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

1$ node benchmarks/index.js
2Benchmarking: sign
3elliptic#sign x 262 ops/sec ±0.51% (177 runs sampled)
4eccjs#sign x 55.91 ops/sec ±0.90% (144 runs sampled)
5------------------------
6Fastest is elliptic#sign
7========================
8Benchmarking: verify
9elliptic#verify x 113 ops/sec ±0.50% (166 runs sampled)
10eccjs#verify x 48.56 ops/sec ±0.36% (125 runs sampled)
11------------------------
12Fastest is elliptic#verify
13========================
14Benchmarking: gen
15elliptic#gen x 294 ops/sec ±0.43% (176 runs sampled)
16eccjs#gen x 62.25 ops/sec ±0.63% (129 runs sampled)
17------------------------
18Fastest is elliptic#gen
19========================
20Benchmarking: ecdh
21elliptic#ecdh x 136 ops/sec ±0.85% (156 runs sampled)
22------------------------
23Fastest is elliptic#ecdh
24========================

API

ECDSA

1var EC = require('elliptic').ec;
2
3// Create and initialize EC context
4// (better do it once and reuse it)
5var ec = new EC('secp256k1');
6
7// Generate keys
8var key = ec.genKeyPair();
9
10// Sign the message's hash (input must be an array, or a hex-string)
11var msgHash = [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ];
12var signature = key.sign(msgHash);
13
14// Export DER encoded signature in Array
15var derSign = signature.toDER();
16
17// Verify signature
18console.log(key.verify(msgHash, derSign));
19
20// CHECK WITH NO PRIVATE KEY
21
22var pubPoint = key.getPublic();
23var x = pubPoint.getX();
24var y = pubPoint.getY();
25
26// Public Key MUST be either:
27// 1) '04' + hex string of x + hex string of y; or
28// 2) object with two hex string properties (x and y); or
29// 3) object with two buffer properties (x and y)
30var pub = pubPoint.encode('hex');                                 // case 1
31var pub = { x: x.toString('hex'), y: y.toString('hex') };         // case 2
32var pub = { x: x.toBuffer(), y: y.toBuffer() };                   // case 3
33var pub = { x: x.toArrayLike(Buffer), y: y.toArrayLike(Buffer) }; // case 3
34
35// Import public key
36var key = ec.keyFromPublic(pub, 'hex');
37
38// Signature MUST be either:
39// 1) DER-encoded signature as hex-string; or
40// 2) DER-encoded signature as buffer; or
41// 3) object with two hex-string properties (r and s); or
42// 4) object with two buffer properties (r and s)
43
44var signature = '3046022100...'; // case 1
45var signature = new Buffer('...'); // case 2
46var signature = { r: 'b1fc...', s: '9c42...' }; // case 3
47
48// Verify signature
49console.log(key.verify(msgHash, signature));

EdDSA

1var EdDSA = require('elliptic').eddsa;
2
3// Create and initialize EdDSA context
4// (better do it once and reuse it)
5var ec = new EdDSA('ed25519');
6
7// Create key pair from secret
8var key = ec.keyFromSecret('693e3c...'); // hex string, array or Buffer
9
10// Sign the message's hash (input must be an array, or a hex-string)
11var msgHash = [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ];
12var signature = key.sign(msgHash).toHex();
13
14// Verify signature
15console.log(key.verify(msgHash, signature));
16
17// CHECK WITH NO PRIVATE KEY
18
19// Import public key
20var pub = '0a1af638...';
21var key = ec.keyFromPublic(pub, 'hex');
22
23// Verify signature
24var signature = '70bed1...';
25console.log(key.verify(msgHash, signature));

ECDH

1var EC = require('elliptic').ec;
2var ec = new EC('curve25519');
3
4// Generate keys
5var key1 = ec.genKeyPair();
6var key2 = ec.genKeyPair();
7
8var shared1 = key1.derive(key2.getPublic());
9var shared2 = key2.derive(key1.getPublic());
10
11console.log('Both shared secrets are BN instances');
12console.log(shared1.toString(16));
13console.log(shared2.toString(16));

three and more members:

1var EC = require('elliptic').ec;
2var ec = new EC('curve25519');
3
4var A = ec.genKeyPair();
5var B = ec.genKeyPair();
6var C = ec.genKeyPair();
7
8var AB = A.getPublic().mul(B.getPrivate())
9var BC = B.getPublic().mul(C.getPrivate())
10var CA = C.getPublic().mul(A.getPrivate())
11
12var ABC = AB.mul(C.getPrivate())
13var BCA = BC.mul(A.getPrivate())
14var CAB = CA.mul(B.getPrivate())
15
16console.log(ABC.getX().toString(16))
17console.log(BCA.getX().toString(16))
18console.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.