 1 <= scalar < L
-            const { p, f } = wnaf.cached(this, n, (p) => normalizeZ(Point, p));
+            // 1 <= scalar < L
+            if (!Fn.isValidNot0(scalar))
+                throw new Error('invalid scalar: expected 1 <= sc < curve.n');
+            const { p, f } = wnaf.cached(this, scalar, (p) => normalizeZ(Point, p));
             return normalizeZ(Point, [p, f])[0];
@@ -255,9 +256,10 @@ }
         multiplyUnsafe(scalar, acc = Point.ZERO) {
-            const n = scalar;
-            aInRange('scalar', n, _0n, CURVE_ORDER); // 0 <= scalar < L
-            if (n === _0n)
+            // 0 <= scalar < L
+            if (!Fn.isValid(scalar))
+                throw new Error('invalid scalar: expected 0 <= sc < curve.n');
+            if (scalar === _0n)
                 return Point.ZERO;
-            if (this.is0() || n === _1n)
+            if (this.is0() || scalar === _1n)
                 return this;
-            return wnaf.unsafe(this, n, (p) => normalizeZ(Point, p), acc);
+            return wnaf.unsafe(this, scalar, (p) => normalizeZ(Point, p), acc);
         }
@@ -274,3 +276,3 @@ // Checks if point is of small order.
         isTorsionFree() {
-            return wnaf.unsafe(this, CURVE_ORDER).is0();
+            return wnaf.unsafe(this, CURVE.n).is0();
         }
@@ -289,10 +291,9 @@ // Converts Extended point to default (x, y) coordinates.
             const { x, y } = this.toAffine();
-            const bytes = numberToBytesLE(y, Fp.BYTES); // each y has 2 x values (x, -y)
-            bytes[bytes.length - 1] |= x & _1n ? 0x80 : 0; // when compressing, it's enough to store y
-            return bytes; // and use the last byte to encode sign of x
+            // Fp.toBytes() allows non-canonical encoding of y (>= p).
+            const bytes = Fp.toBytes(y);
+            // Each y has 2 valid points: (x, y), (x,-y).
+            // When compressing, it's enough to store y and use the last byte to encode sign of x
+            bytes[bytes.length - 1] |= x & _1n ? 0x80 : 0;
+            return bytes;
         }
-        /** @deprecated use `toBytes` */
-        toRawBytes() {
-            return this.toBytes();
-        }
         toHex() {
@@ -326,2 +327,5 @@ return bytesToHex(this.toBytes());
         }
+        toRawBytes() {
+            return this.toBytes();
+        }
     }
@@ -336,3 +340,4 @@ // base / generator point
     Point.Fn = Fn;
-    const wnaf = new wNAF(Point, Fn.BYTES * 8); // Fn.BITS?
+    const wnaf = new wNAF(Point, Fn.BITS);
+    Point.BASE.precompute(8); // Enable precomputes. Slows down first publicKey computation by 20ms.
     return Point;
@@ -373,6 +378,2 @@ }
     }
-    /** @deprecated use `toBytes` */
-    toRawBytes() {
-        return this.toBytes();
-    }
     toHex() {
@@ -413,2 +414,6 @@ return bytesToHex(this.toBytes());
     }
+    /** @deprecated use `toBytes` */
+    toRawBytes() {
+        return this.toBytes();
+    }
 }
@@ -429,6 +434,5 @@ /**
     const { prehash } = eddsaOpts;
-    const { BASE: G, Fp, Fn } = Point;
-    const CURVE_ORDER = Fn.ORDER;
-    const randomBytes_ = eddsaOpts.randomBytes || randomBytes;
-    const adjustScalarBytes = eddsaOpts.adjustScalarBytes || ((bytes) => bytes); // NOOP
+    const { BASE, Fp, Fn } = Point;
+    const randomBytes = eddsaOpts.randomBytes || randomBytesWeb;
+    const adjustScalarBytes = eddsaOpts.adjustScalarBytes || ((bytes) => bytes);
     const domain = eddsaOpts.domain ||
@@ -441,13 +445,9 @@ ((data, ctx, phflag) => {
         }); // NOOP
-    function modN(a) {
-        return Fn.create(a);
-    }
     // Little-endian SHA512 with modulo n
     function modN_LE(hash) {
-        // Not using Fn.fromBytes: hash can be 2*Fn.BYTES
-        return modN(bytesToNumberLE(hash));
+        return Fn.create(bytesToNumberLE(hash)); // Not Fn.fromBytes: it has length limit
     }
     // Get the hashed private scalar per RFC8032 5.1.5
     function getPrivateScalar(key) {
-        const len = lengths.secret;
+        const len = lengths.secretKey;
         key = ensureBytes('private key', key, len);
@@ -465,3 +465,3 @@ // Hash private key with curve's hash function to produce uniformingly random input
         const { head, prefix, scalar } = getPrivateScalar(secretKey);
-        const point = G.multiply(scalar); // Point on Edwards curve aka public key
+        const point = BASE.multiply(scalar); // Point on Edwards curve aka public key
         const pointBytes = point.toBytes();
@@ -486,9 +486,9 @@ return { head, prefix, scalar, point, pointBytes };
         const r = hashDomainToScalar(options.context, prefix, msg); // r = dom2(F, C) || prefix || PH(M)
-        const R = G.multiply(r).toBytes(); // R = rG
+        const R = BASE.multiply(r).toBytes(); // R = rG
         const k = hashDomainToScalar(options.context, R, pointBytes, msg); // R || A || PH(M)
-        const s = modN(r + k * scalar); // S = (r + k * s) mod L
-        aInRange('signature.s', s, _0n, CURVE_ORDER); // 0 <= s < l
-        const L = Fp.BYTES;
-        const res = concatBytes(R, numberToBytesLE(s, L));
-        return ensureBytes('result', res, L * 2); // 64-byte signature
+        const s = Fn.create(r + k * scalar); // S = (r + k * s) mod L
+        if (!Fn.isValid(s))
+            throw new Error('sign failed: invalid s'); // 0 <= s < L
+        const rs = concatBytes(R, Fn.toBytes(s));
+        return abytes(rs, lengths.signature, 'result');
     }
@@ -503,6 +503,6 @@ // verification rule is either zip215 or rfc8032 / nist186-5. Consult fromHex:
         const { context, zip215 } = options;
-        const len = lengths.signature; // Verifies EdDSA signature against message and public key. RFC8032 5.1.7.
-        sig = ensureBytes('signature', sig, len); // An extended group equation is checked.
+        const len = lengths.signature;
+        sig = ensureBytes('signature', sig, len);
         msg = ensureBytes('message', msg);
-        publicKey = ensureBytes('publicKey', publicKey, lengths.public);
+        publicKey = ensureBytes('publicKey', publicKey, lengths.publicKey);
         if (zip215 !== undefined)
@@ -522,3 +522,3 @@ abool(zip215, 'zip215');
             R = Point.fromBytes(r, zip215);
-            SB = G.multiplyUnsafe(s); // 0 <= s < l is done inside
+            SB = BASE.multiplyUnsafe(s); // 0 <= s < l is done inside
         }
@@ -529,3 +529,3 @@ catch (error) {
         if (!zip215 && A.isSmallOrder())
-            return false;
+            return false; // zip215 allows public keys of small order
         const k = hashDomainToScalar(context, R.toBytes(), A.toBytes(), msg);
@@ -537,11 +537,10 @@ const RkA = R.add(A.multiplyUnsafe(k));
     }
-    G.precompute(8); // Enable precomputes. Slows down first publicKey computation by 20ms.
-    const _size = Fp.BYTES;
+    const _size = Fp.BYTES; // 32 for ed25519, 57 for ed448
     const lengths = {
-        secret: _size,
-        public: _size,
+        secretKey: _size,
+        publicKey: _size,
         signature: 2 * _size,
         seed: _size,
     };
-    function randomSecretKey(seed = randomBytes_(lengths.seed)) {
+    function randomSecretKey(seed = randomBytes(lengths.seed)) {
         return abytes(seed, lengths.seed, 'seed');
@@ -554,8 +553,3 @@ }
     function isValidSecretKey(key) {
-        try {
-            return !!Fn.fromBytes(key, false);
-        }
-        catch (error) {
-            return false;
-        }
+        return isBytes(key) && key.length === Fn.BYTES;
     }
@@ -583,11 +577,6 @@ function isValidPublicKey(key, zip215) {
          *   - `(x, y) = (sqrt(156324)*u/v, (1+u)/(1-u))`
-         *
-         * There is NO `fromMontgomery`:
-         * - There are 2 valid ed25519 points for every x25519, with flipped coordinate
-         * - Sometimes there are 0 valid ed25519 points, because x25519 *additionally*
-         *   accepts inputs on the quadratic twist, which can't be moved to ed25519
          */
         toMontgomery(publicKey) {
             const { y } = Point.fromBytes(publicKey);
-            const size = lengths.public;
+            const size = lengths.publicKey;
             const is25519 = size === 32;
@@ -600,3 +589,3 @@ if (!is25519 && size !== 57)
         toMontgomeryPriv(secretKey) {
-            const size = lengths.secret;
+            const size = lengths.secretKey;
             abytes(secretKey, size);
@@ -646,3 +635,9 @@ const hashed = cHash(secretKey.subarray(0, size));
 function _eddsa_new_output_to_legacy(c, eddsa) {
-    const legacy = Object.assign({}, eddsa, { ExtendedPoint: eddsa.Point, CURVE: c });
+    const Point = eddsa.Point;
+    const legacy = Object.assign({}, eddsa, {
+        ExtendedPoint: Point,
+        CURVE: c,
+        nBitLength: Point.Fn.BITS,
+        nByteLength: Point.Fn.BYTES,
+    });
     return legacy;
@@ -649,0 +644,0 @@ }

esm/abstract/edwards.js.map

@@ -1,1 +0,1 @@
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esm/abstract/montgomery.js

@@ -130,4 +130,4 @@ /**
     const lengths = {
-        secret: fieldLen,
-        public: fieldLen,
+        secretKey: fieldLen,
+        publicKey: fieldLen,
         seed: fieldLen,
@@ -134,0 +134,0 @@ };

esm/abstract/montgomery.js.map

@@ -1,1 +0,1 @@
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+{"version":3,"file":"montgomery.js","sourceRoot":"","sources":["../../src/abstract/montgomery.ts"],"names":[],"mappings":"AAAA;;;;;GAKG;AACH,sEAAsE;AACtE,OAAO,EACL,eAAe,EACf,MAAM,EACN,QAAQ,EACR,eAAe,EACf,WAAW,EACX,eAAe,EACf,WAAW,GACZ,MAAM,aAAa,CAAC;AAErB,OAAO,EAAE,GAAG,EAAE,MAAM,cAAc,CAAC;AAEnC,MAAM,GAAG,GAAG,MAAM,CAAC,CAAC,CAAC,CAAC;AACtB,MAAM,GAAG,GAAG,MAAM,CAAC,CAAC,CAAC,CAAC;AACtB,MAAM,GAAG,GAAG,MAAM,CAAC,CAAC,CAAC,CAAC;AA2BtB,SAAS,YAAY,CAAC,KAAgB;IACpC,eAAe,CAAC,KAAK,EAAE;QACrB,iBAAiB,EAAE,UAAU;QAC7B,UAAU,EAAE,UAAU;KACvB,CAAC,CAAC;IACH,OAAO,MAAM,CAAC,MAAM,CAAC,EAAE,GAAG,KAAK,EAAW,CAAC,CAAC;AAC9C,CAAC;AAED,MAAM,UAAU,UAAU,CAAC,QAAmB;IAC5C,MAAM,KAAK,GAAG,YAAY,CAAC,QAAQ,CAAC,CAAC;IACrC,MAAM,EAAE,CAAC,EAAE,IAAI,EAAE,iBAAiB,EAAE,UAAU,EAAE,WAAW,EAAE,IAAI,EAAE,GAAG,KAAK,CAAC;IAC5E,MAAM,OAAO,GAAG,IAAI,KAAK,QAAQ,CAAC;IAClC,IAAI,CAAC,OAAO,IAAI,IAAI,KAAK,MAAM;QAAE,MAAM,IAAI,KAAK,CAAC,cAAc,CAAC,CAAC;IACjE,MAAM,YAAY,GAAG,IAAI,IAAI,WAAW,CAAC;IAEzC,MAAM,cAAc,GAAG,OAAO,CAAC,CAAC,CAAC,GAAG,CAAC,CAAC,CAAC,GAAG,CAAC;IAC3C,MAAM,QAAQ,GAAG,OAAO,CAAC,CAAC,CAAC,EAAE,CAAC,CAAC,CAAC,EAAE,CAAC;IACnC,MAAM,EAAE,GAAG,OAAO,CAAC,CAAC,CAAC,MAAM,CAAC,CAAC,CAAC,CAAC,CAAC,CAAC,MAAM,CAAC,CAAC,CAAC,CAAC;IAC3C,eAAe;IACf,0EAA0E;IAC1E,6CAA6C;IAC7C,yCAAyC;IACzC,MAAM,GAAG,GAAG,OAAO,CAAC,CAAC,CAAC,MAAM,CAAC,MAAM,CAAC,CAAC,CAAC,CAAC,MAAM,CAAC,KAAK,CAAC,CAAC;IACrD,+DAA+D;IAC/D,2DAA2D;IAC3D,4EAA4E;IAC5E,MAAM,SAAS,GAAG,OAAO,CAAC,CAAC,CAAC,GAAG,IAAI,MAAM,CAAC,GAAG,CAAC,CAAC,CAAC,CAAC,GAAG,IAAI,MAAM,CAAC,GAAG,CAAC,CAAC;IACpE,MAAM,QAAQ,GAAG,OAAO;QACtB,CAAC,CAAC,MAAM,CAAC,CAAC,CAAC,GAAG,GAAG,IAAI,MAAM,CAAC,GAAG,CAAC,GAAG,GAAG;QACtC,CAAC,CAAC,MAAM,CAAC,CAAC,CAAC,GAAG,GAAG,IAAI,MAAM,CAAC,GAAG,CAAC,GAAG,GAAG,CAAC;IACzC,MAAM,SAAS,GAAG,SAAS,GAAG,QAAQ,GAAG,GAAG,CAAC,CAAC,cAAc;IAC5D,MAAM,IAAI,GAAG,CAAC,CAAS,EAAE,EAAE,CAAC,GAAG,CAAC,CAAC,EAAE,CAAC,CAAC,CAAC;IACtC,MAAM,OAAO,GAAG,OAAO,CAAC,EAAE,CAAC,CAAC;IAC5B,SAAS,OAAO,CAAC,CAAS;QACxB,OAAO,eAAe,CAAC,IAAI,CAAC,CAAC,CAAC,EAAE,QAAQ,CAAC,CAAC;IAC5C,CAAC;IACD,SAAS,OAAO,CAAC,CAAM;QACrB,MAAM,EAAE,GAAG,WAAW,CAAC,cAAc,EAAE,CAAC,EAAE,QAAQ,CAAC,CAAC;QACpD,+DAA+D;QAC/D,uEAAuE;QACvE,IAAI,OAAO;YAAE,EAAE,CAAC,EAAE,CAAC,IAAI,GAAG,CAAC,CAAC,cAAc;QAC1C,4EAA4E;QAC5E,sEAAsE;QACtE,uEAAuE;QACvE,kCAAkC;QAClC,OAAO,IAAI,CAAC,eAAe,CAAC,EAAE,CAAC,CAAC,CAAC;IACnC,CAAC;IACD,SAAS,YAAY,CAAC,MAAW;QAC/B,OAAO,eAAe,CAAC,iBAAiB,CAAC,WAAW,CAAC,QAAQ,EAAE,MAAM,EAAE,QAAQ,CAAC,CAAC,CAAC,CAAC;IACrF,CAAC;IACD,SAAS,UAAU,CAAC,MAAW,EAAE,CAAM;QACrC,MAAM,EAAE,GAAG,gBAAgB,CAAC,OAAO,CAAC,CAAC,CAAC,EAAE,YAAY,CAAC,MAAM,CAAC,CAAC,CAAC;QAC9D,yEAAyE;QACzE,sDAAsD;QACtD,sCAAsC;QACtC,IAAI,EAAE,KAAK,GAAG;YAAE,MAAM,IAAI,KAAK,CAAC,wCAAwC,CAAC,CAAC;QAC1E,OAAO,OAAO,CAAC,EAAE,CAAC,CAAC;IACrB,CAAC;IACD,kFAAkF;IAClF,SAAS,cAAc,CAAC,MAAW;QACjC,OAAO,UAAU,CAAC,MAAM,EAAE,OAAO,CAAC,CAAC;IACrC,CAAC;IAED,oCAAoC;IACpC,SAAS,KAAK,CAAC,IAAY,EAAE,GAAW,EAAE,GAAW;QACnD,uCAAuC;QACvC,wEAAwE;QACxE,qDAAqD;QACrD,MAAM,KAAK,GAAG,IAAI,CAAC,IAAI,GAAG,CAAC,GAAG,GAAG,GAAG,CAAC,CAAC,CAAC;QACvC,GAAG,GAAG,IAAI,CAAC,GAAG,GAAG,KAAK,CAAC,CAAC,CAAC,sBAAsB;QAC/C,GAAG,GAAG,IAAI,CAAC,GAAG,GAAG,KAAK,CAAC,CAAC,CAAC,sBAAsB;QAC/C,OAAO,EAAE,GAAG,EAAE,GAAG,EAAE,CAAC;IACtB,CAAC;IAED;;;;;OAKG;IACH,SAAS,gBAAgB,CAAC,CAAS,EAAE,MAAc;QACjD,QAAQ,CAAC,GAAG,EAAE,CAAC,EAAE,GAAG,EAAE,CAAC,CAAC,CAAC;QACzB,QAAQ,CAAC,QAAQ,EAAE,MAAM,EAAE,SAAS,EAAE,SAAS,CAAC,CAAC;QACjD,MAAM,CAAC,GAAG,MAAM,CAAC;QACjB,MAAM,GAAG,GAAG,CAAC,CAAC;QACd,IAAI,GAAG,GAAG,GAAG,CAAC;QACd,IAAI,GAAG,GAAG,GAAG,CAAC;QACd,IAAI,GAAG,GAAG,CAAC,CAAC;QACZ,IAAI,GAAG,GAAG,GAAG,CAAC;QACd,IAAI,IAAI,GAAG,GAAG,CAAC;QACf,KAAK,IAAI,CAAC,GAAG,MAAM,CAAC,cAAc,GAAG,CAAC,CAAC,EAAE,CAAC,IAAI,GAAG,EAAE,CAAC,EAAE,EAAE,CAAC;YACvD,MAAM,GAAG,GAAG,CAAC,CAAC,IAAI,CAAC,CAAC,GAAG,GAAG,CAAC;YAC3B,IAAI,IAAI,GAAG,CAAC;YACZ,CAAC,EAAE,GAAG,EAAE,GAAG,EAAE,GAAG,KAAK,CAAC,IAAI,EAAE,GAAG,EAAE,GAAG,CAAC,CAAC,CAAC;YACvC,CAAC,EAAE,GAAG,EAAE,GAAG,EAAE,GAAG,EAAE,GAAG,EAAE,GAAG,KAAK,CAAC,IAAI,EAAE,GAAG,EAAE,GAAG,CAAC,CAAC,CAAC;YACjD,IAAI,GAAG,GAAG,CAAC;YAEX,MAAM,CAAC,GAAG,GAAG,GAAG,GAAG,CAAC;YACpB,MAAM,EAAE,GAAG,IAAI,CAAC,CAAC,GAAG,CAAC,CAAC,CAAC;YACvB,MAAM,CAAC,GAAG,GAAG,GAAG,GAAG,CAAC;YACpB,MAAM,EAAE,GAAG,IAAI,CAAC,CAAC,GAAG,CAAC,CAAC,CAAC;YACvB,MAAM,CAAC,GAAG,EAAE,GAAG,EAAE,CAAC;YAClB,MAAM,CAAC,GAAG,GAAG,GAAG,GAAG,CAAC;YACpB,MAAM,CAAC,GAAG,GAAG,GAAG,GAAG,CAAC;YACpB,MAAM,EAAE,GAAG,IAAI,CAAC,CAAC,GAAG,CAAC,CAAC,CAAC;YACvB,MAAM,EAAE,GAAG,IAAI,CAAC,CAAC,GAAG,CAAC,CAAC,CAAC;YACvB,MAAM,IAAI,GAAG,EAAE,GAAG,EAAE,CAAC;YACrB,MAAM,KAAK,GAAG,EAAE,GAAG,EAAE,CAAC;YACtB,GAAG,GAAG,IAAI,CAAC,IAAI,GAAG,IAAI,CAAC,CAAC;YACxB,GAAG,GAAG,IAAI,CAAC,GAAG,GAAG,IAAI,CAAC,KAAK,GAAG,KAAK,CAAC,CAAC,CAAC;YACtC,GAAG,GAAG,IAAI,CAAC,EAAE,GAAG,EAAE,CAAC,CAAC;YACpB,GAAG,GAAG,IAAI,CAAC,CAAC,GAAG,CAAC,EAAE,GAAG,IAAI,CAAC,GAAG,GAAG,CAAC,CAAC,CAAC,CAAC,CAAC;QACvC,CAAC;QACD,CAAC,EAAE,GAAG,EAAE,GAAG,EAAE,GAAG,KAAK,CAAC,IAAI,EAAE,GAAG,EAAE,GAAG,CAAC,CAAC,CAAC;QACvC,CAAC,EAAE,GAAG,EAAE,GAAG,EAAE,GAAG,EAAE,GAAG,EAAE,GAAG,KAAK,CAAC,IAAI,EAAE,GAAG,EAAE,GAAG,CAAC,CAAC,CAAC;QACjD,MAAM,EAAE,GAAG,UAAU,CAAC,GAAG,CAAC,CAAC,CAAC,iDAAiD;QAC7E,OAAO,IAAI,CAAC,GAA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esm/abstract/tower.d.ts

@@ -34,4 +34,5 @@ import * as mod from './modular.ts';
 export type Fp2Bls = mod.IField<Fp2> & {
+    Fp: mod.IField<Fp>;
     frobeniusMap(num: Fp2, power: number): Fp2;
-    fromBigTuple(num: [bigint, bigint]): Fp2;
+    fromBigTuple(num: BigintTuple): Fp2;
     mulByB: (num: Fp2) => Fp2;
@@ -43,5 +44,10 @@ mulByNonresidue: (num: Fp2) => Fp2;
     };
+    Fp4Square: (a: Fp2, b: Fp2) => {
+        first: Fp2;
+        second: Fp2;
+    };
     NONRESIDUE: Fp2;
 };
 export type Fp6Bls = mod.IField<Fp6> & {
+    Fp2: Fp2Bls;
     frobeniusMap(num: Fp6, power: number): Fp6;
@@ -55,2 +61,3 @@ fromBigSix: (tuple: BigintSix) => Fp6;
 export type Fp12Bls = mod.IField<Fp12> & {
+    Fp6: Fp6Bls;
     frobeniusMap(num: Fp12, power: number): Fp12;
@@ -78,2 +85,3 @@ fromBigTwelve: (t: BigintTwelve) => Fp12;
     ORDER: bigint;
+    X_LEN: number;
     NONRESIDUE?: Fp;
@@ -83,4 +91,2 @@ FP2_NONRESIDUE: BigintTuple;
     Fp2mulByB: (num: Fp2) => Fp2;
-    Fp12cyclotomicSquare: (num: Fp12) => Fp12;
-    Fp12cyclotomicExp: (num: Fp12, n: bigint) => Fp12;
     Fp12finalExponentiate: (num: Fp12) => Fp12;
@@ -93,7 +99,3 @@ };
     Fp12: Fp12Bls;
-    Fp4Square: (a: Fp2, b: Fp2) => {
-        first: Fp2;
-        second: Fp2;
-    };
 };
 //# sourceMappingURL=tower.d.ts.map

esm/abstract/tower.d.ts.map

@@ -1,1 +0,1 @@
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esm/abstract/tower.js

@@ -13,3 +13,3 @@ /**
 /*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
-import { bitLen, bitMask, concatBytes, notImplemented } from "../utils.js";
+import { bitGet, bitLen, concatBytes, notImplemented } from "../utils.js";
 import * as mod from "./modular.js";
@@ -66,19 +66,75 @@ // Be friendly to bad ECMAScript parsers by not using bigint literals
 }
-export function tower12(opts) {
-    const { ORDER } = opts;
-    // Fp
-    const Fp = mod.Field(ORDER);
-    const FpNONRESIDUE = Fp.create(opts.NONRESIDUE || BigInt(-1));
-    const Fpdiv2 = Fp.div(Fp.ONE, _2n); // 1/2
-    // Fp2
-    const FP2_FROBENIUS_COEFFICIENTS = calcFrobeniusCoefficients(Fp, FpNONRESIDUE, Fp.ORDER, 2)[0];
-    const Fp2Add = ({ c0, c1 }, { c0: r0, c1: r1 }) => ({
-        c0: Fp.add(c0, r0),
-        c1: Fp.add(c1, r1),
-    });
-    const Fp2Subtract = ({ c0, c1 }, { c0: r0, c1: r1 }) => ({
-        c0: Fp.sub(c0, r0),
-        c1: Fp.sub(c1, r1),
-    });
-    const Fp2Multiply = ({ c0, c1 }, rhs) => {
+const Fp2fromBigTuple = (Fp, tuple) => {
+    if (tuple.length !== 2)
+        throw new Error('invalid tuple');
+    const fps = tuple.map((n) => Fp.create(n));
+    return { c0: fps[0], c1: fps[1] };
+};
+class _Field2 {
+    constructor(Fp, opts = {}) {
+        this.MASK = _1n;
+        const ORDER = Fp.ORDER;
+        const FP2_ORDER = ORDER * ORDER;
+        this.Fp = Fp;
+        this.ORDER = FP2_ORDER;
+        this.BITS = bitLen(FP2_ORDER);
+        this.BYTES = Math.ceil(bitLen(FP2_ORDER) / 8);
+        this.isLE = Fp.isLE;
+        this.ZERO = { c0: Fp.ZERO, c1: Fp.ZERO };
+        this.ONE = { c0: Fp.ONE, c1: Fp.ZERO };
+        this.Fp_NONRESIDUE = Fp.create(opts.NONRESIDUE || BigInt(-1));
+        this.Fp_div2 = Fp.div(Fp.ONE, _2n); // 1/2
+        this.NONRESIDUE = Fp2fromBigTuple(Fp, opts.FP2_NONRESIDUE);
+        // const Fp2Nonresidue = Fp2fromBigTuple(opts.FP2_NONRESIDUE);
+        this.FROBENIUS_COEFFICIENTS = calcFrobeniusCoefficients(Fp, this.Fp_NONRESIDUE, Fp.ORDER, 2)[0];
+        this.mulByB = opts.Fp2mulByB;
+        Object.seal(this);
+    }
+    fromBigTuple(tuple) {
+        return Fp2fromBigTuple(this.Fp, tuple);
+    }
+    create(num) {
+        return num;
+    }
+    isValid({ c0, c1 }) {
+        function isValidC(num, ORDER) {
+            return typeof num === 'bigint' && _0n <= num && num < ORDER;
+        }
+        return isValidC(c0, this.ORDER) && isValidC(c1, this.ORDER);
+    }
+    is0({ c0, c1 }) {
+        return this.Fp.is0(c0) && this.Fp.is0(c1);
+    }
+    isValidNot0(num) {
+        return !this.is0(num) && this.isValid(num);
+    }
+    eql({ c0, c1 }, { c0: r0, c1: r1 }) {
+        return this.Fp.eql(c0, r0) && this.Fp.eql(c1, r1);
+    }
+    neg({ c0, c1 }) {
+        return { c0: this.Fp.neg(c0), c1: this.Fp.neg(c1) };
+    }
+    pow(num, power) {
+        return mod.FpPow(this, num, power);
+    }
+    invertBatch(nums) {
+        return mod.FpInvertBatch(this, nums);
+    }
+    // Normalized
+    add(f1, f2) {
+        const { c0, c1 } = f1;
+        const { c0: r0, c1: r1 } = f2;
+        return {
+            c0: this.Fp.add(c0, r0),
+            c1: this.Fp.add(c1, r1),
+        };
+    }
+    sub({ c0, c1 }, { c0: r0, c1: r1 }) {
+        return {
+            c0: this.Fp.sub(c0, r0),
+            c1: this.Fp.sub(c1, r1),
+        };
+    }
+    mul({ c0, c1 }, rhs) {
+        const { Fp } = this;
         if (typeof rhs === 'bigint')
@@ -94,4 +150,5 @@ return { c0: Fp.mul(c0, rhs), c1: Fp.mul(c1, rhs) };
         return { c0: o0, c1: o1 };
-    };
-    const Fp2Square = ({ c0, c1 }) => {
+    }
+    sqr({ c0, c1 }) {
+        const { Fp } = this;
         const a = Fp.add(c0, c1);
@@ -101,132 +158,152 @@ const b = Fp.sub(c0, c1);
         return { c0: Fp.mul(a, b), c1: Fp.mul(c, c1) };
-    };
-    const Fp2fromBigTuple = (tuple) => {
-        if (tuple.length !== 2)
-            throw new Error('invalid tuple');
-        const fps = tuple.map((n) => Fp.create(n));
-        return { c0: fps[0], c1: fps[1] };
-    };
-    function isValidC(num, ORDER) {
-        return typeof num === 'bigint' && _0n <= num && num < ORDER;
     }
-    const FP2_ORDER = ORDER * ORDER;
-    const Fp2Nonresidue = Fp2fromBigTuple(opts.FP2_NONRESIDUE);
-    const Fp2 = {
-        ORDER: FP2_ORDER,
-        isLE: Fp.isLE,
-        NONRESIDUE: Fp2Nonresidue,
-        BITS: bitLen(FP2_ORDER),
-        BYTES: Math.ceil(bitLen(FP2_ORDER) / 8),
-        MASK: bitMask(bitLen(FP2_ORDER)),
-        ZERO: { c0: Fp.ZERO, c1: Fp.ZERO },
-        ONE: { c0: Fp.ONE, c1: Fp.ZERO },
-        create: (num) => num,
-        isValid: ({ c0, c1 }) => isValidC(c0, FP2_ORDER) && isValidC(c1, FP2_ORDER),
-        is0: ({ c0, c1 }) => Fp.is0(c0) && Fp.is0(c1),
-        isValidNot0: (num) => !Fp2.is0(num) && Fp2.isValid(num),
-        eql: ({ c0, c1 }, { c0: r0, c1: r1 }) => Fp.eql(c0, r0) && Fp.eql(c1, r1),
-        neg: ({ c0, c1 }) => ({ c0: Fp.neg(c0), c1: Fp.neg(c1) }),
-        pow: (num, power) => mod.FpPow(Fp2, num, power),
-        invertBatch: (nums) => mod.FpInvertBatch(Fp2, nums),
-        // Normalized
-        add: Fp2Add,
-        sub: Fp2Subtract,
-        mul: Fp2Multiply,
-        sqr: Fp2Square,
-        // NonNormalized stuff
-        addN: Fp2Add,
-        subN: Fp2Subtract,
-        mulN: Fp2Multiply,
-        sqrN: Fp2Square,
-        // Why inversion for bigint inside Fp instead of Fp2? it is even used in that context?
-        div: (lhs, rhs) => Fp2.mul(lhs, typeof rhs === 'bigint' ? Fp.inv(Fp.create(rhs)) : Fp2.inv(rhs)),
-        inv: ({ c0: a, c1: b }) => {
-            // We wish to find the multiplicative inverse of a nonzero
-            // element a + bu in Fp2. We leverage an identity
-            //
-            // (a + bu)(a - bu) = a² + b²
-            //
-            // which holds because u² = -1. This can be rewritten as
-            //
-            // (a + bu)(a - bu)/(a² + b²) = 1
-            //
-            // because a² + b² = 0 has no nonzero solutions for (a, b).
-            // This gives that (a - bu)/(a² + b²) is the inverse
-            // of (a + bu). Importantly, this can be computing using
-            // only a single inversion in Fp.
-            const factor = Fp.inv(Fp.create(a * a + b * b));
-            return { c0: Fp.mul(factor, Fp.create(a)), c1: Fp.mul(factor, Fp.create(-b)) };
-        },
-        sqrt: (num) => {
-            if (opts.Fp2sqrt)
-                return opts.Fp2sqrt(num);
-            // This is generic for all quadratic extensions (Fp2)
-            const { c0, c1 } = num;
-            if (Fp.is0(c1)) {
-                // if c0 is quadratic residue
-                if (mod.FpLegendre(Fp, c0) === 1)
-                    return Fp2.create({ c0: Fp.sqrt(c0), c1: Fp.ZERO });
-                else
-                    return Fp2.create({ c0: Fp.ZERO, c1: Fp.sqrt(Fp.div(c0, FpNONRESIDUE)) });
-            }
-            const a = Fp.sqrt(Fp.sub(Fp.sqr(c0), Fp.mul(Fp.sqr(c1), FpNONRESIDUE)));
-            let d = Fp.mul(Fp.add(a, c0), Fpdiv2);
-            const legendre = mod.FpLegendre(Fp, d);
-            // -1, Quadratic non residue
-            if (legendre === -1)
-                d = Fp.sub(d, a);
-            const a0 = Fp.sqrt(d);
-            const candidateSqrt = Fp2.create({ c0: a0, c1: Fp.div(Fp.mul(c1, Fpdiv2), a0) });
-            if (!Fp2.eql(Fp2.sqr(candidateSqrt), num))
-                throw new Error('Cannot find square root');
-            // Normalize root: at this point candidateSqrt ** 2 = num, but also -candidateSqrt ** 2 = num
-            const x1 = candidateSqrt;
-            const x2 = Fp2.neg(x1);
-            const { re: re1, im: im1 } = Fp2.reim(x1);
-            const { re: re2, im: im2 } = Fp2.reim(x2);
-            if (im1 > im2 || (im1 === im2 && re1 > re2))
-                return x1;
-            return x2;
-        },
-        // Same as sgn0_m_eq_2 in RFC 9380
-        isOdd: (x) => {
-            const { re: x0, im: x1 } = Fp2.reim(x);
-            const sign_0 = x0 % _2n;
-            const zero_0 = x0 === _0n;
-            const sign_1 = x1 % _2n;
-            return BigInt(sign_0 || (zero_0 && sign_1)) == _1n;
-        },
-        // Bytes util
-        fromBytes(b) {
-            if (b.length !== Fp2.BYTES)
-                throw new Error('fromBytes invalid length=' + b.length);
-            return { c0: Fp.fromBytes(b.subarray(0, Fp.BYTES)), c1: Fp.fromBytes(b.subarray(Fp.BYTES)) };
-        },
-        toBytes: ({ c0, c1 }) => concatBytes(Fp.toBytes(c0), Fp.toBytes(c1)),
-        cmov: ({ c0, c1 }, { c0: r0, c1: r1 }, c) => ({
-            c0: Fp.cmov(c0, r0, c),
-            c1: Fp.cmov(c1, r1, c),
-        }),
-        reim: ({ c0, c1 }) => ({ re: c0, im: c1 }),
-        // multiply by u + 1
-        mulByNonresidue: ({ c0, c1 }) => Fp2.mul({ c0, c1 }, Fp2Nonresidue),
-        mulByB: opts.Fp2mulByB,
-        fromBigTuple: Fp2fromBigTuple,
-        frobeniusMap: ({ c0, c1 }, power) => ({
+    // NonNormalized stuff
+    addN(a, b) {
+        return this.add(a, b);
+    }
+    subN(a, b) {
+        return this.sub(a, b);
+    }
+    mulN(a, b) {
+        return this.mul(a, b);
+    }
+    sqrN(a) {
+        return this.sqr(a);
+    }
+    // Why inversion for bigint inside Fp instead of Fp2? it is even used in that context?
+    div(lhs, rhs) {
+        const { Fp } = this;
+        // @ts-ignore
+        return this.mul(lhs, typeof rhs === 'bigint' ? Fp.inv(Fp.create(rhs)) : this.inv(rhs));
+    }
+    inv({ c0: a, c1: b }) {
+        // We wish to find the multiplicative inverse of a nonzero
+        // element a + bu in Fp2. We leverage an identity
+        //
+        // (a + bu)(a - bu) = a² + b²
+        //
+        // which holds because u² = -1. This can be rewritten as
+        //
+        // (a + bu)(a - bu)/(a² + b²) = 1
+        //
+        // because a² + b² = 0 has no nonzero solutions for (a, b).
+        // This gives that (a - bu)/(a² + b²) is the inverse
+        // of (a + bu). Importantly, this can be computing using
+        // only a single inversion in Fp.
+        const { Fp } = this;
+        const factor = Fp.inv(Fp.create(a * a + b * b));
+        return { c0: Fp.mul(factor, Fp.create(a)), c1: Fp.mul(factor, Fp.create(-b)) };
+    }
+    sqrt(num) {
+        // This is generic for all quadratic extensions (Fp2)
+        const { Fp } = this;
+        const Fp2 = this;
+        const { c0, c1 } = num;
+        if (Fp.is0(c1)) {
+            // if c0 is quadratic residue
+            if (mod.FpLegendre(Fp, c0) === 1)
+                return Fp2.create({ c0: Fp.sqrt(c0), c1: Fp.ZERO });
+            else
+                return Fp2.create({ c0: Fp.ZERO, c1: Fp.sqrt(Fp.div(c0, this.Fp_NONRESIDUE)) });
+        }
+        const a = Fp.sqrt(Fp.sub(Fp.sqr(c0), Fp.mul(Fp.sqr(c1), this.Fp_NONRESIDUE)));
+        let d = Fp.mul(Fp.add(a, c0), this.Fp_div2);
+        const legendre = mod.FpLegendre(Fp, d);
+        // -1, Quadratic non residue
+        if (legendre === -1)
+            d = Fp.sub(d, a);
+        const a0 = Fp.sqrt(d);
+        const candidateSqrt = Fp2.create({ c0: a0, c1: Fp.div(Fp.mul(c1, this.Fp_div2), a0) });
+        if (!Fp2.eql(Fp2.sqr(candidateSqrt), num))
+            throw new Error('Cannot find square root');
+        // Normalize root: at this point candidateSqrt ** 2 = num, but also -candidateSqrt ** 2 = num
+        const x1 = candidateSqrt;
+        const x2 = Fp2.neg(x1);
+        const { re: re1, im: im1 } = Fp2.reim(x1);
+        const { re: re2, im: im2 } = Fp2.reim(x2);
+        if (im1 > im2 || (im1 === im2 && re1 > re2))
+            return x1;
+        return x2;
+    }
+    // Same as sgn0_m_eq_2 in RFC 9380
+    isOdd(x) {
+        const { re: x0, im: x1 } = this.reim(x);
+        const sign_0 = x0 % _2n;
+        const zero_0 = x0 === _0n;
+        const sign_1 = x1 % _2n;
+        return BigInt(sign_0 || (zero_0 && sign_1)) == _1n;
+    }
+    // Bytes util
+    fromBytes(b) {
+        const { Fp } = this;
+        if (b.length !== this.BYTES)
+            throw new Error('fromBytes invalid length=' + b.length);
+        return { c0: Fp.fromBytes(b.subarray(0, Fp.BYTES)), c1: Fp.fromBytes(b.subarray(Fp.BYTES)) };
+    }
+    toBytes({ c0, c1 }) {
+        return concatBytes(this.Fp.toBytes(c0), this.Fp.toBytes(c1));
+    }
+    cmov({ c0, c1 }, { c0: r0, c1: r1 }, c) {
+        return {
+            c0: this.Fp.cmov(c0, r0, c),
+            c1: this.Fp.cmov(c1, r1, c),
+        };
+    }
+    reim({ c0, c1 }) {
+        return { re: c0, im: c1 };
+    }
+    Fp4Square(a, b) {
+        const Fp2 = this;
+        const a2 = Fp2.sqr(a);
+        const b2 = Fp2.sqr(b);
+        return {
+            first: Fp2.add(Fp2.mulByNonresidue(b2), a2), // b² * Nonresidue + a²
+            second: Fp2.sub(Fp2.sub(Fp2.sqr(Fp2.add(a, b)), a2), b2), // (a + b)² - a² - b²
+        };
+    }
+    // multiply by u + 1
+    mulByNonresidue({ c0, c1 }) {
+        return this.mul({ c0, c1 }, this.NONRESIDUE);
+    }
+    frobeniusMap({ c0, c1 }, power) {
+        return {
             c0,
-            c1: Fp.mul(c1, FP2_FROBENIUS_COEFFICIENTS[power % 2]),
-        }),
-    };
-    // Fp6
-    const Fp6Add = ({ c0, c1, c2 }, { c0: r0, c1: r1, c2: r2 }) => ({
-        c0: Fp2.add(c0, r0),
-        c1: Fp2.add(c1, r1),
-        c2: Fp2.add(c2, r2),
-    });
-    const Fp6Subtract = ({ c0, c1, c2 }, { c0: r0, c1: r1, c2: r2 }) => ({
-        c0: Fp2.sub(c0, r0),
-        c1: Fp2.sub(c1, r1),
-        c2: Fp2.sub(c2, r2),
-    });
-    const Fp6Multiply = ({ c0, c1, c2 }, rhs) => {
+            c1: this.Fp.mul(c1, this.FROBENIUS_COEFFICIENTS[power % 2]),
+        };
+    }
+}
+class _Field6 {
+    constructor(Fp2) {
+        this.MASK = _1n;
+        this.Fp2 = Fp2;
+        this.ORDER = Fp2.ORDER; // TODO: unused, but need to verify
+        this.BITS = 3 * Fp2.BITS;
+        this.BYTES = 3 * Fp2.BYTES;
+        this.isLE = Fp2.isLE;
+        this.ZERO = { c0: Fp2.ZERO, c1: Fp2.ZERO, c2: Fp2.ZERO };
+        this.ONE = { c0: Fp2.ONE, c1: Fp2.ZERO, c2: Fp2.ZERO };
+        const { Fp } = Fp2;
+        const frob = calcFrobeniusCoefficients(Fp2, Fp2.NONRESIDUE, Fp.ORDER, 6, 2, 3);
+        this.FROBENIUS_COEFFICIENTS_1 = frob[0];
+        this.FROBENIUS_COEFFICIENTS_2 = frob[1];
+        Object.seal(this);
+    }
+    add({ c0, c1, c2 }, { c0: r0, c1: r1, c2: r2 }) {
+        const { Fp2 } = this;
+        return {
+            c0: Fp2.add(c0, r0),
+            c1: Fp2.add(c1, r1),
+            c2: Fp2.add(c2, r2),
+        };
+    }
+    sub({ c0, c1, c2 }, { c0: r0, c1: r1, c2: r2 }) {
+        const { Fp2 } = this;
+        return {
+            c0: Fp2.sub(c0, r0),
+            c1: Fp2.sub(c1, r1),
+            c2: Fp2.sub(c2, r2),
+        };
+    }
+    mul({ c0, c1, c2 }, rhs) {
+        const { Fp2 } = this;
         if (typeof rhs === 'bigint') {
@@ -251,4 +328,5 @@ return {
         };
-    };
-    const Fp6Square = ({ c0, c1, c2 }) => {
+    }
+    sqr({ c0, c1, c2 }) {
+        const { Fp2 } = this;
         let t0 = Fp2.sqr(c0); // c0²
@@ -264,108 +342,214 @@ let t1 = Fp2.mul(Fp2.mul(c0, c1), _2n); // 2 * c0 * c1
         };
-    };
-    const [FP6_FROBENIUS_COEFFICIENTS_1, FP6_FROBENIUS_COEFFICIENTS_2] = calcFrobeniusCoefficients(Fp2, Fp2Nonresidue, Fp.ORDER, 6, 2, 3);
-    const Fp6 = {
-        ORDER: Fp2.ORDER, // TODO: unused, but need to verify
-        isLE: Fp2.isLE,
-        BITS: 3 * Fp2.BITS,
-        BYTES: 3 * Fp2.BYTES,
-        MASK: bitMask(3 * Fp2.BITS),
-        ZERO: { c0: Fp2.ZERO, c1: Fp2.ZERO, c2: Fp2.ZERO },
-        ONE: { c0: Fp2.ONE, c1: Fp2.ZERO, c2: Fp2.ZERO },
-        create: (num) => num,
-        isValid: ({ c0, c1, c2 }) => Fp2.isValid(c0) && Fp2.isValid(c1) && Fp2.isValid(c2),
-        is0: ({ c0, c1, c2 }) => Fp2.is0(c0) && Fp2.is0(c1) && Fp2.is0(c2),
-        isValidNot0: (num) => !Fp6.is0(num) && Fp6.isValid(num),
-        neg: ({ c0, c1, c2 }) => ({ c0: Fp2.neg(c0), c1: Fp2.neg(c1), c2: Fp2.neg(c2) }),
-        eql: ({ c0, c1, c2 }, { c0: r0, c1: r1, c2: r2 }) => Fp2.eql(c0, r0) && Fp2.eql(c1, r1) && Fp2.eql(c2, r2),
-        sqrt: notImplemented,
-        // Do we need division by bigint at all? Should be done via order:
-        div: (lhs, rhs) => Fp6.mul(lhs, typeof rhs === 'bigint' ? Fp.inv(Fp.create(rhs)) : Fp6.inv(rhs)),
-        pow: (num, power) => mod.FpPow(Fp6, num, power),
-        invertBatch: (nums) => mod.FpInvertBatch(Fp6, nums),
-        // Normalized
-        add: Fp6Add,
-        sub: Fp6Subtract,
-        mul: Fp6Multiply,
-        sqr: Fp6Square,
-        // NonNormalized stuff
-        addN: Fp6Add,
-        subN: Fp6Subtract,
-        mulN: Fp6Multiply,
-        sqrN: Fp6Square,
-        inv: ({ c0, c1, c2 }) => {
-            let t0 = Fp2.sub(Fp2.sqr(c0), Fp2.mulByNonresidue(Fp2.mul(c2, c1))); // c0² - c2 * c1 * (u + 1)
-            let t1 = Fp2.sub(Fp2.mulByNonresidue(Fp2.sqr(c2)), Fp2.mul(c0, c1)); // c2² * (u + 1) - c0 * c1
-            let t2 = Fp2.sub(Fp2.sqr(c1), Fp2.mul(c0, c2)); // c1² - c0 * c2
-            // 1/(((c2 * T1 + c1 * T2) * v) + c0 * T0)
-            let t4 = Fp2.inv(Fp2.add(Fp2.mulByNonresidue(Fp2.add(Fp2.mul(c2, t1), Fp2.mul(c1, t2))), Fp2.mul(c0, t0)));
-            return { c0: Fp2.mul(t4, t0), c1: Fp2.mul(t4, t1), c2: Fp2.mul(t4, t2) };
-        },
-        // Bytes utils
-        fromBytes: (b) => {
-            if (b.length !== Fp6.BYTES)
-                throw new Error('fromBytes invalid length=' + b.length);
-            return {
-                c0: Fp2.fromBytes(b.subarray(0, Fp2.BYTES)),
-                c1: Fp2.fromBytes(b.subarray(Fp2.BYTES, 2 * Fp2.BYTES)),
-                c2: Fp2.fromBytes(b.subarray(2 * Fp2.BYTES)),
-            };
-        },
-        toBytes: ({ c0, c1, c2 }) => concatBytes(Fp2.toBytes(c0), Fp2.toBytes(c1), Fp2.toBytes(c2)),
-        cmov: ({ c0, c1, c2 }, { c0: r0, c1: r1, c2: r2 }, c) => ({
+    }
+    addN(a, b) {
+        return this.add(a, b);
+    }
+    subN(a, b) {
+        return this.sub(a, b);
+    }
+    mulN(a, b) {
+        return this.mul(a, b);
+    }
+    sqrN(a) {
+        return this.sqr(a);
+    }
+    create(num) {
+        return num;
+    }
+    isValid({ c0, c1, c2 }) {
+        const { Fp2 } = this;
+        return Fp2.isValid(c0) && Fp2.isValid(c1) && Fp2.isValid(c2);
+    }
+    is0({ c0, c1, c2 }) {
+        const { Fp2 } = this;
+        return Fp2.is0(c0) && Fp2.is0(c1) && Fp2.is0(c2);
+    }
+    isValidNot0(num) {
+        return !this.is0(num) && this.isValid(num);
+    }
+    neg({ c0, c1, c2 }) {
+        const { Fp2 } = this;
+        return { c0: Fp2.neg(c0), c1: Fp2.neg(c1), c2: Fp2.neg(c2) };
+    }
+    eql({ c0, c1, c2 }, { c0: r0, c1: r1, c2: r2 }) {
+        const { Fp2 } = this;
+        return Fp2.eql(c0, r0) && Fp2.eql(c1, r1) && Fp2.eql(c2, r2);
+    }
+    sqrt(_) {
+        return notImplemented();
+    }
+    // Do we need division by bigint at all? Should be done via order:
+    div(lhs, rhs) {
+        const { Fp2 } = this;
+        const { Fp } = Fp2;
+        return this.mul(lhs, typeof rhs === 'bigint' ? Fp.inv(Fp.create(rhs)) : this.inv(rhs));
+    }
+    pow(num, power) {
+        return mod.FpPow(this, num, power);
+    }
+    invertBatch(nums) {
+        return mod.FpInvertBatch(this, nums);
+    }
+    inv({ c0, c1, c2 }) {
+        const { Fp2 } = this;
+        let t0 = Fp2.sub(Fp2.sqr(c0), Fp2.mulByNonresidue(Fp2.mul(c2, c1))); // c0² - c2 * c1 * (u + 1)
+        let t1 = Fp2.sub(Fp2.mulByNonresidue(Fp2.sqr(c2)), Fp2.mul(c0, c1)); // c2² * (u + 1) - c0 * c1
+        let t2 = Fp2.sub(Fp2.sqr(c1), Fp2.mul(c0, c2)); // c1² - c0 * c2
+        // 1/(((c2 * T1 + c1 * T2) * v) + c0 * T0)
+        let t4 = Fp2.inv(Fp2.add(Fp2.mulByNonresidue(Fp2.add(Fp2.mul(c2, t1), Fp2.mul(c1, t2))), Fp2.mul(c0, t0)));
+        return { c0: Fp2.mul(t4, t0), c1: Fp2.mul(t4, t1), c2: Fp2.mul(t4, t2) };
+    }
+    // Bytes utils
+    fromBytes(b) {
+        const { Fp2 } = this;
+        if (b.length !== this.BYTES)
+            throw new Error('fromBytes invalid length=' + b.length);
+        const B2 = Fp2.BYTES;
+        return {
+            c0: Fp2.fromBytes(b.subarray(0, B2)),
+            c1: Fp2.fromBytes(b.subarray(B2, B2 * 2)),
+            c2: Fp2.fromBytes(b.subarray(2 * B2)),
+        };
+    }
+    toBytes({ c0, c1, c2 }) {
+        const { Fp2 } = this;
+        return concatBytes(Fp2.toBytes(c0), Fp2.toBytes(c1), Fp2.toBytes(c2));
+    }
+    cmov({ c0, c1, c2 }, { c0: r0, c1: r1, c2: r2 }, c) {
+        const { Fp2 } = this;
+        return {
             c0: Fp2.cmov(c0, r0, c),
             c1: Fp2.cmov(c1, r1, c),
             c2: Fp2.cmov(c2, r2, c),
-        }),
-        fromBigSix: (t) => {
-            if (!Array.isArray(t) || t.length !== 6)
-                throw new Error('invalid Fp6 usage');
-            return {
-                c0: Fp2.fromBigTuple(t.slice(0, 2)),
-                c1: Fp2.fromBigTuple(t.slice(2, 4)),
-                c2: Fp2.fromBigTuple(t.slice(4, 6)),
-            };
-        },
-        frobeniusMap: ({ c0, c1, c2 }, power) => ({
+        };
+    }
+    fromBigSix(t) {
+        const { Fp2 } = this;
+        if (!Array.isArray(t) || t.length !== 6)
+            throw new Error('invalid Fp6 usage');
+        return {
+            c0: Fp2.fromBigTuple(t.slice(0, 2)),
+            c1: Fp2.fromBigTuple(t.slice(2, 4)),
+            c2: Fp2.fromBigTuple(t.slice(4, 6)),
+        };
+    }
+    frobeniusMap({ c0, c1, c2 }, power) {
+        const { Fp2 } = this;
+        return {
             c0: Fp2.frobeniusMap(c0, power),
-            c1: Fp2.mul(Fp2.frobeniusMap(c1, power), FP6_FROBENIUS_COEFFICIENTS_1[power % 6]),
-            c2: Fp2.mul(Fp2.frobeniusMap(c2, power), FP6_FROBENIUS_COEFFICIENTS_2[power % 6]),
-        }),
-        mulByFp2: ({ c0, c1, c2 }, rhs) => ({
+            c1: Fp2.mul(Fp2.frobeniusMap(c1, power), this.FROBENIUS_COEFFICIENTS_1[power % 6]),
+            c2: Fp2.mul(Fp2.frobeniusMap(c2, power), this.FROBENIUS_COEFFICIENTS_2[power % 6]),
+        };
+    }
+    mulByFp2({ c0, c1, c2 }, rhs) {
+        const { Fp2 } = this;
+        return {
             c0: Fp2.mul(c0, rhs),
             c1: Fp2.mul(c1, rhs),
             c2: Fp2.mul(c2, rhs),
-        }),
-        mulByNonresidue: ({ c0, c1, c2 }) => ({ c0: Fp2.mulByNonresidue(c2), c1: c0, c2: c1 }),
-        // Sparse multiplication
-        mul1: ({ c0, c1, c2 }, b1) => ({
+        };
+    }
+    mulByNonresidue({ c0, c1, c2 }) {
+        const { Fp2 } = this;
+        return { c0: Fp2.mulByNonresidue(c2), c1: c0, c2: c1 };
+    }
+    // Sparse multiplication
+    mul1({ c0, c1, c2 }, b1) {
+        const { Fp2 } = this;
+        return {
             c0: Fp2.mulByNonresidue(Fp2.mul(c2, b1)),
             c1: Fp2.mul(c0, b1),
             c2: Fp2.mul(c1, b1),
-        }),
-        // Sparse multiplication
-        mul01({ c0, c1, c2 }, b0, b1) {
-            let t0 = Fp2.mul(c0, b0); // c0 * b0
-            let t1 = Fp2.mul(c1, b1); // c1 * b1
-            return {
-                // ((c1 + c2) * b1 - T1) * (u + 1) + T0
-                c0: Fp2.add(Fp2.mulByNonresidue(Fp2.sub(Fp2.mul(Fp2.add(c1, c2), b1), t1)), t0),
-                // (b0 + b1) * (c0 + c1) - T0 - T1
-                c1: Fp2.sub(Fp2.sub(Fp2.mul(Fp2.add(b0, b1), Fp2.add(c0, c1)), t0), t1),
-                // (c0 + c2) * b0 - T0 + T1
-                c2: Fp2.add(Fp2.sub(Fp2.mul(Fp2.add(c0, c2), b0), t0), t1),
-            };
-        },
-    };
-    // Fp12
-    const FP12_FROBENIUS_COEFFICIENTS = calcFrobeniusCoefficients(Fp2, Fp2Nonresidue, Fp.ORDER, 12, 1, 6)[0];
-    const Fp12Add = ({ c0, c1 }, { c0: r0, c1: r1 }) => ({
-        c0: Fp6.add(c0, r0),
-        c1: Fp6.add(c1, r1),
-    });
-    const Fp12Subtract = ({ c0, c1 }, { c0: r0, c1: r1 }) => ({
-        c0: Fp6.sub(c0, r0),
-        c1: Fp6.sub(c1, r1),
-    });
-    const Fp12Multiply = ({ c0, c1 }, rhs) => {
+        };
+    }
+    // Sparse multiplication
+    mul01({ c0, c1, c2 }, b0, b1) {
+        const { Fp2 } = this;
+        let t0 = Fp2.mul(c0, b0); // c0 * b0
+        let t1 = Fp2.mul(c1, b1); // c1 * b1
+        return {
+            // ((c1 + c2) * b1 - T1) * (u + 1) + T0
+            c0: Fp2.add(Fp2.mulByNonresidue(Fp2.sub(Fp2.mul(Fp2.add(c1, c2), b1), t1)), t0),
+            // (b0 + b1) * (c0 + c1) - T0 - T1
+            c1: Fp2.sub(Fp2.sub(Fp2.mul(Fp2.add(b0, b1), Fp2.add(c0, c1)), t0), t1),
+            // (c0 + c2) * b0 - T0 + T1
+            c2: Fp2.add(Fp2.sub(Fp2.mul(Fp2.add(c0, c2), b0), t0), t1),
+        };
+    }
+}
+class _Field12 {
+    constructor(Fp6, opts) {
+        this.MASK = _1n;
+        const { Fp2 } = Fp6;
+        const { Fp } = Fp2;
+        this.Fp6 = Fp6;
+        this.ORDER = Fp2.ORDER; // TODO: verify if it's unuesd
+        this.BITS = 2 * Fp6.BITS;
+        this.BYTES = 2 * Fp6.BYTES;
+        this.isLE = Fp6.isLE;
+        this.ZERO = { c0: Fp6.ZERO, c1: Fp6.ZERO };
+        this.ONE = { c0: Fp6.ONE, c1: Fp6.ZERO };
+        this.FROBENIUS_COEFFICIENTS = calcFrobeniusCoefficients(Fp2, Fp2.NONRESIDUE, Fp.ORDER, 12, 1, 6)[0];
+        this.X_LEN = opts.X_LEN;
+        this.finalExponentiate = opts.Fp12finalExponentiate;
+    }
+    create(num) {
+        return num;
+    }
+    isValid({ c0, c1 }) {
+        const { Fp6 } = this;
+        return Fp6.isValid(c0) && Fp6.isValid(c1);
+    }
+    is0({ c0, c1 }) {
+        const { Fp6 } = this;
+        return Fp6.is0(c0) && Fp6.is0(c1);
+    }
+    isValidNot0(num) {
+        return !this.is0(num) && this.isValid(num);
+    }
+    neg({ c0, c1 }) {
+        const { Fp6 } = this;
+        return { c0: Fp6.neg(c0), c1: Fp6.neg(c1) };
+    }
+    eql({ c0, c1 }, { c0: r0, c1: r1 }) {
+        const { Fp6 } = this;
+        return Fp6.eql(c0, r0) && Fp6.eql(c1, r1);
+    }
+    sqrt(_) {
+        notImplemented();
+    }
+    inv({ c0, c1 }) {
+        const { Fp6 } = this;
+        let t = Fp6.inv(Fp6.sub(Fp6.sqr(c0), Fp6.mulByNonresidue(Fp6.sqr(c1)))); // 1 / (c0² - c1² * v)
+        return { c0: Fp6.mul(c0, t), c1: Fp6.neg(Fp6.mul(c1, t)) }; // ((C0 * T) * T) + (-C1 * T) * w
+    }
+    div(lhs, rhs) {
+        const { Fp6 } = this;
+        const { Fp2 } = Fp6;
+        const { Fp } = Fp2;
+        return this.mul(lhs, typeof rhs === 'bigint' ? Fp.inv(Fp.create(rhs)) : this.inv(rhs));
+    }
+    pow(num, power) {
+        return mod.FpPow(this, num, power);
+    }
+    invertBatch(nums) {
+        return mod.FpInvertBatch(this, nums);
+    }
+    // Normalized
+    add({ c0, c1 }, { c0: r0, c1: r1 }) {
+        const { Fp6 } = this;
+        return {
+            c0: Fp6.add(c0, r0),
+            c1: Fp6.add(c1, r1),
+        };
+    }
+    sub({ c0, c1 }, { c0: r0, c1: r1 }) {
+        const { Fp6 } = this;
+        return {
+            c0: Fp6.sub(c0, r0),
+            c1: Fp6.sub(c1, r1),
+        };
+    }
+    mul({ c0, c1 }, rhs) {
+        const { Fp6 } = this;
         if (typeof rhs === 'bigint')
@@ -381,4 +565,5 @@ return { c0: Fp6.mul(c0, rhs), c1: Fp6.mul(c1, rhs) };
         };
-    };
-    const Fp12Square = ({ c0, c1 }) => {
+    }
+    sqr({ c0, c1 }) {
+        const { Fp6 } = this;
         let ab = Fp6.mul(c0, c1); // c0 * c1
@@ -390,121 +575,148 @@ return {
         }; // AB + AB
-    };
-    function Fp4Square(a, b) {
-        const a2 = Fp2.sqr(a);
-        const b2 = Fp2.sqr(b);
+    }
+    // NonNormalized stuff
+    addN(a, b) {
+        return this.add(a, b);
+    }
+    subN(a, b) {
+        return this.sub(a, b);
+    }
+    mulN(a, b) {
+        return this.mul(a, b);
+    }
+    sqrN(a) {
+        return this.sqr(a);
+    }
+    // Bytes utils
+    fromBytes(b) {
+        const { Fp6 } = this;
+        if (b.length !== this.BYTES)
+            throw new Error('fromBytes invalid length=' + b.length);
         return {
-            first: Fp2.add(Fp2.mulByNonresidue(b2), a2), // b² * Nonresidue + a²
-            second: Fp2.sub(Fp2.sub(Fp2.sqr(Fp2.add(a, b)), a2), b2), // (a + b)² - a² - b²
+            c0: Fp6.fromBytes(b.subarray(0, Fp6.BYTES)),
+            c1: Fp6.fromBytes(b.subarray(Fp6.BYTES)),
         };
     }
-    const Fp12 = {
-        ORDER: Fp2.ORDER, // TODO: unused, but need to verify
-        isLE: Fp6.isLE,
-        BITS: 2 * Fp6.BITS,
-        BYTES: 2 * Fp6.BYTES,
-        MASK: bitMask(2 * Fp6.BITS),
-        ZERO: { c0: Fp6.ZERO, c1: Fp6.ZERO },
-        ONE: { c0: Fp6.ONE, c1: Fp6.ZERO },
-        create: (num) => num,
-        isValid: ({ c0, c1 }) => Fp6.isValid(c0) && Fp6.isValid(c1),
-        is0: ({ c0, c1 }) => Fp6.is0(c0) && Fp6.is0(c1),
-        isValidNot0: (num) => !Fp12.is0(num) && Fp12.isValid(num),
-        neg: ({ c0, c1 }) => ({ c0: Fp6.neg(c0), c1: Fp6.neg(c1) }),
-        eql: ({ c0, c1 }, { c0: r0, c1: r1 }) => Fp6.eql(c0, r0) && Fp6.eql(c1, r1),
-        sqrt: notImplemented,
-        inv: ({ c0, c1 }) => {
-            let t = Fp6.inv(Fp6.sub(Fp6.sqr(c0), Fp6.mulByNonresidue(Fp6.sqr(c1)))); // 1 / (c0² - c1² * v)
-            return { c0: Fp6.mul(c0, t), c1: Fp6.neg(Fp6.mul(c1, t)) }; // ((C0 * T) * T) + (-C1 * T) * w
-        },
-        div: (lhs, rhs) => Fp12.mul(lhs, typeof rhs === 'bigint' ? Fp.inv(Fp.create(rhs)) : Fp12.inv(rhs)),
-        pow: (num, power) => mod.FpPow(Fp12, num, power),
-        invertBatch: (nums) => mod.FpInvertBatch(Fp12, nums),
-        // Normalized
-        add: Fp12Add,
-        sub: Fp12Subtract,
-        mul: Fp12Multiply,
-        sqr: Fp12Square,
-        // NonNormalized stuff
-        addN: Fp12Add,
-        subN: Fp12Subtract,
-        mulN: Fp12Multiply,
-        sqrN: Fp12Square,
-        // Bytes utils
-        fromBytes: (b) => {
-            if (b.length !== Fp12.BYTES)
-                throw new Error('fromBytes invalid length=' + b.length);
-            return {
-                c0: Fp6.fromBytes(b.subarray(0, Fp6.BYTES)),
-                c1: Fp6.fromBytes(b.subarray(Fp6.BYTES)),
-            };
-        },
-        toBytes: ({ c0, c1 }) => concatBytes(Fp6.toBytes(c0), Fp6.toBytes(c1)),
-        cmov: ({ c0, c1 }, { c0: r0, c1: r1 }, c) => ({
+    toBytes({ c0, c1 }) {
+        const { Fp6 } = this;
+        return concatBytes(Fp6.toBytes(c0), Fp6.toBytes(c1));
+    }
+    cmov({ c0, c1 }, { c0: r0, c1: r1 }, c) {
+        const { Fp6 } = this;
+        return {
             c0: Fp6.cmov(c0, r0, c),
             c1: Fp6.cmov(c1, r1, c),
-        }),
-        // Utils
-        // toString() {
-        //   return '' + 'Fp12(' + this.c0 + this.c1 + '* w');
-        // },
-        // fromTuple(c: [Fp6, Fp6]) {
-        //   return new Fp12(...c);
-        // }
-        fromBigTwelve: (t) => ({
+        };
+    }
+    // Utils
+    // toString() {
+    //   return '' + 'Fp12(' + this.c0 + this.c1 + '* w');
+    // },
+    // fromTuple(c: [Fp6, Fp6]) {
+    //   return new Fp12(...c);
+    // }
+    fromBigTwelve(t) {
+        const { Fp6 } = this;
+        return {
             c0: Fp6.fromBigSix(t.slice(0, 6)),
             c1: Fp6.fromBigSix(t.slice(6, 12)),
-        }),
-        // Raises to q**i -th power
-        frobeniusMap(lhs, power) {
-            const { c0, c1, c2 } = Fp6.frobeniusMap(lhs.c1, power);
-            const coeff = FP12_FROBENIUS_COEFFICIENTS[power % 12];
-            return {
-                c0: Fp6.frobeniusMap(lhs.c0, power),
-                c1: Fp6.create({
-                    c0: Fp2.mul(c0, coeff),
-                    c1: Fp2.mul(c1, coeff),
-                    c2: Fp2.mul(c2, coeff),
-                }),
-            };
-        },
-        mulByFp2: ({ c0, c1 }, rhs) => ({
+        };
+    }
+    // Raises to q**i -th power
+    frobeniusMap(lhs, power) {
+        const { Fp6 } = this;
+        const { Fp2 } = Fp6;
+        const { c0, c1, c2 } = Fp6.frobeniusMap(lhs.c1, power);
+        const coeff = this.FROBENIUS_COEFFICIENTS[power % 12];
+        return {
+            c0: Fp6.frobeniusMap(lhs.c0, power),
+            c1: Fp6.create({
+                c0: Fp2.mul(c0, coeff),
+                c1: Fp2.mul(c1, coeff),
+                c2: Fp2.mul(c2, coeff),
+            }),
+        };
+    }
+    mulByFp2({ c0, c1 }, rhs) {
+        const { Fp6 } = this;
+        return {
             c0: Fp6.mulByFp2(c0, rhs),
             c1: Fp6.mulByFp2(c1, rhs),
-        }),
-        conjugate: ({ c0, c1 }) => ({ c0, c1: Fp6.neg(c1) }),
-        // Sparse multiplication
-        mul014: ({ c0, c1 }, o0, o1, o4) => {
-            let t0 = Fp6.mul01(c0, o0, o1);
-            let t1 = Fp6.mul1(c1, o4);
-            return {
-                c0: Fp6.add(Fp6.mulByNonresidue(t1), t0), // T1 * v + T0
-                // (c1 + c0) * [o0, o1+o4] - T0 - T1
-                c1: Fp6.sub(Fp6.sub(Fp6.mul01(Fp6.add(c1, c0), o0, Fp2.add(o1, o4)), t0), t1),
-            };
-        },
-        mul034: ({ c0, c1 }, o0, o3, o4) => {
-            const a = Fp6.create({
-                c0: Fp2.mul(c0.c0, o0),
-                c1: Fp2.mul(c0.c1, o0),
-                c2: Fp2.mul(c0.c2, o0),
-            });
-            const b = Fp6.mul01(c1, o3, o4);
-            const e = Fp6.mul01(Fp6.add(c0, c1), Fp2.add(o0, o3), o4);
-            return {
-                c0: Fp6.add(Fp6.mulByNonresidue(b), a),
-                c1: Fp6.sub(e, Fp6.add(a, b)),
-            };
-        },
-        // A cyclotomic group is a subgroup of Fp^n defined by
-        //   GΦₙ(p) = {α ∈ Fpⁿ : α^Φₙ(p) = 1}
-        // The result of any pairing is in a cyclotomic subgroup
-        // https://eprint.iacr.org/2009/565.pdf
-        _cyclotomicSquare: opts.Fp12cyclotomicSquare,
-        _cyclotomicExp: opts.Fp12cyclotomicExp,
-        // https://eprint.iacr.org/2010/354.pdf
-        // https://eprint.iacr.org/2009/565.pdf
-        finalExponentiate: opts.Fp12finalExponentiate,
-    };
-    return { Fp, Fp2, Fp6, Fp12, Fp4Square };
+        };
+    }
+    conjugate({ c0, c1 }) {
+        return { c0, c1: this.Fp6.neg(c1) };
+    }
+    // Sparse multiplication
+    mul014({ c0, c1 }, o0, o1, o4) {
+        const { Fp6 } = this;
+        const { Fp2 } = Fp6;
+        let t0 = Fp6.mul01(c0, o0, o1);
+        let t1 = Fp6.mul1(c1, o4);
+        return {
+            c0: Fp6.add(Fp6.mulByNonresidue(t1), t0), // T1 * v + T0
+            // (c1 + c0) * [o0, o1+o4] - T0 - T1
+            c1: Fp6.sub(Fp6.sub(Fp6.mul01(Fp6.add(c1, c0), o0, Fp2.add(o1, o4)), t0), t1),
+        };
+    }
+    mul034({ c0, c1 }, o0, o3, o4) {
+        const { Fp6 } = this;
+        const { Fp2 } = Fp6;
+        const a = Fp6.create({
+            c0: Fp2.mul(c0.c0, o0),
+            c1: Fp2.mul(c0.c1, o0),
+            c2: Fp2.mul(c0.c2, o0),
+        });
+        const b = Fp6.mul01(c1, o3, o4);
+        const e = Fp6.mul01(Fp6.add(c0, c1), Fp2.add(o0, o3), o4);
+        return {
+            c0: Fp6.add(Fp6.mulByNonresidue(b), a),
+            c1: Fp6.sub(e, Fp6.add(a, b)),
+        };
+    }
+    // A cyclotomic group is a subgroup of Fp^n defined by
+    //   GΦₙ(p) = {α ∈ Fpⁿ : α^Φₙ(p) = 1}
+    // The result of any pairing is in a cyclotomic subgroup
+    // https://eprint.iacr.org/2009/565.pdf
+    // https://eprint.iacr.org/2010/354.pdf
+    _cyclotomicSquare({ c0, c1 }) {
+        const { Fp6 } = this;
+        const { Fp2 } = Fp6;
+        const { c0: c0c0, c1: c0c1, c2: c0c2 } = c0;
+        const { c0: c1c0, c1: c1c1, c2: c1c2 } = c1;
+        const { first: t3, second: t4 } = Fp2.Fp4Square(c0c0, c1c1);
+        const { first: t5, second: t6 } = Fp2.Fp4Square(c1c0, c0c2);
+        const { first: t7, second: t8 } = Fp2.Fp4Square(c0c1, c1c2);
+        const t9 = Fp2.mulByNonresidue(t8); // T8 * (u + 1)
+        return {
+            c0: Fp6.create({
+                c0: Fp2.add(Fp2.mul(Fp2.sub(t3, c0c0), _2n), t3), // 2 * (T3 - c0c0)  + T3
+                c1: Fp2.add(Fp2.mul(Fp2.sub(t5, c0c1), _2n), t5), // 2 * (T5 - c0c1)  + T5
+                c2: Fp2.add(Fp2.mul(Fp2.sub(t7, c0c2), _2n), t7),
+            }), // 2 * (T7 - c0c2)  + T7
+            c1: Fp6.create({
+                c0: Fp2.add(Fp2.mul(Fp2.add(t9, c1c0), _2n), t9), // 2 * (T9 + c1c0) + T9
+                c1: Fp2.add(Fp2.mul(Fp2.add(t4, c1c1), _2n), t4), // 2 * (T4 + c1c1) + T4
+                c2: Fp2.add(Fp2.mul(Fp2.add(t6, c1c2), _2n), t6),
+            }),
+        }; // 2 * (T6 + c1c2) + T6
+    }
+    // https://eprint.iacr.org/2009/565.pdf
+    _cyclotomicExp(num, n) {
+        let z = this.ONE;
+        for (let i = this.X_LEN - 1; i >= 0; i--) {
+            z = this._cyclotomicSquare(z);
+            if (bitGet(n, i))
+                z = this.mul(z, num);
+        }
+        return z;
+    }
 }
+export function tower12(opts) {
+    const Fp = mod.Field(opts.ORDER);
+    const Fp2 = new _Field2(Fp, opts);
+    const Fp6 = new _Field6(Fp2);
+    const Fp12 = new _Field12(Fp6, opts);
+    return { Fp, Fp2, Fp6, Fp12 };
+}
 //# sourceMappingURL=tower.js.map

esm/abstract/tower.js.map

@@ -1,1 +0,1 @@
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esm/abstract/weierstrass.d.ts

@@ -323,2 +323,3 @@ import { type CHash, type Hex, type PrivKey } from '../utils.ts';
  * const p256_sha224 = ecdsa(p256_Point, sha224);
+ * const p256_sha224_r = ecdsa(p256_Point, sha224, { randomBytes: (length) => { ... } });
  * ```
@@ -325,0 +326,0 @@ */

esm/abstract/weierstrass.d.ts.map

@@ -1,1 +0,1 @@
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esm/abstract/weierstrass.js

@@ -30,3 +30,3 @@ /**
 import { ahash } from '@noble/hashes/utils';
-import { _validateObject, _abool2 as abool, _abytes2 as abytes, aInRange, bitLen, bitMask, bytesToHex, bytesToNumberBE, concatBytes, createHmacDrbg, ensureBytes, hexToBytes, inRange, isBytes, memoized, numberToHexUnpadded, randomBytes as wcRandomBytes, } from "../utils.js";
+import { _validateObject, _abool2 as abool, _abytes2 as abytes, aInRange, bitLen, bitMask, bytesToHex, bytesToNumberBE, concatBytes, createHmacDrbg, ensureBytes, hexToBytes, inRange, isBytes, memoized, numberToHexUnpadded, randomBytes as randomBytesWeb, } from "../utils.js";
 import { _createCurveFields, mulEndoUnsafe, negateCt, normalizeZ, pippenger, wNAF, } from "./curve.js";
@@ -278,3 +278,3 @@ import { Field, FpInvertBatch, getMinHashLength, mapHashToField, nLength, validateField, } from "./modular.js";
         abytes(bytes, undefined, 'Point');
-        const { public: comp, publicUncompressed: uncomp } = lengths; // e.g. for 32-byte: 33, 65
+        const { publicKey: comp, publicKeyUncompressed: uncomp } = lengths; // e.g. for 32-byte: 33, 65
         const length = bytes.length;
@@ -723,2 +723,3 @@ const head = bytes[0];
     const wnaf = new wNAF(Point, extraOpts.endo ? Math.ceil(bits / 2) : bits);
+    Point.BASE.precompute(8); // Enable precomputes. Slows down first publicKey computation by 20ms.
     return Point;
@@ -856,5 +857,5 @@ }
     return {
-        secret: Fn.BYTES,
-        public: 1 + Fp.BYTES,
-        publicUncompressed: 1 + 2 * Fp.BYTES,
+        secretKey: Fn.BYTES,
+        publicKey: 1 + Fp.BYTES,
+        publicKeyUncompressed: 1 + 2 * Fp.BYTES,
         publicKeyHasPrefix: true,
@@ -870,3 +871,3 @@ signature: 2 * Fn.BYTES,
     const { Fn } = Point;
-    const randomBytes_ = ecdhOpts.randomBytes || wcRandomBytes;
+    const randomBytes_ = ecdhOpts.randomBytes || randomBytesWeb;
     const lengths = Object.assign(getWLengths(Point.Fp, Fn), { seed: getMinHashLength(Fn.ORDER) });
@@ -882,3 +883,3 @@ function isValidSecretKey(secretKey) {
     function isValidPublicKey(publicKey, isCompressed) {
-        const { public: comp, publicUncompressed } = lengths;
+        const { publicKey: comp, publicKeyUncompressed } = lengths;
         try {
@@ -888,3 +889,3 @@ const l = publicKey.length;
                 return false;
-            if (isCompressed === false && l !== publicUncompressed)
+            if (isCompressed === false && l !== publicKeyUncompressed)
                 return false;
@@ -924,6 +925,7 @@ return !!Point.fromBytes(publicKey);
             return true;
-        if (Fn.allowedLengths || lengths.secret === lengths.public)
+        const { secretKey, publicKey, publicKeyUncompressed } = lengths;
+        if (Fn.allowedLengths || secretKey === publicKey)
             return undefined;
         const l = ensureBytes('key', item).length;
-        return l === lengths.public || l === lengths.publicUncompressed;
+        return l === publicKey || l === publicKeyUncompressed;
     }
@@ -974,2 +976,3 @@ /**
  * const p256_sha224 = ecdsa(p256_Point, sha224);
+ * const p256_sha224_r = ecdsa(p256_Point, sha224, { randomBytes: (length) => { ... } });
  * ```
@@ -986,4 +989,4 @@ */
     });
-    const randomBytes_ = ecdsaOpts.randomBytes || wcRandomBytes;
-    const hmac_ = ecdsaOpts.hmac ||
+    const randomBytes = ecdsaOpts.randomBytes || randomBytesWeb;
+    const hmac = ecdsaOpts.hmac ||
         ((key, ...msgs) => nobleHmac(hash, key, concatBytes(...msgs)));
@@ -1004,5 +1007,2 @@ const { Fp, Fn } = Point;
     }
-    function normalizeS(s) {
-        return isBiggerThanHalfOrder(s) ? Fn.neg(s) : s;
-    }
     function validateRS(title, num) {
@@ -1013,2 +1013,8 @@ if (!Fn.isValidNot0(num))
     }
+    function validateSigLength(bytes, format) {
+        validateSigFormat(format);
+        const size = lengths.signature;
+        const sizer = format === 'compact' ? size : format === 'recovered' ? size + 1 : undefined;
+        return abytes(bytes, sizer, `${format} signature`);
+    }
     /**
@@ -1026,4 +1032,3 @@ * ECDSA signature with its (r, s) properties. Supports compact, recovered & DER representations.
         static fromBytes(bytes, format = defaultSigOpts_format) {
-            validateSigFormat(format);
-            const size = lengths.signature;
+            validateSigLength(bytes, format);
             let recid;
@@ -1035,3 +1040,2 @@ if (format === 'der') {
             if (format === 'recovered') {
-                abytes(bytes, size + 1);
                 recid = bytes[0];
@@ -1041,4 +1045,3 @@ format = 'compact';
             }
-            abytes(bytes, size);
-            const L = size / 2;
+            const L = Fn.BYTES;
             const r = bytes.subarray(0, L);
@@ -1054,3 +1057,3 @@ const s = bytes.subarray(L, L * 2);
         }
-        recoverPublicKey(msgHash) {
+        recoverPublicKey(messageHash) {
             const FIELD_ORDER = Fp.ORDER;
@@ -1077,3 +1080,3 @@ const { r, s, recovery: rec } = this;
             const ir = Fn.inv(radj); // r^-1
-            const h = bits2int_modN(ensureBytes('msgHash', msgHash)); // Truncate hash
+            const h = bits2int_modN(ensureBytes('msgHash', messageHash)); // Truncate hash
             const u1 = Fn.create(-h * ir); // -hr^-1
@@ -1137,3 +1140,3 @@ const u2 = Fn.create(s * ir); // sr^-1
     const bits2int = ecdsaOpts.bits2int ||
-        function (bytes) {
+        function bits2int_def(bytes) {
             // Our custom check "just in case", for protection against DoS
@@ -1149,10 +1152,8 @@ if (bytes.length > 8192)
     const bits2int_modN = ecdsaOpts.bits2int_modN ||
-        function (bytes) {
+        function bits2int_modN_def(bytes) {
             return Fn.create(bits2int(bytes)); // can't use bytesToNumberBE here
         };
-    // NOTE: pads output with zero as per spec
+    // Pads output with zero as per spec
     const ORDER_MASK = bitMask(fnBits);
-    /**
-     * Converts to bytes. Checks if num in `[0..ORDER_MASK-1]` e.g.: `[0..2^256-1]`.
-     */
+    /** Converts to bytes. Checks if num in `[0..ORDER_MASK-1]` e.g.: `[0..2^256-1]`. */
     function int2octets(num) {
@@ -1163,2 +1164,6 @@ // IMPORTANT: the check ensures working for case `Fn.BYTES != Fn.BITS * 8`
     }
+    function validateMsgAndHash(message, prehash) {
+        abytes(message, undefined, 'message');
+        return prehash ? abytes(hash(message), undefined, 'prehashed message') : message;
+    }
     /**
@@ -1176,6 +1181,3 @@ * Steps A, D of RFC6979 3.2.
         const { lowS, prehash, extraEntropy } = validateSigOpts(opts, defaultSigOpts);
-        // RFC6979 3.2: we skip step A, because we already provide hash
-        message = abytes(message, undefined, 'message');
-        if (prehash)
-            message = abytes(hash(message), undefined, 'prehashed message');
+        message = validateMsgAndHash(message, prehash); // RFC6979 3.2 A: h1 = H(m)
         // We can't later call bits2octets, since nested bits2int is broken for curves
@@ -1191,3 +1193,3 @@ // with fnBits % 8 !== 0. Because of that, we unwrap it here as int2octets call.
             // gen random bytes OR pass as-is
-            const e = extraEntropy === true ? randomBytes_(lengths.secret) : extraEntropy;
+            const e = extraEntropy === true ? randomBytes(lengths.secretKey) : extraEntropy;
             seedArgs.push(ensureBytes('extraEntropy', e)); // check for being bytes
@@ -1222,3 +1224,3 @@ }
             if (lowS && isBiggerThanHalfOrder(s)) {
-                normS = normalizeS(s); // if lowS was passed, ensure s is always
+                normS = Fn.neg(s); // if lowS was passed, ensure s is always
                 recovery ^= 1; // // in the bottom half of N
@@ -1244,8 +1246,41 @@ }
         const { seed, k2sig } = prepSig(message, secretKey, opts); // Steps A, D of RFC6979 3.2.
-        const drbg = createHmacDrbg(hash.outputLen, Fn.BYTES, hmac_);
+        const drbg = createHmacDrbg(hash.outputLen, Fn.BYTES, hmac);
         const sig = drbg(seed, k2sig); // Steps B, C, D, E, F, G
         return sig;
     }
-    // Enable precomputes. Slows down first publicKey computation by 20ms.
-    Point.BASE.precompute(8);
+    function tryParsingSig(sg) {
+        // Try to deduce format
+        let sig = undefined;
+        const isHex = typeof sg === 'string' || isBytes(sg);
+        const isObj = !isHex &&
+            sg !== null &&
+            typeof sg === 'object' &&
+            typeof sg.r === 'bigint' &&
+            typeof sg.s === 'bigint';
+        if (!isHex && !isObj)
+            throw new Error('invalid signature, expected Uint8Array, hex string or Signature instance');
+        if (isObj) {
+            sig = new Signature(sg.r, sg.s);
+        }
+        else if (isHex) {
+            try {
+                sig = Signature.fromBytes(ensureBytes('sig', sg), 'der');
+            }
+            catch (derError) {
+                if (!(derError instanceof DER.Err))
+                    throw derError;
+            }
+            if (!sig) {
+                try {
+                    sig = Signature.fromBytes(ensureBytes('sig', sg), 'compact');
+                }
+                catch (error) {
+                    return false;
+                }
+            }
+        }
+        if (!sig)
+            return false;
+        return sig;
+    }
     /**
@@ -1265,64 +1300,17 @@ * Verifies a signature against message and public key.
     function verify(signature, message, publicKey, opts = {}) {
-        const sg = signature;
-        message = ensureBytes('msgHash', message);
+        const { lowS, prehash, format } = validateSigOpts(opts, defaultSigOpts);
         publicKey = ensureBytes('publicKey', publicKey);
-        const { lowS, prehash, format } = validateSigOpts(opts, defaultSigOpts);
-        let _sig = undefined;
-        let P;
+        message = validateMsgAndHash(ensureBytes('message', message), prehash);
         if ('strict' in opts)
             throw new Error('options.strict was renamed to lowS');
-        if (format === undefined) {
-            // Try to deduce format
-            const isHex = typeof sg === 'string' || isBytes(sg);
-            const isObj = !isHex &&
-                sg !== null &&
-                typeof sg === 'object' &&
-                typeof sg.r === 'bigint' &&
-                typeof sg.s === 'bigint';
-            if (!isHex && !isObj)
-                throw new Error('invalid signature, expected Uint8Array, hex string or Signature instance');
-            if (isObj) {
-                _sig = new Signature(sg.r, sg.s);
-            }
-            else if (isHex) {
-                // TODO: remove this malleable check
-                // Signature can be represented in 2 ways: compact (2*Fn.BYTES) & DER (variable-length).
-                // Since DER can also be 2*Fn.BYTES bytes, we check for it first.
-                try {
-                    _sig = Signature.fromDER(sg);
-                }
-                catch (derError) {
-                    if (!(derError instanceof DER.Err))
-                        throw derError;
-                }
-                if (!_sig) {
-                    try {
-                        _sig = Signature.fromCompact(sg);
-                    }
-                    catch (error) {
-                        return false;
-                    }
-                }
-            }
-        }
-        else {
-            if (format === 'compact' || format === 'der') {
-                if (typeof sg !== 'string' && !isBytes(sg))
-                    throw new Error('"der" / "compact" format expects Uint8Array signature');
-                _sig = Signature.fromBytes(ensureBytes('sig', sg), format);
-            }
-            else {
-                throw new Error('format must be "compact", "der" or "js"');
-            }
-        }
-        if (!_sig)
+        const sig = format === undefined
+            ? tryParsingSig(signature)
+            : Signature.fromBytes(ensureBytes('sig', signature), format);
+        if (sig === false)
             return false;
         try {
-            P = Point.fromHex(publicKey);
-            if (lowS && _sig.hasHighS())
+            const P = Point.fromBytes(publicKey);
+            if (lowS && sig.hasHighS())
                 return false;
-            // todo: optional.hash => hash
-            if (prehash)
-                message = hash(message);
-            const { r, s } = _sig;
+            const { r, s } = sig;
             const h = bits2int_modN(message); // mod n, not mod p
@@ -1343,7 +1331,4 @@ const is = Fn.inv(s); // s^-1 mod n
     function recoverPublicKey(signature, message, opts = {}) {
-        const prehash = opts.prehash !== undefined ? opts.prehash : defaultSigOpts.prehash;
-        abool(prehash, 'prehash');
-        message = abytes(message, undefined, 'message');
-        if (prehash)
-            message = abytes(hash(message), undefined, 'prehashed message');
+        const { prehash } = validateSigOpts(opts, defaultSigOpts);
+        message = validateMsgAndHash(message, prehash);
         return Signature.fromBytes(signature, 'recovered').recoverPublicKey(message).toBytes();
@@ -1350,0 +1335,0 @@ }

esm/abstract/weierstrass.js.map

@@ -1,1 +0,1 @@
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esm/bls12-381.d.ts.map

@@ -1,1 +0,1 @@
-{"version":3,"file":"bls12-381.d.ts","sourceRoot":"","sources":["../src/bls12-381.ts"],"names":[],"mappings":"AAgFA,OAAO,EAAO,KAAK,OAAO,EAAE,MAAM,mBAAmB,CAAC;AACtD,OAAO,EAAS,KAAK,MAAM,EAAE,MAAM,uBAAuB,CAAC;AAoE3D,eAAO,MAAM,YAAY,EAAE,MAAM,CAAC,MAAM,CAAuD,CAAC;AA0VhG;;;;;;;;;;GAUG;AACH,eAAO,MAAM,SAAS,EAAE,OA8HtB,CAAC"}
+{"version":3,"file":"bls12-381.d.ts","sourceRoot":"","sources":["../src/bls12-381.ts"],"names":[],"mappings":"AAgFA,OAAO,EAAO,KAAK,OAAO,EAAE,MAAM,mBAAmB,CAAC;AACtD,OAAO,EAAS,KAAK,MAAM,EAAE,MAAM,uBAAuB,CAAC;AAmE3D,eAAO,MAAM,YAAY,EAAE,MAAM,CAAC,MAAM,CAGtC,CAAC;AAuTH;;;;;;;;;;GAUG;AACH,eAAO,MAAM,SAAS,EAAE,OA8HtB,CAAC"}

esm/bls12-381.js

@@ -83,3 +83,3 @@ /**
 import { Field } from "./abstract/modular.js";
-import { abytes, bitGet, bitLen, bitMask, bytesToHex, bytesToNumberBE, concatBytes, ensureBytes, numberToBytesBE, } from "./utils.js";
+import { abytes, bitLen, bitMask, bytesToHex, bytesToNumberBE, concatBytes, ensureBytes, numberToBytesBE, } from "./utils.js";
 // Types
@@ -122,6 +122,9 @@ import { isogenyMap } from "./abstract/hash-to-curve.js";
 // CURVE FIELDS
-export const bls12_381_Fr = Field(bls12_381_CURVE_G1.n, { modFromBytes: true });
-const { Fp, Fp2, Fp6, Fp4Square, Fp12 } = tower12({
-    // Order of Fp
+export const bls12_381_Fr = Field(bls12_381_CURVE_G1.n, {
+    modFromBytes: true,
+    isLE: true,
+});
+const { Fp, Fp2, Fp6, Fp12 } = tower12({
     ORDER: bls12_381_CURVE_G1.p,
+    X_LEN: BLS_X_LEN,
     // Finite extension field over irreducible polynominal.
@@ -136,38 +139,2 @@ // Fp(u) / (u² - β) where β = -1
     },
-    // Fp12
-    // A cyclotomic group is a subgroup of Fp^n defined by
-    //   GΦₙ(p) = {α ∈ Fpⁿ : α^Φₙ(p) = 1}
-    // The result of any pairing is in a cyclotomic subgroup
-    // https://eprint.iacr.org/2009/565.pdf
-    Fp12cyclotomicSquare: ({ c0, c1 }) => {
-        const { c0: c0c0, c1: c0c1, c2: c0c2 } = c0;
-        const { c0: c1c0, c1: c1c1, c2: c1c2 } = c1;
-        const { first: t3, second: t4 } = Fp4Square(c0c0, c1c1);
-        const { first: t5, second: t6 } = Fp4Square(c1c0, c0c2);
-        const { first: t7, second: t8 } = Fp4Square(c0c1, c1c2);
-        const t9 = Fp2.mulByNonresidue(t8); // T8 * (u + 1)
-        return {
-            c0: Fp6.create({
-                c0: Fp2.add(Fp2.mul(Fp2.sub(t3, c0c0), _2n), t3), // 2 * (T3 - c0c0)  + T3
-                c1: Fp2.add(Fp2.mul(Fp2.sub(t5, c0c1), _2n), t5), // 2 * (T5 - c0c1)  + T5
-                c2: Fp2.add(Fp2.mul(Fp2.sub(t7, c0c2), _2n), t7),
-            }), // 2 * (T7 - c0c2)  + T7
-            c1: Fp6.create({
-                c0: Fp2.add(Fp2.mul(Fp2.add(t9, c1c0), _2n), t9), // 2 * (T9 + c1c0) + T9
-                c1: Fp2.add(Fp2.mul(Fp2.add(t4, c1c1), _2n), t4), // 2 * (T4 + c1c1) + T4
-                c2: Fp2.add(Fp2.mul(Fp2.add(t6, c1c2), _2n), t6),
-            }),
-        }; // 2 * (T6 + c1c2) + T6
-    },
-    Fp12cyclotomicExp(num, n) {
-        let z = Fp12.ONE;
-        for (let i = BLS_X_LEN - 1; i >= 0; i--) {
-            z = Fp12._cyclotomicSquare(z);
-            if (bitGet(n, i))
-                z = Fp12.mul(z, num);
-        }
-        return z;
-    },
-    // https://eprint.iacr.org/2010/354.pdf
-    // https://eprint.iacr.org/2009/565.pdf
     Fp12finalExponentiate: (num) => {
@@ -174,0 +141,0 @@ const x = BLS_X;

esm/bls12-381.js.map

@@ -1,1 +0,1 @@
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esm/bn254.d.ts.map

@@ -1,1 +0,1 @@
-{"version":3,"file":"bn254.d.ts","sourceRoot":"","sources":["../src/bn254.ts"],"names":[],"mappings":"AAyDA,OAAO,EAEL,KAAK,OAAO,IAAI,UAAU,EAC1B,KAAK,gBAAgB,EAEtB,MAAM,mBAAmB,CAAC;AAC3B,OAAO,EAAS,KAAK,MAAM,EAAE,MAAM,uBAAuB,CAAC;AAG3D,OAAO,EAAE,KAAK,OAAO,EAAqC,MAAM,2BAA2B,CAAC;AAsB5F,eAAO,MAAM,QAAQ,EAAE,MAAM,CAAC,MAAM,CAA2B,CAAC;AAqFhE,eAAO,MAAM,eAAe,EAAE,gBAY7B,CAAC;AAmBF;;;GAGG;AACH,eAAO,MAAM,KAAK,EAAE,UAgDlB,CAAC;AAEH;;;;;GAKG;AACH,eAAO,MAAM,iBAAiB,EAAE,OAS9B,CAAC"}
+{"version":3,"file":"bn254.d.ts","sourceRoot":"","sources":["../src/bn254.ts"],"names":[],"mappings":"AAyDA,OAAO,EAEL,KAAK,OAAO,IAAI,UAAU,EAC1B,KAAK,gBAAgB,EAEtB,MAAM,mBAAmB,CAAC;AAC3B,OAAO,EAAS,KAAK,MAAM,EAAE,MAAM,uBAAuB,CAAC;AAG3D,OAAO,EAAE,KAAK,OAAO,EAAqC,MAAM,2BAA2B,CAAC;AAsB5F,eAAO,MAAM,QAAQ,EAAE,MAAM,CAAC,MAAM,CAA2B,CAAC;AAsDhE,eAAO,MAAM,eAAe,EAAE,gBAY7B,CAAC;AAmBF;;;GAGG;AACH,eAAO,MAAM,KAAK,EAAE,UAgDlB,CAAC;AAEH;;;;;GAKG;AACH,eAAO,MAAM,iBAAiB,EAAE,OAS9B,CAAC"}

esm/bn254.js

@@ -62,3 +62,3 @@ /**
 import { weierstrass } from "./abstract/weierstrass.js";
-import { bitGet, bitLen, notImplemented } from "./utils.js";
+import { bitLen, notImplemented } from "./utils.js";
 // prettier-ignore
@@ -87,39 +87,7 @@ const _0n = BigInt(0), _1n = BigInt(1), _2n = BigInt(2), _3n = BigInt(3);
 };
-const { Fp, Fp2, Fp6, Fp4Square, Fp12 } = tower12({
+const { Fp, Fp2, Fp6, Fp12 } = tower12({
     ORDER: bn254_G1_CURVE.p,
+    X_LEN: BN_X_LEN,
     FP2_NONRESIDUE: [BigInt(9), _1n],
     Fp2mulByB: (num) => Fp2.mul(num, Fp2B),
-    // The result of any pairing is in a cyclotomic subgroup
-    // https://eprint.iacr.org/2009/565.pdf
-    Fp12cyclotomicSquare: ({ c0, c1 }) => {
-        const { c0: c0c0, c1: c0c1, c2: c0c2 } = c0;
-        const { c0: c1c0, c1: c1c1, c2: c1c2 } = c1;
-        const { first: t3, second: t4 } = Fp4Square(c0c0, c1c1);
-        const { first: t5, second: t6 } = Fp4Square(c1c0, c0c2);
-        const { first: t7, second: t8 } = Fp4Square(c0c1, c1c2);
-        let t9 = Fp2.mulByNonresidue(t8); // T8 * (u + 1)
-        return {
-            c0: Fp6.create({
-                c0: Fp2.add(Fp2.mul(Fp2.sub(t3, c0c0), _2n), t3), // 2 * (T3 - c0c0)  + T3
-                c1: Fp2.add(Fp2.mul(Fp2.sub(t5, c0c1), _2n), t5), // 2 * (T5 - c0c1)  + T5
-                c2: Fp2.add(Fp2.mul(Fp2.sub(t7, c0c2), _2n), t7),
-            }), // 2 * (T7 - c0c2)  + T7
-            c1: Fp6.create({
-                c0: Fp2.add(Fp2.mul(Fp2.add(t9, c1c0), _2n), t9), // 2 * (T9 + c1c0) + T9
-                c1: Fp2.add(Fp2.mul(Fp2.add(t4, c1c1), _2n), t4), // 2 * (T4 + c1c1) + T4
-                c2: Fp2.add(Fp2.mul(Fp2.add(t6, c1c2), _2n), t6),
-            }),
-        }; // 2 * (T6 + c1c2) + T6
-    },
-    Fp12cyclotomicExp(num, n) {
-        let z = Fp12.ONE;
-        for (let i = BN_X_LEN - 1; i >= 0; i--) {
-            z = Fp12._cyclotomicSquare(z);
-            if (bitGet(n, i))
-                z = Fp12.mul(z, num);
-        }
-        return z;
-    },
-    // https://eprint.iacr.org/2010/354.pdf
-    // https://eprint.iacr.org/2009/565.pdf
     Fp12finalExponentiate: (num) => {
@@ -126,0 +94,0 @@ const powMinusX = (num) => Fp12.conjugate(Fp12._cyclotomicExp(num, BN_X));

esm/bn254.js.map

@@ -1,1 +0,1 @@
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esm/ed25519.js

@@ -16,14 +16,13 @@ /**
 import { montgomery } from "./abstract/montgomery.js";
-import { bytesToNumberLE, ensureBytes, equalBytes, numberToBytesLE } from "./utils.js";
+import { bytesToNumberLE, ensureBytes, equalBytes } from "./utils.js";
 // prettier-ignore
-const _0n = BigInt(0), _1n = BigInt(1), _2n = BigInt(2), _3n = BigInt(3);
+const _0n = /* @__PURE__ */ BigInt(0), _1n = BigInt(1), _2n = BigInt(2), _3n = BigInt(3);
 // prettier-ignore
 const _5n = BigInt(5), _8n = BigInt(8);
-// 2n**255n-19n
+// P = 2n**255n-19n
 const ed25519_CURVE_p = BigInt('0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffed');
-// P = 2n**255n - 19n
 // N = 2n**252n + 27742317777372353535851937790883648493n
 // a = Fp.create(BigInt(-1))
 // d = -121665/121666 a.k.a. Fp.neg(121665 * Fp.inv(121666))
-const ed25519_CURVE = {
+const ed25519_CURVE = /* @__PURE__ */ (() => ({
     p: ed25519_CURVE_p,
@@ -36,3 +35,3 @@ n: BigInt('0x1000000000000000000000000000000014def9dea2f79cd65812631a5cf5d3ed'),
     Gy: BigInt('0x6666666666666666666666666666666666666666666666666666666666666658'),
-};
+}))();
 function ed25519_pow_2_252_3(x) {
@@ -141,3 +140,3 @@ // prettier-ignore
 export const x25519 = /* @__PURE__ */ (() => {
-    const P = ed25519.CURVE.Fp.ORDER;
+    const P = Fp.ORDER;
     return montgomery({
@@ -157,3 +156,3 @@ P,
 // SageMath returns different root first and everything falls apart
-const ELL2_C1 = /* @__PURE__ */ (() => (Fp.ORDER + _3n) / _8n)(); // 1. c1 = (q + 3) / 8       # Integer arithmetic
+const ELL2_C1 = /* @__PURE__ */ (() => (ed25519_CURVE_p + _3n) / _8n)(); // 1. c1 = (q + 3) / 8       # Integer arithmetic
 const ELL2_C2 = /* @__PURE__ */ (() => Fp.pow(_2n, ELL2_C1))(); // 2. c2 = 2^c1
@@ -163,3 +162,3 @@ const ELL2_C3 = /* @__PURE__ */ (() => Fp.sqrt(Fp.neg(Fp.ONE)))(); // 3. c3 = sqrt(-1)
 function map_to_curve_elligator2_curve25519(u) {
-    const ELL2_C4 = (Fp.ORDER - _5n) / _8n; // 4. c4 = (q - 5) / 8       # Integer arithmetic
+    const ELL2_C4 = (ed25519_CURVE_p - _5n) / _8n; // 4. c4 = (q - 5) / 8       # Integer arithmetic
     const ELL2_J = BigInt(486662);
@@ -228,3 +227,3 @@ let tv1 = Fp.sqr(u); //  1.  tv1 = u^2
     encodeDST: 'edwards25519_XMD:SHA-512_ELL2_NU_',
-    p: Fp.ORDER,
+    p: ed25519_CURVE_p,
     m: 1,
@@ -256,3 +255,3 @@ k: 128,
     const { d } = ed25519_CURVE;
-    const P = Fp.ORDER;
+    const P = ed25519_CURVE_p;
     const mod = (n) => Fp.create(n);
@@ -322,3 +321,3 @@ const r = mod(SQRT_M1 * r0 * r0); // 1
         // 3. Check that s is non-negative, or else abort
-        if (!equalBytes(numberToBytesLE(s, 32), bytes) || isNegativeLE(s, P))
+        if (!equalBytes(Fp.toBytes(s), bytes) || isNegativeLE(s, P))
             throw new Error('invalid ristretto255 encoding 1');
@@ -386,3 +385,3 @@ const s2 = mod(s * s);
             s = mod(-s);
-        return numberToBytesLE(s, 32); // 11
+        return Fp.toBytes(s); // 11
     }
@@ -426,7 +425,8 @@ /**
         const DST = options?.DST || 'ristretto255_XMD:SHA-512_R255MAP_RO_';
-        return ristretto255_map(expand_message_xmd(msg, DST, 64, sha512));
+        const xmd = expand_message_xmd(msg, DST, 64, sha512);
+        return ristretto255_map(xmd);
     },
     hashToScalar(msg, options = { DST: _DST_scalar }) {
         const xmd = expand_message_xmd(msg, options.DST, 64, sha512);
-        return ristretto255.Point.Fn.create(bytesToNumberLE(xmd));
+        return Fn.create(bytesToNumberLE(xmd));
     },
@@ -433,0 +433,0 @@ };

esm/ed25519.js.map

@@ -1,1 +0,1 @@
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esm/ed448.d.ts

@@ -33,7 +33,6 @@ import type { AffinePoint } from './abstract/curve.ts';
 export declare const ed448_hasher: H2CHasher<bigint>;
-type ExtendedPoint = EdwardsPoint;
 /**
- * Each ed448/ExtendedPoint has 4 different equivalent points. This can be
+ * Each ed448/EdwardsPoint has 4 different equivalent points. This can be
  * a source of bugs for protocols like ring signatures. Decaf was created to solve this.
- * Decaf point operates in X:Y:Z:T extended coordinates like ExtendedPoint,
+ * Decaf point operates in X:Y:Z:T extended coordinates like EdwardsPoint,
  * but it should work in its own namespace: do not combine those two.
@@ -47,3 +46,3 @@ * See [RFC9496](https://www.rfc-editor.org/rfc/rfc9496).
     static Fn: IField<bigint>;
-    constructor(ep: ExtendedPoint);
+    constructor(ep: EdwardsPoint);
     static fromAffine(ap: AffinePoint<bigint>): _DecafPoint;
@@ -50,0 +49,0 @@ protected assertSame(other: _DecafPoint): void;

esm/ed448.d.ts.map

@@ -1,1 +0,1 @@
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esm/ed448.js

@@ -11,3 +11,3 @@ /**
 import { shake256 } from '@noble/hashes/sha3.js';
-import { abytes, concatBytes, utf8ToBytes, createHasher as wrapConstructor, } from '@noble/hashes/utils.js';
+import { abytes, concatBytes, createHasher as wrapConstructor } from '@noble/hashes/utils.js';
 import { pippenger } from "./abstract/curve.js";
@@ -18,3 +18,3 @@ import { edwards, PrimeEdwardsPoint, twistedEdwards, } from "./abstract/edwards.js";
 import { montgomery } from "./abstract/montgomery.js";
-import { bytesToNumberLE, ensureBytes, equalBytes, numberToBytesLE } from "./utils.js";
+import { asciiToBytes, bytesToNumberLE, ensureBytes, equalBytes } from "./utils.js";
 // edwards448 curve
@@ -99,6 +99,10 @@ // a = 1n
 // Finite field 2n**448n - 2n**224n - 1n
+// The value fits in 448 bits, but we use 456-bit (57-byte) elements because of bitflags.
+// - ed25519 fits in 255 bits, allowing using last 1 byte for specifying bit flag of point negation.
+// - ed448 fits in 448 bits. We can't use last 1 byte: we can only use a bit 224 in the middle.
 const Fp = /* @__PURE__ */ (() => Field(ed448_CURVE.p, { BITS: 456, isLE: true }))();
-// RFC 7748 has 56-byte keys, RFC 8032 has 57-byte keys
-const Fn = /* @__PURE__ */ (() => Field(ed448_CURVE.n, { BITS: 448, isLE: true }))();
-// Fn456 has BITS: 456
+const Fn = /* @__PURE__ */ (() => Field(ed448_CURVE.n, { BITS: 456, isLE: true }))();
+// decaf448 uses 448-bit (56-byte) keys
+const Fp448 = /* @__PURE__ */ (() => Field(ed448_CURVE.p, { BITS: 448, isLE: true }))();
+const Fn448 = /* @__PURE__ */ (() => Field(ed448_CURVE.n, { BITS: 448, isLE: true }))();
 // SHAKE256(dom4(phflag,context)||x, 114)
@@ -108,3 +112,3 @@ function dom4(data, ctx, phflag) {
         throw new Error('context must be smaller than 255, got: ' + ctx.length);
-    return concatBytes(utf8ToBytes('SigEd448'), new Uint8Array([phflag ? 1 : 0, ctx.length]), ctx, data);
+    return concatBytes(asciiToBytes('SigEd448'), new Uint8Array([phflag ? 1 : 0, ctx.length]), ctx, data);
 }
@@ -117,2 +121,3 @@ // const ed448_eddsa_opts = { adjustScalarBytes, domain: dom4 };
     Fn,
+    nBitLength: Fn.BITS,
     hash: shake256_114,
@@ -256,4 +261,2 @@ adjustScalarBytes,
 const invertSqrt = (number) => uvRatio(_1n, number);
-const MAX_448B = /* @__PURE__ */ BigInt('0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff');
-const bytes448ToNumberLE = (bytes) => Fp.create(bytesToNumberLE(bytes) & MAX_448B);
 /**
@@ -291,5 +294,9 @@ * Elligator map for hash-to-curve of decaf448.
     abytes(bytes, 112);
-    const r1 = bytes448ToNumberLE(bytes.slice(0, 56));
+    const skipValidation = true;
+    // Note: Similar to the field element decoding described in
+    // [RFC7748], and unlike the field element decoding described in
+    // Section 5.3.1, non-canonical values are accepted.
+    const r1 = Fp448.create(Fp448.fromBytes(bytes.subarray(0, 56), skipValidation));
     const R1 = calcElligatorDecafMap(r1);
-    const r2 = bytes448ToNumberLE(bytes.slice(56, 112));
+    const r2 = Fp448.create(Fp448.fromBytes(bytes.subarray(56, 112), skipValidation));
     const R2 = calcElligatorDecafMap(r2);
@@ -299,5 +306,5 @@ return new _DecafPoint(R1.add(R2));
 /**
- * Each ed448/ExtendedPoint has 4 different equivalent points. This can be
+ * Each ed448/EdwardsPoint has 4 different equivalent points. This can be
  * a source of bugs for protocols like ring signatures. Decaf was created to solve this.
- * Decaf point operates in X:Y:Z:T extended coordinates like ExtendedPoint,
+ * Decaf point operates in X:Y:Z:T extended coordinates like EdwardsPoint,
  * but it should work in its own namespace: do not combine those two.
@@ -328,7 +335,7 @@ * See [RFC9496](https://www.rfc-editor.org/rfc/rfc9496).
         const P = Fp.ORDER;
-        const mod = (n) => Fp.create(n);
-        const s = bytes448ToNumberLE(bytes);
+        const mod = (n) => Fp448.create(n);
+        const s = Fp448.fromBytes(bytes);
         // 1. Check that s_bytes is the canonical encoding of a field element, or else abort.
         // 2. Check that s is non-negative, or else abort
-        if (!equalBytes(numberToBytesLE(s, 56), bytes) || isNegativeLE(s, P))
+        if (!equalBytes(Fn448.toBytes(s), bytes) || isNegativeLE(s, P))
             throw new Error('invalid decaf448 encoding 1');
@@ -380,3 +387,3 @@ const s2 = mod(s * s); // 1
             s = mod(-s);
-        return numberToBytesLE(s, 56);
+        return Fn448.toBytes(s);
     }
@@ -391,5 +398,4 @@ /**
         const { X: X2, Y: Y2 } = other.ep;
-        const mod = (n) => Fp.create(n);
         // (x1 * y2 == y1 * x2)
-        return mod(X1 * Y2) === mod(Y1 * X2);
+        return Fp.create(X1 * Y2) === Fp.create(Y1 * X2);
     }
@@ -409,6 +415,6 @@ is0() {
 _DecafPoint.Fp = 
-/* @__PURE__ */ (() => Fp)();
+/* @__PURE__ */ (() => Fp448)();
 // prettier-ignore
 _DecafPoint.Fn = 
-/* @__PURE__ */ (() => Fn)();
+/* @__PURE__ */ (() => Fn448)();
 export const decaf448 = { Point: _DecafPoint };
@@ -421,4 +427,9 @@ /** Hashing to decaf448 points / field. RFC 9380 methods. */
     },
+    // Warning: has big modulo bias of 2^-64.
+    // RFC is invalid. RFC says "use 64-byte xof", while for 2^-112 bias
+    // it must use 84-byte xof (56+56/2), not 64.
     hashToScalar(msg, options = { DST: _DST_scalar }) {
-        return Fn.create(bytesToNumberLE(expand_message_xof(msg, options.DST, 64, 256, shake256)));
+        // Can't use `Fn448.fromBytes()`. 64-byte input => 56-byte field element
+        const xof = expand_message_xof(msg, options.DST, 64, 256, shake256);
+        return Fn448.create(bytesToNumberLE(xof));
     },
@@ -425,0 +436,0 @@ };

esm/ed448.js.map

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esm/secp256k1.d.ts.map

@@ -1,1 +0,1 @@
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esm/secp256k1.js

@@ -15,3 +15,3 @@ /**
 import { _normFnElement, mapToCurveSimpleSWU, } from "./abstract/weierstrass.js";
-import { aInRange, bytesToNumberBE, concatBytes, ensureBytes, inRange, numberToBytesBE, utf8ToBytes, } from "./utils.js";
+import { bytesToNumberBE, concatBytes, ensureBytes, inRange, numberToBytesBE, utf8ToBytes, } from "./utils.js";
 // Seems like generator was produced from some seed:
@@ -98,13 +98,10 @@ // `Point.BASE.multiply(Point.Fn.inv(2n, N)).toAffine().x`
 const pointToBytes = (point) => point.toBytes(true).slice(1);
-const numTo32b = (n) => numberToBytesBE(n, 32);
-const modP = (x) => mod(x, secp256k1_CURVE.p);
-const modN = (x) => mod(x, secp256k1_CURVE.n);
-const Point = /* @__PURE__ */ (() => secp256k1.Point)();
+const Pointk1 = /* @__PURE__ */ (() => secp256k1.Point)();
 const hasEven = (y) => y % _2n === _0n;
 // Calculate point, scalar and bytes
 function schnorrGetExtPubKey(priv) {
-    // TODO: replace with Point.Fn.fromBytes(priv)
-    let d_ = _normFnElement(Point.Fn, priv);
-    let p = Point.BASE.multiply(d_); // P = d'⋅G; 0 < d' < n check is done inside
-    const scalar = hasEven(p.y) ? d_ : modN(-d_);
+    const { Fn, BASE } = Pointk1;
+    const d_ = _normFnElement(Fn, priv);
+    const p = BASE.multiply(d_); // P = d'⋅G; 0 < d' < n check is done inside
+    const scalar = hasEven(p.y) ? d_ : Fn.neg(d_);
     return { scalar, bytes: pointToBytes(p) };
@@ -117,9 +114,13 @@ }
 function lift_x(x) {
-    aInRange('x', x, _1n, secp256k1_CURVE.p); // Fail if x ≥ p.
-    const xx = modP(x * x);
-    const c = modP(xx * x + BigInt(7)); // Let c = x³ + 7 mod p.
-    let y = sqrtMod(c); // Let y = c^(p+1)/4 mod p.
+    const Fp = Fpk1;
+    if (!Fp.isValidNot0(x))
+        throw new Error('invalid x: Fail if x ≥ p');
+    const xx = Fp.create(x * x);
+    const c = Fp.create(xx * x + BigInt(7)); // Let c = x³ + 7 mod p.
+    let y = Fp.sqrt(c); // Let y = c^(p+1)/4 mod p. Same as sqrt().
+    // Return the unique point P such that x(P) = x and
+    // y(P) = y if y mod 2 = 0 or y(P) = p-y otherwise.
     if (!hasEven(y))
-        y = modP(-y); // Return the unique point P such that x(P) = x and
-    const p = Point.fromAffine({ x, y }); // y(P) = y if y mod 2 = 0 or y(P) = p-y otherwise.
+        y = Fp.neg(y);
+    const p = Pointk1.fromAffine({ x, y });
     p.assertValidity();
@@ -133,3 +134,3 @@ return p;
 function challenge(...args) {
-    return modN(num(taggedHash('BIP0340/challenge', ...args)));
+    return Pointk1.Fn.create(num(taggedHash('BIP0340/challenge', ...args)));
 }
@@ -147,15 +148,14 @@ /**
 function schnorrSign(message, secretKey, auxRand = randomBytes(32)) {
+    const { Fn } = Pointk1;
     const m = ensureBytes('message', message);
     const { bytes: px, scalar: d } = schnorrGetExtPubKey(secretKey); // checks for isWithinCurveOrder
     const a = ensureBytes('auxRand', auxRand, 32); // Auxiliary random data a: a 32-byte array
-    const t = numTo32b(d ^ num(taggedHash('BIP0340/aux', a))); // Let t be the byte-wise xor of bytes(d) and hash/aux(a)
+    const t = Fn.toBytes(d ^ num(taggedHash('BIP0340/aux', a))); // Let t be the byte-wise xor of bytes(d) and hash/aux(a)
     const rand = taggedHash('BIP0340/nonce', t, px, m); // Let rand = hash/nonce(t || bytes(P) || m)
-    const k_ = modN(num(rand)); // Let k' = int(rand) mod n
-    if (k_ === _0n)
-        throw new Error('sign failed: k is zero'); // Fail if k' = 0.
-    const { bytes: rx, scalar: k } = schnorrGetExtPubKey(k_); // Let R = k'⋅G.
+    // Let k' = int(rand) mod n. Fail if k' = 0. Let R = k'⋅G
+    const { bytes: rx, scalar: k } = schnorrGetExtPubKey(rand);
     const e = challenge(rx, px, m); // Let e = int(hash/challenge(bytes(R) || bytes(P) || m)) mod n.
     const sig = new Uint8Array(64); // Let sig = bytes(R) || bytes((k + ed) mod n).
     sig.set(rx, 0);
-    sig.set(numTo32b(modN(k + e * d)), 32);
+    sig.set(Fn.toBytes(Fn.create(k + e * d)), 32);
     // If Verify(bytes(P), m, sig) (see below) returns failure, abort
@@ -171,2 +171,3 @@ if (!schnorrVerify(sig, m, px))
 function schnorrVerify(signature, message, publicKey) {
+    const { Fn, BASE } = Pointk1;
     const sig = ensureBytes('signature', signature, 64);
@@ -183,5 +184,6 @@ const m = ensureBytes('message', message);
             return false;
-        const e = challenge(numTo32b(r), pointToBytes(P), m); // int(challenge(bytes(r)||bytes(P)||m))%n
+        // int(challenge(bytes(r)||bytes(P)||m))%n
+        const e = challenge(Fn.toBytes(r), pointToBytes(P), m);
         // R = s⋅G - e⋅P, where -eP == (n-e)P
-        const R = Point.BASE.multiplyUnsafe(s).add(P.multiplyUnsafe(modN(-e)));
+        const R = BASE.multiplyUnsafe(s).add(P.multiplyUnsafe(Fn.neg(e)));
         const { x, y } = R.toAffine();
@@ -227,3 +229,3 @@ // Fail if is_infinite(R) / not has_even_y(R) / x(R) ≠ r.
         verify: schnorrVerify,
-        Point,
+        Point: Pointk1,
         utils: {
@@ -241,7 +243,7 @@ randomSecretKey: randomSecretKey,
         lengths: {
-            secret: size,
-            public: size,
+            secretKey: size,
+            publicKey: size,
+            publicKeyHasPrefix: false,
             signature: size * 2,
             seed: seedLength,
-            publicKeyHasPrefix: false,
         },
@@ -248,0 +250,0 @@ };

esm/secp256k1.js.map

@@ -1,1 +0,1 @@
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esm/utils.js

@@ -29,3 +29,3 @@ /**
     if (!bytes || (needsLen && len !== length)) {
-        const prefix = title && `"${title}"`;
+        const prefix = title && `"${title}" `;
         const ofLen = needsLen ? ` of length ${length}` : '';
@@ -32,0 +32,0 @@ const got = bytes ? `length=${len}` : `type=${typeof value}`;

esm/utils.js.map

@@ -1,1 +0,1 @@
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package.json

 {
   "name": "@noble/curves",
-  "version": "1.9.5",
+  "version": "1.9.6",
   "description": "Audited & minimal JS implementation of elliptic curve cryptography",
@@ -24,3 +24,3 @@ "files": [
     "format": "prettier --write 'src/**/*.{js,ts}' 'test/*.js'",
-    "test": "node test/index.js",
+    "test": "node --disable-warning=ExperimentalWarning test/index.js",
     "test:bun": "bun test/index.js",
@@ -27,0 +27,0 @@ "test:deno": "deno --allow-env --allow-read test/index.js",

secp256k1.d.ts.map

@@ -1,1 +0,1 @@
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secp256k1.js

@@ -100,13 +100,10 @@ "use strict";
 const pointToBytes = (point) => point.toBytes(true).slice(1);
-const numTo32b = (n) => (0, utils_ts_1.numberToBytesBE)(n, 32);
-const modP = (x) => (0, modular_ts_1.mod)(x, secp256k1_CURVE.p);
-const modN = (x) => (0, modular_ts_1.mod)(x, secp256k1_CURVE.n);
-const Point = /* @__PURE__ */ (() => exports.secp256k1.Point)();
+const Pointk1 = /* @__PURE__ */ (() => exports.secp256k1.Point)();
 const hasEven = (y) => y % _2n === _0n;
 // Calculate point, scalar and bytes
 function schnorrGetExtPubKey(priv) {
-    // TODO: replace with Point.Fn.fromBytes(priv)
-    let d_ = (0, weierstrass_ts_1._normFnElement)(Point.Fn, priv);
-    let p = Point.BASE.multiply(d_); // P = d'⋅G; 0 < d' < n check is done inside
-    const scalar = hasEven(p.y) ? d_ : modN(-d_);
+    const { Fn, BASE } = Pointk1;
+    const d_ = (0, weierstrass_ts_1._normFnElement)(Fn, priv);
+    const p = BASE.multiply(d_); // P = d'⋅G; 0 < d' < n check is done inside
+    const scalar = hasEven(p.y) ? d_ : Fn.neg(d_);
     return { scalar, bytes: pointToBytes(p) };
@@ -119,9 +116,13 @@ }
 function lift_x(x) {
-    (0, utils_ts_1.aInRange)('x', x, _1n, secp256k1_CURVE.p); // Fail if x ≥ p.
-    const xx = modP(x * x);
-    const c = modP(xx * x + BigInt(7)); // Let c = x³ + 7 mod p.
-    let y = sqrtMod(c); // Let y = c^(p+1)/4 mod p.
+    const Fp = Fpk1;
+    if (!Fp.isValidNot0(x))
+        throw new Error('invalid x: Fail if x ≥ p');
+    const xx = Fp.create(x * x);
+    const c = Fp.create(xx * x + BigInt(7)); // Let c = x³ + 7 mod p.
+    let y = Fp.sqrt(c); // Let y = c^(p+1)/4 mod p. Same as sqrt().
+    // Return the unique point P such that x(P) = x and
+    // y(P) = y if y mod 2 = 0 or y(P) = p-y otherwise.
     if (!hasEven(y))
-        y = modP(-y); // Return the unique point P such that x(P) = x and
-    const p = Point.fromAffine({ x, y }); // y(P) = y if y mod 2 = 0 or y(P) = p-y otherwise.
+        y = Fp.neg(y);
+    const p = Pointk1.fromAffine({ x, y });
     p.assertValidity();
@@ -135,3 +136,3 @@ return p;
 function challenge(...args) {
-    return modN(num(taggedHash('BIP0340/challenge', ...args)));
+    return Pointk1.Fn.create(num(taggedHash('BIP0340/challenge', ...args)));
 }
@@ -149,15 +150,14 @@ /**
 function schnorrSign(message, secretKey, auxRand = (0, utils_js_1.randomBytes)(32)) {
+    const { Fn } = Pointk1;
     const m = (0, utils_ts_1.ensureBytes)('message', message);
     const { bytes: px, scalar: d } = schnorrGetExtPubKey(secretKey); // checks for isWithinCurveOrder
     const a = (0, utils_ts_1.ensureBytes)('auxRand', auxRand, 32); // Auxiliary random data a: a 32-byte array
-    const t = numTo32b(d ^ num(taggedHash('BIP0340/aux', a))); // Let t be the byte-wise xor of bytes(d) and hash/aux(a)
+    const t = Fn.toBytes(d ^ num(taggedHash('BIP0340/aux', a))); // Let t be the byte-wise xor of bytes(d) and hash/aux(a)
     const rand = taggedHash('BIP0340/nonce', t, px, m); // Let rand = hash/nonce(t || bytes(P) || m)
-    const k_ = modN(num(rand)); // Let k' = int(rand) mod n
-    if (k_ === _0n)
-        throw new Error('sign failed: k is zero'); // Fail if k' = 0.
-    const { bytes: rx, scalar: k } = schnorrGetExtPubKey(k_); // Let R = k'⋅G.
+    // Let k' = int(rand) mod n. Fail if k' = 0. Let R = k'⋅G
+    const { bytes: rx, scalar: k } = schnorrGetExtPubKey(rand);
     const e = challenge(rx, px, m); // Let e = int(hash/challenge(bytes(R) || bytes(P) || m)) mod n.
     const sig = new Uint8Array(64); // Let sig = bytes(R) || bytes((k + ed) mod n).
     sig.set(rx, 0);
-    sig.set(numTo32b(modN(k + e * d)), 32);
+    sig.set(Fn.toBytes(Fn.create(k + e * d)), 32);
     // If Verify(bytes(P), m, sig) (see below) returns failure, abort
@@ -173,2 +173,3 @@ if (!schnorrVerify(sig, m, px))
 function schnorrVerify(signature, message, publicKey) {
+    const { Fn, BASE } = Pointk1;
     const sig = (0, utils_ts_1.ensureBytes)('signature', signature, 64);
@@ -185,5 +186,6 @@ const m = (0, utils_ts_1.ensureBytes)('message', message);
             return false;
-        const e = challenge(numTo32b(r), pointToBytes(P), m); // int(challenge(bytes(r)||bytes(P)||m))%n
+        // int(challenge(bytes(r)||bytes(P)||m))%n
+        const e = challenge(Fn.toBytes(r), pointToBytes(P), m);
         // R = s⋅G - e⋅P, where -eP == (n-e)P
-        const R = Point.BASE.multiplyUnsafe(s).add(P.multiplyUnsafe(modN(-e)));
+        const R = BASE.multiplyUnsafe(s).add(P.multiplyUnsafe(Fn.neg(e)));
         const { x, y } = R.toAffine();
@@ -229,3 +231,3 @@ // Fail if is_infinite(R) / not has_even_y(R) / x(R) ≠ r.
         verify: schnorrVerify,
-        Point,
+        Point: Pointk1,
         utils: {
@@ -243,7 +245,7 @@ randomSecretKey: randomSecretKey,
         lengths: {
-            secret: size,
-            public: size,
+            secretKey: size,
+            publicKey: size,
+            publicKeyHasPrefix: false,
             signature: size * 2,
             seed: seedLength,
-            publicKeyHasPrefix: false,
         },
@@ -250,0 +252,0 @@ };

secp256k1.js.map

@@ -1,1 +0,1 @@
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src/abstract/bls.ts

@@ -59,5 +59,5 @@ /**
   toBytes(point: WeierstrassPoint<Fp>): Uint8Array;
+  toHex(point: WeierstrassPoint<Fp>): string;
   /** @deprecated use `toBytes` */
   toRawBytes(point: WeierstrassPoint<Fp>): Uint8Array;
-  toHex(point: WeierstrassPoint<Fp>): string;
 };
@@ -69,5 +69,5 @@
   toBytes(point: WeierstrassPoint<Fp>): Uint8Array;
+  toHex(point: WeierstrassPoint<Fp>): string;
   /** @deprecated use `toBytes` */
   toRawBytes(point: WeierstrassPoint<Fp>): Uint8Array;
-  toHex(point: WeierstrassPoint<Fp>): string;
 };
@@ -74,0 +74,0 @@

src/abstract/curve.ts

@@ -130,5 +130,5 @@ /**
 export interface CurveLengths {
-  secret?: number;
-  public?: number;
-  publicUncompressed?: number;
+  secretKey?: number;
+  publicKey?: number;
+  publicKeyUncompressed?: number;
   publicKeyHasPrefix?: boolean;
@@ -135,0 +135,0 @@ signature?: number;

src/abstract/edwards.ts

@@ -18,6 +18,6 @@ /**
   ensureBytes,
+  isBytes,
   memoized,
   notImplemented,
-  numberToBytesLE,
-  randomBytes,
+  randomBytes as randomBytesWeb,
   type FHash,
@@ -159,2 +159,8 @@ type Hex,
      * Converts ed public key to x public key.
+     *
+     * There is NO `fromMontgomery`:
+     * - There are 2 valid ed25519 points for every x25519, with flipped coordinate
+     * - Sometimes there are 0 valid ed25519 points, because x25519 *additionally*
+     *   accepts inputs on the quadratic twist, which can't be moved to ed25519
+     *
      * @example
@@ -206,3 +212,3 @@ * ```js
   let CURVE = validated.CURVE as EdwardsOpts;
-  const { h: cofactor, n: CURVE_ORDER } = CURVE;
+  const { h: cofactor } = CURVE;
   _validateObject(extraOpts, {}, { uvRatio: 'function' });
@@ -306,3 +312,3 @@
     static CURVE(): EdwardsOpts {
-      return CURVE as EdwardsOpts;
+      return CURVE;
     }
@@ -334,3 +340,3 @@
       const max = zip215 ? MASK : Fp.ORDER;
-      aInRange('pointHex.y', y, _0n, max);
+      aInRange('point.y', y, _0n, max);
 
@@ -343,3 +349,3 @@ // Ed25519: x² = (y²-1)/(dy²+1) mod p. Ed448: x² = (y²-1)/(dy²-1) mod p. Generic case:
       let { isValid, value: x } = uvRatio(u, v); // √(u/v)
-      if (!isValid) throw new Error('Point.fromHex: invalid y coordinate');
+      if (!isValid) throw new Error('bad point: invalid y coordinate');
       const isXOdd = (x & _1n) === _1n; // There are 2 square roots. Use x_0 bit to select proper
@@ -349,3 +355,3 @@ const isLastByteOdd = (lastByte & 0x80) !== 0; // x_0, last bit
         // if x=0 and x_0 = 1, fail
-        throw new Error('Point.fromHex: x=0 and x_0=1');
+        throw new Error('bad point: x=0 and x_0=1');
       if (isLastByteOdd !== isXOdd) x = modP(-x); // if x_0 != x mod 2, set x = p-x
@@ -448,5 +454,5 @@ return Point.fromAffine({ x, y });
     multiply(scalar: bigint): Point {
-      const n = scalar;
-      aInRange('scalar', n, _1n, CURVE_ORDER); // 1 <= scalar < L
-      const { p, f } = wnaf.cached(this, n, (p) => normalizeZ(Point, p));
+      // 1 <= scalar < L
+      if (!Fn.isValidNot0(scalar)) throw new Error('invalid scalar: expected 1 <= sc < curve.n');
+      const { p, f } = wnaf.cached(this, scalar, (p) => normalizeZ(Point, p));
       return normalizeZ(Point, [p, f])[0];
@@ -461,7 +467,7 @@ }
     multiplyUnsafe(scalar: bigint, acc = Point.ZERO): Point {
-      const n = scalar;
-      aInRange('scalar', n, _0n, CURVE_ORDER); // 0 <= scalar < L
-      if (n === _0n) return Point.ZERO;
-      if (this.is0() || n === _1n) return this;
-      return wnaf.unsafe(this, n, (p) => normalizeZ(Point, p), acc);
+      // 0 <= scalar < L
+      if (!Fn.isValid(scalar)) throw new Error('invalid scalar: expected 0 <= sc < curve.n');
+      if (scalar === _0n) return Point.ZERO;
+      if (this.is0() || scalar === _1n) return this;
+      return wnaf.unsafe(this, scalar, (p) => normalizeZ(Point, p), acc);
     }
@@ -480,3 +486,3 @@
     isTorsionFree(): boolean {
-      return wnaf.unsafe(this, CURVE_ORDER).is0();
+      return wnaf.unsafe(this, CURVE.n).is0();
     }
@@ -497,10 +503,9 @@
       const { x, y } = this.toAffine();
-      const bytes = numberToBytesLE(y, Fp.BYTES); // each y has 2 x values (x, -y)
-      bytes[bytes.length - 1] |= x & _1n ? 0x80 : 0; // when compressing, it's enough to store y
-      return bytes; // and use the last byte to encode sign of x
+      // Fp.toBytes() allows non-canonical encoding of y (>= p).
+      const bytes = Fp.toBytes(y);
+      // Each y has 2 valid points: (x, y), (x,-y).
+      // When compressing, it's enough to store y and use the last byte to encode sign of x
+      bytes[bytes.length - 1] |= x & _1n ? 0x80 : 0;
+      return bytes;
     }
-    /** @deprecated use `toBytes` */
-    toRawBytes(): Uint8Array {
-      return this.toBytes();
-    }
     toHex(): string {
@@ -536,4 +541,8 @@ return bytesToHex(this.toBytes());
     }
+    toRawBytes(): Uint8Array {
+      return this.toBytes();
+    }
   }
-  const wnaf = new wNAF(Point, Fn.BYTES * 8); // Fn.BITS?
+  const wnaf = new wNAF(Point, Fn.BITS);
+  Point.BASE.precompute(8); // Enable precomputes. Slows down first publicKey computation by 20ms.
   return Point;
@@ -595,7 +604,2 @@ }
 
-  /** @deprecated use `toBytes` */
-  toRawBytes(): Uint8Array {
-    return this.toBytes();
-  }
-
   toHex(): string {
@@ -651,2 +655,7 @@ return bytesToHex(this.toBytes());
   protected abstract init(ep: EdwardsPoint): T;
+
+  /** @deprecated use `toBytes` */
+  toRawBytes(): Uint8Array {
+    return this.toBytes();
+  }
 }
@@ -672,7 +681,6 @@
   const { prehash } = eddsaOpts;
-  const { BASE: G, Fp, Fn } = Point;
-  const CURVE_ORDER = Fn.ORDER;
+  const { BASE, Fp, Fn } = Point;
 
-  const randomBytes_ = eddsaOpts.randomBytes || randomBytes;
-  const adjustScalarBytes = eddsaOpts.adjustScalarBytes || ((bytes: Uint8Array) => bytes); // NOOP
+  const randomBytes = eddsaOpts.randomBytes || randomBytesWeb;
+  const adjustScalarBytes = eddsaOpts.adjustScalarBytes || ((bytes: Uint8Array) => bytes);
   const domain =
@@ -686,10 +694,5 @@ eddsaOpts.domain ||
 
-  function modN(a: bigint) {
-    return Fn.create(a);
-  }
-
   // Little-endian SHA512 with modulo n
   function modN_LE(hash: Uint8Array): bigint {
-    // Not using Fn.fromBytes: hash can be 2*Fn.BYTES
-    return modN(bytesToNumberLE(hash));
+    return Fn.create(bytesToNumberLE(hash)); // Not Fn.fromBytes: it has length limit
   }
@@ -699,3 +702,3 @@
   function getPrivateScalar(key: Hex) {
-    const len = lengths.secret;
+    const len = lengths.secretKey;
     key = ensureBytes('private key', key, len);
@@ -714,3 +717,3 @@ // Hash private key with curve's hash function to produce uniformingly random input
     const { head, prefix, scalar } = getPrivateScalar(secretKey);
-    const point = G.multiply(scalar); // Point on Edwards curve aka public key
+    const point = BASE.multiply(scalar); // Point on Edwards curve aka public key
     const pointBytes = point.toBytes();
@@ -737,9 +740,8 @@ return { head, prefix, scalar, point, pointBytes };
     const r = hashDomainToScalar(options.context, prefix, msg); // r = dom2(F, C) || prefix || PH(M)
-    const R = G.multiply(r).toBytes(); // R = rG
+    const R = BASE.multiply(r).toBytes(); // R = rG
     const k = hashDomainToScalar(options.context, R, pointBytes, msg); // R || A || PH(M)
-    const s = modN(r + k * scalar); // S = (r + k * s) mod L
-    aInRange('signature.s', s, _0n, CURVE_ORDER); // 0 <= s < l
-    const L = Fp.BYTES;
-    const res = concatBytes(R, numberToBytesLE(s, L));
-    return ensureBytes('result', res, L * 2); // 64-byte signature
+    const s = Fn.create(r + k * scalar); // S = (r + k * s) mod L
+    if (!Fn.isValid(s)) throw new Error('sign failed: invalid s'); // 0 <= s < L
+    const rs = concatBytes(R, Fn.toBytes(s));
+    return abytes(rs, lengths.signature, 'result');
   }
@@ -756,6 +758,6 @@
     const { context, zip215 } = options;
-    const len = lengths.signature; // Verifies EdDSA signature against message and public key. RFC8032 5.1.7.
-    sig = ensureBytes('signature', sig, len); // An extended group equation is checked.
+    const len = lengths.signature;
+    sig = ensureBytes('signature', sig, len);
     msg = ensureBytes('message', msg);
-    publicKey = ensureBytes('publicKey', publicKey, lengths.public);
+    publicKey = ensureBytes('publicKey', publicKey, lengths.publicKey);
     if (zip215 !== undefined) abool(zip215, 'zip215');
@@ -774,7 +776,7 @@ if (prehash) msg = prehash(msg); // for ed25519ph, etc
       R = Point.fromBytes(r, zip215);
-      SB = G.multiplyUnsafe(s); // 0 <= s < l is done inside
+      SB = BASE.multiplyUnsafe(s); // 0 <= s < l is done inside
     } catch (error) {
       return false;
     }
-    if (!zip215 && A.isSmallOrder()) return false;
+    if (!zip215 && A.isSmallOrder()) return false; // zip215 allows public keys of small order
 
@@ -788,12 +790,10 @@ const k = hashDomainToScalar(context, R.toBytes(), A.toBytes(), msg);
 
-  G.precompute(8); // Enable precomputes. Slows down first publicKey computation by 20ms.
-
-  const _size = Fp.BYTES;
+  const _size = Fp.BYTES; // 32 for ed25519, 57 for ed448
   const lengths = {
-    secret: _size,
-    public: _size,
+    secretKey: _size,
+    publicKey: _size,
     signature: 2 * _size,
     seed: _size,
   };
-  function randomSecretKey(seed = randomBytes_!(lengths.seed)): Uint8Array {
+  function randomSecretKey(seed = randomBytes(lengths.seed)): Uint8Array {
     return abytes(seed, lengths.seed, 'seed');
@@ -805,11 +805,5 @@ }
   }
-
   function isValidSecretKey(key: Uint8Array): boolean {
-    try {
-      return !!Fn.fromBytes(key, false);
-    } catch (error) {
-      return false;
-    }
+    return isBytes(key) && key.length === Fn.BYTES;
   }
-
   function isValidPublicKey(key: Uint8Array, zip215?: boolean): boolean {
@@ -836,11 +830,6 @@ try {
      *   - `(x, y) = (sqrt(156324)*u/v, (1+u)/(1-u))`
-     *
-     * There is NO `fromMontgomery`:
-     * - There are 2 valid ed25519 points for every x25519, with flipped coordinate
-     * - Sometimes there are 0 valid ed25519 points, because x25519 *additionally*
-     *   accepts inputs on the quadratic twist, which can't be moved to ed25519
      */
     toMontgomery(publicKey: Uint8Array): Uint8Array {
       const { y } = Point.fromBytes(publicKey);
-      const size = lengths.public;
+      const size = lengths.publicKey;
       const is25519 = size === 32;
@@ -853,3 +842,3 @@ if (!is25519 && size !== 57) throw new Error('only defined for 25519 and 448');
     toMontgomeryPriv(secretKey: Uint8Array): Uint8Array {
-      const size = lengths.secret;
+      const size = lengths.secretKey;
       abytes(secretKey, size);
@@ -935,3 +924,9 @@ const hashed = cHash(secretKey.subarray(0, size));
 function _eddsa_new_output_to_legacy(c: CurveTypeWithLength, eddsa: EdDSA): CurveFn {
-  const legacy = Object.assign({}, eddsa, { ExtendedPoint: eddsa.Point, CURVE: c });
+  const Point = eddsa.Point;
+  const legacy = Object.assign({}, eddsa, {
+    ExtendedPoint: Point,
+    CURVE: c,
+    nBitLength: Point.Fn.BITS,
+    nByteLength: Point.Fn.BYTES,
+  });
   return legacy;
@@ -938,0 +933,0 @@ }

src/abstract/montgomery.ts

@@ -168,4 +168,4 @@ /**
   const lengths = {
-    secret: fieldLen,
-    public: fieldLen,
+    secretKey: fieldLen,
+    publicKey: fieldLen,
     seed: fieldLen,
@@ -172,0 +172,0 @@ };

src/abstract/tower.ts

@@ -13,3 +13,3 @@ /**
 /*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
-import { bitLen, bitMask, concatBytes, notImplemented } from '../utils.ts';
+import { bitGet, bitLen, concatBytes, notImplemented } from '../utils.ts';
 import * as mod from './modular.ts';
@@ -38,7 +38,9 @@ import type { WeierstrassPoint, WeierstrassPointCons } from './weierstrass.ts';
 export type Fp2Bls = mod.IField<Fp2> & {
+  Fp: mod.IField<Fp>;
   frobeniusMap(num: Fp2, power: number): Fp2;
-  fromBigTuple(num: [bigint, bigint]): Fp2;
+  fromBigTuple(num: BigintTuple): Fp2;
   mulByB: (num: Fp2) => Fp2;
   mulByNonresidue: (num: Fp2) => Fp2;
   reim: (num: Fp2) => { re: Fp; im: Fp };
+  Fp4Square: (a: Fp2, b: Fp2) => { first: Fp2; second: Fp2 };
   NONRESIDUE: Fp2;
@@ -48,2 +50,3 @@ };
 export type Fp6Bls = mod.IField<Fp6> & {
+  Fp2: Fp2Bls;
   frobeniusMap(num: Fp6, power: number): Fp6;
@@ -58,2 +61,3 @@ fromBigSix: (tuple: BigintSix) => Fp6;
 export type Fp12Bls = mod.IField<Fp12> & {
+  Fp6: Fp6Bls;
   frobeniusMap(num: Fp12, power: number): Fp12;
@@ -142,37 +146,106 @@ fromBigTwelve: (t: BigintTwelve) => Fp12;
   ORDER: bigint;
+  X_LEN: number;
   NONRESIDUE?: Fp;
-  // Fp2
   FP2_NONRESIDUE: BigintTuple;
   Fp2sqrt?: (num: Fp2) => Fp2;
   Fp2mulByB: (num: Fp2) => Fp2;
-  // Fp12
-  Fp12cyclotomicSquare: (num: Fp12) => Fp12;
-  Fp12cyclotomicExp: (num: Fp12, n: bigint) => Fp12;
   Fp12finalExponentiate: (num: Fp12) => Fp12;
 };
 
-export function tower12(opts: Tower12Opts): {
-  Fp: Readonly<mod.IField<bigint> & Required<Pick<mod.IField<bigint>, 'isOdd'>>>;
-  Fp2: Fp2Bls;
-  Fp6: Fp6Bls;
-  Fp12: Fp12Bls;
-  Fp4Square: (a: Fp2, b: Fp2) => { first: Fp2; second: Fp2 };
-} {
-  const { ORDER } = opts;
-  // Fp
-  const Fp = mod.Field(ORDER);
-  const FpNONRESIDUE = Fp.create(opts.NONRESIDUE || BigInt(-1));
-  const Fpdiv2 = Fp.div(Fp.ONE, _2n); // 1/2
+const Fp2fromBigTuple = (Fp: mod.IField<bigint>, tuple: BigintTuple | bigint[]) => {
+  if (tuple.length !== 2) throw new Error('invalid tuple');
+  const fps = tuple.map((n) => Fp.create(n)) as BigintTuple;
+  return { c0: fps[0], c1: fps[1] };
+};
 
-  // Fp2
-  const FP2_FROBENIUS_COEFFICIENTS = calcFrobeniusCoefficients(Fp, FpNONRESIDUE, Fp.ORDER, 2)[0];
-  const Fp2Add = ({ c0, c1 }: Fp2, { c0: r0, c1: r1 }: Fp2) => ({
-    c0: Fp.add(c0, r0),
-    c1: Fp.add(c1, r1),
-  });
-  const Fp2Subtract = ({ c0, c1 }: Fp2, { c0: r0, c1: r1 }: Fp2) => ({
-    c0: Fp.sub(c0, r0),
-    c1: Fp.sub(c1, r1),
-  });
-  const Fp2Multiply = ({ c0, c1 }: Fp2, rhs: Fp2) => {
+class _Field2 implements mod.IField<Fp2> {
+  readonly ORDER: bigint;
+  readonly BITS: number;
+  readonly BYTES: number;
+  readonly isLE: boolean;
+  readonly MASK = _1n;
+
+  readonly ZERO: Fp2;
+  readonly ONE: Fp2;
+  readonly Fp: mod.IField<bigint>;
+
+  readonly NONRESIDUE: Fp2;
+  readonly mulByB: Tower12Opts['Fp2mulByB'];
+  readonly Fp_NONRESIDUE: bigint;
+  readonly Fp_div2: bigint;
+  readonly FROBENIUS_COEFFICIENTS: Fp[];
+
+  constructor(
+    Fp: mod.IField<bigint>,
+    opts: Partial<{
+      NONRESIDUE: bigint;
+      FP2_NONRESIDUE: BigintTuple;
+      Fp2mulByB: Tower12Opts['Fp2mulByB'];
+    }> = {}
+  ) {
+    const ORDER = Fp.ORDER;
+    const FP2_ORDER = ORDER * ORDER;
+    this.Fp = Fp;
+    this.ORDER = FP2_ORDER;
+    this.BITS = bitLen(FP2_ORDER);
+    this.BYTES = Math.ceil(bitLen(FP2_ORDER) / 8);
+    this.isLE = Fp.isLE;
+    this.ZERO = { c0: Fp.ZERO, c1: Fp.ZERO };
+    this.ONE = { c0: Fp.ONE, c1: Fp.ZERO };
+
+    this.Fp_NONRESIDUE = Fp.create(opts.NONRESIDUE || BigInt(-1));
+    this.Fp_div2 = Fp.div(Fp.ONE, _2n); // 1/2
+    this.NONRESIDUE = Fp2fromBigTuple(Fp, opts.FP2_NONRESIDUE!);
+    // const Fp2Nonresidue = Fp2fromBigTuple(opts.FP2_NONRESIDUE);
+    this.FROBENIUS_COEFFICIENTS = calcFrobeniusCoefficients(Fp, this.Fp_NONRESIDUE, Fp.ORDER, 2)[0];
+    this.mulByB = opts.Fp2mulByB!;
+    Object.seal(this);
+  }
+  fromBigTuple(tuple: BigintTuple) {
+    return Fp2fromBigTuple(this.Fp, tuple);
+  }
+  create(num: Fp2) {
+    return num;
+  }
+  isValid({ c0, c1 }: Fp2) {
+    function isValidC(num: bigint, ORDER: bigint) {
+      return typeof num === 'bigint' && _0n <= num && num < ORDER;
+    }
+    return isValidC(c0, this.ORDER) && isValidC(c1, this.ORDER);
+  }
+  is0({ c0, c1 }: Fp2) {
+    return this.Fp.is0(c0) && this.Fp.is0(c1);
+  }
+  isValidNot0(num: Fp2) {
+    return !this.is0(num) && this.isValid(num);
+  }
+  eql({ c0, c1 }: Fp2, { c0: r0, c1: r1 }: Fp2) {
+    return this.Fp.eql(c0, r0) && this.Fp.eql(c1, r1);
+  }
+  neg({ c0, c1 }: Fp2) {
+    return { c0: this.Fp.neg(c0), c1: this.Fp.neg(c1) };
+  }
+  pow(num: Fp2, power: bigint): Fp2 {
+    return mod.FpPow(this, num, power);
+  }
+  invertBatch(nums: Fp2[]): Fp2[] {
+    return mod.FpInvertBatch(this, nums);
+  }
+  // Normalized
+  add(f1: Fp2, f2: Fp2): Fp2 {
+    const { c0, c1 } = f1;
+    const { c0: r0, c1: r1 } = f2;
+    return {
+      c0: this.Fp.add(c0, r0),
+      c1: this.Fp.add(c1, r1),
+    };
+  }
+  sub({ c0, c1 }: Fp2, { c0: r0, c1: r1 }: Fp2) {
+    return {
+      c0: this.Fp.sub(c0, r0),
+      c1: this.Fp.sub(c1, r1),
+    };
+  }
+  mul({ c0, c1 }: Fp2, rhs: Fp2) {
+    const { Fp } = this;
     if (typeof rhs === 'bigint') return { c0: Fp.mul(c0, rhs), c1: Fp.mul(c1, rhs) };
@@ -187,4 +260,5 @@ // (a+bi)(c+di) = (ac−bd) + (ad+bc)i
     return { c0: o0, c1: o1 };
-  };
-  const Fp2Square = ({ c0, c1 }: Fp2) => {
+  }
+  sqr({ c0, c1 }: Fp2) {
+    const { Fp } = this;
     const a = Fp.add(c0, c1);
@@ -194,127 +268,158 @@ const b = Fp.sub(c0, c1);
     return { c0: Fp.mul(a, b), c1: Fp.mul(c, c1) };
-  };
-  const Fp2fromBigTuple = (tuple: BigintTuple | bigint[]) => {
-    if (tuple.length !== 2) throw new Error('invalid tuple');
-    const fps = tuple.map((n) => Fp.create(n)) as [Fp, Fp];
-    return { c0: fps[0], c1: fps[1] };
-  };
+  }
+  // NonNormalized stuff
+  addN(a: Fp2, b: Fp2): Fp2 {
+    return this.add(a, b);
+  }
+  subN(a: Fp2, b: Fp2): Fp2 {
+    return this.sub(a, b);
+  }
+  mulN(a: Fp2, b: Fp2): Fp2 {
+    return this.mul(a, b);
+  }
+  sqrN(a: Fp2): Fp2 {
+    return this.sqr(a);
+  }
+  // Why inversion for bigint inside Fp instead of Fp2? it is even used in that context?
+  div(lhs: Fp2, rhs: Fp2): Fp2 {
+    const { Fp } = this;
+    // @ts-ignore
+    return this.mul(lhs, typeof rhs === 'bigint' ? Fp.inv(Fp.create(rhs)) : this.inv(rhs));
+  }
+  inv({ c0: a, c1: b }: Fp2): Fp2 {
+    // We wish to find the multiplicative inverse of a nonzero
+    // element a + bu in Fp2. We leverage an identity
+    //
+    // (a + bu)(a - bu) = a² + b²
+    //
+    // which holds because u² = -1. This can be rewritten as
+    //
+    // (a + bu)(a - bu)/(a² + b²) = 1
+    //
+    // because a² + b² = 0 has no nonzero solutions for (a, b).
+    // This gives that (a - bu)/(a² + b²) is the inverse
+    // of (a + bu). Importantly, this can be computing using
+    // only a single inversion in Fp.
+    const { Fp } = this;
+    const factor = Fp.inv(Fp.create(a * a + b * b));
+    return { c0: Fp.mul(factor, Fp.create(a)), c1: Fp.mul(factor, Fp.create(-b)) };
+  }
+  sqrt(num: Fp2) {
+    // This is generic for all quadratic extensions (Fp2)
+    const { Fp } = this;
+    const Fp2 = this;
+    const { c0, c1 } = num;
+    if (Fp.is0(c1)) {
+      // if c0 is quadratic residue
+      if (mod.FpLegendre(Fp, c0) === 1) return Fp2.create({ c0: Fp.sqrt(c0), c1: Fp.ZERO });
+      else return Fp2.create({ c0: Fp.ZERO, c1: Fp.sqrt(Fp.div(c0, this.Fp_NONRESIDUE)) });
+    }
+    const a = Fp.sqrt(Fp.sub(Fp.sqr(c0), Fp.mul(Fp.sqr(c1), this.Fp_NONRESIDUE)));
+    let d = Fp.mul(Fp.add(a, c0), this.Fp_div2);
+    const legendre = mod.FpLegendre(Fp, d);
+    // -1, Quadratic non residue
+    if (legendre === -1) d = Fp.sub(d, a);
+    const a0 = Fp.sqrt(d);
+    const candidateSqrt = Fp2.create({ c0: a0, c1: Fp.div(Fp.mul(c1, this.Fp_div2), a0) });
+    if (!Fp2.eql(Fp2.sqr(candidateSqrt), num)) throw new Error('Cannot find square root');
+    // Normalize root: at this point candidateSqrt ** 2 = num, but also -candidateSqrt ** 2 = num
+    const x1 = candidateSqrt;
+    const x2 = Fp2.neg(x1);
+    const { re: re1, im: im1 } = Fp2.reim(x1);
+    const { re: re2, im: im2 } = Fp2.reim(x2);
+    if (im1 > im2 || (im1 === im2 && re1 > re2)) return x1;
+    return x2;
+  }
+  // Same as sgn0_m_eq_2 in RFC 9380
+  isOdd(x: Fp2) {
+    const { re: x0, im: x1 } = this.reim(x);
+    const sign_0 = x0 % _2n;
+    const zero_0 = x0 === _0n;
+    const sign_1 = x1 % _2n;
+    return BigInt(sign_0 || (zero_0 && sign_1)) == _1n;
+  }
+  // Bytes util
+  fromBytes(b: Uint8Array): Fp2 {
+    const { Fp } = this;
+    if (b.length !== this.BYTES) throw new Error('fromBytes invalid length=' + b.length);
+    return { c0: Fp.fromBytes(b.subarray(0, Fp.BYTES)), c1: Fp.fromBytes(b.subarray(Fp.BYTES)) };
+  }
+  toBytes({ c0, c1 }: Fp2) {
+    return concatBytes(this.Fp.toBytes(c0), this.Fp.toBytes(c1));
+  }
+  cmov({ c0, c1 }: Fp2, { c0: r0, c1: r1 }: Fp2, c: boolean) {
+    return {
+      c0: this.Fp.cmov(c0, r0, c),
+      c1: this.Fp.cmov(c1, r1, c),
+    };
+  }
+  reim({ c0, c1 }: Fp2) {
+    return { re: c0, im: c1 };
+  }
+  Fp4Square(a: Fp2, b: Fp2): { first: Fp2; second: Fp2 } {
+    const Fp2 = this;
+    const a2 = Fp2.sqr(a);
+    const b2 = Fp2.sqr(b);
+    return {
+      first: Fp2.add(Fp2.mulByNonresidue(b2), a2), // b² * Nonresidue + a²
+      second: Fp2.sub(Fp2.sub(Fp2.sqr(Fp2.add(a, b)), a2), b2), // (a + b)² - a² - b²
+    };
+  }
+  // multiply by u + 1
+  mulByNonresidue({ c0, c1 }: Fp2) {
+    return this.mul({ c0, c1 }, this.NONRESIDUE);
+  }
+  frobeniusMap({ c0, c1 }: Fp2, power: number): Fp2 {
+    return {
+      c0,
+      c1: this.Fp.mul(c1, this.FROBENIUS_COEFFICIENTS[power % 2]),
+    };
+  }
+}
 
-  function isValidC(num: bigint, ORDER: bigint) {
-    return typeof num === 'bigint' && _0n <= num && num < ORDER;
+class _Field6 implements Fp6Bls {
+  readonly ORDER: bigint;
+  readonly BITS: number;
+  readonly BYTES: number;
+  readonly isLE: boolean;
+  readonly MASK = _1n;
+
+  readonly ZERO: Fp6;
+  readonly ONE: Fp6;
+  readonly Fp2: Fp2Bls;
+  readonly FROBENIUS_COEFFICIENTS_1: Fp2[];
+  readonly FROBENIUS_COEFFICIENTS_2: Fp2[];
+
+  constructor(Fp2: Fp2Bls) {
+    this.Fp2 = Fp2;
+    this.ORDER = Fp2.ORDER; // TODO: unused, but need to verify
+    this.BITS = 3 * Fp2.BITS;
+    this.BYTES = 3 * Fp2.BYTES;
+    this.isLE = Fp2.isLE;
+    this.ZERO = { c0: Fp2.ZERO, c1: Fp2.ZERO, c2: Fp2.ZERO };
+    this.ONE = { c0: Fp2.ONE, c1: Fp2.ZERO, c2: Fp2.ZERO };
+    const { Fp } = Fp2;
+    const frob = calcFrobeniusCoefficients(Fp2, Fp2.NONRESIDUE, Fp.ORDER, 6, 2, 3);
+    this.FROBENIUS_COEFFICIENTS_1 = frob[0];
+    this.FROBENIUS_COEFFICIENTS_2 = frob[1];
+    Object.seal(this);
   }
-
-  const FP2_ORDER = ORDER * ORDER;
-  const Fp2Nonresidue = Fp2fromBigTuple(opts.FP2_NONRESIDUE);
-  const Fp2: Fp2Bls = {
-    ORDER: FP2_ORDER,
-    isLE: Fp.isLE,
-    NONRESIDUE: Fp2Nonresidue,
-    BITS: bitLen(FP2_ORDER),
-    BYTES: Math.ceil(bitLen(FP2_ORDER) / 8),
-    MASK: bitMask(bitLen(FP2_ORDER)),
-    ZERO: { c0: Fp.ZERO, c1: Fp.ZERO },
-    ONE: { c0: Fp.ONE, c1: Fp.ZERO },
-    create: (num) => num,
-    isValid: ({ c0, c1 }) => isValidC(c0, FP2_ORDER) && isValidC(c1, FP2_ORDER),
-    is0: ({ c0, c1 }) => Fp.is0(c0) && Fp.is0(c1),
-    isValidNot0: (num) => !Fp2.is0(num) && Fp2.isValid(num),
-    eql: ({ c0, c1 }: Fp2, { c0: r0, c1: r1 }: Fp2) => Fp.eql(c0, r0) && Fp.eql(c1, r1),
-    neg: ({ c0, c1 }) => ({ c0: Fp.neg(c0), c1: Fp.neg(c1) }),
-    pow: (num, power) => mod.FpPow(Fp2, num, power),
-    invertBatch: (nums) => mod.FpInvertBatch(Fp2, nums),
-    // Normalized
-    add: Fp2Add,
-    sub: Fp2Subtract,
-    mul: Fp2Multiply,
-    sqr: Fp2Square,
-    // NonNormalized stuff
-    addN: Fp2Add,
-    subN: Fp2Subtract,
-    mulN: Fp2Multiply,
-    sqrN: Fp2Square,
-    // Why inversion for bigint inside Fp instead of Fp2? it is even used in that context?
-    div: (lhs, rhs) =>
-      Fp2.mul(lhs, typeof rhs === 'bigint' ? Fp.inv(Fp.create(rhs)) : Fp2.inv(rhs)),
-    inv: ({ c0: a, c1: b }) => {
-      // We wish to find the multiplicative inverse of a nonzero
-      // element a + bu in Fp2. We leverage an identity
-      //
-      // (a + bu)(a - bu) = a² + b²
-      //
-      // which holds because u² = -1. This can be rewritten as
-      //
-      // (a + bu)(a - bu)/(a² + b²) = 1
-      //
-      // because a² + b² = 0 has no nonzero solutions for (a, b).
-      // This gives that (a - bu)/(a² + b²) is the inverse
-      // of (a + bu). Importantly, this can be computing using
-      // only a single inversion in Fp.
-      const factor = Fp.inv(Fp.create(a * a + b * b));
-      return { c0: Fp.mul(factor, Fp.create(a)), c1: Fp.mul(factor, Fp.create(-b)) };
-    },
-    sqrt: (num) => {
-      if (opts.Fp2sqrt) return opts.Fp2sqrt(num);
-      // This is generic for all quadratic extensions (Fp2)
-      const { c0, c1 } = num;
-      if (Fp.is0(c1)) {
-        // if c0 is quadratic residue
-        if (mod.FpLegendre(Fp, c0) === 1) return Fp2.create({ c0: Fp.sqrt(c0), c1: Fp.ZERO });
-        else return Fp2.create({ c0: Fp.ZERO, c1: Fp.sqrt(Fp.div(c0, FpNONRESIDUE)) });
-      }
-      const a = Fp.sqrt(Fp.sub(Fp.sqr(c0), Fp.mul(Fp.sqr(c1), FpNONRESIDUE)));
-      let d = Fp.mul(Fp.add(a, c0), Fpdiv2);
-      const legendre = mod.FpLegendre(Fp, d);
-      // -1, Quadratic non residue
-      if (legendre === -1) d = Fp.sub(d, a);
-      const a0 = Fp.sqrt(d);
-      const candidateSqrt = Fp2.create({ c0: a0, c1: Fp.div(Fp.mul(c1, Fpdiv2), a0) });
-      if (!Fp2.eql(Fp2.sqr(candidateSqrt), num)) throw new Error('Cannot find square root');
-      // Normalize root: at this point candidateSqrt ** 2 = num, but also -candidateSqrt ** 2 = num
-      const x1 = candidateSqrt;
-      const x2 = Fp2.neg(x1);
-      const { re: re1, im: im1 } = Fp2.reim(x1);
-      const { re: re2, im: im2 } = Fp2.reim(x2);
-      if (im1 > im2 || (im1 === im2 && re1 > re2)) return x1;
-      return x2;
-    },
-    // Same as sgn0_m_eq_2 in RFC 9380
-    isOdd: (x: Fp2) => {
-      const { re: x0, im: x1 } = Fp2.reim(x);
-      const sign_0 = x0 % _2n;
-      const zero_0 = x0 === _0n;
-      const sign_1 = x1 % _2n;
-      return BigInt(sign_0 || (zero_0 && sign_1)) == _1n;
-    },
-    // Bytes util
-    fromBytes(b: Uint8Array): Fp2 {
-      if (b.length !== Fp2.BYTES) throw new Error('fromBytes invalid length=' + b.length);
-      return { c0: Fp.fromBytes(b.subarray(0, Fp.BYTES)), c1: Fp.fromBytes(b.subarray(Fp.BYTES)) };
-    },
-    toBytes: ({ c0, c1 }) => concatBytes(Fp.toBytes(c0), Fp.toBytes(c1)),
-    cmov: ({ c0, c1 }, { c0: r0, c1: r1 }, c) => ({
-      c0: Fp.cmov(c0, r0, c),
-      c1: Fp.cmov(c1, r1, c),
-    }),
-    reim: ({ c0, c1 }) => ({ re: c0, im: c1 }),
-    // multiply by u + 1
-    mulByNonresidue: ({ c0, c1 }) => Fp2.mul({ c0, c1 }, Fp2Nonresidue),
-    mulByB: opts.Fp2mulByB,
-    fromBigTuple: Fp2fromBigTuple,
-    frobeniusMap: ({ c0, c1 }, power: number): Fp2 => ({
-      c0,
-      c1: Fp.mul(c1, FP2_FROBENIUS_COEFFICIENTS[power % 2]),
-    }),
-  };
-  // Fp6
-  const Fp6Add = ({ c0, c1, c2 }: Fp6, { c0: r0, c1: r1, c2: r2 }: Fp6) => ({
-    c0: Fp2.add(c0, r0),
-    c1: Fp2.add(c1, r1),
-    c2: Fp2.add(c2, r2),
-  });
-  const Fp6Subtract = ({ c0, c1, c2 }: Fp6, { c0: r0, c1: r1, c2: r2 }: Fp6) => ({
-    c0: Fp2.sub(c0, r0),
-    c1: Fp2.sub(c1, r1),
-    c2: Fp2.sub(c2, r2),
-  });
-  const Fp6Multiply = ({ c0, c1, c2 }: Fp6, rhs: Fp6 | bigint) => {
+  add({ c0, c1, c2 }: Fp6, { c0: r0, c1: r1, c2: r2 }: Fp6) {
+    const { Fp2 } = this;
+    return {
+      c0: Fp2.add(c0, r0),
+      c1: Fp2.add(c1, r1),
+      c2: Fp2.add(c2, r2),
+    };
+  }
+  sub({ c0, c1, c2 }: Fp6, { c0: r0, c1: r1, c2: r2 }: Fp6) {
+    const { Fp2 } = this;
+    return {
+      c0: Fp2.sub(c0, r0),
+      c1: Fp2.sub(c1, r1),
+      c2: Fp2.sub(c2, r2),
+    };
+  }
+  mul({ c0, c1, c2 }: Fp6, rhs: Fp6 | bigint) {
+    const { Fp2 } = this;
     if (typeof rhs === 'bigint') {
@@ -345,4 +450,5 @@ return {
     };
-  };
-  const Fp6Square = ({ c0, c1, c2 }: Fp6) => {
+  }
+  sqr({ c0, c1, c2 }: Fp6) {
+    const { Fp2 } = this;
     let t0 = Fp2.sqr(c0); // c0²
@@ -358,129 +464,241 @@ let t1 = Fp2.mul(Fp2.mul(c0, c1), _2n); // 2 * c0 * c1
     };
-  };
-  const [FP6_FROBENIUS_COEFFICIENTS_1, FP6_FROBENIUS_COEFFICIENTS_2] = calcFrobeniusCoefficients(
-    Fp2,
-    Fp2Nonresidue,
-    Fp.ORDER,
-    6,
-    2,
-    3
-  );
+  }
+  addN(a: Fp6, b: Fp6): Fp6 {
+    return this.add(a, b);
+  }
+  subN(a: Fp6, b: Fp6): Fp6 {
+    return this.sub(a, b);
+  }
+  mulN(a: Fp6, b: Fp6): Fp6 {
+    return this.mul(a, b);
+  }
+  sqrN(a: Fp6): Fp6 {
+    return this.sqr(a);
+  }
 
-  const Fp6: Fp6Bls = {
-    ORDER: Fp2.ORDER, // TODO: unused, but need to verify
-    isLE: Fp2.isLE,
-    BITS: 3 * Fp2.BITS,
-    BYTES: 3 * Fp2.BYTES,
-    MASK: bitMask(3 * Fp2.BITS),
-    ZERO: { c0: Fp2.ZERO, c1: Fp2.ZERO, c2: Fp2.ZERO },
-    ONE: { c0: Fp2.ONE, c1: Fp2.ZERO, c2: Fp2.ZERO },
-    create: (num) => num,
-    isValid: ({ c0, c1, c2 }) => Fp2.isValid(c0) && Fp2.isValid(c1) && Fp2.isValid(c2),
-    is0: ({ c0, c1, c2 }) => Fp2.is0(c0) && Fp2.is0(c1) && Fp2.is0(c2),
-    isValidNot0: (num) => !Fp6.is0(num) && Fp6.isValid(num),
-    neg: ({ c0, c1, c2 }) => ({ c0: Fp2.neg(c0), c1: Fp2.neg(c1), c2: Fp2.neg(c2) }),
-    eql: ({ c0, c1, c2 }, { c0: r0, c1: r1, c2: r2 }) =>
-      Fp2.eql(c0, r0) && Fp2.eql(c1, r1) && Fp2.eql(c2, r2),
-    sqrt: notImplemented,
-    // Do we need division by bigint at all? Should be done via order:
-    div: (lhs, rhs) =>
-      Fp6.mul(lhs, typeof rhs === 'bigint' ? Fp.inv(Fp.create(rhs)) : Fp6.inv(rhs)),
-    pow: (num, power) => mod.FpPow(Fp6, num, power),
-    invertBatch: (nums) => mod.FpInvertBatch(Fp6, nums),
-    // Normalized
-    add: Fp6Add,
-    sub: Fp6Subtract,
-    mul: Fp6Multiply,
-    sqr: Fp6Square,
-    // NonNormalized stuff
-    addN: Fp6Add,
-    subN: Fp6Subtract,
-    mulN: Fp6Multiply,
-    sqrN: Fp6Square,
+  create(num: Fp6) {
+    return num;
+  }
 
-    inv: ({ c0, c1, c2 }) => {
-      let t0 = Fp2.sub(Fp2.sqr(c0), Fp2.mulByNonresidue(Fp2.mul(c2, c1))); // c0² - c2 * c1 * (u + 1)
-      let t1 = Fp2.sub(Fp2.mulByNonresidue(Fp2.sqr(c2)), Fp2.mul(c0, c1)); // c2² * (u + 1) - c0 * c1
-      let t2 = Fp2.sub(Fp2.sqr(c1), Fp2.mul(c0, c2)); // c1² - c0 * c2
-      // 1/(((c2 * T1 + c1 * T2) * v) + c0 * T0)
-      let t4 = Fp2.inv(
-        Fp2.add(Fp2.mulByNonresidue(Fp2.add(Fp2.mul(c2, t1), Fp2.mul(c1, t2))), Fp2.mul(c0, t0))
-      );
-      return { c0: Fp2.mul(t4, t0), c1: Fp2.mul(t4, t1), c2: Fp2.mul(t4, t2) };
-    },
-    // Bytes utils
-    fromBytes: (b: Uint8Array): Fp6 => {
-      if (b.length !== Fp6.BYTES) throw new Error('fromBytes invalid length=' + b.length);
-      return {
-        c0: Fp2.fromBytes(b.subarray(0, Fp2.BYTES)),
-        c1: Fp2.fromBytes(b.subarray(Fp2.BYTES, 2 * Fp2.BYTES)),
-        c2: Fp2.fromBytes(b.subarray(2 * Fp2.BYTES)),
-      };
-    },
-    toBytes: ({ c0, c1, c2 }): Uint8Array =>
-      concatBytes(Fp2.toBytes(c0), Fp2.toBytes(c1), Fp2.toBytes(c2)),
-    cmov: ({ c0, c1, c2 }: Fp6, { c0: r0, c1: r1, c2: r2 }: Fp6, c) => ({
+  isValid({ c0, c1, c2 }: Fp6) {
+    const { Fp2 } = this;
+    return Fp2.isValid(c0) && Fp2.isValid(c1) && Fp2.isValid(c2);
+  }
+  is0({ c0, c1, c2 }: Fp6) {
+    const { Fp2 } = this;
+    return Fp2.is0(c0) && Fp2.is0(c1) && Fp2.is0(c2);
+  }
+  isValidNot0(num: Fp6) {
+    return !this.is0(num) && this.isValid(num);
+  }
+  neg({ c0, c1, c2 }: Fp6) {
+    const { Fp2 } = this;
+    return { c0: Fp2.neg(c0), c1: Fp2.neg(c1), c2: Fp2.neg(c2) };
+  }
+  eql({ c0, c1, c2 }: Fp6, { c0: r0, c1: r1, c2: r2 }: Fp6) {
+    const { Fp2 } = this;
+    return Fp2.eql(c0, r0) && Fp2.eql(c1, r1) && Fp2.eql(c2, r2);
+  }
+  sqrt(_: Fp6) {
+    return notImplemented();
+  }
+  // Do we need division by bigint at all? Should be done via order:
+  div(lhs: Fp6, rhs: Fp6) {
+    const { Fp2 } = this;
+    const { Fp } = Fp2;
+    return this.mul(lhs, typeof rhs === 'bigint' ? Fp.inv(Fp.create(rhs)) : this.inv(rhs));
+  }
+  pow(num: Fp6, power: Fp): Fp6 {
+    return mod.FpPow(this, num, power);
+  }
+  invertBatch(nums: Fp6[]): Fp6[] {
+    return mod.FpInvertBatch(this, nums);
+  }
+
+  inv({ c0, c1, c2 }: Fp6) {
+    const { Fp2 } = this;
+    let t0 = Fp2.sub(Fp2.sqr(c0), Fp2.mulByNonresidue(Fp2.mul(c2, c1))); // c0² - c2 * c1 * (u + 1)
+    let t1 = Fp2.sub(Fp2.mulByNonresidue(Fp2.sqr(c2)), Fp2.mul(c0, c1)); // c2² * (u + 1) - c0 * c1
+    let t2 = Fp2.sub(Fp2.sqr(c1), Fp2.mul(c0, c2)); // c1² - c0 * c2
+    // 1/(((c2 * T1 + c1 * T2) * v) + c0 * T0)
+    let t4 = Fp2.inv(
+      Fp2.add(Fp2.mulByNonresidue(Fp2.add(Fp2.mul(c2, t1), Fp2.mul(c1, t2))), Fp2.mul(c0, t0))
+    );
+    return { c0: Fp2.mul(t4, t0), c1: Fp2.mul(t4, t1), c2: Fp2.mul(t4, t2) };
+  }
+  // Bytes utils
+  fromBytes(b: Uint8Array): Fp6 {
+    const { Fp2 } = this;
+    if (b.length !== this.BYTES) throw new Error('fromBytes invalid length=' + b.length);
+    const B2 = Fp2.BYTES;
+    return {
+      c0: Fp2.fromBytes(b.subarray(0, B2)),
+      c1: Fp2.fromBytes(b.subarray(B2, B2 * 2)),
+      c2: Fp2.fromBytes(b.subarray(2 * B2)),
+    };
+  }
+  toBytes({ c0, c1, c2 }: Fp6): Uint8Array {
+    const { Fp2 } = this;
+    return concatBytes(Fp2.toBytes(c0), Fp2.toBytes(c1), Fp2.toBytes(c2));
+  }
+  cmov({ c0, c1, c2 }: Fp6, { c0: r0, c1: r1, c2: r2 }: Fp6, c: boolean) {
+    const { Fp2 } = this;
+    return {
       c0: Fp2.cmov(c0, r0, c),
       c1: Fp2.cmov(c1, r1, c),
       c2: Fp2.cmov(c2, r2, c),
-    }),
-    fromBigSix: (t: BigintSix): Fp6 => {
-      if (!Array.isArray(t) || t.length !== 6) throw new Error('invalid Fp6 usage');
-      return {
-        c0: Fp2.fromBigTuple(t.slice(0, 2) as BigintTuple),
-        c1: Fp2.fromBigTuple(t.slice(2, 4) as BigintTuple),
-        c2: Fp2.fromBigTuple(t.slice(4, 6) as BigintTuple),
-      };
-    },
-    frobeniusMap: ({ c0, c1, c2 }, power: number) => ({
+    };
+  }
+  fromBigSix(t: BigintSix): Fp6 {
+    const { Fp2 } = this;
+    if (!Array.isArray(t) || t.length !== 6) throw new Error('invalid Fp6 usage');
+    return {
+      c0: Fp2.fromBigTuple(t.slice(0, 2) as BigintTuple),
+      c1: Fp2.fromBigTuple(t.slice(2, 4) as BigintTuple),
+      c2: Fp2.fromBigTuple(t.slice(4, 6) as BigintTuple),
+    };
+  }
+  frobeniusMap({ c0, c1, c2 }: Fp6, power: number) {
+    const { Fp2 } = this;
+    return {
       c0: Fp2.frobeniusMap(c0, power),
-      c1: Fp2.mul(Fp2.frobeniusMap(c1, power), FP6_FROBENIUS_COEFFICIENTS_1[power % 6]),
-      c2: Fp2.mul(Fp2.frobeniusMap(c2, power), FP6_FROBENIUS_COEFFICIENTS_2[power % 6]),
-    }),
-    mulByFp2: ({ c0, c1, c2 }, rhs: Fp2): Fp6 => ({
+      c1: Fp2.mul(Fp2.frobeniusMap(c1, power), this.FROBENIUS_COEFFICIENTS_1[power % 6]),
+      c2: Fp2.mul(Fp2.frobeniusMap(c2, power), this.FROBENIUS_COEFFICIENTS_2[power % 6]),
+    };
+  }
+  mulByFp2({ c0, c1, c2 }: Fp6, rhs: Fp2): Fp6 {
+    const { Fp2 } = this;
+    return {
       c0: Fp2.mul(c0, rhs),
       c1: Fp2.mul(c1, rhs),
       c2: Fp2.mul(c2, rhs),
-    }),
-    mulByNonresidue: ({ c0, c1, c2 }) => ({ c0: Fp2.mulByNonresidue(c2), c1: c0, c2: c1 }),
-    // Sparse multiplication
-    mul1: ({ c0, c1, c2 }, b1: Fp2): Fp6 => ({
+    };
+  }
+  mulByNonresidue({ c0, c1, c2 }: Fp6) {
+    const { Fp2 } = this;
+    return { c0: Fp2.mulByNonresidue(c2), c1: c0, c2: c1 };
+  }
+  // Sparse multiplication
+  mul1({ c0, c1, c2 }: Fp6, b1: Fp2): Fp6 {
+    const { Fp2 } = this;
+    return {
       c0: Fp2.mulByNonresidue(Fp2.mul(c2, b1)),
       c1: Fp2.mul(c0, b1),
       c2: Fp2.mul(c1, b1),
-    }),
-    // Sparse multiplication
-    mul01({ c0, c1, c2 }, b0: Fp2, b1: Fp2): Fp6 {
-      let t0 = Fp2.mul(c0, b0); // c0 * b0
-      let t1 = Fp2.mul(c1, b1); // c1 * b1
-      return {
-        // ((c1 + c2) * b1 - T1) * (u + 1) + T0
-        c0: Fp2.add(Fp2.mulByNonresidue(Fp2.sub(Fp2.mul(Fp2.add(c1, c2), b1), t1)), t0),
-        // (b0 + b1) * (c0 + c1) - T0 - T1
-        c1: Fp2.sub(Fp2.sub(Fp2.mul(Fp2.add(b0, b1), Fp2.add(c0, c1)), t0), t1),
-        // (c0 + c2) * b0 - T0 + T1
-        c2: Fp2.add(Fp2.sub(Fp2.mul(Fp2.add(c0, c2), b0), t0), t1),
-      };
-    },
-  };
+    };
+  }
+  // Sparse multiplication
+  mul01({ c0, c1, c2 }: Fp6, b0: Fp2, b1: Fp2): Fp6 {
+    const { Fp2 } = this;
+    let t0 = Fp2.mul(c0, b0); // c0 * b0
+    let t1 = Fp2.mul(c1, b1); // c1 * b1
+    return {
+      // ((c1 + c2) * b1 - T1) * (u + 1) + T0
+      c0: Fp2.add(Fp2.mulByNonresidue(Fp2.sub(Fp2.mul(Fp2.add(c1, c2), b1), t1)), t0),
+      // (b0 + b1) * (c0 + c1) - T0 - T1
+      c1: Fp2.sub(Fp2.sub(Fp2.mul(Fp2.add(b0, b1), Fp2.add(c0, c1)), t0), t1),
+      // (c0 + c2) * b0 - T0 + T1
+      c2: Fp2.add(Fp2.sub(Fp2.mul(Fp2.add(c0, c2), b0), t0), t1),
+    };
+  }
+}
 
-  // Fp12
-  const FP12_FROBENIUS_COEFFICIENTS = calcFrobeniusCoefficients(
-    Fp2,
-    Fp2Nonresidue,
-    Fp.ORDER,
-    12,
-    1,
-    6
-  )[0];
+class _Field12 implements Fp12Bls {
+  readonly ORDER: bigint;
+  readonly BITS: number;
+  readonly BYTES: number;
+  readonly isLE: boolean;
+  readonly MASK = _1n;
 
-  const Fp12Add = ({ c0, c1 }: Fp12, { c0: r0, c1: r1 }: Fp12) => ({
-    c0: Fp6.add(c0, r0),
-    c1: Fp6.add(c1, r1),
-  });
-  const Fp12Subtract = ({ c0, c1 }: Fp12, { c0: r0, c1: r1 }: Fp12) => ({
-    c0: Fp6.sub(c0, r0),
-    c1: Fp6.sub(c1, r1),
-  });
-  const Fp12Multiply = ({ c0, c1 }: Fp12, rhs: Fp12 | bigint) => {
+  readonly ZERO: Fp12;
+  readonly ONE: Fp12;
+
+  readonly Fp6: Fp6Bls;
+  readonly FROBENIUS_COEFFICIENTS: Fp2[];
+  readonly X_LEN: number;
+  readonly finalExponentiate: Tower12Opts['Fp12finalExponentiate'];
+
+  constructor(Fp6: Fp6Bls, opts: Tower12Opts) {
+    const { Fp2 } = Fp6;
+    const { Fp } = Fp2;
+    this.Fp6 = Fp6;
+
+    this.ORDER = Fp2.ORDER; // TODO: verify if it's unuesd
+    this.BITS = 2 * Fp6.BITS;
+    this.BYTES = 2 * Fp6.BYTES;
+    this.isLE = Fp6.isLE;
+    this.ZERO = { c0: Fp6.ZERO, c1: Fp6.ZERO };
+    this.ONE = { c0: Fp6.ONE, c1: Fp6.ZERO };
+
+    this.FROBENIUS_COEFFICIENTS = calcFrobeniusCoefficients(
+      Fp2,
+      Fp2.NONRESIDUE,
+      Fp.ORDER,
+      12,
+      1,
+      6
+    )[0];
+    this.X_LEN = opts.X_LEN;
+    this.finalExponentiate = opts.Fp12finalExponentiate;
+  }
+  create(num: Fp12) {
+    return num;
+  }
+  isValid({ c0, c1 }: Fp12) {
+    const { Fp6 } = this;
+    return Fp6.isValid(c0) && Fp6.isValid(c1);
+  }
+  is0({ c0, c1 }: Fp12) {
+    const { Fp6 } = this;
+    return Fp6.is0(c0) && Fp6.is0(c1);
+  }
+  isValidNot0(num: Fp12) {
+    return !this.is0(num) && this.isValid(num);
+  }
+  neg({ c0, c1 }: Fp12) {
+    const { Fp6 } = this;
+    return { c0: Fp6.neg(c0), c1: Fp6.neg(c1) };
+  }
+  eql({ c0, c1 }: Fp12, { c0: r0, c1: r1 }: Fp12) {
+    const { Fp6 } = this;
+    return Fp6.eql(c0, r0) && Fp6.eql(c1, r1);
+  }
+  sqrt(_: any): any {
+    notImplemented();
+  }
+  inv({ c0, c1 }: Fp12) {
+    const { Fp6 } = this;
+    let t = Fp6.inv(Fp6.sub(Fp6.sqr(c0), Fp6.mulByNonresidue(Fp6.sqr(c1)))); // 1 / (c0² - c1² * v)
+    return { c0: Fp6.mul(c0, t), c1: Fp6.neg(Fp6.mul(c1, t)) }; // ((C0 * T) * T) + (-C1 * T) * w
+  }
+  div(lhs: Fp12, rhs: Fp12) {
+    const { Fp6 } = this;
+    const { Fp2 } = Fp6;
+    const { Fp } = Fp2;
+    return this.mul(lhs, typeof rhs === 'bigint' ? Fp.inv(Fp.create(rhs)) : this.inv(rhs));
+  }
+  pow(num: Fp12, power: bigint): Fp12 {
+    return mod.FpPow(this, num, power);
+  }
+  invertBatch(nums: Fp12[]): Fp12[] {
+    return mod.FpInvertBatch(this, nums);
+  }
+
+  // Normalized
+  add({ c0, c1 }: Fp12, { c0: r0, c1: r1 }: Fp12) {
+    const { Fp6 } = this;
+    return {
+      c0: Fp6.add(c0, r0),
+      c1: Fp6.add(c1, r1),
+    };
+  }
+  sub({ c0, c1 }: Fp12, { c0: r0, c1: r1 }: Fp12) {
+    const { Fp6 } = this;
+    return {
+      c0: Fp6.sub(c0, r0),
+      c1: Fp6.sub(c1, r1),
+    };
+  }
+  mul({ c0, c1 }: Fp12, rhs: Fp12 | bigint) {
+    const { Fp6 } = this;
     if (typeof rhs === 'bigint') return { c0: Fp6.mul(c0, rhs), c1: Fp6.mul(c1, rhs) };
@@ -495,4 +713,5 @@ let { c0: r0, c1: r1 } = rhs;
     };
-  };
-  const Fp12Square = ({ c0, c1 }: Fp12) => {
+  }
+  sqr({ c0, c1 }: Fp12) {
+    const { Fp6 } = this;
     let ab = Fp6.mul(c0, c1); // c0 * c1
@@ -507,124 +726,153 @@ return {
     }; // AB + AB
-  };
-  function Fp4Square(a: Fp2, b: Fp2): { first: Fp2; second: Fp2 } {
-    const a2 = Fp2.sqr(a);
-    const b2 = Fp2.sqr(b);
+  }
+  // NonNormalized stuff
+  addN(a: Fp12, b: Fp12): Fp12 {
+    return this.add(a, b);
+  }
+  subN(a: Fp12, b: Fp12): Fp12 {
+    return this.sub(a, b);
+  }
+  mulN(a: Fp12, b: Fp12): Fp12 {
+    return this.mul(a, b);
+  }
+  sqrN(a: Fp12): Fp12 {
+    return this.sqr(a);
+  }
+
+  // Bytes utils
+  fromBytes(b: Uint8Array): Fp12 {
+    const { Fp6 } = this;
+    if (b.length !== this.BYTES) throw new Error('fromBytes invalid length=' + b.length);
     return {
-      first: Fp2.add(Fp2.mulByNonresidue(b2), a2), // b² * Nonresidue + a²
-      second: Fp2.sub(Fp2.sub(Fp2.sqr(Fp2.add(a, b)), a2), b2), // (a + b)² - a² - b²
+      c0: Fp6.fromBytes(b.subarray(0, Fp6.BYTES)),
+      c1: Fp6.fromBytes(b.subarray(Fp6.BYTES)),
     };
   }
-
-  const Fp12: Fp12Bls = {
-    ORDER: Fp2.ORDER, // TODO: unused, but need to verify
-    isLE: Fp6.isLE,
-    BITS: 2 * Fp6.BITS,
-    BYTES: 2 * Fp6.BYTES,
-    MASK: bitMask(2 * Fp6.BITS),
-    ZERO: { c0: Fp6.ZERO, c1: Fp6.ZERO },
-    ONE: { c0: Fp6.ONE, c1: Fp6.ZERO },
-    create: (num) => num,
-    isValid: ({ c0, c1 }) => Fp6.isValid(c0) && Fp6.isValid(c1),
-    is0: ({ c0, c1 }) => Fp6.is0(c0) && Fp6.is0(c1),
-    isValidNot0: (num) => !Fp12.is0(num) && Fp12.isValid(num),
-    neg: ({ c0, c1 }) => ({ c0: Fp6.neg(c0), c1: Fp6.neg(c1) }),
-    eql: ({ c0, c1 }, { c0: r0, c1: r1 }) => Fp6.eql(c0, r0) && Fp6.eql(c1, r1),
-    sqrt: notImplemented,
-    inv: ({ c0, c1 }) => {
-      let t = Fp6.inv(Fp6.sub(Fp6.sqr(c0), Fp6.mulByNonresidue(Fp6.sqr(c1)))); // 1 / (c0² - c1² * v)
-      return { c0: Fp6.mul(c0, t), c1: Fp6.neg(Fp6.mul(c1, t)) }; // ((C0 * T) * T) + (-C1 * T) * w
-    },
-    div: (lhs, rhs) =>
-      Fp12.mul(lhs, typeof rhs === 'bigint' ? Fp.inv(Fp.create(rhs)) : Fp12.inv(rhs)),
-    pow: (num, power) => mod.FpPow(Fp12, num, power),
-    invertBatch: (nums) => mod.FpInvertBatch(Fp12, nums),
-    // Normalized
-    add: Fp12Add,
-    sub: Fp12Subtract,
-    mul: Fp12Multiply,
-    sqr: Fp12Square,
-    // NonNormalized stuff
-    addN: Fp12Add,
-    subN: Fp12Subtract,
-    mulN: Fp12Multiply,
-    sqrN: Fp12Square,
-
-    // Bytes utils
-    fromBytes: (b: Uint8Array): Fp12 => {
-      if (b.length !== Fp12.BYTES) throw new Error('fromBytes invalid length=' + b.length);
-      return {
-        c0: Fp6.fromBytes(b.subarray(0, Fp6.BYTES)),
-        c1: Fp6.fromBytes(b.subarray(Fp6.BYTES)),
-      };
-    },
-    toBytes: ({ c0, c1 }): Uint8Array => concatBytes(Fp6.toBytes(c0), Fp6.toBytes(c1)),
-    cmov: ({ c0, c1 }, { c0: r0, c1: r1 }, c) => ({
+  toBytes({ c0, c1 }: Fp12): Uint8Array {
+    const { Fp6 } = this;
+    return concatBytes(Fp6.toBytes(c0), Fp6.toBytes(c1));
+  }
+  cmov({ c0, c1 }: Fp12, { c0: r0, c1: r1 }: Fp12, c: boolean) {
+    const { Fp6 } = this;
+    return {
       c0: Fp6.cmov(c0, r0, c),
       c1: Fp6.cmov(c1, r1, c),
-    }),
-    // Utils
-    // toString() {
-    //   return '' + 'Fp12(' + this.c0 + this.c1 + '* w');
-    // },
-    // fromTuple(c: [Fp6, Fp6]) {
-    //   return new Fp12(...c);
-    // }
-    fromBigTwelve: (t: BigintTwelve): Fp12 => ({
+    };
+  }
+  // Utils
+  // toString() {
+  //   return '' + 'Fp12(' + this.c0 + this.c1 + '* w');
+  // },
+  // fromTuple(c: [Fp6, Fp6]) {
+  //   return new Fp12(...c);
+  // }
+  fromBigTwelve(t: BigintTwelve): Fp12 {
+    const { Fp6 } = this;
+    return {
       c0: Fp6.fromBigSix(t.slice(0, 6) as BigintSix),
       c1: Fp6.fromBigSix(t.slice(6, 12) as BigintSix),
-    }),
-    // Raises to q**i -th power
-    frobeniusMap(lhs, power: number) {
-      const { c0, c1, c2 } = Fp6.frobeniusMap(lhs.c1, power);
-      const coeff = FP12_FROBENIUS_COEFFICIENTS[power % 12];
-      return {
-        c0: Fp6.frobeniusMap(lhs.c0, power),
-        c1: Fp6.create({
-          c0: Fp2.mul(c0, coeff),
-          c1: Fp2.mul(c1, coeff),
-          c2: Fp2.mul(c2, coeff),
-        }),
-      };
-    },
-    mulByFp2: ({ c0, c1 }, rhs: Fp2): Fp12 => ({
+    };
+  }
+  // Raises to q**i -th power
+  frobeniusMap(lhs: Fp12, power: number) {
+    const { Fp6 } = this;
+    const { Fp2 } = Fp6;
+    const { c0, c1, c2 } = Fp6.frobeniusMap(lhs.c1, power);
+    const coeff = this.FROBENIUS_COEFFICIENTS[power % 12];
+    return {
+      c0: Fp6.frobeniusMap(lhs.c0, power),
+      c1: Fp6.create({
+        c0: Fp2.mul(c0, coeff),
+        c1: Fp2.mul(c1, coeff),
+        c2: Fp2.mul(c2, coeff),
+      }),
+    };
+  }
+  mulByFp2({ c0, c1 }: Fp12, rhs: Fp2): Fp12 {
+    const { Fp6 } = this;
+    return {
       c0: Fp6.mulByFp2(c0, rhs),
       c1: Fp6.mulByFp2(c1, rhs),
-    }),
-    conjugate: ({ c0, c1 }): Fp12 => ({ c0, c1: Fp6.neg(c1) }),
-    // Sparse multiplication
-    mul014: ({ c0, c1 }, o0: Fp2, o1: Fp2, o4: Fp2) => {
-      let t0 = Fp6.mul01(c0, o0, o1);
-      let t1 = Fp6.mul1(c1, o4);
-      return {
-        c0: Fp6.add(Fp6.mulByNonresidue(t1), t0), // T1 * v + T0
-        // (c1 + c0) * [o0, o1+o4] - T0 - T1
-        c1: Fp6.sub(Fp6.sub(Fp6.mul01(Fp6.add(c1, c0), o0, Fp2.add(o1, o4)), t0), t1),
-      };
-    },
-    mul034: ({ c0, c1 }, o0: Fp2, o3: Fp2, o4: Fp2) => {
-      const a = Fp6.create({
-        c0: Fp2.mul(c0.c0, o0),
-        c1: Fp2.mul(c0.c1, o0),
-        c2: Fp2.mul(c0.c2, o0),
-      });
-      const b = Fp6.mul01(c1, o3, o4);
-      const e = Fp6.mul01(Fp6.add(c0, c1), Fp2.add(o0, o3), o4);
-      return {
-        c0: Fp6.add(Fp6.mulByNonresidue(b), a),
-        c1: Fp6.sub(e, Fp6.add(a, b)),
-      };
-    },
+    };
+  }
+  conjugate({ c0, c1 }: Fp12): Fp12 {
+    return { c0, c1: this.Fp6.neg(c1) };
+  }
+  // Sparse multiplication
+  mul014({ c0, c1 }: Fp12, o0: Fp2, o1: Fp2, o4: Fp2) {
+    const { Fp6 } = this;
+    const { Fp2 } = Fp6;
+    let t0 = Fp6.mul01(c0, o0, o1);
+    let t1 = Fp6.mul1(c1, o4);
+    return {
+      c0: Fp6.add(Fp6.mulByNonresidue(t1), t0), // T1 * v + T0
+      // (c1 + c0) * [o0, o1+o4] - T0 - T1
+      c1: Fp6.sub(Fp6.sub(Fp6.mul01(Fp6.add(c1, c0), o0, Fp2.add(o1, o4)), t0), t1),
+    };
+  }
+  mul034({ c0, c1 }: Fp12, o0: Fp2, o3: Fp2, o4: Fp2) {
+    const { Fp6 } = this;
+    const { Fp2 } = Fp6;
+    const a = Fp6.create({
+      c0: Fp2.mul(c0.c0, o0),
+      c1: Fp2.mul(c0.c1, o0),
+      c2: Fp2.mul(c0.c2, o0),
+    });
+    const b = Fp6.mul01(c1, o3, o4);
+    const e = Fp6.mul01(Fp6.add(c0, c1), Fp2.add(o0, o3), o4);
+    return {
+      c0: Fp6.add(Fp6.mulByNonresidue(b), a),
+      c1: Fp6.sub(e, Fp6.add(a, b)),
+    };
+  }
 
-    // A cyclotomic group is a subgroup of Fp^n defined by
-    //   GΦₙ(p) = {α ∈ Fpⁿ : α^Φₙ(p) = 1}
-    // The result of any pairing is in a cyclotomic subgroup
-    // https://eprint.iacr.org/2009/565.pdf
-    _cyclotomicSquare: opts.Fp12cyclotomicSquare,
-    _cyclotomicExp: opts.Fp12cyclotomicExp,
-    // https://eprint.iacr.org/2010/354.pdf
-    // https://eprint.iacr.org/2009/565.pdf
-    finalExponentiate: opts.Fp12finalExponentiate,
-  };
+  // A cyclotomic group is a subgroup of Fp^n defined by
+  //   GΦₙ(p) = {α ∈ Fpⁿ : α^Φₙ(p) = 1}
+  // The result of any pairing is in a cyclotomic subgroup
+  // https://eprint.iacr.org/2009/565.pdf
+  // https://eprint.iacr.org/2010/354.pdf
+  _cyclotomicSquare({ c0, c1 }: Fp12): Fp12 {
+    const { Fp6 } = this;
+    const { Fp2 } = Fp6;
+    const { c0: c0c0, c1: c0c1, c2: c0c2 } = c0;
+    const { c0: c1c0, c1: c1c1, c2: c1c2 } = c1;
+    const { first: t3, second: t4 } = Fp2.Fp4Square(c0c0, c1c1);
+    const { first: t5, second: t6 } = Fp2.Fp4Square(c1c0, c0c2);
+    const { first: t7, second: t8 } = Fp2.Fp4Square(c0c1, c1c2);
+    const t9 = Fp2.mulByNonresidue(t8); // T8 * (u + 1)
+    return {
+      c0: Fp6.create({
+        c0: Fp2.add(Fp2.mul(Fp2.sub(t3, c0c0), _2n), t3), // 2 * (T3 - c0c0)  + T3
+        c1: Fp2.add(Fp2.mul(Fp2.sub(t5, c0c1), _2n), t5), // 2 * (T5 - c0c1)  + T5
+        c2: Fp2.add(Fp2.mul(Fp2.sub(t7, c0c2), _2n), t7),
+      }), // 2 * (T7 - c0c2)  + T7
+      c1: Fp6.create({
+        c0: Fp2.add(Fp2.mul(Fp2.add(t9, c1c0), _2n), t9), // 2 * (T9 + c1c0) + T9
+        c1: Fp2.add(Fp2.mul(Fp2.add(t4, c1c1), _2n), t4), // 2 * (T4 + c1c1) + T4
+        c2: Fp2.add(Fp2.mul(Fp2.add(t6, c1c2), _2n), t6),
+      }),
+    }; // 2 * (T6 + c1c2) + T6
+  }
+  // https://eprint.iacr.org/2009/565.pdf
+  _cyclotomicExp(num: Fp12, n: bigint): Fp12 {
+    let z = this.ONE;
+    for (let i = this.X_LEN - 1; i >= 0; i--) {
+      z = this._cyclotomicSquare(z);
+      if (bitGet(n, i)) z = this.mul(z, num);
+    }
+    return z;
+  }
+}
 
-  return { Fp, Fp2, Fp6, Fp12, Fp4Square };
+export function tower12(opts: Tower12Opts): {
+  Fp: Readonly<mod.IField<bigint> & Required<Pick<mod.IField<bigint>, 'isOdd'>>>;
+  Fp2: Fp2Bls;
+  Fp6: Fp6Bls;
+  Fp12: Fp12Bls;
+} {
+  const Fp = mod.Field(opts.ORDER);
+  const Fp2 = new _Field2(Fp, opts);
+  const Fp6 = new _Field6(Fp2);
+  const Fp12 = new _Field12(Fp6, opts);
+  return { Fp, Fp2, Fp6, Fp12 };
 }

src/bls12-381.ts

@@ -85,3 +85,2 @@ /**
   abytes,
-  bitGet,
   bitLen,
@@ -151,6 +150,9 @@ bitMask,
 // CURVE FIELDS
-export const bls12_381_Fr: IField<bigint> = Field(bls12_381_CURVE_G1.n, { modFromBytes: true });
-const { Fp, Fp2, Fp6, Fp4Square, Fp12 } = tower12({
-  // Order of Fp
+export const bls12_381_Fr: IField<bigint> = Field(bls12_381_CURVE_G1.n, {
+  modFromBytes: true,
+  isLE: true,
+});
+const { Fp, Fp2, Fp6, Fp12 } = tower12({
   ORDER: bls12_381_CURVE_G1.p,
+  X_LEN: BLS_X_LEN,
   // Finite extension field over irreducible polynominal.
@@ -165,37 +167,2 @@ // Fp(u) / (u² - β) where β = -1
   },
-  // Fp12
-  // A cyclotomic group is a subgroup of Fp^n defined by
-  //   GΦₙ(p) = {α ∈ Fpⁿ : α^Φₙ(p) = 1}
-  // The result of any pairing is in a cyclotomic subgroup
-  // https://eprint.iacr.org/2009/565.pdf
-  Fp12cyclotomicSquare: ({ c0, c1 }): Fp12 => {
-    const { c0: c0c0, c1: c0c1, c2: c0c2 } = c0;
-    const { c0: c1c0, c1: c1c1, c2: c1c2 } = c1;
-    const { first: t3, second: t4 } = Fp4Square(c0c0, c1c1);
-    const { first: t5, second: t6 } = Fp4Square(c1c0, c0c2);
-    const { first: t7, second: t8 } = Fp4Square(c0c1, c1c2);
-    const t9 = Fp2.mulByNonresidue(t8); // T8 * (u + 1)
-    return {
-      c0: Fp6.create({
-        c0: Fp2.add(Fp2.mul(Fp2.sub(t3, c0c0), _2n), t3), // 2 * (T3 - c0c0)  + T3
-        c1: Fp2.add(Fp2.mul(Fp2.sub(t5, c0c1), _2n), t5), // 2 * (T5 - c0c1)  + T5
-        c2: Fp2.add(Fp2.mul(Fp2.sub(t7, c0c2), _2n), t7),
-      }), // 2 * (T7 - c0c2)  + T7
-      c1: Fp6.create({
-        c0: Fp2.add(Fp2.mul(Fp2.add(t9, c1c0), _2n), t9), // 2 * (T9 + c1c0) + T9
-        c1: Fp2.add(Fp2.mul(Fp2.add(t4, c1c1), _2n), t4), // 2 * (T4 + c1c1) + T4
-        c2: Fp2.add(Fp2.mul(Fp2.add(t6, c1c2), _2n), t6),
-      }),
-    }; // 2 * (T6 + c1c2) + T6
-  },
-  Fp12cyclotomicExp(num, n) {
-    let z = Fp12.ONE;
-    for (let i = BLS_X_LEN - 1; i >= 0; i--) {
-      z = Fp12._cyclotomicSquare(z);
-      if (bitGet(n, i)) z = Fp12.mul(z, num);
-    }
-    return z;
-  },
-  // https://eprint.iacr.org/2010/354.pdf
-  // https://eprint.iacr.org/2009/565.pdf
   Fp12finalExponentiate: (num) => {
@@ -202,0 +169,0 @@ const x = BLS_X;

src/bn254.ts

@@ -68,3 +68,3 @@ /**
 import { type CurveFn, weierstrass, type WeierstrassOpts } from './abstract/weierstrass.ts';
-import { bitGet, bitLen, notImplemented } from './utils.ts';
+import { bitLen, notImplemented } from './utils.ts';
 // prettier-ignore
@@ -98,38 +98,7 @@ const _0n = BigInt(0), _1n = BigInt(1), _2n = BigInt(2), _3n = BigInt(3);
 
-const { Fp, Fp2, Fp6, Fp4Square, Fp12 } = tower12({
+const { Fp, Fp2, Fp6, Fp12 } = tower12({
   ORDER: bn254_G1_CURVE.p,
+  X_LEN: BN_X_LEN,
   FP2_NONRESIDUE: [BigInt(9), _1n],
   Fp2mulByB: (num) => Fp2.mul(num, Fp2B),
-  // The result of any pairing is in a cyclotomic subgroup
-  // https://eprint.iacr.org/2009/565.pdf
-  Fp12cyclotomicSquare: ({ c0, c1 }): Fp12 => {
-    const { c0: c0c0, c1: c0c1, c2: c0c2 } = c0;
-    const { c0: c1c0, c1: c1c1, c2: c1c2 } = c1;
-    const { first: t3, second: t4 } = Fp4Square(c0c0, c1c1);
-    const { first: t5, second: t6 } = Fp4Square(c1c0, c0c2);
-    const { first: t7, second: t8 } = Fp4Square(c0c1, c1c2);
-    let t9 = Fp2.mulByNonresidue(t8); // T8 * (u + 1)
-    return {
-      c0: Fp6.create({
-        c0: Fp2.add(Fp2.mul(Fp2.sub(t3, c0c0), _2n), t3), // 2 * (T3 - c0c0)  + T3
-        c1: Fp2.add(Fp2.mul(Fp2.sub(t5, c0c1), _2n), t5), // 2 * (T5 - c0c1)  + T5
-        c2: Fp2.add(Fp2.mul(Fp2.sub(t7, c0c2), _2n), t7),
-      }), // 2 * (T7 - c0c2)  + T7
-      c1: Fp6.create({
-        c0: Fp2.add(Fp2.mul(Fp2.add(t9, c1c0), _2n), t9), // 2 * (T9 + c1c0) + T9
-        c1: Fp2.add(Fp2.mul(Fp2.add(t4, c1c1), _2n), t4), // 2 * (T4 + c1c1) + T4
-        c2: Fp2.add(Fp2.mul(Fp2.add(t6, c1c2), _2n), t6),
-      }),
-    }; // 2 * (T6 + c1c2) + T6
-  },
-  Fp12cyclotomicExp(num, n) {
-    let z = Fp12.ONE;
-    for (let i = BN_X_LEN - 1; i >= 0; i--) {
-      z = Fp12._cyclotomicSquare(z);
-      if (bitGet(n, i)) z = Fp12.mul(z, num);
-    }
-    return z;
-  },
-  // https://eprint.iacr.org/2010/354.pdf
-  // https://eprint.iacr.org/2009/565.pdf
   Fp12finalExponentiate: (num) => {
@@ -136,0 +105,0 @@ const powMinusX = (num: Fp12) => Fp12.conjugate(Fp12._cyclotomicExp(num, BN_X));

src/ed25519.ts

@@ -38,10 +38,10 @@ /**
 import { montgomery, type MontgomeryECDH as XCurveFn } from './abstract/montgomery.ts';
-import { bytesToNumberLE, ensureBytes, equalBytes, numberToBytesLE, type Hex } from './utils.ts';
+import { bytesToNumberLE, ensureBytes, equalBytes, type Hex } from './utils.ts';
 
 // prettier-ignore
-const _0n = BigInt(0), _1n = BigInt(1), _2n = BigInt(2), _3n = BigInt(3);
+const _0n = /* @__PURE__ */ BigInt(0), _1n = BigInt(1), _2n = BigInt(2), _3n = BigInt(3);
 // prettier-ignore
 const _5n = BigInt(5), _8n = BigInt(8);
 
-// 2n**255n-19n
+// P = 2n**255n-19n
 const ed25519_CURVE_p = BigInt(
@@ -51,7 +51,6 @@ '0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffed'
 
-// P = 2n**255n - 19n
 // N = 2n**252n + 27742317777372353535851937790883648493n
 // a = Fp.create(BigInt(-1))
 // d = -121665/121666 a.k.a. Fp.neg(121665 * Fp.inv(121666))
-const ed25519_CURVE: EdwardsOpts = {
+const ed25519_CURVE: EdwardsOpts = /* @__PURE__ */ (() => ({
   p: ed25519_CURVE_p,
@@ -64,3 +63,3 @@ n: BigInt('0x1000000000000000000000000000000014def9dea2f79cd65812631a5cf5d3ed'),
   Gy: BigInt('0x6666666666666666666666666666666666666666666666666666666666666658'),
-};
+}))();
 
@@ -186,3 +185,3 @@ function ed25519_pow_2_252_3(x: bigint) {
 export const x25519: XCurveFn = /* @__PURE__ */ (() => {
-  const P = ed25519.CURVE.Fp.ORDER;
+  const P = Fp.ORDER;
   return montgomery({
@@ -203,4 +202,3 @@ P,
 // SageMath returns different root first and everything falls apart
-
-const ELL2_C1 = /* @__PURE__ */ (() => (Fp.ORDER + _3n) / _8n)(); // 1. c1 = (q + 3) / 8       # Integer arithmetic
+const ELL2_C1 = /* @__PURE__ */ (() => (ed25519_CURVE_p + _3n) / _8n)(); // 1. c1 = (q + 3) / 8       # Integer arithmetic
 const ELL2_C2 = /* @__PURE__ */ (() => Fp.pow(_2n, ELL2_C1))(); // 2. c2 = 2^c1
@@ -211,3 +209,3 @@ const ELL2_C3 = /* @__PURE__ */ (() => Fp.sqrt(Fp.neg(Fp.ONE)))(); // 3. c3 = sqrt(-1)
 function map_to_curve_elligator2_curve25519(u: bigint) {
-  const ELL2_C4 = (Fp.ORDER - _5n) / _8n; // 4. c4 = (q - 5) / 8       # Integer arithmetic
+  const ELL2_C4 = (ed25519_CURVE_p - _5n) / _8n; // 4. c4 = (q - 5) / 8       # Integer arithmetic
   const ELL2_J = BigInt(486662);
@@ -283,3 +281,3 @@
       encodeDST: 'edwards25519_XMD:SHA-512_ELL2_NU_',
-      p: Fp.ORDER,
+      p: ed25519_CURVE_p,
       m: 1,
@@ -328,3 +326,3 @@ k: 128,
   const { d } = ed25519_CURVE;
-  const P = Fp.ORDER;
+  const P = ed25519_CURVE_p;
   const mod = (n: bigint) => Fp.create(n);
@@ -412,3 +410,3 @@ const r = mod(SQRT_M1 * r0 * r0); // 1
     // 3. Check that s is non-negative, or else abort
-    if (!equalBytes(numberToBytesLE(s, 32), bytes) || isNegativeLE(s, P))
+    if (!equalBytes(Fp.toBytes(s), bytes) || isNegativeLE(s, P))
       throw new Error('invalid ristretto255 encoding 1');
@@ -475,3 +473,3 @@ const s2 = mod(s * s);
     if (isNegativeLE(s, P)) s = mod(-s);
-    return numberToBytesLE(s, 32); // 11
+    return Fp.toBytes(s); // 11
   }
@@ -507,7 +505,8 @@
     const DST = options?.DST || 'ristretto255_XMD:SHA-512_R255MAP_RO_';
-    return ristretto255_map(expand_message_xmd(msg, DST, 64, sha512));
+    const xmd = expand_message_xmd(msg, DST, 64, sha512);
+    return ristretto255_map(xmd);
   },
   hashToScalar(msg: Uint8Array, options: htfBasicOpts = { DST: _DST_scalar }) {
     const xmd = expand_message_xmd(msg, options.DST, 64, sha512);
-    return ristretto255.Point.Fn.create(bytesToNumberLE(xmd));
+    return Fn.create(bytesToNumberLE(xmd));
   },
@@ -514,0 +513,0 @@ };

src/ed448.ts

@@ -11,8 +11,3 @@ /**
 import { shake256 } from '@noble/hashes/sha3.js';
-import {
-  abytes,
-  concatBytes,
-  utf8ToBytes,
-  createHasher as wrapConstructor,
-} from '@noble/hashes/utils.js';
+import { abytes, concatBytes, createHasher as wrapConstructor } from '@noble/hashes/utils.js';
 import type { AffinePoint } from './abstract/curve.ts';
@@ -40,3 +35,3 @@ import { pippenger } from './abstract/curve.ts';
 import { montgomery, type MontgomeryECDH as XCurveFn } from './abstract/montgomery.ts';
-import { bytesToNumberLE, ensureBytes, equalBytes, numberToBytesLE, type Hex } from './utils.ts';
+import { asciiToBytes, bytesToNumberLE, ensureBytes, equalBytes, type Hex } from './utils.ts';
 
@@ -145,6 +140,10 @@ // edwards448 curve
 // Finite field 2n**448n - 2n**224n - 1n
+// The value fits in 448 bits, but we use 456-bit (57-byte) elements because of bitflags.
+// - ed25519 fits in 255 bits, allowing using last 1 byte for specifying bit flag of point negation.
+// - ed448 fits in 448 bits. We can't use last 1 byte: we can only use a bit 224 in the middle.
 const Fp = /* @__PURE__ */ (() => Field(ed448_CURVE.p, { BITS: 456, isLE: true }))();
-// RFC 7748 has 56-byte keys, RFC 8032 has 57-byte keys
-const Fn = /* @__PURE__ */ (() => Field(ed448_CURVE.n, { BITS: 448, isLE: true }))();
-// Fn456 has BITS: 456
+const Fn = /* @__PURE__ */ (() => Field(ed448_CURVE.n, { BITS: 456, isLE: true }))();
+// decaf448 uses 448-bit (56-byte) keys
+const Fp448 = /* @__PURE__ */ (() => Field(ed448_CURVE.p, { BITS: 448, isLE: true }))();
+const Fn448 = /* @__PURE__ */ (() => Field(ed448_CURVE.n, { BITS: 448, isLE: true }))();
 
@@ -155,3 +154,3 @@ // SHAKE256(dom4(phflag,context)||x, 114)
   return concatBytes(
-    utf8ToBytes('SigEd448'),
+    asciiToBytes('SigEd448'),
     new Uint8Array([phflag ? 1 : 0, ctx.length]),
@@ -169,2 +168,3 @@ ctx,
   Fn,
+  nBitLength: Fn.BITS,
   hash: shake256_114,
@@ -325,9 +325,2 @@ adjustScalarBytes,
 
-const MAX_448B = /* @__PURE__ */ BigInt(
-  '0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff'
-);
-const bytes448ToNumberLE = (bytes: Uint8Array) => Fp.create(bytesToNumberLE(bytes) & MAX_448B);
-
-type ExtendedPoint = EdwardsPoint;
-
 /**
@@ -338,3 +331,3 @@ * Elligator map for hash-to-curve of decaf448.
  */
-function calcElligatorDecafMap(r0: bigint): ExtendedPoint {
+function calcElligatorDecafMap(r0: bigint): EdwardsPoint {
   const { d } = ed448_CURVE;
@@ -370,5 +363,9 @@ const P = Fp.ORDER;
   abytes(bytes, 112);
-  const r1 = bytes448ToNumberLE(bytes.slice(0, 56));
+  const skipValidation = true;
+  // Note: Similar to the field element decoding described in
+  // [RFC7748], and unlike the field element decoding described in
+  // Section 5.3.1, non-canonical values are accepted.
+  const r1 = Fp448.create(Fp448.fromBytes(bytes.subarray(0, 56), skipValidation));
   const R1 = calcElligatorDecafMap(r1);
-  const r2 = bytes448ToNumberLE(bytes.slice(56, 112));
+  const r2 = Fp448.create(Fp448.fromBytes(bytes.subarray(56, 112), skipValidation));
   const R2 = calcElligatorDecafMap(r2);
@@ -379,5 +376,5 @@ return new _DecafPoint(R1.add(R2));
 /**
- * Each ed448/ExtendedPoint has 4 different equivalent points. This can be
+ * Each ed448/EdwardsPoint has 4 different equivalent points. This can be
  * a source of bugs for protocols like ring signatures. Decaf was created to solve this.
- * Decaf point operates in X:Y:Z:T extended coordinates like ExtendedPoint,
+ * Decaf point operates in X:Y:Z:T extended coordinates like EdwardsPoint,
  * but it should work in its own namespace: do not combine those two.
@@ -396,8 +393,8 @@ * See [RFC9496](https://www.rfc-editor.org/rfc/rfc9496).
   static Fp: IField<bigint> =
-    /* @__PURE__ */ (() => Fp)();
+    /* @__PURE__ */ (() => Fp448)();
   // prettier-ignore
   static Fn: IField<bigint> =
-    /* @__PURE__ */ (() => Fn)();
+    /* @__PURE__ */ (() => Fn448)();
 
-  constructor(ep: ExtendedPoint) {
+  constructor(ep: EdwardsPoint) {
     super(ep);
@@ -427,8 +424,9 @@ }
     const P = Fp.ORDER;
-    const mod = (n: bigint) => Fp.create(n);
-    const s = bytes448ToNumberLE(bytes);
+    const mod = (n: bigint) => Fp448.create(n);
+    const s = Fp448.fromBytes(bytes);
 
     // 1. Check that s_bytes is the canonical encoding of a field element, or else abort.
     // 2. Check that s is non-negative, or else abort
-    if (!equalBytes(numberToBytesLE(s, 56), bytes) || isNegativeLE(s, P))
+
+    if (!equalBytes(Fn448.toBytes(s), bytes) || isNegativeLE(s, P))
       throw new Error('invalid decaf448 encoding 1');
@@ -476,16 +474,11 @@
     const mod = (n: bigint) => Fp.create(n);
-
     const u1 = mod(mod(X + T) * mod(X - T)); // 1
     const x2 = mod(X * X);
     const { value: invsqrt } = invertSqrt(mod(u1 * ONE_MINUS_D * x2)); // 2
-
     let ratio = mod(invsqrt * u1 * SQRT_MINUS_D); // 3
     if (isNegativeLE(ratio, P)) ratio = mod(-ratio);
-
     const u2 = mod(INVSQRT_MINUS_D * ratio * Z - T); // 4
-
     let s = mod(ONE_MINUS_D * invsqrt * X * u2); // 5
     if (isNegativeLE(s, P)) s = mod(-s);
-
-    return numberToBytesLE(s, 56);
+    return Fn448.toBytes(s);
   }
@@ -501,5 +494,4 @@
     const { X: X2, Y: Y2 } = other.ep;
-    const mod = (n: bigint) => Fp.create(n);
     // (x1 * y2 == y1 * x2)
-    return mod(X1 * Y2) === mod(Y1 * X2);
+    return Fp.create(X1 * Y2) === Fp.create(Y1 * X2);
   }
@@ -522,4 +514,9 @@
   },
+  // Warning: has big modulo bias of 2^-64.
+  // RFC is invalid. RFC says "use 64-byte xof", while for 2^-112 bias
+  // it must use 84-byte xof (56+56/2), not 64.
   hashToScalar(msg: Uint8Array, options: htfBasicOpts = { DST: _DST_scalar }) {
-    return Fn.create(bytesToNumberLE(expand_message_xof(msg, options.DST, 64, 256, shake256)));
+    // Can't use `Fn448.fromBytes()`. 64-byte input => 56-byte field element
+    const xof = expand_message_xof(msg, options.DST, 64, 256, shake256);
+    return Fn448.create(bytesToNumberLE(xof));
   },
@@ -564,3 +561,2 @@ };
   decaf448_hasher.hashToCurve as DcfHasher)();
-
 /** @deprecated use `ed448.utils.toMontgomery` */
@@ -570,4 +566,3 @@ export function edwardsToMontgomeryPub(edwardsPub: string | Uint8Array): Uint8Array {
 }
-
 /** @deprecated use `ed448.utils.toMontgomery` */
 export const edwardsToMontgomery: typeof edwardsToMontgomeryPub = edwardsToMontgomeryPub;

src/secp256k1.ts

@@ -30,3 +30,2 @@ /**
 import {
-  aInRange,
   bytesToNumberBE,
@@ -130,6 +129,3 @@ concatBytes,
 const pointToBytes = (point: PointType<bigint>) => point.toBytes(true).slice(1);
-const numTo32b = (n: bigint) => numberToBytesBE(n, 32);
-const modP = (x: bigint) => mod(x, secp256k1_CURVE.p);
-const modN = (x: bigint) => mod(x, secp256k1_CURVE.n);
-const Point = /* @__PURE__ */ (() => secp256k1.Point)();
+const Pointk1 = /* @__PURE__ */ (() => secp256k1.Point)();
 const hasEven = (y: bigint) => y % _2n === _0n;
@@ -139,6 +135,6 @@
 function schnorrGetExtPubKey(priv: PrivKey) {
-  // TODO: replace with Point.Fn.fromBytes(priv)
-  let d_ = _normFnElement(Point.Fn, priv);
-  let p = Point.BASE.multiply(d_); // P = d'⋅G; 0 < d' < n check is done inside
-  const scalar = hasEven(p.y) ? d_ : modN(-d_);
+  const { Fn, BASE } = Pointk1;
+  const d_ = _normFnElement(Fn, priv);
+  const p = BASE.multiply(d_); // P = d'⋅G; 0 < d' < n check is done inside
+  const scalar = hasEven(p.y) ? d_ : Fn.neg(d_);
   return { scalar, bytes: pointToBytes(p) };
@@ -151,8 +147,11 @@ }
 function lift_x(x: bigint): PointType<bigint> {
-  aInRange('x', x, _1n, secp256k1_CURVE.p); // Fail if x ≥ p.
-  const xx = modP(x * x);
-  const c = modP(xx * x + BigInt(7)); // Let c = x³ + 7 mod p.
-  let y = sqrtMod(c); // Let y = c^(p+1)/4 mod p.
-  if (!hasEven(y)) y = modP(-y); // Return the unique point P such that x(P) = x and
-  const p = Point.fromAffine({ x, y }); // y(P) = y if y mod 2 = 0 or y(P) = p-y otherwise.
+  const Fp = Fpk1;
+  if (!Fp.isValidNot0(x)) throw new Error('invalid x: Fail if x ≥ p');
+  const xx = Fp.create(x * x);
+  const c = Fp.create(xx * x + BigInt(7)); // Let c = x³ + 7 mod p.
+  let y = Fp.sqrt(c); // Let y = c^(p+1)/4 mod p. Same as sqrt().
+  // Return the unique point P such that x(P) = x and
+  // y(P) = y if y mod 2 = 0 or y(P) = p-y otherwise.
+  if (!hasEven(y)) y = Fp.neg(y);
+  const p = Pointk1.fromAffine({ x, y });
   p.assertValidity();
@@ -166,3 +165,3 @@ return p;
 function challenge(...args: Uint8Array[]): bigint {
-  return modN(num(taggedHash('BIP0340/challenge', ...args)));
+  return Pointk1.Fn.create(num(taggedHash('BIP0340/challenge', ...args)));
 }
@@ -182,14 +181,14 @@
 function schnorrSign(message: Hex, secretKey: PrivKey, auxRand: Hex = randomBytes(32)): Uint8Array {
+  const { Fn } = Pointk1;
   const m = ensureBytes('message', message);
   const { bytes: px, scalar: d } = schnorrGetExtPubKey(secretKey); // checks for isWithinCurveOrder
   const a = ensureBytes('auxRand', auxRand, 32); // Auxiliary random data a: a 32-byte array
-  const t = numTo32b(d ^ num(taggedHash('BIP0340/aux', a))); // Let t be the byte-wise xor of bytes(d) and hash/aux(a)
+  const t = Fn.toBytes(d ^ num(taggedHash('BIP0340/aux', a))); // Let t be the byte-wise xor of bytes(d) and hash/aux(a)
   const rand = taggedHash('BIP0340/nonce', t, px, m); // Let rand = hash/nonce(t || bytes(P) || m)
-  const k_ = modN(num(rand)); // Let k' = int(rand) mod n
-  if (k_ === _0n) throw new Error('sign failed: k is zero'); // Fail if k' = 0.
-  const { bytes: rx, scalar: k } = schnorrGetExtPubKey(k_); // Let R = k'⋅G.
+  // Let k' = int(rand) mod n. Fail if k' = 0. Let R = k'⋅G
+  const { bytes: rx, scalar: k } = schnorrGetExtPubKey(rand);
   const e = challenge(rx, px, m); // Let e = int(hash/challenge(bytes(R) || bytes(P) || m)) mod n.
   const sig = new Uint8Array(64); // Let sig = bytes(R) || bytes((k + ed) mod n).
   sig.set(rx, 0);
-  sig.set(numTo32b(modN(k + e * d)), 32);
+  sig.set(Fn.toBytes(Fn.create(k + e * d)), 32);
   // If Verify(bytes(P), m, sig) (see below) returns failure, abort
@@ -205,2 +204,3 @@ if (!schnorrVerify(sig, m, px)) throw new Error('sign: Invalid signature produced');
 function schnorrVerify(signature: Hex, message: Hex, publicKey: Hex): boolean {
+  const { Fn, BASE } = Pointk1;
   const sig = ensureBytes('signature', signature, 64);
@@ -215,5 +215,6 @@ const m = ensureBytes('message', message);
     if (!inRange(s, _1n, secp256k1_CURVE.n)) return false;
-    const e = challenge(numTo32b(r), pointToBytes(P), m); // int(challenge(bytes(r)||bytes(P)||m))%n
+    // int(challenge(bytes(r)||bytes(P)||m))%n
+    const e = challenge(Fn.toBytes(r), pointToBytes(P), m);
     // R = s⋅G - e⋅P, where -eP == (n-e)P
-    const R = Point.BASE.multiplyUnsafe(s).add(P.multiplyUnsafe(modN(-e)));
+    const R = BASE.multiplyUnsafe(s).add(P.multiplyUnsafe(Fn.neg(e)));
     const { x, y } = R.toAffine();
@@ -281,3 +282,3 @@ // Fail if is_infinite(R) / not has_even_y(R) / x(R) ≠ r.
     verify: schnorrVerify,
-    Point,
+    Point: Pointk1,
     utils: {
@@ -296,7 +297,7 @@ randomSecretKey: randomSecretKey,
     lengths: {
-      secret: size,
-      public: size,
+      secretKey: size,
+      publicKey: size,
+      publicKeyHasPrefix: false,
       signature: size * 2,
       seed: seedLength,
-      publicKeyHasPrefix: false,
     },
@@ -303,0 +304,0 @@ };

src/utils.ts

@@ -56,3 +56,3 @@ /**
   if (!bytes || (needsLen && len !== length)) {
-    const prefix = title && `"${title}"`;
+    const prefix = title && `"${title}" `;
     const ofLen = needsLen ? ` of length ${length}` : '';
@@ -59,0 +59,0 @@ const got = bytes ? `length=${len}` : `type=${typeof value}`;

utils.js

@@ -65,3 +65,3 @@ "use strict";
     if (!bytes || (needsLen && len !== length)) {
-        const prefix = title && `"${title}"`;
+        const prefix = title && `"${title}" `;
         const ofLen = needsLen ? ` of length ${length}` : '';
@@ -68,0 +68,0 @@ const got = bytes ? `length=${len}` : `type=${typeof value}`;

utils.js.map

@@ -1,1 +0,1 @@
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Improved metrics

Total package byte prevSize

2032871

0.28%

Lines of code

30301

1.55%

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