elliptic

What is elliptic?

The elliptic npm package provides a collection of utilities for elliptic curve cryptography. It supports various elliptic curve operations such as key pair generation, digital signature creation and verification, and ECDH (Elliptic Curve Diffie-Hellman) key agreement. This makes it a versatile tool for implementing secure cryptographic functions in Node.js applications.

What are elliptic's main functionalities?

Key Pair Generation

This feature allows the generation of elliptic curve key pairs, which are fundamental for cryptographic operations. The example demonstrates generating a new key pair using the secp256k1 curve, which is widely used in blockchain technologies.

const EC = require('elliptic').ec;
const ec = new EC('secp256k1');

// Generate a new key pair
const keyPair = ec.genKeyPair();

// Get the public and private keys as hex strings
const publicKey = keyPair.getPublic().encode('hex');
const privateKey = keyPair.getPrivate().toString('hex');

Digital Signature

This feature enables the creation and verification of digital signatures, which are crucial for ensuring the integrity and authenticity of data. The code sample shows how to sign a message and then export the signature in DER format.

const EC = require('elliptic').ec;
const ec = new EC('secp256k1');

// Generate keys
const key = ec.genKeyPair();

// Sign a message
const msg = 'Hello world';
const signature = key.sign(msg);

// Export the signature to DER format
const derSign = signature.toDER();

ECDH Key Agreement

This feature supports Elliptic Curve Diffie-Hellman (ECDH), a key agreement protocol that allows two parties to establish a shared secret over an insecure channel. The example demonstrates how two parties can generate a shared secret.

const EC = require('elliptic').ec;
const ec = new EC('curve25519');

// Generate keys for two parties
const key1 = ec.genKeyPair();
const key2 = ec.genKeyPair();

// Derive shared secret
const shared1 = key1.derive(key2.getPublic());
const shared2 = key2.derive(key1.getPublic());

// Shared secrets should be the same
console.log(shared1.toString(16) === shared2.toString(16));

Other packages similar to elliptic

secp256k1

This package focuses specifically on the secp256k1 elliptic curve, offering functionalities similar to elliptic but with optimizations for speed and security. It is often used in Bitcoin and Ethereum projects.

node-forge

node-forge is a comprehensive Node.js library that includes a wide range of cryptographic operations, including those related to elliptic curves. While it covers more than elliptic curve cryptography, it is generally heavier and more complex to use for specific elliptic curve operations.

tweetnacl

tweetnacl is a port of NaCl, the Networking and Cryptography library, to JavaScript. It offers a variety of cryptographic primitives, including elliptic curve cryptography, with a focus on simplicity and small size. It's a good alternative for projects requiring lightweight cryptography solutions.

README

Elliptic

Fast elliptic-curve cryptography in a plain javascript implementation.

NOTE: Please take a look at http://safecurves.cr.yp.to/ before choosing a curve for your cryptography operations.

Incentive

ECC is much slower than regular RSA cryptography, the JS implementations are even more slower.

Benchmarks

$ node benchmarks/index.js
Benchmarking: sign
elliptic#sign x 262 ops/sec ±0.51% (177 runs sampled)
eccjs#sign x 55.91 ops/sec ±0.90% (144 runs sampled)
------------------------
Fastest is elliptic#sign
========================
Benchmarking: verify
elliptic#verify x 113 ops/sec ±0.50% (166 runs sampled)
eccjs#verify x 48.56 ops/sec ±0.36% (125 runs sampled)
------------------------
Fastest is elliptic#verify
========================
Benchmarking: gen
elliptic#gen x 294 ops/sec ±0.43% (176 runs sampled)
eccjs#gen x 62.25 ops/sec ±0.63% (129 runs sampled)
------------------------
Fastest is elliptic#gen
========================
Benchmarking: ecdh
elliptic#ecdh x 136 ops/sec ±0.85% (156 runs sampled)
------------------------
Fastest is elliptic#ecdh
========================

API

ECDSA

var EC = require('elliptic').ec;

// Create and initialize EC context
// (better do it once and reuse it)
var ec = new EC('secp256k1');

// Generate keys
var key = ec.genKeyPair();

// Sign the message's hash (input must be an array, or a hex-string)
var msgHash = [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ];
var signature = key.sign(msgHash);

// Export DER encoded signature in Array
var derSign = signature.toDER();

// Verify signature
console.log(key.verify(msgHash, derSign));

// CHECK WITH NO PRIVATE KEY

var pubPoint = key.getPublic();
var x = pubPoint.getX();
var y = pubPoint.getY();

// Public Key MUST be either:
// 1) '04' + hex string of x + hex string of y; or
// 2) object with two hex string properties (x and y); or
// 3) object with two buffer properties (x and y)
var pub = pubPoint.encode('hex');                                 // case 1
var pub = { x: x.toString('hex'), y: y.toString('hex') };         // case 2
var pub = { x: x.toBuffer(), y: y.toBuffer() };                   // case 3
var pub = { x: x.toArrayLike(Buffer), y: y.toArrayLike(Buffer) }; // case 3

// Import public key
var key = ec.keyFromPublic(pub, 'hex');

// Signature MUST be either:
// 1) DER-encoded signature as hex-string; or
// 2) DER-encoded signature as buffer; or
// 3) object with two hex-string properties (r and s); or
// 4) object with two buffer properties (r and s)

var signature = '3046022100...'; // case 1
var signature = new Buffer('...'); // case 2
var signature = { r: 'b1fc...', s: '9c42...' }; // case 3

// Verify signature
console.log(key.verify(msgHash, signature));

EdDSA

var EdDSA = require('elliptic').eddsa;

// Create and initialize EdDSA context
// (better do it once and reuse it)
var ec = new EdDSA('ed25519');

// Create key pair from secret
var key = ec.keyFromSecret('693e3c...'); // hex string, array or Buffer

// Sign the message's hash (input must be an array, or a hex-string)
var msgHash = [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ];
var signature = key.sign(msgHash).toHex();

// Verify signature
console.log(key.verify(msgHash, signature));

// CHECK WITH NO PRIVATE KEY

// Import public key
var pub = '0a1af638...';
var key = ec.keyFromPublic(pub, 'hex');

// Verify signature
var signature = '70bed1...';
console.log(key.verify(msgHash, signature));

ECDH

var EC = require('elliptic').ec;
var ec = new EC('curve25519');

// Generate keys
var key1 = ec.genKeyPair();
var key2 = ec.genKeyPair();

var shared1 = key1.derive(key2.getPublic());
var shared2 = key2.derive(key1.getPublic());

console.log('Both shared secrets are BN instances');
console.log(shared1.toString(16));
console.log(shared2.toString(16));

three and more members:

var EC = require('elliptic').ec;
var ec = new EC('curve25519');

var A = ec.genKeyPair();
var B = ec.genKeyPair();
var C = ec.genKeyPair();

var AB = A.getPublic().mul(B.getPrivate())
var BC = B.getPublic().mul(C.getPrivate())
var CA = C.getPublic().mul(A.getPrivate())

var ABC = AB.mul(C.getPrivate())
var BCA = BC.mul(A.getPrivate())
var CAB = CA.mul(B.getPrivate())

console.log(ABC.getX().toString(16))
console.log(BCA.getX().toString(16))
console.log(CAB.getX().toString(16))

NOTE: .derive() returns a BN instance.

Supported curves

Elliptic.js support following curve types:

• Short Weierstrass
• Montgomery
• Edwards
• Twisted Edwards

Following curve 'presets' are embedded into the library:

• secp256k1
• p192
• p224
• p256
• p384
• p521
• curve25519
• ed25519

NOTE: That curve25519 could not be used for ECDSA, use ed25519 instead.

Implementation details

ECDSA is using deterministic k value generation as per RFC6979. Most of the curve operations are performed on non-affine coordinates (either projective or extended), various windowing techniques are used for different cases.

All operations are performed in reduction context using bn.js, hashing is provided by hash.js

Related projects

• eccrypto: isomorphic implementation of ECDSA, ECDH and ECIES for both browserify and node (uses elliptic for browser and secp256k1-node for node)

LICENSE

This software is licensed under the MIT License.

Copyright Fedor Indutny, 2014.

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.