elliptic - npm Package Compare versions

Comparing version 0.13.2 to 0.14.0

lib/elliptic.js

 var elliptic = exports;
 
+elliptic.version = require('../package.json').version;
 elliptic.utils = require('./elliptic/utils');
@@ -4,0 +5,0 @@ elliptic.rand = require('./elliptic/rand');

lib/elliptic/curve.js

@@ -14,7 +14,165 @@ var assert = require('assert');
   this.mOne = new bn(1).toRed(this.red);
+  this.n = conf.n && new bn(conf.n, 16);
 
-  this.zeroA = this.a.cmpn(0) === 0;
+  this.zeroA = this.a.fromRed().cmpn(0) === 0;
+  this.threeA = this.a.fromRed().sub(this.p).cmpn(-3) === 0;
+
+  // If the curve is endomorphic, precalculate beta and lambda
+  this.endo = this._getEndomorphism(conf);
+
+  // Temporary arrays
+  this.t1 = new Array(4);
+  this.t2 = new Array(4);
+  this.t3 = new Array(4);
+  this.t4 = new Array(4);
+  this.t5 = new Array(4);
+  this.t6 = new Array(4);
 }
 module.exports = Curve;
 
+Curve.prototype._getEndomorphism = function _getEndomorphism(conf) {
+  // No efficient endomorphism
+  if (!this.zeroA || !this.n || this.p.modn(3) !== 1)
+    return;
+
+  // Compute beta and lambda, that lambda * P = (beta * Px; Py)
+  var beta = conf.beta ? new bn(conf.beta, 16).toRed(this.red) :
+      this._getEndoRoot(this.p).toRed(this.red);
+  var lambda = conf.lambda ? new bn(conf.lambda, 16) :
+      this.n && this._getEndoRoot(this.n);
+
+  // Get basis vectors, used for balanced length-two representation
+  var basis;
+  if (conf.basis) {
+    basis = conf.basis.map(function(vec) {
+      return {
+        a: new bn(vec.a, 16),
+        b: new bn(vec.b, 16),
+      };
+    });
+  } else {
+    basis = this._getEndoBasis(lambda);
+  }
+
+  return {
+    beta: beta,
+    lambda: lambda,
+    basis: basis
+  };
+};
+
+Curve.prototype._getEndoRoot = function _getEndoRoot(num) {
+  // Need to find smallest root for x^2 + x + 1 in F
+  // Lambda = (-1 +- Sqrt(-3)) / 2
+  //
+  var red = num === this.p ? this.red : bn.mont(num);
+  var tinv = new bn(2).toRed(red).redInvm();
+  var ntinv = tinv.redNeg();
+  var one = new bn(1).toRed(red);
+
+  var s = new bn(3).toRed(red).redNeg().redSqrt().redMul(tinv);
+
+  // XXX: This seems to be a bit wrong... It should verify that
+  // lambda and beta are actually from one endomorphism
+  var l1 = ntinv.redAdd(s).fromRed();
+  var l2 = ntinv.redSub(s).fromRed();
+  if (l1.cmp(l2) < 0)
+    return l1;
+  else
+    return l2;
+};
+
+Curve.prototype._getEndoBasis = function _getEndoBasis(lambda) {
+  // aprxSqrt >= sqrt(this.n)
+  var aprxSqrt = this.n.shrn(Math.floor(this.n.bitLength() / 2));
+
+  // 3.74
+  // Run EGCD, until r(L + 1) < aprxSqrt
+  var u = lambda;
+  var v = this.n.clone();
+  var x1 = new bn(1);
+  var y1 = new bn(0);
+  var x2 = new bn(0);
+  var y2 = new bn(1);
+
+  // NOTE: all vectors are roots of: a + b * lambda = 0 (mod n)
+  var a0;
+  var b0;
+  // First vector
+  var a1;
+  var b1;
+  // Second vector
+  var a2;
+  var b2;
+
+  var prevR;
+  var i = 0;
+  while (u.cmpn(0) !== 0) {
+    var q = v.div(u);
+    var r = v.sub(q.mul(u));
+    var x = x2.sub(q.mul(x1));
+    var y = y2.sub(q.mul(y1));
+
+    if (!a1 && r.cmp(aprxSqrt) < 0) {
+      a0 = prevR.neg();
+      b0 = x1;
+      a1 = r.neg();
+      b1 = x;
+    } else if (a1 && ++i === 2) {
+      break;
+    }
+    prevR = r;
+
+    v = u;
+    u = r;
+    x2 = x1;
+    x1 = x;
+    y2 = y1;
+    y1 = y;
+  }
+  a2 = r.neg();
+  b2 = x;
+
+  var len1 = a1.sqr().add(b1.sqr());
+  var len2 = a2.sqr().add(b2.sqr());
+  if (len2.cmp(len1) >= 0) {
+    a2 = a0;
+    b2 = b0;
+  }
+
+  // Normalize signs
+  if (a1.sign) {
+    a1 = a1.neg();
+    b1 = b1.neg();
+  }
+  if (a2.sign) {
+    a2 = a2.neg();
+    b2 = b2.neg();
+  }
+
+  return [
+    { a: a1, b: b1 },
+    { a: a2, b: b2 }
+  ];
+};
+
+Curve.prototype._endoSplit = function _endoSplit(k) {
+  var basis = this.endo.basis;
+  var v1 = basis[0];
+  var v2 = basis[1];
+
+  var c1 = v2.b.mul(k).divRound(this.n);
+  var c2 = v1.b.neg().mul(k).divRound(this.n);
+
+  var p1 = c1.mul(v1.a);
+  var p2 = c2.mul(v2.a);
+  var q1 = c1.mul(v1.b);
+  var q2 = c2.mul(v2.b);
+
+  // Calculate answer
+  var k1 = k.sub(p1).sub(p2);
+  var k2 = q1.add(q2).neg();
+  return { k1: k1, k2: k2 };
+};
+
 Curve.prototype.point = function point(x, y, isRed) {
@@ -29,3 +187,3 @@ return new Point(this, x, y, isRed);
 
-  var y2 = x.redSqr().redMul(x).redAdd(x.redMul(this.a)).redAdd(this.b);
+  var y2 = x.redSqr().redMul(x).redIAdd(x.redMul(this.a)).redIAdd(this.b);
   var y = y2.redSqrt();
@@ -62,16 +220,31 @@
 
-Curve.prototype._nafMul = function _nafMul(p, k) {
+Curve.prototype._fixedNafMul = function _fixedNafMul(p, k) {
+  var doubles = p._getDoubles();
+
   var naf = getNAF(k, 2);
-  var acc = this.jpoint(null, null, null);
-  var q = p;
-  for (var i = 0; i < naf.length; i++, q = q.dbl()) {
-    var z = naf[i];
-    if (z === 1)
-      acc = acc.mixedAdd(q);
-    else if (z === -1)
-      acc = acc.mixedAdd(q.neg());
-    else
-      continue;
+  var I = (1 << (doubles.step + 1)) - (doubles.step % 2 === 0 ? 2 : 1);
+  I /= 3;
+
+  // Translate into more windowed form
+  var repr = [];
+  for (var j = 0; j < naf.length; j += doubles.step) {
+    var nafW = 0;
+    for (var k = j + doubles.step - 1; k >= j; k--)
+      nafW = (nafW << 1) + naf[k];
+    repr.push(nafW);
   }
-  return acc.toP();
+
+  var a = this.jpoint(null, null, null);
+  var b = this.jpoint(null, null, null);
+  for (var i = I; i > 0; i--) {
+    for (var j = 0; j < repr.length; j++) {
+      var nafW = repr[j];
+      if (nafW === i)
+        b = b.mixedAdd(doubles.points[j]);
+      else if (nafW === -i)
+        b = b.mixedAdd(doubles.points[j].neg());
+    }
+    a = a.add(b);
+  }
+  return a.toP();
 };
@@ -81,13 +254,11 @@
   var w = 4;
-  var naf = getNAF(k, w);
 
   // Precompute window
-  var wnd = [ p ];
-  var dbl;
-  for (var i = 1; i < (1 << (w - 1)); i++) {
-    if (!dbl)
-      dbl = p.dbl();
-    wnd[i] = wnd[i - 1].add(dbl);
-  }
+  var nafPoints = p._getNAFPoints(w);
+  w = nafPoints.wnd;
+  var wnd = nafPoints.points;
 
+  // Get NAF form
+  var naf = getNAF(k, w);
+
   // Add `this`*(N+1) for every w-NAF index
@@ -124,2 +295,80 @@ var acc = this.jpoint(null, null, null);
 
+Curve.prototype._wnafMulAdd = function _wnafMulAdd(points, coeffs) {
+  assert.equal(points.length, coeffs.length);
+  var len = points.length;
+  var wndWidth = this.t1;
+  var wnd = this.t2;
+  var naf = this.t3;
+
+  // Fill all arrays
+  var defW = 2;
+  var max = 0;
+  for (var i = 0; i < len; i++) {
+    var p = points[i];
+    var nafPoints = p._getNAFPoints(defW);
+    wndWidth[i] = nafPoints.wnd;
+    wnd[i] = nafPoints.points;
+    naf[i] = getNAF(coeffs[i], nafPoints.wnd);
+
+    max = Math.max(naf[i].length, max);
+  }
+
+  var acc = this.jpoint(null, null, null);
+  var tmp = this.t4;
+  for (var i = max; i >= 0; i--) {
+    var k = 0;
+
+    while (i >= 0) {
+      var zero = true;
+      for (var j = 0; j < len; j++) {
+        tmp[j] = naf[j][i];
+        if (tmp[j] !== 0)
+          zero = false;
+      }
+      if (!zero)
+        break;
+      k++;
+      i--;
+    }
+    if (i >= 0)
+      k++;
+    acc = acc.dblp(k);
+    if (i < 0)
+      break;
+
+    for (var j = 0; j < tmp.length; j++) {
+      var z = tmp[j];
+      if (z > 0)
+        acc = acc.mixedAdd(wnd[j][(z - 1) >> 1]);
+      else if (z < 0)
+        acc = acc.mixedAdd(wnd[j][(-z - 1) >> 1].neg());
+    }
+  }
+  return acc.toP();
+};
+
+Curve.prototype._endoWnafMulAdd = function _endoWnafMulAdd(points, coeffs) {
+  var npoints = this.t5;
+  var ncoeffs = this.t6;
+  for (var i = 0; i < points.length; i++) {
+    var split = this._endoSplit(coeffs[i]);
+    var p = points[i];
+    var beta = p._getBeta();
+
+    if (split.k1.sign) {
+      split.k1.sign = !split.k1.sign;
+      p = p.neg(true);
+    }
+    if (split.k2.sign) {
+      split.k2.sign = !split.k2.sign;
+      beta = beta.neg(true);
+    }
+    npoints[i * 2] = p;
+    npoints[i * 2 + 1] = beta;
+    ncoeffs[i * 2] = split.k1;
+    ncoeffs[i * 2 + 1] = split.k2;
+  }
+  return this._wnafMulAdd(npoints, ncoeffs);
+};
+
 function Point(curve, x, y, isRed) {
@@ -147,4 +396,2 @@ this.type = 'affine';
   this.precomputed = null;
-  this.precomputedW = null;
-  this.precomputedW = null;
 }
@@ -156,14 +403,16 @@
 
-Point.prototype.precompute = function precompute(power) {
+Point.prototype.toJSON = function toJSON() {
   if (!this.precomputed)
-    this.precomputed = [];
-  for (var i = this.precomputed.length; i < power; i++) {
-    var q = (i === 0 ? this : this.precomputed[i - 1]).dbl();
-    this.precomputed.push(q);
-  }
-};
+    return [ this.x, this.y ];
 
-Point.prototype.toJSON = function toJSON() {
-  return this.precomputed ? [ this.x, this.y, this.precomputed ] :
-                            [ this.x, this.y ];
+  return [ this.x, this.y, this.precomputed && {
+    doubles: this.precomputed.doubles && {
+      step: this.precomputed.doubles.step,
+      points: this.precomputed.doubles.points.slice(1)
+    },
+    naf: this.precomputed.naf && {
+      wnd: this.precomputed.naf.wnd,
+      points: this.precomputed.naf.points.slice(1)
+    }
+  }];
 };
@@ -177,8 +426,100 @@
     return res;
-  res.precomputed = obj[2].map(function(obj) {
+
+  function obj2point(obj) {
     return curve.point(obj[0], obj[1], red);
-  });
+  }
+
+  var pre = obj[2];
+  res.precomputed = {
+    beta: null,
+    doubles: pre.doubles && {
+      step: pre.doubles.step,
+      points: [ res ].concat(pre.doubles.points.map(obj2point))
+    },
+    naf: pre.naf && {
+      wnd: pre.naf.wnd,
+      points: [ res ].concat(pre.naf.points.map(obj2point))
+    }
+  };
   return res;
 };
 
+Point.prototype.precompute = function precompute(power, order, _beta) {
+  if (this.precomputed)
+    return this;
+
+  var precomputed = {
+    doubles: null,
+    naf: null,
+    beta: null
+  };
+  precomputed.naf = this._getNAFPoints(8);
+  precomputed.beta = this._getBeta();
+  this.precomputed = precomputed;
+
+  return this;
+};
+
+Point.prototype._getDoubles = function _getDoubles(step, power) {
+  if (this.precomputed && this.precomputed.doubles)
+    return this.precomputed.doubles;
+
+  var doubles = [ this ];
+  var acc = this;
+  for (var i = 0; i < power; i += step) {
+    for (var j = 0; j < step; j++)
+      acc = acc.dbl();
+    doubles.push(acc);
+  }
+  return {
+    step: step,
+    points: doubles
+  };
+};
+
+Point.prototype._getNAFPoints = function _getNAFPoints(wnd) {
+  if (this.precomputed && this.precomputed.naf)
+    return this.precomputed.naf;
+
+  var res = [ this ];
+  var max = (1 << (wnd - 1)) - 1;
+  var dbl = max === 1 ? null : this.dbl();
+  for (var i = 1; i < max; i++)
+    res[i] = res[i - 1].add(dbl);
+  return {
+    wnd: wnd,
+    points: res
+  };
+};
+
+Point.prototype._getBeta = function _getBeta() {
+  if (!this.curve.endo)
+    return;
+
+  var pre = this.precomputed;
+  if (pre && pre.beta)
+    return pre.beta;
+
+  var beta = this.curve.point(this.x.redMul(this.curve.endo.beta), this.y);
+  if (pre) {
+    var curve = this.curve;
+    function endoMul(p) {
+      return curve.point(p.x.redMul(curve.endo.beta), p.y);
+    }
+    pre.beta = beta;
+    beta.precomputed = {
+      beta: null,
+      naf: pre.naf && {
+        wnd: pre.naf.wnd,
+        points: pre.naf.points.map(endoMul)
+      },
+      doubles: pre.doubles && {
+        step: pre.doubles.step,
+        points: pre.doubles.points.map(endoMul)
+      }
+    };
+  }
+  return beta;
+};
+
 Point.prototype.inspect = function inspect() {
@@ -188,4 +529,3 @@ if (this.isInfinity())
   return '<EC Point x: ' + this.x.fromRed().toString(16) +
-      ' y: ' + this.y.fromRed().toString(16) +
-      ' pc: ' + (this.precomputed && this.precomputed.length || 0) + '>';
+      ' y: ' + this.y.fromRed().toString(16) + '>';
 };
@@ -227,9 +567,2 @@
     return this;
-  if (this.precomputed && this.precomputed.length) {
-    var cached = this.precomputed[0];
-    var res = this.curve.point(cached.x, cached.y);
-    if (this.precomputed.length > 1)
-      res.precomputed = this.precomputed.slice(1);
-    return res;
-  }
 
@@ -325,4 +658,4 @@ // 2P = O
 
-  if (this.precomputed && this.precomputed.length)
-    return this.curve._nafMul(this, k);
+  if (this.precomputed && this.precomputed.doubles)
+    return this.curve._fixedNafMul(this, k);
   else
@@ -406,135 +739,7 @@ return this.curve._wnafMul(this, k);
 
-Point.prototype._wnafMulAdd = function _wnafMulAdd(k1, p2, k2) {
-  var a = this;
-  var b = p2;
-  assert.equal(b.type, 'affine');
-
-  var w = {
-    a: 8,
-    b: 4
-  };
-  var naf = {
-    a: getNAF(k1, w.a),
-    b: getNAF(k2, w.b)
-  };
-
-  // Precompute window
-  var dbl = {
-    a: a.dbl(),
-    b: b.dbl()
-  };
-  var wnd = {
-    a: [ a ],
-    b: [ b ]
-  };
-  if (a.precomputed && a.precomputed.length) {
-    if (a.precomputedW) {
-      wnd.a = wnd.a.concat(a.precomputedW);
-    } else {
-      for (var i = 1; i < (1 << (w.a - 1)); i++)
-        wnd.a[i] = wnd.a[i - 1].add(dbl.a);
-      a.precomputedW = wnd.a.slice(1);
-    }
-  } else {
-    for (var i = 1; i < (1 << (w.a - 1)); i++)
-      wnd.a[i] = wnd.a[i - 1].add(dbl.a);
-  }
-  for (var i = 1; i < (1 << (w.b - 1)); i++)
-    wnd.b[i] = wnd.b[i - 1].add(dbl.b);
-
-  // Add `this`*(N+1) for every w-NAF index
-  var acc = this.curve.jpoint(null, null, null);
-  for (var i = Math.max(naf.b.length - 1, naf.a.length - 1); i >= 0; i--) {
-    var k = 0;
-    var za = naf.a[i] | 0;
-    var zb = naf.b[i] | 0;
-
-    while (i >= 0 && za === 0 && zb === 0) {
-      k++;
-      i--;
-      var za = naf.a[i] | 0;
-      var zb = naf.b[i] | 0;
-    }
-    if (i >= 0)
-      k++;
-    acc = acc.dblp(k);
-    if (i < 0)
-      break;
-
-    if (za > 0)
-      acc = acc.mixedAdd(wnd.a[(za - 1) >> 1]);
-    else if (za < 0)
-      acc = acc.mixedAdd(wnd.a[(-za - 1) >> 1].neg());
-    if (zb > 0)
-      acc = acc.mixedAdd(wnd.b[(zb - 1) >> 1]);
-    else if (zb < 0)
-      acc = acc.mixedAdd(wnd.b[(-zb - 1) >> 1].neg());
-  }
-  return acc.toP();
-};
-
-Point.prototype._naiveMulAdd = function _naiveMulAdd(k1, p2, k2) {
-  var a = this;
-  var b = p2;
-  assert.equal(b.type, 'affine');
-
-  // Precompute window
-  var w = 4;
-  var mask = (1 << w) - 1;
-  var wnd = {
-    a: [ a ],
-    b: [ b ]
-  };
-  if (a.precomputed && a.precomputed.length) {
-    if (a.precomputedN) {
-      wnd.a = a.precomputedN;
-    } else {
-      for (var i = 1; i < (1 << w) - 1; i++)
-        wnd.a[i] = wnd.a[i - 1].add(a);
-      a.precomputedN = wnd.a;
-    }
-  } else {
-    for (var i = 1; i < (1 << w) - 1; i++)
-      wnd.a[i] = wnd.a[i - 1].add(a);
-  }
-  for (var i = 1; i < (1 << w) - 1; i++)
-    wnd.b[i] = wnd.b[i - 1].add(b);
-
-  // Compute binary form
-  var bform = {
-    a: [],
-    b: []
-  };
-  k1 = k1.clone();
-  k2 = k2.clone();
-  while (k1.cmpn(0) !== 0) {
-    bform.a.push(k1.andln(mask));
-    k1.ishrn(w);
-  }
-  while (k2.cmpn(0) !== 0) {
-    bform.b.push(k2.andln(mask));
-    k2.ishrn(w);
-  }
-
-  var acc = this.curve.jpoint(null, null, null);
-  for (var i = Math.max(bform.a.length, bform.b.length) - 1; i >= 0; ) {
-    var k = 0;
-    do {
-      var za = bform.a[i] | 0;
-      var zb = bform.b[i] | 0;
-      k++;
-      i--;
-    } while (i >= 0 && za === 0 && zb === 0);
-    acc = acc.dblp(k * w);
-
-    if (za !== 0)
-      acc = acc.mixedAdd(wnd.a[za - 1]);
-    if (zb !== 0)
-      acc = acc.mixedAdd(wnd.b[zb - 1]);
-  }
-  return acc.toP();
-};
-
 Point.prototype.mulAdd = function mulAdd(k1, p2, k2) {
-  return this._wnafMulAdd(k1, p2, k2);
+  if (this.curve.endo)
+    return this.curve._endoWnafMulAdd([ this, p2 ], [ k1, k2 ]);
+  else
+    return this.curve._wnafMulAdd([ this, p2 ], [ k1, k2 ]);
 };
@@ -548,7 +753,24 @@
 
-Point.prototype.neg = function neg() {
+Point.prototype.neg = function neg(_precompute) {
   if (this.inf)
     return this;
 
-  return this.curve.point(this.x, this.y.redNeg());
+  var res = this.curve.point(this.x, this.y.redNeg());
+  if (_precompute && this.precomputed) {
+    var pre = this.precomputed;
+    function negate(p) {
+      return p.neg();
+    }
+    res.precomputed = {
+      naf: pre.naf && {
+        wnd: pre.naf.wnd,
+        points: pre.naf.points.map(negate)
+      },
+      doubles: pre.doubles && {
+        step: pre.doubles.step,
+        step: pre.doubles.points.map(negate)
+      }
+    };
+  }
+  return res;
 };
@@ -683,3 +905,3 @@
 
-  if (this.curve.zeroA) {
+  if (this.curve.zeroA || this.curve.threeA) {
     var r = this;
@@ -691,2 +913,4 @@ for (var i = 0; i < pow; i++)
 
+  // 1M + 2S + 1A + N * (4S + 5M + 8A)
+  // N = 1 => 6M + 6S + 9A
   var a = this.curve.a;
@@ -731,2 +955,4 @@ var tinv = this.curve.tinv;
     return this._zeroDbl();
+  else if (this.curve.threeA)
+    return this._threeDbl();
   else
@@ -802,2 +1028,61 @@ return this._dbl();
 
+JPoint.prototype._threeDbl = function _threeDbl() {
+  // Z = 1
+  if (this.zOne) {
+    // http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#doubling-mdbl-2007-bl
+    // 1M + 5S + 15A
+
+    // XX = X1^2
+    var xx = this.x.redSqr();
+    // YY = Y1^2
+    var yy = this.y.redSqr();
+    // YYYY = YY^2
+    var yyyy = yy.redSqr();
+    // S = 2 * ((X1 + YY)^2 - XX - YYYY)
+    var s = this.x.redAdd(yy).redSqr().redISub(xx).redISub(yyyy);
+    s = s.redIAdd(s);
+    // M = 3 * XX + a
+    var m = xx.redAdd(xx).redIAdd(xx).redIAdd(this.curve.a);
+    // T = M^2 - 2 * S
+    var t = m.redSqr().redISub(s).redISub(s);
+    // X3 = T
+    var nx = t;
+    // Y3 = M * (S - T) - 8 * YYYY
+    var yyyy8 = yyyy.redIAdd(yyyy);
+    yyyy8 = yyyy8.redIAdd(yyyy8);
+    yyyy8 = yyyy8.redIAdd(yyyy8);
+    var ny = m.redMul(s.redISub(t)).redISub(yyyy8);
+    // Z3 = 2 * Y1
+    var nz = this.y.redAdd(this.y);
+  } else {
+    // http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#doubling-dbl-2001-b
+    // 3M + 5S
+
+    // delta = Z1^2
+    var delta = this.z.redSqr();
+    // gamma = Y1^2
+    var gamma = this.y.redSqr();
+    // beta = X1 * gamma
+    var beta = this.x.redMul(gamma);
+    // alpha = 3 * (X1 - delta) * (X1 + delta)
+    var alpha = this.x.redSub(delta).redMul(this.x.redAdd(delta));
+    alpha = alpha.redAdd(alpha).redIAdd(alpha);
+    // X3 = alpha^2 - 8 * beta
+    var beta4 = beta.redIAdd(beta);
+    beta4 = beta4.redIAdd(beta4);
+    var beta8 = beta4.redAdd(beta4);
+    var nx = alpha.redSqr().redISub(beta8);
+    // Z3 = (Y1 + Z1)^2 - gamma - delta
+    var nz = this.y.redAdd(this.z).redSqr().redISub(gamma).redISub(delta);
+    // Y3 = alpha * (4 * beta - X3) - 8 * gamma^2
+    var ggamma8 = gamma.redSqr();
+    ggamma8 = ggamma8.redIAdd(ggamma8);
+    ggamma8 = ggamma8.redIAdd(ggamma8);
+    ggamma8 = ggamma8.redIAdd(ggamma8);
+    var ny = alpha.redMul(beta4.redISub(nx)).redISub(ggamma8);
+  }
+
+  return this.curve.jpoint(nx, ny, nz);
+};
+
 JPoint.prototype._dbl = function _dbl() {
@@ -804,0 +1089,0 @@ var a = this.curve.a;

lib/elliptic/ecdsa/index.js

@@ -18,7 +18,7 @@ var assert = require('assert');
   this.curve = options.curve.curve;
+  // Order of the point
+  this.n = options.curve.n;
   // Point on curve
   this.g = options.curve.g;
-  this.g.precompute(options.curve.n.bitLength());
-  // Order of the point
-  this.n = options.curve.n;
+  this.g.precompute(options.curve.n.bitLength() + 1, this.n);
   // Hash for function for DRBG
@@ -105,3 +105,3 @@ this.hash = options.hash || options.curve.hash;
 
-    var s = k.invm(this.n).mul(msg.add(r.mul(key.getPrivate()))).mod(this.n);
+    var s = k.invm(this.n).mul(r.mul(key.getPrivate()).iadd(msg)).mod(this.n);
     if (s.cmpn(0) === 0)
@@ -108,0 +108,0 @@ continue;

lib/elliptic/nist.js

@@ -36,3 +36,3 @@ var nist = exports;
 defineCurve('p192', {
-  prime: null,
+  prime: 'p192',
   p: 'ffffffff ffffffff ffffffff fffffffe ffffffff ffffffff',
@@ -51,3 +51,3 @@ a: 'ffffffff ffffffff ffffffff fffffffe ffffffff fffffffc',
 defineCurve('p224', {
-  prime: null,
+  prime: 'p224',
   p: 'ffffffff ffffffff ffffffff ffffffff 00000000 00000000 00000001',
@@ -88,3 +88,16 @@ a: 'ffffffff ffffffff ffffffff fffffffe ffffffff ffffffff fffffffe',
 
-  // Point and precomputed 2^N powers of it
+  // Precomputed endomorphism
+  beta: '7ae96a2b657c07106e64479eac3434e99cf0497512f58995c1396c28719501ee',
+  lambda: '5363ad4cc05c30e0a5261c028812645a122e22ea20816678df02967c1b23bd72',
+  basis: [
+    {
+      a: '3086d221a7d46bcde86c90e49284eb15',
+      b: '-e4437ed6010e88286f547fa90abfe4c3'
+    },
+    {
+      a: '114ca50f7a8e2f3f657c1108d9d44cfd8',
+      b: '3086d221a7d46bcde86c90e49284eb15'
+    }
+  ],
+
   gRed: false,
@@ -94,1029 +107,783 @@ g: [
     '483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8',
-    [
-      [
-        'c6047f9441ed7d6d3045406e95c07cd85c778e4b8cef3ca7abac09b95c709ee5',
-        '1ae168fea63dc339a3c58419466ceaeef7f632653266d0e1236431a950cfe52a'
-      ],
-      [
-        'e493dbf1c10d80f3581e4904930b1404cc6c13900ee0758474fa94abe8c4cd13',
-        '51ed993ea0d455b75642e2098ea51448d967ae33bfbdfe40cfe97bdc47739922'
-      ],
-      [
-        '2f01e5e15cca351daff3843fb70f3c2f0a1bdd05e5af888a67784ef3e10a2a01',
-        '5c4da8a741539949293d082a132d13b4c2e213d6ba5b7617b5da2cb76cbde904'
-      ],
-      [
-        'e60fce93b59e9ec53011aabc21c23e97b2a31369b87a5ae9c44ee89e2a6dec0a',
-        'f7e3507399e595929db99f34f57937101296891e44d23f0be1f32cce69616821'
-      ],
-      [
-        'd30199d74fb5a22d47b6e054e2f378cedacffcb89904a61d75d0dbd407143e65',
-        '95038d9d0ae3d5c3b3d6dec9e98380651f760cc364ed819605b3ff1f24106ab9'
-      ],
-      [
-        'bf23c1542d16eab70b1051eaf832823cfc4c6f1dcdbafd81e37918e6f874ef8b',
-        '5cb3866fc33003737ad928a0ba5392e4c522fc54811e2f784dc37efe66831d9f'
-      ],
-      [
-        '34ff3be4033f7a06696c3d09f7d1671cbcf55cd700535655647077456769a24e',
-        '5d9d11623a236c553f6619d89832098c55df16c3e8f8b6818491067a73cc2f1a'
-      ],
-      [
-        '8282263212c609d9ea2a6e3e172de238d8c39cabd5ac1ca10646e23fd5f51508',
-        '11f8a8098557dfe45e8256e830b60ace62d613ac2f7b17bed31b6eaff6e26caf'
-      ],
-      [
-        '465370b287a79ff3905a857a9cf918d50adbc968d9e159d0926e2c00ef34a24d',
-        '35e531b38368c082a4af8bdafdeec2c1588e09b215d37a10a2f8fb20b33887f4'
-      ],
-      [
-        '241febb8e23cbd77d664a18f66ad6240aaec6ecdc813b088d5b901b2e285131f',
-        '513378d9ff94f8d3d6c420bd13981df8cd50fd0fbd0cb5afabb3e66f2750026d'
-      ],
-      [
-        '5d1bdb4ea172fa79fce4cc2983d8f8d9fc318b85f423de0dedcb63069b920471',
-        '2843826779379e2e794bb99438a2265679eb1e9996c56e7b70330666f7b83103'
-      ],
-      [
-        '175e159f728b865a72f99cc6c6fc846de0b93833fd2222ed73fce5b551e5b739',
-        'd3506e0d9e3c79eba4ef97a51ff71f5eacb5955add24345c6efa6ffee9fed695'
-      ],
-      [
-        '423a013f03ff32d7a5ffbcc8e139c62130fdfeb5c6da121bce78049e46bc47d6',
-        'b91ae00fe1e1d970a1179f7bbaf6b3c7720d8ec3524f009ed1236e6d8b548a34'
-      ],
-      [
-        '111d6a45ac1fb90508907a7abcd6877649df662f3b3e2741302df6f78416824a',
-        '696911c478eaffbb90d48dbff065952f070008996daca4ca9a111d42108e9d0'
-      ],
-      [
-        '4a4a6dc97ac7c8b8ad795dbebcb9dcff7290b68a5ef74e56ab5edde01bced775',
-        '529911b016631e72943ef9f739c0f4571de90cdb424742acb2bf8f68a78dd66d'
-      ],
-      [
-        '363d90d447b00c9c99ceac05b6262ee053441c7e55552ffe526bad8f83ff4640',
-        '4e273adfc732221953b445397f3363145b9a89008199ecb62003c7f3bee9de9'
-      ],
-      [
-        '4c1b9866ed9a7e9b553973c6c93b02bf0b62fb012edfb59dd2712a5caf92c541',
-        'c1f792d320be8a0f7fbcb753ce56e69cc652ead7e43eb1ad72c4f3fdc68fe020'
-      ],
-      [
-        'a4083877ba83b12b529a2f3c0780b54e3233edbc1a28f135e0c8f28cbeaaf3d1',
-        '40e9f612feefbc79b8bf83d69361b3e22001e7576ed1ef90b12b534df0b254b9'
-      ],
-      [
-        'a804c641d28cc0b53a4e3e1a2f56c86f6e0d880a454203b98cd3db5a7940d33a',
-        '95be83252b2fa6d03dec2842c16047e81af18ca89cf736a943ce95fa6d46967a'
-      ],
-      [
-        '8b4b5f165df3c2be8c6244b5b745638843e4a781a15bcd1b69f79a55dffdf80c',
-        '4aad0a6f68d308b4b3fbd7813ab0da04f9e336546162ee56b3eff0c65fd4fd36'
-      ],
-      [
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-      ],
-      [
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-        'cc09b5e90e9ecb57fc2e02c6ec2fb13d9c32b286b85e2e2e8981dfd9ab155070'
-      ],
-      [
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-        '945bb2b2afeee3b9b6f9dd284f863e850f54a840f4752d5364130627c3811c80'
-      ],
-      [
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-        '96e867b5595cc498a921137488824d6e2660a0653779494801dc069d9eb39f5f'
-      ],
-      [
-        '57efa786437b744d343d7dc45773a3c62d240a43079849071fd383d60ca030d5',
-        'd712db0bd1b48518893627c928de03ec689b6d2ae5e9974ab07ab44274b02f9e'
-      ],
-      [
-        '264bbd436a28bc42a2df7e9cd5226cb91080577e327b012a7fafc7770c584dd5',
-        'd87c6fa94ee093b4d4f75ce24c33be226a118243717b8d8de61227937704ab11'
-      ],
-      [
-        'a94c6524bd40d2bbdac85c056236a79da78bc61fd5bdec9d2bf26bd84b2438e8',
-        'b5201fd992f96280fd79219505019e3a7e5d3c60a0e39b2bc2e2c8dbf18661f4'
-      ],
-      [
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-      ],
-      [
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-      ],
-      [
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-        'ecb4530d8af9be7b0154c1ffe477123464e3244a7a2d4c6ad9fd233a8913797'
-      ],
-      [
-        '5318f9b1a2697010c5ac235e9af475a8c7e5419f33d47b18d33feeb329eb99a4',
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-      ],
-      [
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-        'cdd9e13192a00b772ec8f3300c090666b7ff4a18ff5195ac0fbd5cd62bc65a09'
-      ],
-      [
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-        'fb4dbd044f432034ffd2172cb9dc966c60de6bf5156511aa736ac5a35d72fa98'
-      ],
-      [
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-        '6ca27a9dc5e0621816fa11d9b4bccd531dde1389ac542613090a45ddd949b095'
-      ],
-      [
-        'e747333fd75d51755a0cc9f0a728708465a02c587737a7b8b8fa1b8b4bb2629a',
-        'f2affe0145070c114cc43603804c2581c88376aa6e1a969a9f8d961a6946f6d6'
-      ],
-      [
-        'e1031be262c7ed1b1dc9227a4a04c017a77f8d4464f3b3852c8acde6e534fd2d',
-        '9d7061928940405e6bb6a4176597535af292dd419e1ced79a44f18f29456a00d'
-      ],
-      [
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-        'a67a92ec062962dfb0e5f6a7a40eee90c37ef1344915609abd5861b9be001fd3'
-      ],
-      [
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-        '1153188f5101f0c63e56692ce0d8c27e6fe9e0ee9212b5e534e050c57ca04c44'
-      ],
-      [
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-        'd9592fe2bfb30fcfbea4f3ceaac10cb2f00a60ddb15955977ec3c69cf75f5956'
-      ],
-      [
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-      ],
-      [
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-        '6a0d5b8f18e0d255cb6d825582d972cccb7df5f119c7293a3e72851f48302cea'
-      ],
-      [
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-      ],
-      [
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-      ],
-      [
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-      ],
-      [
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-      ],
-      [
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-        '6008391fa991961dcecb9337b1b758bda4ad01206d5bd127e0db419ddb191c19'
-      ],
-      [
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-        '24d9c605d959efeaf5a44180c0372a6e394f8ac53e90576527df01a78d3b6bc7'
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-      [
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-      [
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+          ],
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+            'ed8cc9d04b29eb877d270b4878dc43c19aefd31f4eee09ee7b47834c1fa4b1c3'
+          ],
+          [
+            '75d46efea3771e6e68abb89a13ad747ecf1892393dfc4f1b7004788c50374da8',
+            '9852390a99507679fd0b86fd2b39a868d7efc22151346e1a3ca4726586a6bed8'
+          ],
+          [
+            '809a20c67d64900ffb698c4c825f6d5f2310fb0451c869345b7319f645605721',
+            '9e994980d9917e22b76b061927fa04143d096ccc54963e6a5ebfa5f3f8e286c1'
+          ],
+          [
+            '1b38903a43f7f114ed4500b4eac7083fdefece1cf29c63528d563446f972c180',
+            '4036edc931a60ae889353f77fd53de4a2708b26b6f5da72ad3394119daf408f9'
+          ]
+        ]
+      }
+    }
   ]
 });

Makefile

 BROWSERIFY ?= ./node_modules/.bin/browserify
+UGLIFY ?= ./node_modules/.bin/uglifyjs
 
-all: dist/elliptic.js
+all: dist/elliptic.js dist/elliptic.min.js
 
 dist/elliptic.js: lib/elliptic.js
-	$(BROWSERIFY) $< -o $@
+	$(BROWSERIFY) --standalone ellipticjs $< -o $@
 
+dist/elliptic.min.js: dist/elliptic.js
+	$(UGLIFY) --compress --mangle < $< > $@
+
 .PHONY: all

package.json

 {
   "name": "elliptic",
-  "version": "0.13.2",
+  "version": "0.14.0",
   "description": "EC cryptography",
@@ -30,5 +30,6 @@ "main": "lib/elliptic.js",
   "dependencies": {
-    "bn.js": "^0.8.0",
-    "hash.js": "^0.2.0"
+    "bn.js": "^0.10.0",
+    "hash.js": "^0.2.0",
+    "uglify-js": "^2.4.13"
   }
 }

test/curve-test.js

@@ -40,3 +40,5 @@ var assert = require('assert');
       a: '0',
-      b: '7'
+      b: '7',
+      n: 'ffffffff ffffffff ffffffff fffffffe ' +
+             'baaedce6 af48a03b bfd25e8c d0364141'
     });
@@ -55,3 +57,18 @@
     assert(j.trpl().eq(j.dbl().add(j)));
+
+    // Endomorphism test
+    assert(curve.endo);
+    assert.equal(
+      curve.endo.beta.fromRed().toString(16),
+      '7ae96a2b657c07106e64479eac3434e99cf0497512f58995c1396c28719501ee');
+    assert.equal(
+      curve.endo.lambda.toString(16),
+      '5363ad4cc05c30e0a5261c028812645a122e22ea20816678df02967c1b23bd72');
+
+    var k = new bn('1234567890123456789012345678901234', 16);
+    var split = curve._endoSplit(k);
+    assert.equal(
+      split.k1.add(split.k2.mul(curve.endo.lambda)).mod(curve.n).toString(16),
+      k.toString(16));
   });
 });

No alert changes

Improved metrics

Lines of code

2925

0.97%

Worsened metrics

Total package byte prevSize

111814

-92.97%

Dependency count

3

50%

Number of package files

19

-5%

Dependency changes

• + Added

  uglify-js@^2.4.13

• + Added

  align-text@0.1.4
  (transitive)

• + Added

  bn.js@0.10.1
  (transitive)

• + Added

  camelcase@1.2.1
  (transitive)

• + Added

  center-align@0.1.3
  (transitive)

• + Added

  cliui@2.1.0
  (transitive)

• + Added

  decamelize@1.2.0
  (transitive)

• + Added

  is-buffer@1.1.6
  (transitive)

• + Added

  kind-of@3.2.2
  (transitive)

• + Added

  lazy-cache@1.0.4
  (transitive)

• + Added

  longest@1.0.1
  (transitive)

• + Added

  repeat-string@1.6.1
  (transitive)

• + Added

  right-align@0.1.3
  (transitive)

• + Added

  source-map@0.5.7
  (transitive)

• + Added

  uglify-js@2.8.29
  (transitive)

• + Added

  uglify-to-browserify@1.0.2
  (transitive)

• + Added

  window-size@0.1.0
  (transitive)

• + Added

  wordwrap@0.0.2
  (transitive)

• + Added

  yargs@3.10.0
  (transitive)

• - Removed

  bn.js@0.8.1
  (transitive)

• Updated

  bn.js@^0.10.0