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0.2.0 - Mid migration
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238
web/node_modules/elliptic/README.md
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web/node_modules/elliptic/README.md
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# Elliptic [](http://travis-ci.org/indutny/elliptic) [](https://coveralls.io/github/indutny/elliptic?branch=master) [](https://codeclimate.com/github/indutny/elliptic)
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[](https://saucelabs.com/u/gh-indutny-elliptic)
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Fast elliptic-curve cryptography in a plain javascript implementation.
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NOTE: Please take a look at http://safecurves.cr.yp.to/ before choosing a curve
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for your cryptography operations.
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## Incentive
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ECC is much slower than regular RSA cryptography, the JS implementations are
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even more slower.
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## Benchmarks
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```bash
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$ node benchmarks/index.js
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Benchmarking: sign
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elliptic#sign x 262 ops/sec ±0.51% (177 runs sampled)
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eccjs#sign x 55.91 ops/sec ±0.90% (144 runs sampled)
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------------------------
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Fastest is elliptic#sign
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========================
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Benchmarking: verify
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elliptic#verify x 113 ops/sec ±0.50% (166 runs sampled)
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eccjs#verify x 48.56 ops/sec ±0.36% (125 runs sampled)
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------------------------
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Fastest is elliptic#verify
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========================
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Benchmarking: gen
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elliptic#gen x 294 ops/sec ±0.43% (176 runs sampled)
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eccjs#gen x 62.25 ops/sec ±0.63% (129 runs sampled)
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------------------------
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Fastest is elliptic#gen
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========================
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Benchmarking: ecdh
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elliptic#ecdh x 136 ops/sec ±0.85% (156 runs sampled)
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------------------------
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Fastest is elliptic#ecdh
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========================
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```
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## API
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### ECDSA
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```javascript
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var EC = require('elliptic').ec;
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// Create and initialize EC context
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// (better do it once and reuse it)
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var ec = new EC('secp256k1');
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// Generate keys
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var key = ec.genKeyPair();
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// Sign the message's hash (input must be an array, or a hex-string)
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var msgHash = [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ];
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var signature = key.sign(msgHash);
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// Export DER encoded signature in Array
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var derSign = signature.toDER();
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// Verify signature
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console.log(key.verify(msgHash, derSign));
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// CHECK WITH NO PRIVATE KEY
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var pubPoint = key.getPublic();
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var x = pubPoint.getX();
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var y = pubPoint.getY();
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// Public Key MUST be either:
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// 1) '04' + hex string of x + hex string of y; or
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// 2) object with two hex string properties (x and y); or
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// 3) object with two buffer properties (x and y)
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var pub = pubPoint.encode('hex'); // case 1
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var pub = { x: x.toString('hex'), y: y.toString('hex') }; // case 2
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var pub = { x: x.toBuffer(), y: y.toBuffer() }; // case 3
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var pub = { x: x.toArrayLike(Buffer), y: y.toArrayLike(Buffer) }; // case 3
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// Import public key
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var key = ec.keyFromPublic(pub, 'hex');
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// Signature MUST be either:
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// 1) DER-encoded signature as hex-string; or
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// 2) DER-encoded signature as buffer; or
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// 3) object with two hex-string properties (r and s); or
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// 4) object with two buffer properties (r and s)
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var signature = '3046022100...'; // case 1
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var signature = new Buffer('...'); // case 2
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var signature = { r: 'b1fc...', s: '9c42...' }; // case 3
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// Verify signature
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console.log(key.verify(msgHash, signature));
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```
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### EdDSA
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```javascript
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var EdDSA = require('elliptic').eddsa;
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// Create and initialize EdDSA context
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// (better do it once and reuse it)
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var ec = new EdDSA('ed25519');
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// Create key pair from secret
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var key = ec.keyFromSecret('693e3c...'); // hex string, array or Buffer
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// Sign the message's hash (input must be an array, or a hex-string)
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var msgHash = [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ];
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var signature = key.sign(msgHash).toHex();
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// Verify signature
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console.log(key.verify(msgHash, signature));
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// CHECK WITH NO PRIVATE KEY
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// Import public key
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var pub = '0a1af638...';
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var key = ec.keyFromPublic(pub, 'hex');
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// Verify signature
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var signature = '70bed1...';
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console.log(key.verify(msgHash, signature));
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```
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### ECDH
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```javascript
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var EC = require('elliptic').ec;
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var ec = new EC('curve25519');
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// Generate keys
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var key1 = ec.genKeyPair();
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var key2 = ec.genKeyPair();
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var shared1 = key1.derive(key2.getPublic());
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var shared2 = key2.derive(key1.getPublic());
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console.log('Both shared secrets are BN instances');
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console.log(shared1.toString(16));
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console.log(shared2.toString(16));
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```
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three and more members:
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```javascript
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var EC = require('elliptic').ec;
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var ec = new EC('curve25519');
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var A = ec.genKeyPair();
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var B = ec.genKeyPair();
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var C = ec.genKeyPair();
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var AB = A.getPublic().mul(B.getPrivate())
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var BC = B.getPublic().mul(C.getPrivate())
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var CA = C.getPublic().mul(A.getPrivate())
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var ABC = AB.mul(C.getPrivate())
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var BCA = BC.mul(A.getPrivate())
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var CAB = CA.mul(B.getPrivate())
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console.log(ABC.getX().toString(16))
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console.log(BCA.getX().toString(16))
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console.log(CAB.getX().toString(16))
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```
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NOTE: `.derive()` returns a [BN][1] instance.
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## Supported curves
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Elliptic.js support following curve types:
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* Short Weierstrass
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* Montgomery
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* Edwards
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* Twisted Edwards
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Following curve 'presets' are embedded into the library:
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* `secp256k1`
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* `p192`
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* `p224`
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* `p256`
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* `p384`
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* `p521`
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* `curve25519`
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* `ed25519`
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NOTE: That `curve25519` could not be used for ECDSA, use `ed25519` instead.
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### Implementation details
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ECDSA is using deterministic `k` value generation as per [RFC6979][0]. Most of
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the curve operations are performed on non-affine coordinates (either projective
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or extended), various windowing techniques are used for different cases.
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All operations are performed in reduction context using [bn.js][1], hashing is
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provided by [hash.js][2]
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### Related projects
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* [eccrypto][3]: isomorphic implementation of ECDSA, ECDH and ECIES for both
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browserify and node (uses `elliptic` for browser and [secp256k1-node][4] for
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node)
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#### LICENSE
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This software is licensed under the MIT License.
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Copyright Fedor Indutny, 2014.
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Permission is hereby granted, free of charge, to any person obtaining a
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copy of this software and associated documentation files (the
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"Software"), to deal in the Software without restriction, including
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without limitation the rights to use, copy, modify, merge, publish,
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distribute, sublicense, and/or sell copies of the Software, and to permit
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persons to whom the Software is furnished to do so, subject to the
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following conditions:
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The above copyright notice and this permission notice shall be included
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in all copies or substantial portions of the Software.
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THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
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OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
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MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN
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NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM,
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DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR
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OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE
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USE OR OTHER DEALINGS IN THE SOFTWARE.
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[0]: http://tools.ietf.org/html/rfc6979
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[1]: https://github.com/indutny/bn.js
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[2]: https://github.com/indutny/hash.js
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[3]: https://github.com/bitchan/eccrypto
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[4]: https://github.com/wanderer/secp256k1-node
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13
web/node_modules/elliptic/lib/elliptic.js
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13
web/node_modules/elliptic/lib/elliptic.js
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'use strict';
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var elliptic = exports;
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elliptic.version = require('../package.json').version;
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elliptic.utils = require('./elliptic/utils');
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elliptic.rand = require('brorand');
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elliptic.curve = require('./elliptic/curve');
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elliptic.curves = require('./elliptic/curves');
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// Protocols
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elliptic.ec = require('./elliptic/ec');
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elliptic.eddsa = require('./elliptic/eddsa');
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381
web/node_modules/elliptic/lib/elliptic/curve/base.js
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'use strict';
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var BN = require('bn.js');
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var utils = require('../utils');
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var getNAF = utils.getNAF;
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var getJSF = utils.getJSF;
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var assert = utils.assert;
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function BaseCurve(type, conf) {
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this.type = type;
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this.p = new BN(conf.p, 16);
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// Use Montgomery, when there is no fast reduction for the prime
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this.red = conf.prime ? BN.red(conf.prime) : BN.mont(this.p);
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// Useful for many curves
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this.zero = new BN(0).toRed(this.red);
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this.one = new BN(1).toRed(this.red);
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this.two = new BN(2).toRed(this.red);
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// Curve configuration, optional
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this.n = conf.n && new BN(conf.n, 16);
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this.g = conf.g && this.pointFromJSON(conf.g, conf.gRed);
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// Temporary arrays
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this._wnafT1 = new Array(4);
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this._wnafT2 = new Array(4);
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this._wnafT3 = new Array(4);
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this._wnafT4 = new Array(4);
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this._bitLength = this.n ? this.n.bitLength() : 0;
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// Generalized Greg Maxwell's trick
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var adjustCount = this.n && this.p.div(this.n);
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if (!adjustCount || adjustCount.cmpn(100) > 0) {
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this.redN = null;
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} else {
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this._maxwellTrick = true;
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this.redN = this.n.toRed(this.red);
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}
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}
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module.exports = BaseCurve;
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BaseCurve.prototype.point = function point() {
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throw new Error('Not implemented');
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};
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BaseCurve.prototype.validate = function validate() {
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throw new Error('Not implemented');
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};
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BaseCurve.prototype._fixedNafMul = function _fixedNafMul(p, k) {
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assert(p.precomputed);
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var doubles = p._getDoubles();
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var naf = getNAF(k, 1, this._bitLength);
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var I = (1 << (doubles.step + 1)) - (doubles.step % 2 === 0 ? 2 : 1);
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I /= 3;
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// Translate into more windowed form
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var repr = [];
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var j;
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var nafW;
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for (j = 0; j < naf.length; j += doubles.step) {
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nafW = 0;
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for (var l = j + doubles.step - 1; l >= j; l--)
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nafW = (nafW << 1) + naf[l];
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repr.push(nafW);
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}
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var a = this.jpoint(null, null, null);
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var b = this.jpoint(null, null, null);
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for (var i = I; i > 0; i--) {
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for (j = 0; j < repr.length; j++) {
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nafW = repr[j];
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if (nafW === i)
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b = b.mixedAdd(doubles.points[j]);
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else if (nafW === -i)
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b = b.mixedAdd(doubles.points[j].neg());
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}
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a = a.add(b);
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}
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return a.toP();
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};
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BaseCurve.prototype._wnafMul = function _wnafMul(p, k) {
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var w = 4;
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// Precompute window
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var nafPoints = p._getNAFPoints(w);
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w = nafPoints.wnd;
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var wnd = nafPoints.points;
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// Get NAF form
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var naf = getNAF(k, w, this._bitLength);
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// Add `this`*(N+1) for every w-NAF index
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var acc = this.jpoint(null, null, null);
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for (var i = naf.length - 1; i >= 0; i--) {
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// Count zeroes
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for (var l = 0; i >= 0 && naf[i] === 0; i--)
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l++;
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if (i >= 0)
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l++;
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acc = acc.dblp(l);
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if (i < 0)
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break;
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var z = naf[i];
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assert(z !== 0);
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if (p.type === 'affine') {
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// J +- P
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if (z > 0)
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acc = acc.mixedAdd(wnd[(z - 1) >> 1]);
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else
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acc = acc.mixedAdd(wnd[(-z - 1) >> 1].neg());
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} else {
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// J +- J
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if (z > 0)
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acc = acc.add(wnd[(z - 1) >> 1]);
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else
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acc = acc.add(wnd[(-z - 1) >> 1].neg());
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}
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}
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return p.type === 'affine' ? acc.toP() : acc;
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};
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BaseCurve.prototype._wnafMulAdd = function _wnafMulAdd(defW,
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points,
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coeffs,
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len,
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jacobianResult) {
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var wndWidth = this._wnafT1;
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var wnd = this._wnafT2;
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var naf = this._wnafT3;
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// Fill all arrays
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var max = 0;
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var i;
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var j;
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var p;
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for (i = 0; i < len; i++) {
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p = points[i];
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var nafPoints = p._getNAFPoints(defW);
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wndWidth[i] = nafPoints.wnd;
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wnd[i] = nafPoints.points;
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}
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// Comb small window NAFs
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for (i = len - 1; i >= 1; i -= 2) {
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var a = i - 1;
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var b = i;
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if (wndWidth[a] !== 1 || wndWidth[b] !== 1) {
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naf[a] = getNAF(coeffs[a], wndWidth[a], this._bitLength);
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naf[b] = getNAF(coeffs[b], wndWidth[b], this._bitLength);
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max = Math.max(naf[a].length, max);
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max = Math.max(naf[b].length, max);
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continue;
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}
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var comb = [
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points[a], /* 1 */
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null, /* 3 */
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null, /* 5 */
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points[b], /* 7 */
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];
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// Try to avoid Projective points, if possible
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if (points[a].y.cmp(points[b].y) === 0) {
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comb[1] = points[a].add(points[b]);
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comb[2] = points[a].toJ().mixedAdd(points[b].neg());
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} else if (points[a].y.cmp(points[b].y.redNeg()) === 0) {
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comb[1] = points[a].toJ().mixedAdd(points[b]);
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comb[2] = points[a].add(points[b].neg());
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} else {
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comb[1] = points[a].toJ().mixedAdd(points[b]);
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comb[2] = points[a].toJ().mixedAdd(points[b].neg());
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}
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var index = [
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-3, /* -1 -1 */
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-1, /* -1 0 */
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-5, /* -1 1 */
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-7, /* 0 -1 */
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0, /* 0 0 */
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7, /* 0 1 */
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5, /* 1 -1 */
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1, /* 1 0 */
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3, /* 1 1 */
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];
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var jsf = getJSF(coeffs[a], coeffs[b]);
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max = Math.max(jsf[0].length, max);
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naf[a] = new Array(max);
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naf[b] = new Array(max);
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for (j = 0; j < max; j++) {
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var ja = jsf[0][j] | 0;
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var jb = jsf[1][j] | 0;
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naf[a][j] = index[(ja + 1) * 3 + (jb + 1)];
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naf[b][j] = 0;
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wnd[a] = comb;
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}
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}
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||||
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var acc = this.jpoint(null, null, null);
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var tmp = this._wnafT4;
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for (i = max; i >= 0; i--) {
|
||||
var k = 0;
|
||||
|
||||
while (i >= 0) {
|
||||
var zero = true;
|
||||
for (j = 0; j < len; j++) {
|
||||
tmp[j] = naf[j][i] | 0;
|
||||
if (tmp[j] !== 0)
|
||||
zero = false;
|
||||
}
|
||||
if (!zero)
|
||||
break;
|
||||
k++;
|
||||
i--;
|
||||
}
|
||||
if (i >= 0)
|
||||
k++;
|
||||
acc = acc.dblp(k);
|
||||
if (i < 0)
|
||||
break;
|
||||
|
||||
for (j = 0; j < len; j++) {
|
||||
var z = tmp[j];
|
||||
p;
|
||||
if (z === 0)
|
||||
continue;
|
||||
else if (z > 0)
|
||||
p = wnd[j][(z - 1) >> 1];
|
||||
else if (z < 0)
|
||||
p = wnd[j][(-z - 1) >> 1].neg();
|
||||
|
||||
if (p.type === 'affine')
|
||||
acc = acc.mixedAdd(p);
|
||||
else
|
||||
acc = acc.add(p);
|
||||
}
|
||||
}
|
||||
// Zeroify references
|
||||
for (i = 0; i < len; i++)
|
||||
wnd[i] = null;
|
||||
|
||||
if (jacobianResult)
|
||||
return acc;
|
||||
else
|
||||
return acc.toP();
|
||||
};
|
||||
|
||||
function BasePoint(curve, type) {
|
||||
this.curve = curve;
|
||||
this.type = type;
|
||||
this.precomputed = null;
|
||||
}
|
||||
BaseCurve.BasePoint = BasePoint;
|
||||
|
||||
BasePoint.prototype.eq = function eq(/*other*/) {
|
||||
throw new Error('Not implemented');
|
||||
};
|
||||
|
||||
BasePoint.prototype.validate = function validate() {
|
||||
return this.curve.validate(this);
|
||||
};
|
||||
|
||||
BaseCurve.prototype.decodePoint = function decodePoint(bytes, enc) {
|
||||
bytes = utils.toArray(bytes, enc);
|
||||
|
||||
var len = this.p.byteLength();
|
||||
|
||||
// uncompressed, hybrid-odd, hybrid-even
|
||||
if ((bytes[0] === 0x04 || bytes[0] === 0x06 || bytes[0] === 0x07) &&
|
||||
bytes.length - 1 === 2 * len) {
|
||||
if (bytes[0] === 0x06)
|
||||
assert(bytes[bytes.length - 1] % 2 === 0);
|
||||
else if (bytes[0] === 0x07)
|
||||
assert(bytes[bytes.length - 1] % 2 === 1);
|
||||
|
||||
var res = this.point(bytes.slice(1, 1 + len),
|
||||
bytes.slice(1 + len, 1 + 2 * len));
|
||||
|
||||
return res;
|
||||
} else if ((bytes[0] === 0x02 || bytes[0] === 0x03) &&
|
||||
bytes.length - 1 === len) {
|
||||
return this.pointFromX(bytes.slice(1, 1 + len), bytes[0] === 0x03);
|
||||
}
|
||||
throw new Error('Unknown point format');
|
||||
};
|
||||
|
||||
BasePoint.prototype.encodeCompressed = function encodeCompressed(enc) {
|
||||
return this.encode(enc, true);
|
||||
};
|
||||
|
||||
BasePoint.prototype._encode = function _encode(compact) {
|
||||
var len = this.curve.p.byteLength();
|
||||
var x = this.getX().toArray('be', len);
|
||||
|
||||
if (compact)
|
||||
return [ this.getY().isEven() ? 0x02 : 0x03 ].concat(x);
|
||||
|
||||
return [ 0x04 ].concat(x, this.getY().toArray('be', len));
|
||||
};
|
||||
|
||||
BasePoint.prototype.encode = function encode(enc, compact) {
|
||||
return utils.encode(this._encode(compact), enc);
|
||||
};
|
||||
|
||||
BasePoint.prototype.precompute = function precompute(power) {
|
||||
if (this.precomputed)
|
||||
return this;
|
||||
|
||||
var precomputed = {
|
||||
doubles: null,
|
||||
naf: null,
|
||||
beta: null,
|
||||
};
|
||||
precomputed.naf = this._getNAFPoints(8);
|
||||
precomputed.doubles = this._getDoubles(4, power);
|
||||
precomputed.beta = this._getBeta();
|
||||
this.precomputed = precomputed;
|
||||
|
||||
return this;
|
||||
};
|
||||
|
||||
BasePoint.prototype._hasDoubles = function _hasDoubles(k) {
|
||||
if (!this.precomputed)
|
||||
return false;
|
||||
|
||||
var doubles = this.precomputed.doubles;
|
||||
if (!doubles)
|
||||
return false;
|
||||
|
||||
return doubles.points.length >= Math.ceil((k.bitLength() + 1) / doubles.step);
|
||||
};
|
||||
|
||||
BasePoint.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,
|
||||
};
|
||||
};
|
||||
|
||||
BasePoint.prototype._getNAFPoints = function _getNAFPoints(wnd) {
|
||||
if (this.precomputed && this.precomputed.naf)
|
||||
return this.precomputed.naf;
|
||||
|
||||
var res = [ this ];
|
||||
var max = (1 << wnd) - 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,
|
||||
};
|
||||
};
|
||||
|
||||
BasePoint.prototype._getBeta = function _getBeta() {
|
||||
return null;
|
||||
};
|
||||
|
||||
BasePoint.prototype.dblp = function dblp(k) {
|
||||
var r = this;
|
||||
for (var i = 0; i < k; i++)
|
||||
r = r.dbl();
|
||||
return r;
|
||||
};
|
||||
435
web/node_modules/elliptic/lib/elliptic/curve/edwards.js
generated
vendored
Normal file
435
web/node_modules/elliptic/lib/elliptic/curve/edwards.js
generated
vendored
Normal file
|
|
@ -0,0 +1,435 @@
|
|||
'use strict';
|
||||
|
||||
var utils = require('../utils');
|
||||
var BN = require('bn.js');
|
||||
var inherits = require('inherits');
|
||||
var Base = require('./base');
|
||||
|
||||
var assert = utils.assert;
|
||||
|
||||
function EdwardsCurve(conf) {
|
||||
// NOTE: Important as we are creating point in Base.call()
|
||||
this.twisted = (conf.a | 0) !== 1;
|
||||
this.mOneA = this.twisted && (conf.a | 0) === -1;
|
||||
this.extended = this.mOneA;
|
||||
|
||||
Base.call(this, 'edwards', conf);
|
||||
|
||||
this.a = new BN(conf.a, 16).umod(this.red.m);
|
||||
this.a = this.a.toRed(this.red);
|
||||
this.c = new BN(conf.c, 16).toRed(this.red);
|
||||
this.c2 = this.c.redSqr();
|
||||
this.d = new BN(conf.d, 16).toRed(this.red);
|
||||
this.dd = this.d.redAdd(this.d);
|
||||
|
||||
assert(!this.twisted || this.c.fromRed().cmpn(1) === 0);
|
||||
this.oneC = (conf.c | 0) === 1;
|
||||
}
|
||||
inherits(EdwardsCurve, Base);
|
||||
module.exports = EdwardsCurve;
|
||||
|
||||
EdwardsCurve.prototype._mulA = function _mulA(num) {
|
||||
if (this.mOneA)
|
||||
return num.redNeg();
|
||||
else
|
||||
return this.a.redMul(num);
|
||||
};
|
||||
|
||||
EdwardsCurve.prototype._mulC = function _mulC(num) {
|
||||
if (this.oneC)
|
||||
return num;
|
||||
else
|
||||
return this.c.redMul(num);
|
||||
};
|
||||
|
||||
// Just for compatibility with Short curve
|
||||
EdwardsCurve.prototype.jpoint = function jpoint(x, y, z, t) {
|
||||
return this.point(x, y, z, t);
|
||||
};
|
||||
|
||||
EdwardsCurve.prototype.pointFromX = function pointFromX(x, odd) {
|
||||
x = new BN(x, 16);
|
||||
if (!x.red)
|
||||
x = x.toRed(this.red);
|
||||
|
||||
var x2 = x.redSqr();
|
||||
var rhs = this.c2.redSub(this.a.redMul(x2));
|
||||
var lhs = this.one.redSub(this.c2.redMul(this.d).redMul(x2));
|
||||
|
||||
var y2 = rhs.redMul(lhs.redInvm());
|
||||
var y = y2.redSqrt();
|
||||
if (y.redSqr().redSub(y2).cmp(this.zero) !== 0)
|
||||
throw new Error('invalid point');
|
||||
|
||||
var isOdd = y.fromRed().isOdd();
|
||||
if (odd && !isOdd || !odd && isOdd)
|
||||
y = y.redNeg();
|
||||
|
||||
return this.point(x, y);
|
||||
};
|
||||
|
||||
EdwardsCurve.prototype.pointFromY = function pointFromY(y, odd) {
|
||||
y = new BN(y, 16);
|
||||
if (!y.red)
|
||||
y = y.toRed(this.red);
|
||||
|
||||
// x^2 = (y^2 - c^2) / (c^2 d y^2 - a)
|
||||
var y2 = y.redSqr();
|
||||
var lhs = y2.redSub(this.c2);
|
||||
var rhs = y2.redMul(this.d).redMul(this.c2).redSub(this.a);
|
||||
var x2 = lhs.redMul(rhs.redInvm());
|
||||
|
||||
if (x2.cmp(this.zero) === 0) {
|
||||
if (odd)
|
||||
throw new Error('invalid point');
|
||||
else
|
||||
return this.point(this.zero, y);
|
||||
}
|
||||
|
||||
var x = x2.redSqrt();
|
||||
if (x.redSqr().redSub(x2).cmp(this.zero) !== 0)
|
||||
throw new Error('invalid point');
|
||||
|
||||
if (x.fromRed().isOdd() !== odd)
|
||||
x = x.redNeg();
|
||||
|
||||
return this.point(x, y);
|
||||
};
|
||||
|
||||
EdwardsCurve.prototype.validate = function validate(point) {
|
||||
if (point.isInfinity())
|
||||
return true;
|
||||
|
||||
// Curve: A * X^2 + Y^2 = C^2 * (1 + D * X^2 * Y^2)
|
||||
point.normalize();
|
||||
|
||||
var x2 = point.x.redSqr();
|
||||
var y2 = point.y.redSqr();
|
||||
var lhs = x2.redMul(this.a).redAdd(y2);
|
||||
var rhs = this.c2.redMul(this.one.redAdd(this.d.redMul(x2).redMul(y2)));
|
||||
|
||||
return lhs.cmp(rhs) === 0;
|
||||
};
|
||||
|
||||
function Point(curve, x, y, z, t) {
|
||||
Base.BasePoint.call(this, curve, 'projective');
|
||||
if (x === null && y === null && z === null) {
|
||||
this.x = this.curve.zero;
|
||||
this.y = this.curve.one;
|
||||
this.z = this.curve.one;
|
||||
this.t = this.curve.zero;
|
||||
this.zOne = true;
|
||||
} else {
|
||||
this.x = new BN(x, 16);
|
||||
this.y = new BN(y, 16);
|
||||
this.z = z ? new BN(z, 16) : this.curve.one;
|
||||
this.t = t && new BN(t, 16);
|
||||
if (!this.x.red)
|
||||
this.x = this.x.toRed(this.curve.red);
|
||||
if (!this.y.red)
|
||||
this.y = this.y.toRed(this.curve.red);
|
||||
if (!this.z.red)
|
||||
this.z = this.z.toRed(this.curve.red);
|
||||
if (this.t && !this.t.red)
|
||||
this.t = this.t.toRed(this.curve.red);
|
||||
this.zOne = this.z === this.curve.one;
|
||||
|
||||
// Use extended coordinates
|
||||
if (this.curve.extended && !this.t) {
|
||||
this.t = this.x.redMul(this.y);
|
||||
if (!this.zOne)
|
||||
this.t = this.t.redMul(this.z.redInvm());
|
||||
}
|
||||
}
|
||||
}
|
||||
inherits(Point, Base.BasePoint);
|
||||
|
||||
EdwardsCurve.prototype.pointFromJSON = function pointFromJSON(obj) {
|
||||
return Point.fromJSON(this, obj);
|
||||
};
|
||||
|
||||
EdwardsCurve.prototype.point = function point(x, y, z, t) {
|
||||
return new Point(this, x, y, z, t);
|
||||
};
|
||||
|
||||
Point.fromJSON = function fromJSON(curve, obj) {
|
||||
return new Point(curve, obj[0], obj[1], obj[2]);
|
||||
};
|
||||
|
||||
Point.prototype.inspect = function inspect() {
|
||||
if (this.isInfinity())
|
||||
return '<EC Point Infinity>';
|
||||
return '<EC Point x: ' + this.x.fromRed().toString(16, 2) +
|
||||
' y: ' + this.y.fromRed().toString(16, 2) +
|
||||
' z: ' + this.z.fromRed().toString(16, 2) + '>';
|
||||
};
|
||||
|
||||
Point.prototype.isInfinity = function isInfinity() {
|
||||
// XXX This code assumes that zero is always zero in red
|
||||
return this.x.cmpn(0) === 0 &&
|
||||
(this.y.cmp(this.z) === 0 ||
|
||||
(this.zOne && this.y.cmp(this.curve.c) === 0));
|
||||
};
|
||||
|
||||
Point.prototype._extDbl = function _extDbl() {
|
||||
// hyperelliptic.org/EFD/g1p/auto-twisted-extended-1.html
|
||||
// #doubling-dbl-2008-hwcd
|
||||
// 4M + 4S
|
||||
|
||||
// A = X1^2
|
||||
var a = this.x.redSqr();
|
||||
// B = Y1^2
|
||||
var b = this.y.redSqr();
|
||||
// C = 2 * Z1^2
|
||||
var c = this.z.redSqr();
|
||||
c = c.redIAdd(c);
|
||||
// D = a * A
|
||||
var d = this.curve._mulA(a);
|
||||
// E = (X1 + Y1)^2 - A - B
|
||||
var e = this.x.redAdd(this.y).redSqr().redISub(a).redISub(b);
|
||||
// G = D + B
|
||||
var g = d.redAdd(b);
|
||||
// F = G - C
|
||||
var f = g.redSub(c);
|
||||
// H = D - B
|
||||
var h = d.redSub(b);
|
||||
// X3 = E * F
|
||||
var nx = e.redMul(f);
|
||||
// Y3 = G * H
|
||||
var ny = g.redMul(h);
|
||||
// T3 = E * H
|
||||
var nt = e.redMul(h);
|
||||
// Z3 = F * G
|
||||
var nz = f.redMul(g);
|
||||
return this.curve.point(nx, ny, nz, nt);
|
||||
};
|
||||
|
||||
Point.prototype._projDbl = function _projDbl() {
|
||||
// hyperelliptic.org/EFD/g1p/auto-twisted-projective.html
|
||||
// #doubling-dbl-2008-bbjlp
|
||||
// #doubling-dbl-2007-bl
|
||||
// and others
|
||||
// Generally 3M + 4S or 2M + 4S
|
||||
|
||||
// B = (X1 + Y1)^2
|
||||
var b = this.x.redAdd(this.y).redSqr();
|
||||
// C = X1^2
|
||||
var c = this.x.redSqr();
|
||||
// D = Y1^2
|
||||
var d = this.y.redSqr();
|
||||
|
||||
var nx;
|
||||
var ny;
|
||||
var nz;
|
||||
var e;
|
||||
var h;
|
||||
var j;
|
||||
if (this.curve.twisted) {
|
||||
// E = a * C
|
||||
e = this.curve._mulA(c);
|
||||
// F = E + D
|
||||
var f = e.redAdd(d);
|
||||
if (this.zOne) {
|
||||
// X3 = (B - C - D) * (F - 2)
|
||||
nx = b.redSub(c).redSub(d).redMul(f.redSub(this.curve.two));
|
||||
// Y3 = F * (E - D)
|
||||
ny = f.redMul(e.redSub(d));
|
||||
// Z3 = F^2 - 2 * F
|
||||
nz = f.redSqr().redSub(f).redSub(f);
|
||||
} else {
|
||||
// H = Z1^2
|
||||
h = this.z.redSqr();
|
||||
// J = F - 2 * H
|
||||
j = f.redSub(h).redISub(h);
|
||||
// X3 = (B-C-D)*J
|
||||
nx = b.redSub(c).redISub(d).redMul(j);
|
||||
// Y3 = F * (E - D)
|
||||
ny = f.redMul(e.redSub(d));
|
||||
// Z3 = F * J
|
||||
nz = f.redMul(j);
|
||||
}
|
||||
} else {
|
||||
// E = C + D
|
||||
e = c.redAdd(d);
|
||||
// H = (c * Z1)^2
|
||||
h = this.curve._mulC(this.z).redSqr();
|
||||
// J = E - 2 * H
|
||||
j = e.redSub(h).redSub(h);
|
||||
// X3 = c * (B - E) * J
|
||||
nx = this.curve._mulC(b.redISub(e)).redMul(j);
|
||||
// Y3 = c * E * (C - D)
|
||||
ny = this.curve._mulC(e).redMul(c.redISub(d));
|
||||
// Z3 = E * J
|
||||
nz = e.redMul(j);
|
||||
}
|
||||
return this.curve.point(nx, ny, nz);
|
||||
};
|
||||
|
||||
Point.prototype.dbl = function dbl() {
|
||||
if (this.isInfinity())
|
||||
return this;
|
||||
|
||||
// Double in extended coordinates
|
||||
if (this.curve.extended)
|
||||
return this._extDbl();
|
||||
else
|
||||
return this._projDbl();
|
||||
};
|
||||
|
||||
Point.prototype._extAdd = function _extAdd(p) {
|
||||
// hyperelliptic.org/EFD/g1p/auto-twisted-extended-1.html
|
||||
// #addition-add-2008-hwcd-3
|
||||
// 8M
|
||||
|
||||
// A = (Y1 - X1) * (Y2 - X2)
|
||||
var a = this.y.redSub(this.x).redMul(p.y.redSub(p.x));
|
||||
// B = (Y1 + X1) * (Y2 + X2)
|
||||
var b = this.y.redAdd(this.x).redMul(p.y.redAdd(p.x));
|
||||
// C = T1 * k * T2
|
||||
var c = this.t.redMul(this.curve.dd).redMul(p.t);
|
||||
// D = Z1 * 2 * Z2
|
||||
var d = this.z.redMul(p.z.redAdd(p.z));
|
||||
// E = B - A
|
||||
var e = b.redSub(a);
|
||||
// F = D - C
|
||||
var f = d.redSub(c);
|
||||
// G = D + C
|
||||
var g = d.redAdd(c);
|
||||
// H = B + A
|
||||
var h = b.redAdd(a);
|
||||
// X3 = E * F
|
||||
var nx = e.redMul(f);
|
||||
// Y3 = G * H
|
||||
var ny = g.redMul(h);
|
||||
// T3 = E * H
|
||||
var nt = e.redMul(h);
|
||||
// Z3 = F * G
|
||||
var nz = f.redMul(g);
|
||||
return this.curve.point(nx, ny, nz, nt);
|
||||
};
|
||||
|
||||
Point.prototype._projAdd = function _projAdd(p) {
|
||||
// hyperelliptic.org/EFD/g1p/auto-twisted-projective.html
|
||||
// #addition-add-2008-bbjlp
|
||||
// #addition-add-2007-bl
|
||||
// 10M + 1S
|
||||
|
||||
// A = Z1 * Z2
|
||||
var a = this.z.redMul(p.z);
|
||||
// B = A^2
|
||||
var b = a.redSqr();
|
||||
// C = X1 * X2
|
||||
var c = this.x.redMul(p.x);
|
||||
// D = Y1 * Y2
|
||||
var d = this.y.redMul(p.y);
|
||||
// E = d * C * D
|
||||
var e = this.curve.d.redMul(c).redMul(d);
|
||||
// F = B - E
|
||||
var f = b.redSub(e);
|
||||
// G = B + E
|
||||
var g = b.redAdd(e);
|
||||
// X3 = A * F * ((X1 + Y1) * (X2 + Y2) - C - D)
|
||||
var tmp = this.x.redAdd(this.y).redMul(p.x.redAdd(p.y)).redISub(c).redISub(d);
|
||||
var nx = a.redMul(f).redMul(tmp);
|
||||
var ny;
|
||||
var nz;
|
||||
if (this.curve.twisted) {
|
||||
// Y3 = A * G * (D - a * C)
|
||||
ny = a.redMul(g).redMul(d.redSub(this.curve._mulA(c)));
|
||||
// Z3 = F * G
|
||||
nz = f.redMul(g);
|
||||
} else {
|
||||
// Y3 = A * G * (D - C)
|
||||
ny = a.redMul(g).redMul(d.redSub(c));
|
||||
// Z3 = c * F * G
|
||||
nz = this.curve._mulC(f).redMul(g);
|
||||
}
|
||||
return this.curve.point(nx, ny, nz);
|
||||
};
|
||||
|
||||
Point.prototype.add = function add(p) {
|
||||
if (this.isInfinity())
|
||||
return p;
|
||||
if (p.isInfinity())
|
||||
return this;
|
||||
|
||||
if (this.curve.extended)
|
||||
return this._extAdd(p);
|
||||
else
|
||||
return this._projAdd(p);
|
||||
};
|
||||
|
||||
Point.prototype.mul = function mul(k) {
|
||||
if (this._hasDoubles(k))
|
||||
return this.curve._fixedNafMul(this, k);
|
||||
else
|
||||
return this.curve._wnafMul(this, k);
|
||||
};
|
||||
|
||||
Point.prototype.mulAdd = function mulAdd(k1, p, k2) {
|
||||
return this.curve._wnafMulAdd(1, [ this, p ], [ k1, k2 ], 2, false);
|
||||
};
|
||||
|
||||
Point.prototype.jmulAdd = function jmulAdd(k1, p, k2) {
|
||||
return this.curve._wnafMulAdd(1, [ this, p ], [ k1, k2 ], 2, true);
|
||||
};
|
||||
|
||||
Point.prototype.normalize = function normalize() {
|
||||
if (this.zOne)
|
||||
return this;
|
||||
|
||||
// Normalize coordinates
|
||||
var zi = this.z.redInvm();
|
||||
this.x = this.x.redMul(zi);
|
||||
this.y = this.y.redMul(zi);
|
||||
if (this.t)
|
||||
this.t = this.t.redMul(zi);
|
||||
this.z = this.curve.one;
|
||||
this.zOne = true;
|
||||
return this;
|
||||
};
|
||||
|
||||
Point.prototype.neg = function neg() {
|
||||
return this.curve.point(this.x.redNeg(),
|
||||
this.y,
|
||||
this.z,
|
||||
this.t && this.t.redNeg());
|
||||
};
|
||||
|
||||
Point.prototype.getX = function getX() {
|
||||
this.normalize();
|
||||
return this.x.fromRed();
|
||||
};
|
||||
|
||||
Point.prototype.getY = function getY() {
|
||||
this.normalize();
|
||||
return this.y.fromRed();
|
||||
};
|
||||
|
||||
Point.prototype.eq = function eq(other) {
|
||||
return this === other ||
|
||||
this.getX().cmp(other.getX()) === 0 &&
|
||||
this.getY().cmp(other.getY()) === 0;
|
||||
};
|
||||
|
||||
Point.prototype.eqXToP = function eqXToP(x) {
|
||||
var rx = x.toRed(this.curve.red).redMul(this.z);
|
||||
if (this.x.cmp(rx) === 0)
|
||||
return true;
|
||||
|
||||
var xc = x.clone();
|
||||
var t = this.curve.redN.redMul(this.z);
|
||||
for (;;) {
|
||||
xc.iadd(this.curve.n);
|
||||
if (xc.cmp(this.curve.p) >= 0)
|
||||
return false;
|
||||
|
||||
rx.redIAdd(t);
|
||||
if (this.x.cmp(rx) === 0)
|
||||
return true;
|
||||
}
|
||||
};
|
||||
|
||||
// Compatibility with BaseCurve
|
||||
Point.prototype.toP = Point.prototype.normalize;
|
||||
Point.prototype.mixedAdd = Point.prototype.add;
|
||||
8
web/node_modules/elliptic/lib/elliptic/curve/index.js
generated
vendored
Normal file
8
web/node_modules/elliptic/lib/elliptic/curve/index.js
generated
vendored
Normal file
|
|
@ -0,0 +1,8 @@
|
|||
'use strict';
|
||||
|
||||
var curve = exports;
|
||||
|
||||
curve.base = require('./base');
|
||||
curve.short = require('./short');
|
||||
curve.mont = require('./mont');
|
||||
curve.edwards = require('./edwards');
|
||||
178
web/node_modules/elliptic/lib/elliptic/curve/mont.js
generated
vendored
Normal file
178
web/node_modules/elliptic/lib/elliptic/curve/mont.js
generated
vendored
Normal file
|
|
@ -0,0 +1,178 @@
|
|||
'use strict';
|
||||
|
||||
var BN = require('bn.js');
|
||||
var inherits = require('inherits');
|
||||
var Base = require('./base');
|
||||
|
||||
var utils = require('../utils');
|
||||
|
||||
function MontCurve(conf) {
|
||||
Base.call(this, 'mont', conf);
|
||||
|
||||
this.a = new BN(conf.a, 16).toRed(this.red);
|
||||
this.b = new BN(conf.b, 16).toRed(this.red);
|
||||
this.i4 = new BN(4).toRed(this.red).redInvm();
|
||||
this.two = new BN(2).toRed(this.red);
|
||||
this.a24 = this.i4.redMul(this.a.redAdd(this.two));
|
||||
}
|
||||
inherits(MontCurve, Base);
|
||||
module.exports = MontCurve;
|
||||
|
||||
MontCurve.prototype.validate = function validate(point) {
|
||||
var x = point.normalize().x;
|
||||
var x2 = x.redSqr();
|
||||
var rhs = x2.redMul(x).redAdd(x2.redMul(this.a)).redAdd(x);
|
||||
var y = rhs.redSqrt();
|
||||
|
||||
return y.redSqr().cmp(rhs) === 0;
|
||||
};
|
||||
|
||||
function Point(curve, x, z) {
|
||||
Base.BasePoint.call(this, curve, 'projective');
|
||||
if (x === null && z === null) {
|
||||
this.x = this.curve.one;
|
||||
this.z = this.curve.zero;
|
||||
} else {
|
||||
this.x = new BN(x, 16);
|
||||
this.z = new BN(z, 16);
|
||||
if (!this.x.red)
|
||||
this.x = this.x.toRed(this.curve.red);
|
||||
if (!this.z.red)
|
||||
this.z = this.z.toRed(this.curve.red);
|
||||
}
|
||||
}
|
||||
inherits(Point, Base.BasePoint);
|
||||
|
||||
MontCurve.prototype.decodePoint = function decodePoint(bytes, enc) {
|
||||
return this.point(utils.toArray(bytes, enc), 1);
|
||||
};
|
||||
|
||||
MontCurve.prototype.point = function point(x, z) {
|
||||
return new Point(this, x, z);
|
||||
};
|
||||
|
||||
MontCurve.prototype.pointFromJSON = function pointFromJSON(obj) {
|
||||
return Point.fromJSON(this, obj);
|
||||
};
|
||||
|
||||
Point.prototype.precompute = function precompute() {
|
||||
// No-op
|
||||
};
|
||||
|
||||
Point.prototype._encode = function _encode() {
|
||||
return this.getX().toArray('be', this.curve.p.byteLength());
|
||||
};
|
||||
|
||||
Point.fromJSON = function fromJSON(curve, obj) {
|
||||
return new Point(curve, obj[0], obj[1] || curve.one);
|
||||
};
|
||||
|
||||
Point.prototype.inspect = function inspect() {
|
||||
if (this.isInfinity())
|
||||
return '<EC Point Infinity>';
|
||||
return '<EC Point x: ' + this.x.fromRed().toString(16, 2) +
|
||||
' z: ' + this.z.fromRed().toString(16, 2) + '>';
|
||||
};
|
||||
|
||||
Point.prototype.isInfinity = function isInfinity() {
|
||||
// XXX This code assumes that zero is always zero in red
|
||||
return this.z.cmpn(0) === 0;
|
||||
};
|
||||
|
||||
Point.prototype.dbl = function dbl() {
|
||||
// http://hyperelliptic.org/EFD/g1p/auto-montgom-xz.html#doubling-dbl-1987-m-3
|
||||
// 2M + 2S + 4A
|
||||
|
||||
// A = X1 + Z1
|
||||
var a = this.x.redAdd(this.z);
|
||||
// AA = A^2
|
||||
var aa = a.redSqr();
|
||||
// B = X1 - Z1
|
||||
var b = this.x.redSub(this.z);
|
||||
// BB = B^2
|
||||
var bb = b.redSqr();
|
||||
// C = AA - BB
|
||||
var c = aa.redSub(bb);
|
||||
// X3 = AA * BB
|
||||
var nx = aa.redMul(bb);
|
||||
// Z3 = C * (BB + A24 * C)
|
||||
var nz = c.redMul(bb.redAdd(this.curve.a24.redMul(c)));
|
||||
return this.curve.point(nx, nz);
|
||||
};
|
||||
|
||||
Point.prototype.add = function add() {
|
||||
throw new Error('Not supported on Montgomery curve');
|
||||
};
|
||||
|
||||
Point.prototype.diffAdd = function diffAdd(p, diff) {
|
||||
// http://hyperelliptic.org/EFD/g1p/auto-montgom-xz.html#diffadd-dadd-1987-m-3
|
||||
// 4M + 2S + 6A
|
||||
|
||||
// A = X2 + Z2
|
||||
var a = this.x.redAdd(this.z);
|
||||
// B = X2 - Z2
|
||||
var b = this.x.redSub(this.z);
|
||||
// C = X3 + Z3
|
||||
var c = p.x.redAdd(p.z);
|
||||
// D = X3 - Z3
|
||||
var d = p.x.redSub(p.z);
|
||||
// DA = D * A
|
||||
var da = d.redMul(a);
|
||||
// CB = C * B
|
||||
var cb = c.redMul(b);
|
||||
// X5 = Z1 * (DA + CB)^2
|
||||
var nx = diff.z.redMul(da.redAdd(cb).redSqr());
|
||||
// Z5 = X1 * (DA - CB)^2
|
||||
var nz = diff.x.redMul(da.redISub(cb).redSqr());
|
||||
return this.curve.point(nx, nz);
|
||||
};
|
||||
|
||||
Point.prototype.mul = function mul(k) {
|
||||
var t = k.clone();
|
||||
var a = this; // (N / 2) * Q + Q
|
||||
var b = this.curve.point(null, null); // (N / 2) * Q
|
||||
var c = this; // Q
|
||||
|
||||
for (var bits = []; t.cmpn(0) !== 0; t.iushrn(1))
|
||||
bits.push(t.andln(1));
|
||||
|
||||
for (var i = bits.length - 1; i >= 0; i--) {
|
||||
if (bits[i] === 0) {
|
||||
// N * Q + Q = ((N / 2) * Q + Q)) + (N / 2) * Q
|
||||
a = a.diffAdd(b, c);
|
||||
// N * Q = 2 * ((N / 2) * Q + Q))
|
||||
b = b.dbl();
|
||||
} else {
|
||||
// N * Q = ((N / 2) * Q + Q) + ((N / 2) * Q)
|
||||
b = a.diffAdd(b, c);
|
||||
// N * Q + Q = 2 * ((N / 2) * Q + Q)
|
||||
a = a.dbl();
|
||||
}
|
||||
}
|
||||
return b;
|
||||
};
|
||||
|
||||
Point.prototype.mulAdd = function mulAdd() {
|
||||
throw new Error('Not supported on Montgomery curve');
|
||||
};
|
||||
|
||||
Point.prototype.jumlAdd = function jumlAdd() {
|
||||
throw new Error('Not supported on Montgomery curve');
|
||||
};
|
||||
|
||||
Point.prototype.eq = function eq(other) {
|
||||
return this.getX().cmp(other.getX()) === 0;
|
||||
};
|
||||
|
||||
Point.prototype.normalize = function normalize() {
|
||||
this.x = this.x.redMul(this.z.redInvm());
|
||||
this.z = this.curve.one;
|
||||
return this;
|
||||
};
|
||||
|
||||
Point.prototype.getX = function getX() {
|
||||
// Normalize coordinates
|
||||
this.normalize();
|
||||
|
||||
return this.x.fromRed();
|
||||
};
|
||||
938
web/node_modules/elliptic/lib/elliptic/curve/short.js
generated
vendored
Normal file
938
web/node_modules/elliptic/lib/elliptic/curve/short.js
generated
vendored
Normal file
|
|
@ -0,0 +1,938 @@
|
|||
'use strict';
|
||||
|
||||
var utils = require('../utils');
|
||||
var BN = require('bn.js');
|
||||
var inherits = require('inherits');
|
||||
var Base = require('./base');
|
||||
|
||||
var assert = utils.assert;
|
||||
|
||||
function ShortCurve(conf) {
|
||||
Base.call(this, 'short', conf);
|
||||
|
||||
this.a = new BN(conf.a, 16).toRed(this.red);
|
||||
this.b = new BN(conf.b, 16).toRed(this.red);
|
||||
this.tinv = this.two.redInvm();
|
||||
|
||||
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);
|
||||
this._endoWnafT1 = new Array(4);
|
||||
this._endoWnafT2 = new Array(4);
|
||||
}
|
||||
inherits(ShortCurve, Base);
|
||||
module.exports = ShortCurve;
|
||||
|
||||
ShortCurve.prototype._getEndomorphism = function _getEndomorphism(conf) {
|
||||
// No efficient endomorphism
|
||||
if (!this.zeroA || !this.g || !this.n || this.p.modn(3) !== 1)
|
||||
return;
|
||||
|
||||
// Compute beta and lambda, that lambda * P = (beta * Px; Py)
|
||||
var beta;
|
||||
var lambda;
|
||||
if (conf.beta) {
|
||||
beta = new BN(conf.beta, 16).toRed(this.red);
|
||||
} else {
|
||||
var betas = this._getEndoRoots(this.p);
|
||||
// Choose the smallest beta
|
||||
beta = betas[0].cmp(betas[1]) < 0 ? betas[0] : betas[1];
|
||||
beta = beta.toRed(this.red);
|
||||
}
|
||||
if (conf.lambda) {
|
||||
lambda = new BN(conf.lambda, 16);
|
||||
} else {
|
||||
// Choose the lambda that is matching selected beta
|
||||
var lambdas = this._getEndoRoots(this.n);
|
||||
if (this.g.mul(lambdas[0]).x.cmp(this.g.x.redMul(beta)) === 0) {
|
||||
lambda = lambdas[0];
|
||||
} else {
|
||||
lambda = lambdas[1];
|
||||
assert(this.g.mul(lambda).x.cmp(this.g.x.redMul(beta)) === 0);
|
||||
}
|
||||
}
|
||||
|
||||
// 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,
|
||||
};
|
||||
};
|
||||
|
||||
ShortCurve.prototype._getEndoRoots = function _getEndoRoots(num) {
|
||||
// Find roots of for x^2 + x + 1 in F
|
||||
// Root = (-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 s = new BN(3).toRed(red).redNeg().redSqrt().redMul(tinv);
|
||||
|
||||
var l1 = ntinv.redAdd(s).fromRed();
|
||||
var l2 = ntinv.redSub(s).fromRed();
|
||||
return [ l1, l2 ];
|
||||
};
|
||||
|
||||
ShortCurve.prototype._getEndoBasis = function _getEndoBasis(lambda) {
|
||||
// aprxSqrt >= sqrt(this.n)
|
||||
var aprxSqrt = this.n.ushrn(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;
|
||||
var r;
|
||||
var x;
|
||||
while (u.cmpn(0) !== 0) {
|
||||
var q = v.div(u);
|
||||
r = v.sub(q.mul(u));
|
||||
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.negative) {
|
||||
a1 = a1.neg();
|
||||
b1 = b1.neg();
|
||||
}
|
||||
if (a2.negative) {
|
||||
a2 = a2.neg();
|
||||
b2 = b2.neg();
|
||||
}
|
||||
|
||||
return [
|
||||
{ a: a1, b: b1 },
|
||||
{ a: a2, b: b2 },
|
||||
];
|
||||
};
|
||||
|
||||
ShortCurve.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 };
|
||||
};
|
||||
|
||||
ShortCurve.prototype.pointFromX = function pointFromX(x, odd) {
|
||||
x = new BN(x, 16);
|
||||
if (!x.red)
|
||||
x = x.toRed(this.red);
|
||||
|
||||
var y2 = x.redSqr().redMul(x).redIAdd(x.redMul(this.a)).redIAdd(this.b);
|
||||
var y = y2.redSqrt();
|
||||
if (y.redSqr().redSub(y2).cmp(this.zero) !== 0)
|
||||
throw new Error('invalid point');
|
||||
|
||||
// XXX Is there any way to tell if the number is odd without converting it
|
||||
// to non-red form?
|
||||
var isOdd = y.fromRed().isOdd();
|
||||
if (odd && !isOdd || !odd && isOdd)
|
||||
y = y.redNeg();
|
||||
|
||||
return this.point(x, y);
|
||||
};
|
||||
|
||||
ShortCurve.prototype.validate = function validate(point) {
|
||||
if (point.inf)
|
||||
return true;
|
||||
|
||||
var x = point.x;
|
||||
var y = point.y;
|
||||
|
||||
var ax = this.a.redMul(x);
|
||||
var rhs = x.redSqr().redMul(x).redIAdd(ax).redIAdd(this.b);
|
||||
return y.redSqr().redISub(rhs).cmpn(0) === 0;
|
||||
};
|
||||
|
||||
ShortCurve.prototype._endoWnafMulAdd =
|
||||
function _endoWnafMulAdd(points, coeffs, jacobianResult) {
|
||||
var npoints = this._endoWnafT1;
|
||||
var ncoeffs = this._endoWnafT2;
|
||||
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.negative) {
|
||||
split.k1.ineg();
|
||||
p = p.neg(true);
|
||||
}
|
||||
if (split.k2.negative) {
|
||||
split.k2.ineg();
|
||||
beta = beta.neg(true);
|
||||
}
|
||||
|
||||
npoints[i * 2] = p;
|
||||
npoints[i * 2 + 1] = beta;
|
||||
ncoeffs[i * 2] = split.k1;
|
||||
ncoeffs[i * 2 + 1] = split.k2;
|
||||
}
|
||||
var res = this._wnafMulAdd(1, npoints, ncoeffs, i * 2, jacobianResult);
|
||||
|
||||
// Clean-up references to points and coefficients
|
||||
for (var j = 0; j < i * 2; j++) {
|
||||
npoints[j] = null;
|
||||
ncoeffs[j] = null;
|
||||
}
|
||||
return res;
|
||||
};
|
||||
|
||||
function Point(curve, x, y, isRed) {
|
||||
Base.BasePoint.call(this, curve, 'affine');
|
||||
if (x === null && y === null) {
|
||||
this.x = null;
|
||||
this.y = null;
|
||||
this.inf = true;
|
||||
} else {
|
||||
this.x = new BN(x, 16);
|
||||
this.y = new BN(y, 16);
|
||||
// Force redgomery representation when loading from JSON
|
||||
if (isRed) {
|
||||
this.x.forceRed(this.curve.red);
|
||||
this.y.forceRed(this.curve.red);
|
||||
}
|
||||
if (!this.x.red)
|
||||
this.x = this.x.toRed(this.curve.red);
|
||||
if (!this.y.red)
|
||||
this.y = this.y.toRed(this.curve.red);
|
||||
this.inf = false;
|
||||
}
|
||||
}
|
||||
inherits(Point, Base.BasePoint);
|
||||
|
||||
ShortCurve.prototype.point = function point(x, y, isRed) {
|
||||
return new Point(this, x, y, isRed);
|
||||
};
|
||||
|
||||
ShortCurve.prototype.pointFromJSON = function pointFromJSON(obj, red) {
|
||||
return Point.fromJSON(this, obj, red);
|
||||
};
|
||||
|
||||
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;
|
||||
var endoMul = function(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.toJSON = function toJSON() {
|
||||
if (!this.precomputed)
|
||||
return [ 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),
|
||||
},
|
||||
} ];
|
||||
};
|
||||
|
||||
Point.fromJSON = function fromJSON(curve, obj, red) {
|
||||
if (typeof obj === 'string')
|
||||
obj = JSON.parse(obj);
|
||||
var res = curve.point(obj[0], obj[1], red);
|
||||
if (!obj[2])
|
||||
return res;
|
||||
|
||||
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.inspect = function inspect() {
|
||||
if (this.isInfinity())
|
||||
return '<EC Point Infinity>';
|
||||
return '<EC Point x: ' + this.x.fromRed().toString(16, 2) +
|
||||
' y: ' + this.y.fromRed().toString(16, 2) + '>';
|
||||
};
|
||||
|
||||
Point.prototype.isInfinity = function isInfinity() {
|
||||
return this.inf;
|
||||
};
|
||||
|
||||
Point.prototype.add = function add(p) {
|
||||
// O + P = P
|
||||
if (this.inf)
|
||||
return p;
|
||||
|
||||
// P + O = P
|
||||
if (p.inf)
|
||||
return this;
|
||||
|
||||
// P + P = 2P
|
||||
if (this.eq(p))
|
||||
return this.dbl();
|
||||
|
||||
// P + (-P) = O
|
||||
if (this.neg().eq(p))
|
||||
return this.curve.point(null, null);
|
||||
|
||||
// P + Q = O
|
||||
if (this.x.cmp(p.x) === 0)
|
||||
return this.curve.point(null, null);
|
||||
|
||||
var c = this.y.redSub(p.y);
|
||||
if (c.cmpn(0) !== 0)
|
||||
c = c.redMul(this.x.redSub(p.x).redInvm());
|
||||
var nx = c.redSqr().redISub(this.x).redISub(p.x);
|
||||
var ny = c.redMul(this.x.redSub(nx)).redISub(this.y);
|
||||
return this.curve.point(nx, ny);
|
||||
};
|
||||
|
||||
Point.prototype.dbl = function dbl() {
|
||||
if (this.inf)
|
||||
return this;
|
||||
|
||||
// 2P = O
|
||||
var ys1 = this.y.redAdd(this.y);
|
||||
if (ys1.cmpn(0) === 0)
|
||||
return this.curve.point(null, null);
|
||||
|
||||
var a = this.curve.a;
|
||||
|
||||
var x2 = this.x.redSqr();
|
||||
var dyinv = ys1.redInvm();
|
||||
var c = x2.redAdd(x2).redIAdd(x2).redIAdd(a).redMul(dyinv);
|
||||
|
||||
var nx = c.redSqr().redISub(this.x.redAdd(this.x));
|
||||
var ny = c.redMul(this.x.redSub(nx)).redISub(this.y);
|
||||
return this.curve.point(nx, ny);
|
||||
};
|
||||
|
||||
Point.prototype.getX = function getX() {
|
||||
return this.x.fromRed();
|
||||
};
|
||||
|
||||
Point.prototype.getY = function getY() {
|
||||
return this.y.fromRed();
|
||||
};
|
||||
|
||||
Point.prototype.mul = function mul(k) {
|
||||
k = new BN(k, 16);
|
||||
if (this.isInfinity())
|
||||
return this;
|
||||
else if (this._hasDoubles(k))
|
||||
return this.curve._fixedNafMul(this, k);
|
||||
else if (this.curve.endo)
|
||||
return this.curve._endoWnafMulAdd([ this ], [ k ]);
|
||||
else
|
||||
return this.curve._wnafMul(this, k);
|
||||
};
|
||||
|
||||
Point.prototype.mulAdd = function mulAdd(k1, p2, k2) {
|
||||
var points = [ this, p2 ];
|
||||
var coeffs = [ k1, k2 ];
|
||||
if (this.curve.endo)
|
||||
return this.curve._endoWnafMulAdd(points, coeffs);
|
||||
else
|
||||
return this.curve._wnafMulAdd(1, points, coeffs, 2);
|
||||
};
|
||||
|
||||
Point.prototype.jmulAdd = function jmulAdd(k1, p2, k2) {
|
||||
var points = [ this, p2 ];
|
||||
var coeffs = [ k1, k2 ];
|
||||
if (this.curve.endo)
|
||||
return this.curve._endoWnafMulAdd(points, coeffs, true);
|
||||
else
|
||||
return this.curve._wnafMulAdd(1, points, coeffs, 2, true);
|
||||
};
|
||||
|
||||
Point.prototype.eq = function eq(p) {
|
||||
return this === p ||
|
||||
this.inf === p.inf &&
|
||||
(this.inf || this.x.cmp(p.x) === 0 && this.y.cmp(p.y) === 0);
|
||||
};
|
||||
|
||||
Point.prototype.neg = function neg(_precompute) {
|
||||
if (this.inf)
|
||||
return this;
|
||||
|
||||
var res = this.curve.point(this.x, this.y.redNeg());
|
||||
if (_precompute && this.precomputed) {
|
||||
var pre = this.precomputed;
|
||||
var negate = function(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,
|
||||
points: pre.doubles.points.map(negate),
|
||||
},
|
||||
};
|
||||
}
|
||||
return res;
|
||||
};
|
||||
|
||||
Point.prototype.toJ = function toJ() {
|
||||
if (this.inf)
|
||||
return this.curve.jpoint(null, null, null);
|
||||
|
||||
var res = this.curve.jpoint(this.x, this.y, this.curve.one);
|
||||
return res;
|
||||
};
|
||||
|
||||
function JPoint(curve, x, y, z) {
|
||||
Base.BasePoint.call(this, curve, 'jacobian');
|
||||
if (x === null && y === null && z === null) {
|
||||
this.x = this.curve.one;
|
||||
this.y = this.curve.one;
|
||||
this.z = new BN(0);
|
||||
} else {
|
||||
this.x = new BN(x, 16);
|
||||
this.y = new BN(y, 16);
|
||||
this.z = new BN(z, 16);
|
||||
}
|
||||
if (!this.x.red)
|
||||
this.x = this.x.toRed(this.curve.red);
|
||||
if (!this.y.red)
|
||||
this.y = this.y.toRed(this.curve.red);
|
||||
if (!this.z.red)
|
||||
this.z = this.z.toRed(this.curve.red);
|
||||
|
||||
this.zOne = this.z === this.curve.one;
|
||||
}
|
||||
inherits(JPoint, Base.BasePoint);
|
||||
|
||||
ShortCurve.prototype.jpoint = function jpoint(x, y, z) {
|
||||
return new JPoint(this, x, y, z);
|
||||
};
|
||||
|
||||
JPoint.prototype.toP = function toP() {
|
||||
if (this.isInfinity())
|
||||
return this.curve.point(null, null);
|
||||
|
||||
var zinv = this.z.redInvm();
|
||||
var zinv2 = zinv.redSqr();
|
||||
var ax = this.x.redMul(zinv2);
|
||||
var ay = this.y.redMul(zinv2).redMul(zinv);
|
||||
|
||||
return this.curve.point(ax, ay);
|
||||
};
|
||||
|
||||
JPoint.prototype.neg = function neg() {
|
||||
return this.curve.jpoint(this.x, this.y.redNeg(), this.z);
|
||||
};
|
||||
|
||||
JPoint.prototype.add = function add(p) {
|
||||
// O + P = P
|
||||
if (this.isInfinity())
|
||||
return p;
|
||||
|
||||
// P + O = P
|
||||
if (p.isInfinity())
|
||||
return this;
|
||||
|
||||
// 12M + 4S + 7A
|
||||
var pz2 = p.z.redSqr();
|
||||
var z2 = this.z.redSqr();
|
||||
var u1 = this.x.redMul(pz2);
|
||||
var u2 = p.x.redMul(z2);
|
||||
var s1 = this.y.redMul(pz2.redMul(p.z));
|
||||
var s2 = p.y.redMul(z2.redMul(this.z));
|
||||
|
||||
var h = u1.redSub(u2);
|
||||
var r = s1.redSub(s2);
|
||||
if (h.cmpn(0) === 0) {
|
||||
if (r.cmpn(0) !== 0)
|
||||
return this.curve.jpoint(null, null, null);
|
||||
else
|
||||
return this.dbl();
|
||||
}
|
||||
|
||||
var h2 = h.redSqr();
|
||||
var h3 = h2.redMul(h);
|
||||
var v = u1.redMul(h2);
|
||||
|
||||
var nx = r.redSqr().redIAdd(h3).redISub(v).redISub(v);
|
||||
var ny = r.redMul(v.redISub(nx)).redISub(s1.redMul(h3));
|
||||
var nz = this.z.redMul(p.z).redMul(h);
|
||||
|
||||
return this.curve.jpoint(nx, ny, nz);
|
||||
};
|
||||
|
||||
JPoint.prototype.mixedAdd = function mixedAdd(p) {
|
||||
// O + P = P
|
||||
if (this.isInfinity())
|
||||
return p.toJ();
|
||||
|
||||
// P + O = P
|
||||
if (p.isInfinity())
|
||||
return this;
|
||||
|
||||
// 8M + 3S + 7A
|
||||
var z2 = this.z.redSqr();
|
||||
var u1 = this.x;
|
||||
var u2 = p.x.redMul(z2);
|
||||
var s1 = this.y;
|
||||
var s2 = p.y.redMul(z2).redMul(this.z);
|
||||
|
||||
var h = u1.redSub(u2);
|
||||
var r = s1.redSub(s2);
|
||||
if (h.cmpn(0) === 0) {
|
||||
if (r.cmpn(0) !== 0)
|
||||
return this.curve.jpoint(null, null, null);
|
||||
else
|
||||
return this.dbl();
|
||||
}
|
||||
|
||||
var h2 = h.redSqr();
|
||||
var h3 = h2.redMul(h);
|
||||
var v = u1.redMul(h2);
|
||||
|
||||
var nx = r.redSqr().redIAdd(h3).redISub(v).redISub(v);
|
||||
var ny = r.redMul(v.redISub(nx)).redISub(s1.redMul(h3));
|
||||
var nz = this.z.redMul(h);
|
||||
|
||||
return this.curve.jpoint(nx, ny, nz);
|
||||
};
|
||||
|
||||
JPoint.prototype.dblp = function dblp(pow) {
|
||||
if (pow === 0)
|
||||
return this;
|
||||
if (this.isInfinity())
|
||||
return this;
|
||||
if (!pow)
|
||||
return this.dbl();
|
||||
|
||||
var i;
|
||||
if (this.curve.zeroA || this.curve.threeA) {
|
||||
var r = this;
|
||||
for (i = 0; i < pow; i++)
|
||||
r = r.dbl();
|
||||
return r;
|
||||
}
|
||||
|
||||
// 1M + 2S + 1A + N * (4S + 5M + 8A)
|
||||
// N = 1 => 6M + 6S + 9A
|
||||
var a = this.curve.a;
|
||||
var tinv = this.curve.tinv;
|
||||
|
||||
var jx = this.x;
|
||||
var jy = this.y;
|
||||
var jz = this.z;
|
||||
var jz4 = jz.redSqr().redSqr();
|
||||
|
||||
// Reuse results
|
||||
var jyd = jy.redAdd(jy);
|
||||
for (i = 0; i < pow; i++) {
|
||||
var jx2 = jx.redSqr();
|
||||
var jyd2 = jyd.redSqr();
|
||||
var jyd4 = jyd2.redSqr();
|
||||
var c = jx2.redAdd(jx2).redIAdd(jx2).redIAdd(a.redMul(jz4));
|
||||
|
||||
var t1 = jx.redMul(jyd2);
|
||||
var nx = c.redSqr().redISub(t1.redAdd(t1));
|
||||
var t2 = t1.redISub(nx);
|
||||
var dny = c.redMul(t2);
|
||||
dny = dny.redIAdd(dny).redISub(jyd4);
|
||||
var nz = jyd.redMul(jz);
|
||||
if (i + 1 < pow)
|
||||
jz4 = jz4.redMul(jyd4);
|
||||
|
||||
jx = nx;
|
||||
jz = nz;
|
||||
jyd = dny;
|
||||
}
|
||||
|
||||
return this.curve.jpoint(jx, jyd.redMul(tinv), jz);
|
||||
};
|
||||
|
||||
JPoint.prototype.dbl = function dbl() {
|
||||
if (this.isInfinity())
|
||||
return this;
|
||||
|
||||
if (this.curve.zeroA)
|
||||
return this._zeroDbl();
|
||||
else if (this.curve.threeA)
|
||||
return this._threeDbl();
|
||||
else
|
||||
return this._dbl();
|
||||
};
|
||||
|
||||
JPoint.prototype._zeroDbl = function _zeroDbl() {
|
||||
var nx;
|
||||
var ny;
|
||||
var nz;
|
||||
// Z = 1
|
||||
if (this.zOne) {
|
||||
// hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html
|
||||
// #doubling-mdbl-2007-bl
|
||||
// 1M + 5S + 14A
|
||||
|
||||
// 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; a = 0
|
||||
var m = xx.redAdd(xx).redIAdd(xx);
|
||||
// T = M ^ 2 - 2*S
|
||||
var t = m.redSqr().redISub(s).redISub(s);
|
||||
|
||||
// 8 * YYYY
|
||||
var yyyy8 = yyyy.redIAdd(yyyy);
|
||||
yyyy8 = yyyy8.redIAdd(yyyy8);
|
||||
yyyy8 = yyyy8.redIAdd(yyyy8);
|
||||
|
||||
// X3 = T
|
||||
nx = t;
|
||||
// Y3 = M * (S - T) - 8 * YYYY
|
||||
ny = m.redMul(s.redISub(t)).redISub(yyyy8);
|
||||
// Z3 = 2*Y1
|
||||
nz = this.y.redAdd(this.y);
|
||||
} else {
|
||||
// hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html
|
||||
// #doubling-dbl-2009-l
|
||||
// 2M + 5S + 13A
|
||||
|
||||
// A = X1^2
|
||||
var a = this.x.redSqr();
|
||||
// B = Y1^2
|
||||
var b = this.y.redSqr();
|
||||
// C = B^2
|
||||
var c = b.redSqr();
|
||||
// D = 2 * ((X1 + B)^2 - A - C)
|
||||
var d = this.x.redAdd(b).redSqr().redISub(a).redISub(c);
|
||||
d = d.redIAdd(d);
|
||||
// E = 3 * A
|
||||
var e = a.redAdd(a).redIAdd(a);
|
||||
// F = E^2
|
||||
var f = e.redSqr();
|
||||
|
||||
// 8 * C
|
||||
var c8 = c.redIAdd(c);
|
||||
c8 = c8.redIAdd(c8);
|
||||
c8 = c8.redIAdd(c8);
|
||||
|
||||
// X3 = F - 2 * D
|
||||
nx = f.redISub(d).redISub(d);
|
||||
// Y3 = E * (D - X3) - 8 * C
|
||||
ny = e.redMul(d.redISub(nx)).redISub(c8);
|
||||
// Z3 = 2 * Y1 * Z1
|
||||
nz = this.y.redMul(this.z);
|
||||
nz = nz.redIAdd(nz);
|
||||
}
|
||||
|
||||
return this.curve.jpoint(nx, ny, nz);
|
||||
};
|
||||
|
||||
JPoint.prototype._threeDbl = function _threeDbl() {
|
||||
var nx;
|
||||
var ny;
|
||||
var nz;
|
||||
// Z = 1
|
||||
if (this.zOne) {
|
||||
// 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
|
||||
nx = t;
|
||||
// Y3 = M * (S - T) - 8 * YYYY
|
||||
var yyyy8 = yyyy.redIAdd(yyyy);
|
||||
yyyy8 = yyyy8.redIAdd(yyyy8);
|
||||
yyyy8 = yyyy8.redIAdd(yyyy8);
|
||||
ny = m.redMul(s.redISub(t)).redISub(yyyy8);
|
||||
// Z3 = 2 * Y1
|
||||
nz = this.y.redAdd(this.y);
|
||||
} else {
|
||||
// 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);
|
||||
nx = alpha.redSqr().redISub(beta8);
|
||||
// Z3 = (Y1 + Z1)^2 - gamma - delta
|
||||
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);
|
||||
ny = alpha.redMul(beta4.redISub(nx)).redISub(ggamma8);
|
||||
}
|
||||
|
||||
return this.curve.jpoint(nx, ny, nz);
|
||||
};
|
||||
|
||||
JPoint.prototype._dbl = function _dbl() {
|
||||
var a = this.curve.a;
|
||||
|
||||
// 4M + 6S + 10A
|
||||
var jx = this.x;
|
||||
var jy = this.y;
|
||||
var jz = this.z;
|
||||
var jz4 = jz.redSqr().redSqr();
|
||||
|
||||
var jx2 = jx.redSqr();
|
||||
var jy2 = jy.redSqr();
|
||||
|
||||
var c = jx2.redAdd(jx2).redIAdd(jx2).redIAdd(a.redMul(jz4));
|
||||
|
||||
var jxd4 = jx.redAdd(jx);
|
||||
jxd4 = jxd4.redIAdd(jxd4);
|
||||
var t1 = jxd4.redMul(jy2);
|
||||
var nx = c.redSqr().redISub(t1.redAdd(t1));
|
||||
var t2 = t1.redISub(nx);
|
||||
|
||||
var jyd8 = jy2.redSqr();
|
||||
jyd8 = jyd8.redIAdd(jyd8);
|
||||
jyd8 = jyd8.redIAdd(jyd8);
|
||||
jyd8 = jyd8.redIAdd(jyd8);
|
||||
var ny = c.redMul(t2).redISub(jyd8);
|
||||
var nz = jy.redAdd(jy).redMul(jz);
|
||||
|
||||
return this.curve.jpoint(nx, ny, nz);
|
||||
};
|
||||
|
||||
JPoint.prototype.trpl = function trpl() {
|
||||
if (!this.curve.zeroA)
|
||||
return this.dbl().add(this);
|
||||
|
||||
// hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html#tripling-tpl-2007-bl
|
||||
// 5M + 10S + ...
|
||||
|
||||
// XX = X1^2
|
||||
var xx = this.x.redSqr();
|
||||
// YY = Y1^2
|
||||
var yy = this.y.redSqr();
|
||||
// ZZ = Z1^2
|
||||
var zz = this.z.redSqr();
|
||||
// YYYY = YY^2
|
||||
var yyyy = yy.redSqr();
|
||||
// M = 3 * XX + a * ZZ2; a = 0
|
||||
var m = xx.redAdd(xx).redIAdd(xx);
|
||||
// MM = M^2
|
||||
var mm = m.redSqr();
|
||||
// E = 6 * ((X1 + YY)^2 - XX - YYYY) - MM
|
||||
var e = this.x.redAdd(yy).redSqr().redISub(xx).redISub(yyyy);
|
||||
e = e.redIAdd(e);
|
||||
e = e.redAdd(e).redIAdd(e);
|
||||
e = e.redISub(mm);
|
||||
// EE = E^2
|
||||
var ee = e.redSqr();
|
||||
// T = 16*YYYY
|
||||
var t = yyyy.redIAdd(yyyy);
|
||||
t = t.redIAdd(t);
|
||||
t = t.redIAdd(t);
|
||||
t = t.redIAdd(t);
|
||||
// U = (M + E)^2 - MM - EE - T
|
||||
var u = m.redIAdd(e).redSqr().redISub(mm).redISub(ee).redISub(t);
|
||||
// X3 = 4 * (X1 * EE - 4 * YY * U)
|
||||
var yyu4 = yy.redMul(u);
|
||||
yyu4 = yyu4.redIAdd(yyu4);
|
||||
yyu4 = yyu4.redIAdd(yyu4);
|
||||
var nx = this.x.redMul(ee).redISub(yyu4);
|
||||
nx = nx.redIAdd(nx);
|
||||
nx = nx.redIAdd(nx);
|
||||
// Y3 = 8 * Y1 * (U * (T - U) - E * EE)
|
||||
var ny = this.y.redMul(u.redMul(t.redISub(u)).redISub(e.redMul(ee)));
|
||||
ny = ny.redIAdd(ny);
|
||||
ny = ny.redIAdd(ny);
|
||||
ny = ny.redIAdd(ny);
|
||||
// Z3 = (Z1 + E)^2 - ZZ - EE
|
||||
var nz = this.z.redAdd(e).redSqr().redISub(zz).redISub(ee);
|
||||
|
||||
return this.curve.jpoint(nx, ny, nz);
|
||||
};
|
||||
|
||||
JPoint.prototype.mul = function mul(k, kbase) {
|
||||
k = new BN(k, kbase);
|
||||
|
||||
return this.curve._wnafMul(this, k);
|
||||
};
|
||||
|
||||
JPoint.prototype.eq = function eq(p) {
|
||||
if (p.type === 'affine')
|
||||
return this.eq(p.toJ());
|
||||
|
||||
if (this === p)
|
||||
return true;
|
||||
|
||||
// x1 * z2^2 == x2 * z1^2
|
||||
var z2 = this.z.redSqr();
|
||||
var pz2 = p.z.redSqr();
|
||||
if (this.x.redMul(pz2).redISub(p.x.redMul(z2)).cmpn(0) !== 0)
|
||||
return false;
|
||||
|
||||
// y1 * z2^3 == y2 * z1^3
|
||||
var z3 = z2.redMul(this.z);
|
||||
var pz3 = pz2.redMul(p.z);
|
||||
return this.y.redMul(pz3).redISub(p.y.redMul(z3)).cmpn(0) === 0;
|
||||
};
|
||||
|
||||
JPoint.prototype.eqXToP = function eqXToP(x) {
|
||||
var zs = this.z.redSqr();
|
||||
var rx = x.toRed(this.curve.red).redMul(zs);
|
||||
if (this.x.cmp(rx) === 0)
|
||||
return true;
|
||||
|
||||
var xc = x.clone();
|
||||
var t = this.curve.redN.redMul(zs);
|
||||
for (;;) {
|
||||
xc.iadd(this.curve.n);
|
||||
if (xc.cmp(this.curve.p) >= 0)
|
||||
return false;
|
||||
|
||||
rx.redIAdd(t);
|
||||
if (this.x.cmp(rx) === 0)
|
||||
return true;
|
||||
}
|
||||
};
|
||||
|
||||
JPoint.prototype.inspect = function inspect() {
|
||||
if (this.isInfinity())
|
||||
return '<EC JPoint Infinity>';
|
||||
return '<EC JPoint x: ' + this.x.toString(16, 2) +
|
||||
' y: ' + this.y.toString(16, 2) +
|
||||
' z: ' + this.z.toString(16, 2) + '>';
|
||||
};
|
||||
|
||||
JPoint.prototype.isInfinity = function isInfinity() {
|
||||
// XXX This code assumes that zero is always zero in red
|
||||
return this.z.cmpn(0) === 0;
|
||||
};
|
||||
206
web/node_modules/elliptic/lib/elliptic/curves.js
generated
vendored
Normal file
206
web/node_modules/elliptic/lib/elliptic/curves.js
generated
vendored
Normal file
|
|
@ -0,0 +1,206 @@
|
|||
'use strict';
|
||||
|
||||
var curves = exports;
|
||||
|
||||
var hash = require('hash.js');
|
||||
var curve = require('./curve');
|
||||
var utils = require('./utils');
|
||||
|
||||
var assert = utils.assert;
|
||||
|
||||
function PresetCurve(options) {
|
||||
if (options.type === 'short')
|
||||
this.curve = new curve.short(options);
|
||||
else if (options.type === 'edwards')
|
||||
this.curve = new curve.edwards(options);
|
||||
else
|
||||
this.curve = new curve.mont(options);
|
||||
this.g = this.curve.g;
|
||||
this.n = this.curve.n;
|
||||
this.hash = options.hash;
|
||||
|
||||
assert(this.g.validate(), 'Invalid curve');
|
||||
assert(this.g.mul(this.n).isInfinity(), 'Invalid curve, G*N != O');
|
||||
}
|
||||
curves.PresetCurve = PresetCurve;
|
||||
|
||||
function defineCurve(name, options) {
|
||||
Object.defineProperty(curves, name, {
|
||||
configurable: true,
|
||||
enumerable: true,
|
||||
get: function() {
|
||||
var curve = new PresetCurve(options);
|
||||
Object.defineProperty(curves, name, {
|
||||
configurable: true,
|
||||
enumerable: true,
|
||||
value: curve,
|
||||
});
|
||||
return curve;
|
||||
},
|
||||
});
|
||||
}
|
||||
|
||||
defineCurve('p192', {
|
||||
type: 'short',
|
||||
prime: 'p192',
|
||||
p: 'ffffffff ffffffff ffffffff fffffffe ffffffff ffffffff',
|
||||
a: 'ffffffff ffffffff ffffffff fffffffe ffffffff fffffffc',
|
||||
b: '64210519 e59c80e7 0fa7e9ab 72243049 feb8deec c146b9b1',
|
||||
n: 'ffffffff ffffffff ffffffff 99def836 146bc9b1 b4d22831',
|
||||
hash: hash.sha256,
|
||||
gRed: false,
|
||||
g: [
|
||||
'188da80e b03090f6 7cbf20eb 43a18800 f4ff0afd 82ff1012',
|
||||
'07192b95 ffc8da78 631011ed 6b24cdd5 73f977a1 1e794811',
|
||||
],
|
||||
});
|
||||
|
||||
defineCurve('p224', {
|
||||
type: 'short',
|
||||
prime: 'p224',
|
||||
p: 'ffffffff ffffffff ffffffff ffffffff 00000000 00000000 00000001',
|
||||
a: 'ffffffff ffffffff ffffffff fffffffe ffffffff ffffffff fffffffe',
|
||||
b: 'b4050a85 0c04b3ab f5413256 5044b0b7 d7bfd8ba 270b3943 2355ffb4',
|
||||
n: 'ffffffff ffffffff ffffffff ffff16a2 e0b8f03e 13dd2945 5c5c2a3d',
|
||||
hash: hash.sha256,
|
||||
gRed: false,
|
||||
g: [
|
||||
'b70e0cbd 6bb4bf7f 321390b9 4a03c1d3 56c21122 343280d6 115c1d21',
|
||||
'bd376388 b5f723fb 4c22dfe6 cd4375a0 5a074764 44d58199 85007e34',
|
||||
],
|
||||
});
|
||||
|
||||
defineCurve('p256', {
|
||||
type: 'short',
|
||||
prime: null,
|
||||
p: 'ffffffff 00000001 00000000 00000000 00000000 ffffffff ffffffff ffffffff',
|
||||
a: 'ffffffff 00000001 00000000 00000000 00000000 ffffffff ffffffff fffffffc',
|
||||
b: '5ac635d8 aa3a93e7 b3ebbd55 769886bc 651d06b0 cc53b0f6 3bce3c3e 27d2604b',
|
||||
n: 'ffffffff 00000000 ffffffff ffffffff bce6faad a7179e84 f3b9cac2 fc632551',
|
||||
hash: hash.sha256,
|
||||
gRed: false,
|
||||
g: [
|
||||
'6b17d1f2 e12c4247 f8bce6e5 63a440f2 77037d81 2deb33a0 f4a13945 d898c296',
|
||||
'4fe342e2 fe1a7f9b 8ee7eb4a 7c0f9e16 2bce3357 6b315ece cbb64068 37bf51f5',
|
||||
],
|
||||
});
|
||||
|
||||
defineCurve('p384', {
|
||||
type: 'short',
|
||||
prime: null,
|
||||
p: 'ffffffff ffffffff ffffffff ffffffff ffffffff ffffffff ffffffff ' +
|
||||
'fffffffe ffffffff 00000000 00000000 ffffffff',
|
||||
a: 'ffffffff ffffffff ffffffff ffffffff ffffffff ffffffff ffffffff ' +
|
||||
'fffffffe ffffffff 00000000 00000000 fffffffc',
|
||||
b: 'b3312fa7 e23ee7e4 988e056b e3f82d19 181d9c6e fe814112 0314088f ' +
|
||||
'5013875a c656398d 8a2ed19d 2a85c8ed d3ec2aef',
|
||||
n: 'ffffffff ffffffff ffffffff ffffffff ffffffff ffffffff c7634d81 ' +
|
||||
'f4372ddf 581a0db2 48b0a77a ecec196a ccc52973',
|
||||
hash: hash.sha384,
|
||||
gRed: false,
|
||||
g: [
|
||||
'aa87ca22 be8b0537 8eb1c71e f320ad74 6e1d3b62 8ba79b98 59f741e0 82542a38 ' +
|
||||
'5502f25d bf55296c 3a545e38 72760ab7',
|
||||
'3617de4a 96262c6f 5d9e98bf 9292dc29 f8f41dbd 289a147c e9da3113 b5f0b8c0 ' +
|
||||
'0a60b1ce 1d7e819d 7a431d7c 90ea0e5f',
|
||||
],
|
||||
});
|
||||
|
||||
defineCurve('p521', {
|
||||
type: 'short',
|
||||
prime: null,
|
||||
p: '000001ff ffffffff ffffffff ffffffff ffffffff ffffffff ' +
|
||||
'ffffffff ffffffff ffffffff ffffffff ffffffff ffffffff ' +
|
||||
'ffffffff ffffffff ffffffff ffffffff ffffffff',
|
||||
a: '000001ff ffffffff ffffffff ffffffff ffffffff ffffffff ' +
|
||||
'ffffffff ffffffff ffffffff ffffffff ffffffff ffffffff ' +
|
||||
'ffffffff ffffffff ffffffff ffffffff fffffffc',
|
||||
b: '00000051 953eb961 8e1c9a1f 929a21a0 b68540ee a2da725b ' +
|
||||
'99b315f3 b8b48991 8ef109e1 56193951 ec7e937b 1652c0bd ' +
|
||||
'3bb1bf07 3573df88 3d2c34f1 ef451fd4 6b503f00',
|
||||
n: '000001ff ffffffff ffffffff ffffffff ffffffff ffffffff ' +
|
||||
'ffffffff ffffffff fffffffa 51868783 bf2f966b 7fcc0148 ' +
|
||||
'f709a5d0 3bb5c9b8 899c47ae bb6fb71e 91386409',
|
||||
hash: hash.sha512,
|
||||
gRed: false,
|
||||
g: [
|
||||
'000000c6 858e06b7 0404e9cd 9e3ecb66 2395b442 9c648139 ' +
|
||||
'053fb521 f828af60 6b4d3dba a14b5e77 efe75928 fe1dc127 ' +
|
||||
'a2ffa8de 3348b3c1 856a429b f97e7e31 c2e5bd66',
|
||||
'00000118 39296a78 9a3bc004 5c8a5fb4 2c7d1bd9 98f54449 ' +
|
||||
'579b4468 17afbd17 273e662c 97ee7299 5ef42640 c550b901 ' +
|
||||
'3fad0761 353c7086 a272c240 88be9476 9fd16650',
|
||||
],
|
||||
});
|
||||
|
||||
defineCurve('curve25519', {
|
||||
type: 'mont',
|
||||
prime: 'p25519',
|
||||
p: '7fffffffffffffff ffffffffffffffff ffffffffffffffff ffffffffffffffed',
|
||||
a: '76d06',
|
||||
b: '1',
|
||||
n: '1000000000000000 0000000000000000 14def9dea2f79cd6 5812631a5cf5d3ed',
|
||||
hash: hash.sha256,
|
||||
gRed: false,
|
||||
g: [
|
||||
'9',
|
||||
],
|
||||
});
|
||||
|
||||
defineCurve('ed25519', {
|
||||
type: 'edwards',
|
||||
prime: 'p25519',
|
||||
p: '7fffffffffffffff ffffffffffffffff ffffffffffffffff ffffffffffffffed',
|
||||
a: '-1',
|
||||
c: '1',
|
||||
// -121665 * (121666^(-1)) (mod P)
|
||||
d: '52036cee2b6ffe73 8cc740797779e898 00700a4d4141d8ab 75eb4dca135978a3',
|
||||
n: '1000000000000000 0000000000000000 14def9dea2f79cd6 5812631a5cf5d3ed',
|
||||
hash: hash.sha256,
|
||||
gRed: false,
|
||||
g: [
|
||||
'216936d3cd6e53fec0a4e231fdd6dc5c692cc7609525a7b2c9562d608f25d51a',
|
||||
|
||||
// 4/5
|
||||
'6666666666666666666666666666666666666666666666666666666666666658',
|
||||
],
|
||||
});
|
||||
|
||||
var pre;
|
||||
try {
|
||||
pre = require('./precomputed/secp256k1');
|
||||
} catch (e) {
|
||||
pre = undefined;
|
||||
}
|
||||
|
||||
defineCurve('secp256k1', {
|
||||
type: 'short',
|
||||
prime: 'k256',
|
||||
p: 'ffffffff ffffffff ffffffff ffffffff ffffffff ffffffff fffffffe fffffc2f',
|
||||
a: '0',
|
||||
b: '7',
|
||||
n: 'ffffffff ffffffff ffffffff fffffffe baaedce6 af48a03b bfd25e8c d0364141',
|
||||
h: '1',
|
||||
hash: hash.sha256,
|
||||
|
||||
// Precomputed endomorphism
|
||||
beta: '7ae96a2b657c07106e64479eac3434e99cf0497512f58995c1396c28719501ee',
|
||||
lambda: '5363ad4cc05c30e0a5261c028812645a122e22ea20816678df02967c1b23bd72',
|
||||
basis: [
|
||||
{
|
||||
a: '3086d221a7d46bcde86c90e49284eb15',
|
||||
b: '-e4437ed6010e88286f547fa90abfe4c3',
|
||||
},
|
||||
{
|
||||
a: '114ca50f7a8e2f3f657c1108d9d44cfd8',
|
||||
b: '3086d221a7d46bcde86c90e49284eb15',
|
||||
},
|
||||
],
|
||||
|
||||
gRed: false,
|
||||
g: [
|
||||
'79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798',
|
||||
'483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8',
|
||||
pre,
|
||||
],
|
||||
});
|
||||
243
web/node_modules/elliptic/lib/elliptic/ec/index.js
generated
vendored
Normal file
243
web/node_modules/elliptic/lib/elliptic/ec/index.js
generated
vendored
Normal file
|
|
@ -0,0 +1,243 @@
|
|||
'use strict';
|
||||
|
||||
var BN = require('bn.js');
|
||||
var HmacDRBG = require('hmac-drbg');
|
||||
var utils = require('../utils');
|
||||
var curves = require('../curves');
|
||||
var rand = require('brorand');
|
||||
var assert = utils.assert;
|
||||
|
||||
var KeyPair = require('./key');
|
||||
var Signature = require('./signature');
|
||||
|
||||
function EC(options) {
|
||||
if (!(this instanceof EC))
|
||||
return new EC(options);
|
||||
|
||||
// Shortcut `elliptic.ec(curve-name)`
|
||||
if (typeof options === 'string') {
|
||||
assert(Object.prototype.hasOwnProperty.call(curves, options),
|
||||
'Unknown curve ' + options);
|
||||
|
||||
options = curves[options];
|
||||
}
|
||||
|
||||
// Shortcut for `elliptic.ec(elliptic.curves.curveName)`
|
||||
if (options instanceof curves.PresetCurve)
|
||||
options = { curve: options };
|
||||
|
||||
this.curve = options.curve.curve;
|
||||
this.n = this.curve.n;
|
||||
this.nh = this.n.ushrn(1);
|
||||
this.g = this.curve.g;
|
||||
|
||||
// Point on curve
|
||||
this.g = options.curve.g;
|
||||
this.g.precompute(options.curve.n.bitLength() + 1);
|
||||
|
||||
// Hash for function for DRBG
|
||||
this.hash = options.hash || options.curve.hash;
|
||||
}
|
||||
module.exports = EC;
|
||||
|
||||
EC.prototype.keyPair = function keyPair(options) {
|
||||
return new KeyPair(this, options);
|
||||
};
|
||||
|
||||
EC.prototype.keyFromPrivate = function keyFromPrivate(priv, enc) {
|
||||
return KeyPair.fromPrivate(this, priv, enc);
|
||||
};
|
||||
|
||||
EC.prototype.keyFromPublic = function keyFromPublic(pub, enc) {
|
||||
return KeyPair.fromPublic(this, pub, enc);
|
||||
};
|
||||
|
||||
EC.prototype.genKeyPair = function genKeyPair(options) {
|
||||
if (!options)
|
||||
options = {};
|
||||
|
||||
// Instantiate Hmac_DRBG
|
||||
var drbg = new HmacDRBG({
|
||||
hash: this.hash,
|
||||
pers: options.pers,
|
||||
persEnc: options.persEnc || 'utf8',
|
||||
entropy: options.entropy || rand(this.hash.hmacStrength),
|
||||
entropyEnc: options.entropy && options.entropyEnc || 'utf8',
|
||||
nonce: this.n.toArray(),
|
||||
});
|
||||
|
||||
var bytes = this.n.byteLength();
|
||||
var ns2 = this.n.sub(new BN(2));
|
||||
for (;;) {
|
||||
var priv = new BN(drbg.generate(bytes));
|
||||
if (priv.cmp(ns2) > 0)
|
||||
continue;
|
||||
|
||||
priv.iaddn(1);
|
||||
return this.keyFromPrivate(priv);
|
||||
}
|
||||
};
|
||||
|
||||
EC.prototype._truncateToN = function _truncateToN(msg, truncOnly) {
|
||||
var delta = msg.byteLength() * 8 - this.n.bitLength();
|
||||
if (delta > 0)
|
||||
msg = msg.ushrn(delta);
|
||||
if (!truncOnly && msg.cmp(this.n) >= 0)
|
||||
return msg.sub(this.n);
|
||||
else
|
||||
return msg;
|
||||
};
|
||||
|
||||
EC.prototype.sign = function sign(msg, key, enc, options) {
|
||||
if (typeof enc === 'object') {
|
||||
options = enc;
|
||||
enc = null;
|
||||
}
|
||||
if (!options)
|
||||
options = {};
|
||||
|
||||
key = this.keyFromPrivate(key, enc);
|
||||
msg = this._truncateToN(new BN(msg, 16));
|
||||
|
||||
// Zero-extend key to provide enough entropy
|
||||
var bytes = this.n.byteLength();
|
||||
var bkey = key.getPrivate().toArray('be', bytes);
|
||||
|
||||
// Zero-extend nonce to have the same byte size as N
|
||||
var nonce = msg.toArray('be', bytes);
|
||||
|
||||
// Instantiate Hmac_DRBG
|
||||
var drbg = new HmacDRBG({
|
||||
hash: this.hash,
|
||||
entropy: bkey,
|
||||
nonce: nonce,
|
||||
pers: options.pers,
|
||||
persEnc: options.persEnc || 'utf8',
|
||||
});
|
||||
|
||||
// Number of bytes to generate
|
||||
var ns1 = this.n.sub(new BN(1));
|
||||
|
||||
for (var iter = 0; ; iter++) {
|
||||
var k = options.k ?
|
||||
options.k(iter) :
|
||||
new BN(drbg.generate(this.n.byteLength()));
|
||||
k = this._truncateToN(k, true);
|
||||
if (k.cmpn(1) <= 0 || k.cmp(ns1) >= 0)
|
||||
continue;
|
||||
|
||||
var kp = this.g.mul(k);
|
||||
if (kp.isInfinity())
|
||||
continue;
|
||||
|
||||
var kpX = kp.getX();
|
||||
var r = kpX.umod(this.n);
|
||||
if (r.cmpn(0) === 0)
|
||||
continue;
|
||||
|
||||
var s = k.invm(this.n).mul(r.mul(key.getPrivate()).iadd(msg));
|
||||
s = s.umod(this.n);
|
||||
if (s.cmpn(0) === 0)
|
||||
continue;
|
||||
|
||||
var recoveryParam = (kp.getY().isOdd() ? 1 : 0) |
|
||||
(kpX.cmp(r) !== 0 ? 2 : 0);
|
||||
|
||||
// Use complement of `s`, if it is > `n / 2`
|
||||
if (options.canonical && s.cmp(this.nh) > 0) {
|
||||
s = this.n.sub(s);
|
||||
recoveryParam ^= 1;
|
||||
}
|
||||
|
||||
return new Signature({ r: r, s: s, recoveryParam: recoveryParam });
|
||||
}
|
||||
};
|
||||
|
||||
EC.prototype.verify = function verify(msg, signature, key, enc) {
|
||||
msg = this._truncateToN(new BN(msg, 16));
|
||||
key = this.keyFromPublic(key, enc);
|
||||
signature = new Signature(signature, 'hex');
|
||||
|
||||
// Perform primitive values validation
|
||||
var r = signature.r;
|
||||
var s = signature.s;
|
||||
if (r.cmpn(1) < 0 || r.cmp(this.n) >= 0)
|
||||
return false;
|
||||
if (s.cmpn(1) < 0 || s.cmp(this.n) >= 0)
|
||||
return false;
|
||||
|
||||
// Validate signature
|
||||
var sinv = s.invm(this.n);
|
||||
var u1 = sinv.mul(msg).umod(this.n);
|
||||
var u2 = sinv.mul(r).umod(this.n);
|
||||
var p;
|
||||
|
||||
if (!this.curve._maxwellTrick) {
|
||||
p = this.g.mulAdd(u1, key.getPublic(), u2);
|
||||
if (p.isInfinity())
|
||||
return false;
|
||||
|
||||
return p.getX().umod(this.n).cmp(r) === 0;
|
||||
}
|
||||
|
||||
// NOTE: Greg Maxwell's trick, inspired by:
|
||||
// https://git.io/vad3K
|
||||
|
||||
p = this.g.jmulAdd(u1, key.getPublic(), u2);
|
||||
if (p.isInfinity())
|
||||
return false;
|
||||
|
||||
// Compare `p.x` of Jacobian point with `r`,
|
||||
// this will do `p.x == r * p.z^2` instead of multiplying `p.x` by the
|
||||
// inverse of `p.z^2`
|
||||
return p.eqXToP(r);
|
||||
};
|
||||
|
||||
EC.prototype.recoverPubKey = function(msg, signature, j, enc) {
|
||||
assert((3 & j) === j, 'The recovery param is more than two bits');
|
||||
signature = new Signature(signature, enc);
|
||||
|
||||
var n = this.n;
|
||||
var e = new BN(msg);
|
||||
var r = signature.r;
|
||||
var s = signature.s;
|
||||
|
||||
// A set LSB signifies that the y-coordinate is odd
|
||||
var isYOdd = j & 1;
|
||||
var isSecondKey = j >> 1;
|
||||
if (r.cmp(this.curve.p.umod(this.curve.n)) >= 0 && isSecondKey)
|
||||
throw new Error('Unable to find sencond key candinate');
|
||||
|
||||
// 1.1. Let x = r + jn.
|
||||
if (isSecondKey)
|
||||
r = this.curve.pointFromX(r.add(this.curve.n), isYOdd);
|
||||
else
|
||||
r = this.curve.pointFromX(r, isYOdd);
|
||||
|
||||
var rInv = signature.r.invm(n);
|
||||
var s1 = n.sub(e).mul(rInv).umod(n);
|
||||
var s2 = s.mul(rInv).umod(n);
|
||||
|
||||
// 1.6.1 Compute Q = r^-1 (sR - eG)
|
||||
// Q = r^-1 (sR + -eG)
|
||||
return this.g.mulAdd(s1, r, s2);
|
||||
};
|
||||
|
||||
EC.prototype.getKeyRecoveryParam = function(e, signature, Q, enc) {
|
||||
signature = new Signature(signature, enc);
|
||||
if (signature.recoveryParam !== null)
|
||||
return signature.recoveryParam;
|
||||
|
||||
for (var i = 0; i < 4; i++) {
|
||||
var Qprime;
|
||||
try {
|
||||
Qprime = this.recoverPubKey(e, signature, i);
|
||||
} catch (e) {
|
||||
continue;
|
||||
}
|
||||
|
||||
if (Qprime.eq(Q))
|
||||
return i;
|
||||
}
|
||||
throw new Error('Unable to find valid recovery factor');
|
||||
};
|
||||
121
web/node_modules/elliptic/lib/elliptic/ec/key.js
generated
vendored
Normal file
121
web/node_modules/elliptic/lib/elliptic/ec/key.js
generated
vendored
Normal file
|
|
@ -0,0 +1,121 @@
|
|||
'use strict';
|
||||
|
||||
var BN = require('bn.js');
|
||||
var utils = require('../utils');
|
||||
var assert = utils.assert;
|
||||
|
||||
function KeyPair(ec, options) {
|
||||
this.ec = ec;
|
||||
this.priv = null;
|
||||
this.pub = null;
|
||||
|
||||
// KeyPair(ec, { priv: ..., pub: ... })
|
||||
if (options.priv)
|
||||
this._importPrivate(options.priv, options.privEnc);
|
||||
if (options.pub)
|
||||
this._importPublic(options.pub, options.pubEnc);
|
||||
}
|
||||
module.exports = KeyPair;
|
||||
|
||||
KeyPair.fromPublic = function fromPublic(ec, pub, enc) {
|
||||
if (pub instanceof KeyPair)
|
||||
return pub;
|
||||
|
||||
return new KeyPair(ec, {
|
||||
pub: pub,
|
||||
pubEnc: enc,
|
||||
});
|
||||
};
|
||||
|
||||
KeyPair.fromPrivate = function fromPrivate(ec, priv, enc) {
|
||||
if (priv instanceof KeyPair)
|
||||
return priv;
|
||||
|
||||
return new KeyPair(ec, {
|
||||
priv: priv,
|
||||
privEnc: enc,
|
||||
});
|
||||
};
|
||||
|
||||
KeyPair.prototype.validate = function validate() {
|
||||
var pub = this.getPublic();
|
||||
|
||||
if (pub.isInfinity())
|
||||
return { result: false, reason: 'Invalid public key' };
|
||||
if (!pub.validate())
|
||||
return { result: false, reason: 'Public key is not a point' };
|
||||
if (!pub.mul(this.ec.curve.n).isInfinity())
|
||||
return { result: false, reason: 'Public key * N != O' };
|
||||
|
||||
return { result: true, reason: null };
|
||||
};
|
||||
|
||||
KeyPair.prototype.getPublic = function getPublic(compact, enc) {
|
||||
// compact is optional argument
|
||||
if (typeof compact === 'string') {
|
||||
enc = compact;
|
||||
compact = null;
|
||||
}
|
||||
|
||||
if (!this.pub)
|
||||
this.pub = this.ec.g.mul(this.priv);
|
||||
|
||||
if (!enc)
|
||||
return this.pub;
|
||||
|
||||
return this.pub.encode(enc, compact);
|
||||
};
|
||||
|
||||
KeyPair.prototype.getPrivate = function getPrivate(enc) {
|
||||
if (enc === 'hex')
|
||||
return this.priv.toString(16, 2);
|
||||
else
|
||||
return this.priv;
|
||||
};
|
||||
|
||||
KeyPair.prototype._importPrivate = function _importPrivate(key, enc) {
|
||||
this.priv = new BN(key, enc || 16);
|
||||
|
||||
// Ensure that the priv won't be bigger than n, otherwise we may fail
|
||||
// in fixed multiplication method
|
||||
this.priv = this.priv.umod(this.ec.curve.n);
|
||||
};
|
||||
|
||||
KeyPair.prototype._importPublic = function _importPublic(key, enc) {
|
||||
if (key.x || key.y) {
|
||||
// Montgomery points only have an `x` coordinate.
|
||||
// Weierstrass/Edwards points on the other hand have both `x` and
|
||||
// `y` coordinates.
|
||||
if (this.ec.curve.type === 'mont') {
|
||||
assert(key.x, 'Need x coordinate');
|
||||
} else if (this.ec.curve.type === 'short' ||
|
||||
this.ec.curve.type === 'edwards') {
|
||||
assert(key.x && key.y, 'Need both x and y coordinate');
|
||||
}
|
||||
this.pub = this.ec.curve.point(key.x, key.y);
|
||||
return;
|
||||
}
|
||||
this.pub = this.ec.curve.decodePoint(key, enc);
|
||||
};
|
||||
|
||||
// ECDH
|
||||
KeyPair.prototype.derive = function derive(pub) {
|
||||
if(!pub.validate()) {
|
||||
assert(pub.validate(), 'public point not validated');
|
||||
}
|
||||
return pub.mul(this.priv).getX();
|
||||
};
|
||||
|
||||
// ECDSA
|
||||
KeyPair.prototype.sign = function sign(msg, enc, options) {
|
||||
return this.ec.sign(msg, this, enc, options);
|
||||
};
|
||||
|
||||
KeyPair.prototype.verify = function verify(msg, signature) {
|
||||
return this.ec.verify(msg, signature, this);
|
||||
};
|
||||
|
||||
KeyPair.prototype.inspect = function inspect() {
|
||||
return '<Key priv: ' + (this.priv && this.priv.toString(16, 2)) +
|
||||
' pub: ' + (this.pub && this.pub.inspect()) + ' >';
|
||||
};
|
||||
166
web/node_modules/elliptic/lib/elliptic/ec/signature.js
generated
vendored
Normal file
166
web/node_modules/elliptic/lib/elliptic/ec/signature.js
generated
vendored
Normal file
|
|
@ -0,0 +1,166 @@
|
|||
'use strict';
|
||||
|
||||
var BN = require('bn.js');
|
||||
|
||||
var utils = require('../utils');
|
||||
var assert = utils.assert;
|
||||
|
||||
function Signature(options, enc) {
|
||||
if (options instanceof Signature)
|
||||
return options;
|
||||
|
||||
if (this._importDER(options, enc))
|
||||
return;
|
||||
|
||||
assert(options.r && options.s, 'Signature without r or s');
|
||||
this.r = new BN(options.r, 16);
|
||||
this.s = new BN(options.s, 16);
|
||||
if (options.recoveryParam === undefined)
|
||||
this.recoveryParam = null;
|
||||
else
|
||||
this.recoveryParam = options.recoveryParam;
|
||||
}
|
||||
module.exports = Signature;
|
||||
|
||||
function Position() {
|
||||
this.place = 0;
|
||||
}
|
||||
|
||||
function getLength(buf, p) {
|
||||
var initial = buf[p.place++];
|
||||
if (!(initial & 0x80)) {
|
||||
return initial;
|
||||
}
|
||||
var octetLen = initial & 0xf;
|
||||
|
||||
// Indefinite length or overflow
|
||||
if (octetLen === 0 || octetLen > 4) {
|
||||
return false;
|
||||
}
|
||||
|
||||
var val = 0;
|
||||
for (var i = 0, off = p.place; i < octetLen; i++, off++) {
|
||||
val <<= 8;
|
||||
val |= buf[off];
|
||||
val >>>= 0;
|
||||
}
|
||||
|
||||
// Leading zeroes
|
||||
if (val <= 0x7f) {
|
||||
return false;
|
||||
}
|
||||
|
||||
p.place = off;
|
||||
return val;
|
||||
}
|
||||
|
||||
function rmPadding(buf) {
|
||||
var i = 0;
|
||||
var len = buf.length - 1;
|
||||
while (!buf[i] && !(buf[i + 1] & 0x80) && i < len) {
|
||||
i++;
|
||||
}
|
||||
if (i === 0) {
|
||||
return buf;
|
||||
}
|
||||
return buf.slice(i);
|
||||
}
|
||||
|
||||
Signature.prototype._importDER = function _importDER(data, enc) {
|
||||
data = utils.toArray(data, enc);
|
||||
var p = new Position();
|
||||
if (data[p.place++] !== 0x30) {
|
||||
return false;
|
||||
}
|
||||
var len = getLength(data, p);
|
||||
if (len === false) {
|
||||
return false;
|
||||
}
|
||||
if ((len + p.place) !== data.length) {
|
||||
return false;
|
||||
}
|
||||
if (data[p.place++] !== 0x02) {
|
||||
return false;
|
||||
}
|
||||
var rlen = getLength(data, p);
|
||||
if (rlen === false) {
|
||||
return false;
|
||||
}
|
||||
var r = data.slice(p.place, rlen + p.place);
|
||||
p.place += rlen;
|
||||
if (data[p.place++] !== 0x02) {
|
||||
return false;
|
||||
}
|
||||
var slen = getLength(data, p);
|
||||
if (slen === false) {
|
||||
return false;
|
||||
}
|
||||
if (data.length !== slen + p.place) {
|
||||
return false;
|
||||
}
|
||||
var s = data.slice(p.place, slen + p.place);
|
||||
if (r[0] === 0) {
|
||||
if (r[1] & 0x80) {
|
||||
r = r.slice(1);
|
||||
} else {
|
||||
// Leading zeroes
|
||||
return false;
|
||||
}
|
||||
}
|
||||
if (s[0] === 0) {
|
||||
if (s[1] & 0x80) {
|
||||
s = s.slice(1);
|
||||
} else {
|
||||
// Leading zeroes
|
||||
return false;
|
||||
}
|
||||
}
|
||||
|
||||
this.r = new BN(r);
|
||||
this.s = new BN(s);
|
||||
this.recoveryParam = null;
|
||||
|
||||
return true;
|
||||
};
|
||||
|
||||
function constructLength(arr, len) {
|
||||
if (len < 0x80) {
|
||||
arr.push(len);
|
||||
return;
|
||||
}
|
||||
var octets = 1 + (Math.log(len) / Math.LN2 >>> 3);
|
||||
arr.push(octets | 0x80);
|
||||
while (--octets) {
|
||||
arr.push((len >>> (octets << 3)) & 0xff);
|
||||
}
|
||||
arr.push(len);
|
||||
}
|
||||
|
||||
Signature.prototype.toDER = function toDER(enc) {
|
||||
var r = this.r.toArray();
|
||||
var s = this.s.toArray();
|
||||
|
||||
// Pad values
|
||||
if (r[0] & 0x80)
|
||||
r = [ 0 ].concat(r);
|
||||
// Pad values
|
||||
if (s[0] & 0x80)
|
||||
s = [ 0 ].concat(s);
|
||||
|
||||
r = rmPadding(r);
|
||||
s = rmPadding(s);
|
||||
|
||||
while (!s[0] && !(s[1] & 0x80)) {
|
||||
s = s.slice(1);
|
||||
}
|
||||
var arr = [ 0x02 ];
|
||||
constructLength(arr, r.length);
|
||||
arr = arr.concat(r);
|
||||
arr.push(0x02);
|
||||
constructLength(arr, s.length);
|
||||
var backHalf = arr.concat(s);
|
||||
var res = [ 0x30 ];
|
||||
constructLength(res, backHalf.length);
|
||||
res = res.concat(backHalf);
|
||||
return utils.encode(res, enc);
|
||||
};
|
||||
118
web/node_modules/elliptic/lib/elliptic/eddsa/index.js
generated
vendored
Normal file
118
web/node_modules/elliptic/lib/elliptic/eddsa/index.js
generated
vendored
Normal file
|
|
@ -0,0 +1,118 @@
|
|||
'use strict';
|
||||
|
||||
var hash = require('hash.js');
|
||||
var curves = require('../curves');
|
||||
var utils = require('../utils');
|
||||
var assert = utils.assert;
|
||||
var parseBytes = utils.parseBytes;
|
||||
var KeyPair = require('./key');
|
||||
var Signature = require('./signature');
|
||||
|
||||
function EDDSA(curve) {
|
||||
assert(curve === 'ed25519', 'only tested with ed25519 so far');
|
||||
|
||||
if (!(this instanceof EDDSA))
|
||||
return new EDDSA(curve);
|
||||
|
||||
curve = curves[curve].curve;
|
||||
this.curve = curve;
|
||||
this.g = curve.g;
|
||||
this.g.precompute(curve.n.bitLength() + 1);
|
||||
|
||||
this.pointClass = curve.point().constructor;
|
||||
this.encodingLength = Math.ceil(curve.n.bitLength() / 8);
|
||||
this.hash = hash.sha512;
|
||||
}
|
||||
|
||||
module.exports = EDDSA;
|
||||
|
||||
/**
|
||||
* @param {Array|String} message - message bytes
|
||||
* @param {Array|String|KeyPair} secret - secret bytes or a keypair
|
||||
* @returns {Signature} - signature
|
||||
*/
|
||||
EDDSA.prototype.sign = function sign(message, secret) {
|
||||
message = parseBytes(message);
|
||||
var key = this.keyFromSecret(secret);
|
||||
var r = this.hashInt(key.messagePrefix(), message);
|
||||
var R = this.g.mul(r);
|
||||
var Rencoded = this.encodePoint(R);
|
||||
var s_ = this.hashInt(Rencoded, key.pubBytes(), message)
|
||||
.mul(key.priv());
|
||||
var S = r.add(s_).umod(this.curve.n);
|
||||
return this.makeSignature({ R: R, S: S, Rencoded: Rencoded });
|
||||
};
|
||||
|
||||
/**
|
||||
* @param {Array} message - message bytes
|
||||
* @param {Array|String|Signature} sig - sig bytes
|
||||
* @param {Array|String|Point|KeyPair} pub - public key
|
||||
* @returns {Boolean} - true if public key matches sig of message
|
||||
*/
|
||||
EDDSA.prototype.verify = function verify(message, sig, pub) {
|
||||
message = parseBytes(message);
|
||||
sig = this.makeSignature(sig);
|
||||
var key = this.keyFromPublic(pub);
|
||||
var h = this.hashInt(sig.Rencoded(), key.pubBytes(), message);
|
||||
var SG = this.g.mul(sig.S());
|
||||
var RplusAh = sig.R().add(key.pub().mul(h));
|
||||
return RplusAh.eq(SG);
|
||||
};
|
||||
|
||||
EDDSA.prototype.hashInt = function hashInt() {
|
||||
var hash = this.hash();
|
||||
for (var i = 0; i < arguments.length; i++)
|
||||
hash.update(arguments[i]);
|
||||
return utils.intFromLE(hash.digest()).umod(this.curve.n);
|
||||
};
|
||||
|
||||
EDDSA.prototype.keyFromPublic = function keyFromPublic(pub) {
|
||||
return KeyPair.fromPublic(this, pub);
|
||||
};
|
||||
|
||||
EDDSA.prototype.keyFromSecret = function keyFromSecret(secret) {
|
||||
return KeyPair.fromSecret(this, secret);
|
||||
};
|
||||
|
||||
EDDSA.prototype.makeSignature = function makeSignature(sig) {
|
||||
if (sig instanceof Signature)
|
||||
return sig;
|
||||
return new Signature(this, sig);
|
||||
};
|
||||
|
||||
/**
|
||||
* * https://tools.ietf.org/html/draft-josefsson-eddsa-ed25519-03#section-5.2
|
||||
*
|
||||
* EDDSA defines methods for encoding and decoding points and integers. These are
|
||||
* helper convenience methods, that pass along to utility functions implied
|
||||
* parameters.
|
||||
*
|
||||
*/
|
||||
EDDSA.prototype.encodePoint = function encodePoint(point) {
|
||||
var enc = point.getY().toArray('le', this.encodingLength);
|
||||
enc[this.encodingLength - 1] |= point.getX().isOdd() ? 0x80 : 0;
|
||||
return enc;
|
||||
};
|
||||
|
||||
EDDSA.prototype.decodePoint = function decodePoint(bytes) {
|
||||
bytes = utils.parseBytes(bytes);
|
||||
|
||||
var lastIx = bytes.length - 1;
|
||||
var normed = bytes.slice(0, lastIx).concat(bytes[lastIx] & ~0x80);
|
||||
var xIsOdd = (bytes[lastIx] & 0x80) !== 0;
|
||||
|
||||
var y = utils.intFromLE(normed);
|
||||
return this.curve.pointFromY(y, xIsOdd);
|
||||
};
|
||||
|
||||
EDDSA.prototype.encodeInt = function encodeInt(num) {
|
||||
return num.toArray('le', this.encodingLength);
|
||||
};
|
||||
|
||||
EDDSA.prototype.decodeInt = function decodeInt(bytes) {
|
||||
return utils.intFromLE(bytes);
|
||||
};
|
||||
|
||||
EDDSA.prototype.isPoint = function isPoint(val) {
|
||||
return val instanceof this.pointClass;
|
||||
};
|
||||
95
web/node_modules/elliptic/lib/elliptic/eddsa/key.js
generated
vendored
Normal file
95
web/node_modules/elliptic/lib/elliptic/eddsa/key.js
generated
vendored
Normal file
|
|
@ -0,0 +1,95 @@
|
|||
'use strict';
|
||||
|
||||
var utils = require('../utils');
|
||||
var assert = utils.assert;
|
||||
var parseBytes = utils.parseBytes;
|
||||
var cachedProperty = utils.cachedProperty;
|
||||
|
||||
/**
|
||||
* @param {EDDSA} eddsa - instance
|
||||
* @param {Object} params - public/private key parameters
|
||||
*
|
||||
* @param {Array<Byte>} [params.secret] - secret seed bytes
|
||||
* @param {Point} [params.pub] - public key point (aka `A` in eddsa terms)
|
||||
* @param {Array<Byte>} [params.pub] - public key point encoded as bytes
|
||||
*
|
||||
*/
|
||||
function KeyPair(eddsa, params) {
|
||||
this.eddsa = eddsa;
|
||||
this._secret = parseBytes(params.secret);
|
||||
if (eddsa.isPoint(params.pub))
|
||||
this._pub = params.pub;
|
||||
else
|
||||
this._pubBytes = parseBytes(params.pub);
|
||||
}
|
||||
|
||||
KeyPair.fromPublic = function fromPublic(eddsa, pub) {
|
||||
if (pub instanceof KeyPair)
|
||||
return pub;
|
||||
return new KeyPair(eddsa, { pub: pub });
|
||||
};
|
||||
|
||||
KeyPair.fromSecret = function fromSecret(eddsa, secret) {
|
||||
if (secret instanceof KeyPair)
|
||||
return secret;
|
||||
return new KeyPair(eddsa, { secret: secret });
|
||||
};
|
||||
|
||||
KeyPair.prototype.secret = function secret() {
|
||||
return this._secret;
|
||||
};
|
||||
|
||||
cachedProperty(KeyPair, 'pubBytes', function pubBytes() {
|
||||
return this.eddsa.encodePoint(this.pub());
|
||||
});
|
||||
|
||||
cachedProperty(KeyPair, 'pub', function pub() {
|
||||
if (this._pubBytes)
|
||||
return this.eddsa.decodePoint(this._pubBytes);
|
||||
return this.eddsa.g.mul(this.priv());
|
||||
});
|
||||
|
||||
cachedProperty(KeyPair, 'privBytes', function privBytes() {
|
||||
var eddsa = this.eddsa;
|
||||
var hash = this.hash();
|
||||
var lastIx = eddsa.encodingLength - 1;
|
||||
|
||||
var a = hash.slice(0, eddsa.encodingLength);
|
||||
a[0] &= 248;
|
||||
a[lastIx] &= 127;
|
||||
a[lastIx] |= 64;
|
||||
|
||||
return a;
|
||||
});
|
||||
|
||||
cachedProperty(KeyPair, 'priv', function priv() {
|
||||
return this.eddsa.decodeInt(this.privBytes());
|
||||
});
|
||||
|
||||
cachedProperty(KeyPair, 'hash', function hash() {
|
||||
return this.eddsa.hash().update(this.secret()).digest();
|
||||
});
|
||||
|
||||
cachedProperty(KeyPair, 'messagePrefix', function messagePrefix() {
|
||||
return this.hash().slice(this.eddsa.encodingLength);
|
||||
});
|
||||
|
||||
KeyPair.prototype.sign = function sign(message) {
|
||||
assert(this._secret, 'KeyPair can only verify');
|
||||
return this.eddsa.sign(message, this);
|
||||
};
|
||||
|
||||
KeyPair.prototype.verify = function verify(message, sig) {
|
||||
return this.eddsa.verify(message, sig, this);
|
||||
};
|
||||
|
||||
KeyPair.prototype.getSecret = function getSecret(enc) {
|
||||
assert(this._secret, 'KeyPair is public only');
|
||||
return utils.encode(this.secret(), enc);
|
||||
};
|
||||
|
||||
KeyPair.prototype.getPublic = function getPublic(enc) {
|
||||
return utils.encode(this.pubBytes(), enc);
|
||||
};
|
||||
|
||||
module.exports = KeyPair;
|
||||
65
web/node_modules/elliptic/lib/elliptic/eddsa/signature.js
generated
vendored
Normal file
65
web/node_modules/elliptic/lib/elliptic/eddsa/signature.js
generated
vendored
Normal file
|
|
@ -0,0 +1,65 @@
|
|||
'use strict';
|
||||
|
||||
var BN = require('bn.js');
|
||||
var utils = require('../utils');
|
||||
var assert = utils.assert;
|
||||
var cachedProperty = utils.cachedProperty;
|
||||
var parseBytes = utils.parseBytes;
|
||||
|
||||
/**
|
||||
* @param {EDDSA} eddsa - eddsa instance
|
||||
* @param {Array<Bytes>|Object} sig -
|
||||
* @param {Array<Bytes>|Point} [sig.R] - R point as Point or bytes
|
||||
* @param {Array<Bytes>|bn} [sig.S] - S scalar as bn or bytes
|
||||
* @param {Array<Bytes>} [sig.Rencoded] - R point encoded
|
||||
* @param {Array<Bytes>} [sig.Sencoded] - S scalar encoded
|
||||
*/
|
||||
function Signature(eddsa, sig) {
|
||||
this.eddsa = eddsa;
|
||||
|
||||
if (typeof sig !== 'object')
|
||||
sig = parseBytes(sig);
|
||||
|
||||
if (Array.isArray(sig)) {
|
||||
sig = {
|
||||
R: sig.slice(0, eddsa.encodingLength),
|
||||
S: sig.slice(eddsa.encodingLength),
|
||||
};
|
||||
}
|
||||
|
||||
assert(sig.R && sig.S, 'Signature without R or S');
|
||||
|
||||
if (eddsa.isPoint(sig.R))
|
||||
this._R = sig.R;
|
||||
if (sig.S instanceof BN)
|
||||
this._S = sig.S;
|
||||
|
||||
this._Rencoded = Array.isArray(sig.R) ? sig.R : sig.Rencoded;
|
||||
this._Sencoded = Array.isArray(sig.S) ? sig.S : sig.Sencoded;
|
||||
}
|
||||
|
||||
cachedProperty(Signature, 'S', function S() {
|
||||
return this.eddsa.decodeInt(this.Sencoded());
|
||||
});
|
||||
|
||||
cachedProperty(Signature, 'R', function R() {
|
||||
return this.eddsa.decodePoint(this.Rencoded());
|
||||
});
|
||||
|
||||
cachedProperty(Signature, 'Rencoded', function Rencoded() {
|
||||
return this.eddsa.encodePoint(this.R());
|
||||
});
|
||||
|
||||
cachedProperty(Signature, 'Sencoded', function Sencoded() {
|
||||
return this.eddsa.encodeInt(this.S());
|
||||
});
|
||||
|
||||
Signature.prototype.toBytes = function toBytes() {
|
||||
return this.Rencoded().concat(this.Sencoded());
|
||||
};
|
||||
|
||||
Signature.prototype.toHex = function toHex() {
|
||||
return utils.encode(this.toBytes(), 'hex').toUpperCase();
|
||||
};
|
||||
|
||||
module.exports = Signature;
|
||||
780
web/node_modules/elliptic/lib/elliptic/precomputed/secp256k1.js
generated
vendored
Normal file
780
web/node_modules/elliptic/lib/elliptic/precomputed/secp256k1.js
generated
vendored
Normal file
|
|
@ -0,0 +1,780 @@
|
|||
module.exports = {
|
||||
doubles: {
|
||||
step: 4,
|
||||
points: [
|
||||
[
|
||||
'e60fce93b59e9ec53011aabc21c23e97b2a31369b87a5ae9c44ee89e2a6dec0a',
|
||||
'f7e3507399e595929db99f34f57937101296891e44d23f0be1f32cce69616821',
|
||||
],
|
||||
[
|
||||
'8282263212c609d9ea2a6e3e172de238d8c39cabd5ac1ca10646e23fd5f51508',
|
||||
'11f8a8098557dfe45e8256e830b60ace62d613ac2f7b17bed31b6eaff6e26caf',
|
||||
],
|
||||
[
|
||||
'175e159f728b865a72f99cc6c6fc846de0b93833fd2222ed73fce5b551e5b739',
|
||||
'd3506e0d9e3c79eba4ef97a51ff71f5eacb5955add24345c6efa6ffee9fed695',
|
||||
],
|
||||
[
|
||||
'363d90d447b00c9c99ceac05b6262ee053441c7e55552ffe526bad8f83ff4640',
|
||||
'4e273adfc732221953b445397f3363145b9a89008199ecb62003c7f3bee9de9',
|
||||
],
|
||||
[
|
||||
'8b4b5f165df3c2be8c6244b5b745638843e4a781a15bcd1b69f79a55dffdf80c',
|
||||
'4aad0a6f68d308b4b3fbd7813ab0da04f9e336546162ee56b3eff0c65fd4fd36',
|
||||
],
|
||||
[
|
||||
'723cbaa6e5db996d6bf771c00bd548c7b700dbffa6c0e77bcb6115925232fcda',
|
||||
'96e867b5595cc498a921137488824d6e2660a0653779494801dc069d9eb39f5f',
|
||||
],
|
||||
[
|
||||
'eebfa4d493bebf98ba5feec812c2d3b50947961237a919839a533eca0e7dd7fa',
|
||||
'5d9a8ca3970ef0f269ee7edaf178089d9ae4cdc3a711f712ddfd4fdae1de8999',
|
||||
],
|
||||
[
|
||||
'100f44da696e71672791d0a09b7bde459f1215a29b3c03bfefd7835b39a48db0',
|
||||
'cdd9e13192a00b772ec8f3300c090666b7ff4a18ff5195ac0fbd5cd62bc65a09',
|
||||
],
|
||||
[
|
||||
'e1031be262c7ed1b1dc9227a4a04c017a77f8d4464f3b3852c8acde6e534fd2d',
|
||||
'9d7061928940405e6bb6a4176597535af292dd419e1ced79a44f18f29456a00d',
|
||||
],
|
||||
[
|
||||
'feea6cae46d55b530ac2839f143bd7ec5cf8b266a41d6af52d5e688d9094696d',
|
||||
'e57c6b6c97dce1bab06e4e12bf3ecd5c981c8957cc41442d3155debf18090088',
|
||||
],
|
||||
[
|
||||
'da67a91d91049cdcb367be4be6ffca3cfeed657d808583de33fa978bc1ec6cb1',
|
||||
'9bacaa35481642bc41f463f7ec9780e5dec7adc508f740a17e9ea8e27a68be1d',
|
||||
],
|
||||
[
|
||||
'53904faa0b334cdda6e000935ef22151ec08d0f7bb11069f57545ccc1a37b7c0',
|
||||
'5bc087d0bc80106d88c9eccac20d3c1c13999981e14434699dcb096b022771c8',
|
||||
],
|
||||
[
|
||||
'8e7bcd0bd35983a7719cca7764ca906779b53a043a9b8bcaeff959f43ad86047',
|
||||
'10b7770b2a3da4b3940310420ca9514579e88e2e47fd68b3ea10047e8460372a',
|
||||
],
|
||||
[
|
||||
'385eed34c1cdff21e6d0818689b81bde71a7f4f18397e6690a841e1599c43862',
|
||||
'283bebc3e8ea23f56701de19e9ebf4576b304eec2086dc8cc0458fe5542e5453',
|
||||
],
|
||||
[
|
||||
'6f9d9b803ecf191637c73a4413dfa180fddf84a5947fbc9c606ed86c3fac3a7',
|
||||
'7c80c68e603059ba69b8e2a30e45c4d47ea4dd2f5c281002d86890603a842160',
|
||||
],
|
||||
[
|
||||
'3322d401243c4e2582a2147c104d6ecbf774d163db0f5e5313b7e0e742d0e6bd',
|
||||
'56e70797e9664ef5bfb019bc4ddaf9b72805f63ea2873af624f3a2e96c28b2a0',
|
||||
],
|
||||
[
|
||||
'85672c7d2de0b7da2bd1770d89665868741b3f9af7643397721d74d28134ab83',
|
||||
'7c481b9b5b43b2eb6374049bfa62c2e5e77f17fcc5298f44c8e3094f790313a6',
|
||||
],
|
||||
[
|
||||
'948bf809b1988a46b06c9f1919413b10f9226c60f668832ffd959af60c82a0a',
|
||||
'53a562856dcb6646dc6b74c5d1c3418c6d4dff08c97cd2bed4cb7f88d8c8e589',
|
||||
],
|
||||
[
|
||||
'6260ce7f461801c34f067ce0f02873a8f1b0e44dfc69752accecd819f38fd8e8',
|
||||
'bc2da82b6fa5b571a7f09049776a1ef7ecd292238051c198c1a84e95b2b4ae17',
|
||||
],
|
||||
[
|
||||
'e5037de0afc1d8d43d8348414bbf4103043ec8f575bfdc432953cc8d2037fa2d',
|
||||
'4571534baa94d3b5f9f98d09fb990bddbd5f5b03ec481f10e0e5dc841d755bda',
|
||||
],
|
||||
[
|
||||
'e06372b0f4a207adf5ea905e8f1771b4e7e8dbd1c6a6c5b725866a0ae4fce725',
|
||||
'7a908974bce18cfe12a27bb2ad5a488cd7484a7787104870b27034f94eee31dd',
|
||||
],
|
||||
[
|
||||
'213c7a715cd5d45358d0bbf9dc0ce02204b10bdde2a3f58540ad6908d0559754',
|
||||
'4b6dad0b5ae462507013ad06245ba190bb4850f5f36a7eeddff2c27534b458f2',
|
||||
],
|
||||
[
|
||||
'4e7c272a7af4b34e8dbb9352a5419a87e2838c70adc62cddf0cc3a3b08fbd53c',
|
||||
'17749c766c9d0b18e16fd09f6def681b530b9614bff7dd33e0b3941817dcaae6',
|
||||
],
|
||||
[
|
||||
'fea74e3dbe778b1b10f238ad61686aa5c76e3db2be43057632427e2840fb27b6',
|
||||
'6e0568db9b0b13297cf674deccb6af93126b596b973f7b77701d3db7f23cb96f',
|
||||
],
|
||||
[
|
||||
'76e64113f677cf0e10a2570d599968d31544e179b760432952c02a4417bdde39',
|
||||
'c90ddf8dee4e95cf577066d70681f0d35e2a33d2b56d2032b4b1752d1901ac01',
|
||||
],
|
||||
[
|
||||
'c738c56b03b2abe1e8281baa743f8f9a8f7cc643df26cbee3ab150242bcbb891',
|
||||
'893fb578951ad2537f718f2eacbfbbbb82314eef7880cfe917e735d9699a84c3',
|
||||
],
|
||||
[
|
||||
'd895626548b65b81e264c7637c972877d1d72e5f3a925014372e9f6588f6c14b',
|
||||
'febfaa38f2bc7eae728ec60818c340eb03428d632bb067e179363ed75d7d991f',
|
||||
],
|
||||
[
|
||||
'b8da94032a957518eb0f6433571e8761ceffc73693e84edd49150a564f676e03',
|
||||
'2804dfa44805a1e4d7c99cc9762808b092cc584d95ff3b511488e4e74efdf6e7',
|
||||
],
|
||||
[
|
||||
'e80fea14441fb33a7d8adab9475d7fab2019effb5156a792f1a11778e3c0df5d',
|
||||
'eed1de7f638e00771e89768ca3ca94472d155e80af322ea9fcb4291b6ac9ec78',
|
||||
],
|
||||
[
|
||||
'a301697bdfcd704313ba48e51d567543f2a182031efd6915ddc07bbcc4e16070',
|
||||
'7370f91cfb67e4f5081809fa25d40f9b1735dbf7c0a11a130c0d1a041e177ea1',
|
||||
],
|
||||
[
|
||||
'90ad85b389d6b936463f9d0512678de208cc330b11307fffab7ac63e3fb04ed4',
|
||||
'e507a3620a38261affdcbd9427222b839aefabe1582894d991d4d48cb6ef150',
|
||||
],
|
||||
[
|
||||
'8f68b9d2f63b5f339239c1ad981f162ee88c5678723ea3351b7b444c9ec4c0da',
|
||||
'662a9f2dba063986de1d90c2b6be215dbbea2cfe95510bfdf23cbf79501fff82',
|
||||
],
|
||||
[
|
||||
'e4f3fb0176af85d65ff99ff9198c36091f48e86503681e3e6686fd5053231e11',
|
||||
'1e63633ad0ef4f1c1661a6d0ea02b7286cc7e74ec951d1c9822c38576feb73bc',
|
||||
],
|
||||
[
|
||||
'8c00fa9b18ebf331eb961537a45a4266c7034f2f0d4e1d0716fb6eae20eae29e',
|
||||
'efa47267fea521a1a9dc343a3736c974c2fadafa81e36c54e7d2a4c66702414b',
|
||||
],
|
||||
[
|
||||
'e7a26ce69dd4829f3e10cec0a9e98ed3143d084f308b92c0997fddfc60cb3e41',
|
||||
'2a758e300fa7984b471b006a1aafbb18d0a6b2c0420e83e20e8a9421cf2cfd51',
|
||||
],
|
||||
[
|
||||
'b6459e0ee3662ec8d23540c223bcbdc571cbcb967d79424f3cf29eb3de6b80ef',
|
||||
'67c876d06f3e06de1dadf16e5661db3c4b3ae6d48e35b2ff30bf0b61a71ba45',
|
||||
],
|
||||
[
|
||||
'd68a80c8280bb840793234aa118f06231d6f1fc67e73c5a5deda0f5b496943e8',
|
||||
'db8ba9fff4b586d00c4b1f9177b0e28b5b0e7b8f7845295a294c84266b133120',
|
||||
],
|
||||
[
|
||||
'324aed7df65c804252dc0270907a30b09612aeb973449cea4095980fc28d3d5d',
|
||||
'648a365774b61f2ff130c0c35aec1f4f19213b0c7e332843967224af96ab7c84',
|
||||
],
|
||||
[
|
||||
'4df9c14919cde61f6d51dfdbe5fee5dceec4143ba8d1ca888e8bd373fd054c96',
|
||||
'35ec51092d8728050974c23a1d85d4b5d506cdc288490192ebac06cad10d5d',
|
||||
],
|
||||
[
|
||||
'9c3919a84a474870faed8a9c1cc66021523489054d7f0308cbfc99c8ac1f98cd',
|
||||
'ddb84f0f4a4ddd57584f044bf260e641905326f76c64c8e6be7e5e03d4fc599d',
|
||||
],
|
||||
[
|
||||
'6057170b1dd12fdf8de05f281d8e06bb91e1493a8b91d4cc5a21382120a959e5',
|
||||
'9a1af0b26a6a4807add9a2daf71df262465152bc3ee24c65e899be932385a2a8',
|
||||
],
|
||||
[
|
||||
'a576df8e23a08411421439a4518da31880cef0fba7d4df12b1a6973eecb94266',
|
||||
'40a6bf20e76640b2c92b97afe58cd82c432e10a7f514d9f3ee8be11ae1b28ec8',
|
||||
],
|
||||
[
|
||||
'7778a78c28dec3e30a05fe9629de8c38bb30d1f5cf9a3a208f763889be58ad71',
|
||||
'34626d9ab5a5b22ff7098e12f2ff580087b38411ff24ac563b513fc1fd9f43ac',
|
||||
],
|
||||
[
|
||||
'928955ee637a84463729fd30e7afd2ed5f96274e5ad7e5cb09eda9c06d903ac',
|
||||
'c25621003d3f42a827b78a13093a95eeac3d26efa8a8d83fc5180e935bcd091f',
|
||||
],
|
||||
[
|
||||
'85d0fef3ec6db109399064f3a0e3b2855645b4a907ad354527aae75163d82751',
|
||||
'1f03648413a38c0be29d496e582cf5663e8751e96877331582c237a24eb1f962',
|
||||
],
|
||||
[
|
||||
'ff2b0dce97eece97c1c9b6041798b85dfdfb6d8882da20308f5404824526087e',
|
||||
'493d13fef524ba188af4c4dc54d07936c7b7ed6fb90e2ceb2c951e01f0c29907',
|
||||
],
|
||||
[
|
||||
'827fbbe4b1e880ea9ed2b2e6301b212b57f1ee148cd6dd28780e5e2cf856e241',
|
||||
'c60f9c923c727b0b71bef2c67d1d12687ff7a63186903166d605b68baec293ec',
|
||||
],
|
||||
[
|
||||
'eaa649f21f51bdbae7be4ae34ce6e5217a58fdce7f47f9aa7f3b58fa2120e2b3',
|
||||
'be3279ed5bbbb03ac69a80f89879aa5a01a6b965f13f7e59d47a5305ba5ad93d',
|
||||
],
|
||||
[
|
||||
'e4a42d43c5cf169d9391df6decf42ee541b6d8f0c9a137401e23632dda34d24f',
|
||||
'4d9f92e716d1c73526fc99ccfb8ad34ce886eedfa8d8e4f13a7f7131deba9414',
|
||||
],
|
||||
[
|
||||
'1ec80fef360cbdd954160fadab352b6b92b53576a88fea4947173b9d4300bf19',
|
||||
'aeefe93756b5340d2f3a4958a7abbf5e0146e77f6295a07b671cdc1cc107cefd',
|
||||
],
|
||||
[
|
||||
'146a778c04670c2f91b00af4680dfa8bce3490717d58ba889ddb5928366642be',
|
||||
'b318e0ec3354028add669827f9d4b2870aaa971d2f7e5ed1d0b297483d83efd0',
|
||||
],
|
||||
[
|
||||
'fa50c0f61d22e5f07e3acebb1aa07b128d0012209a28b9776d76a8793180eef9',
|
||||
'6b84c6922397eba9b72cd2872281a68a5e683293a57a213b38cd8d7d3f4f2811',
|
||||
],
|
||||
[
|
||||
'da1d61d0ca721a11b1a5bf6b7d88e8421a288ab5d5bba5220e53d32b5f067ec2',
|
||||
'8157f55a7c99306c79c0766161c91e2966a73899d279b48a655fba0f1ad836f1',
|
||||
],
|
||||
[
|
||||
'a8e282ff0c9706907215ff98e8fd416615311de0446f1e062a73b0610d064e13',
|
||||
'7f97355b8db81c09abfb7f3c5b2515888b679a3e50dd6bd6cef7c73111f4cc0c',
|
||||
],
|
||||
[
|
||||
'174a53b9c9a285872d39e56e6913cab15d59b1fa512508c022f382de8319497c',
|
||||
'ccc9dc37abfc9c1657b4155f2c47f9e6646b3a1d8cb9854383da13ac079afa73',
|
||||
],
|
||||
[
|
||||
'959396981943785c3d3e57edf5018cdbe039e730e4918b3d884fdff09475b7ba',
|
||||
'2e7e552888c331dd8ba0386a4b9cd6849c653f64c8709385e9b8abf87524f2fd',
|
||||
],
|
||||
[
|
||||
'd2a63a50ae401e56d645a1153b109a8fcca0a43d561fba2dbb51340c9d82b151',
|
||||
'e82d86fb6443fcb7565aee58b2948220a70f750af484ca52d4142174dcf89405',
|
||||
],
|
||||
[
|
||||
'64587e2335471eb890ee7896d7cfdc866bacbdbd3839317b3436f9b45617e073',
|
||||
'd99fcdd5bf6902e2ae96dd6447c299a185b90a39133aeab358299e5e9faf6589',
|
||||
],
|
||||
[
|
||||
'8481bde0e4e4d885b3a546d3e549de042f0aa6cea250e7fd358d6c86dd45e458',
|
||||
'38ee7b8cba5404dd84a25bf39cecb2ca900a79c42b262e556d64b1b59779057e',
|
||||
],
|
||||
[
|
||||
'13464a57a78102aa62b6979ae817f4637ffcfed3c4b1ce30bcd6303f6caf666b',
|
||||
'69be159004614580ef7e433453ccb0ca48f300a81d0942e13f495a907f6ecc27',
|
||||
],
|
||||
[
|
||||
'bc4a9df5b713fe2e9aef430bcc1dc97a0cd9ccede2f28588cada3a0d2d83f366',
|
||||
'd3a81ca6e785c06383937adf4b798caa6e8a9fbfa547b16d758d666581f33c1',
|
||||
],
|
||||
[
|
||||
'8c28a97bf8298bc0d23d8c749452a32e694b65e30a9472a3954ab30fe5324caa',
|
||||
'40a30463a3305193378fedf31f7cc0eb7ae784f0451cb9459e71dc73cbef9482',
|
||||
],
|
||||
[
|
||||
'8ea9666139527a8c1dd94ce4f071fd23c8b350c5a4bb33748c4ba111faccae0',
|
||||
'620efabbc8ee2782e24e7c0cfb95c5d735b783be9cf0f8e955af34a30e62b945',
|
||||
],
|
||||
[
|
||||
'dd3625faef5ba06074669716bbd3788d89bdde815959968092f76cc4eb9a9787',
|
||||
'7a188fa3520e30d461da2501045731ca941461982883395937f68d00c644a573',
|
||||
],
|
||||
[
|
||||
'f710d79d9eb962297e4f6232b40e8f7feb2bc63814614d692c12de752408221e',
|
||||
'ea98e67232d3b3295d3b535532115ccac8612c721851617526ae47a9c77bfc82',
|
||||
],
|
||||
],
|
||||
},
|
||||
naf: {
|
||||
wnd: 7,
|
||||
points: [
|
||||
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'b4c4fe99c775a606e2d8862179139ffda61dc861c019e55cd2876eb2a27d84b',
|
||||
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|
||||
[
|
||||
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|
||||
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|
||||
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|
||||
[
|
||||
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|
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|
||||
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||||
[
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||||
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|
||||
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||||
[
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||||
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||||
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|
||||
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||||
[
|
||||
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||||
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|
||||
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|
||||
[
|
||||
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||||
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|
||||
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|
||||
[
|
||||
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|
||||
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|
||||
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|
||||
[
|
||||
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|
||||
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|
||||
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|
||||
[
|
||||
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||||
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|
||||
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|
||||
[
|
||||
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||||
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|
||||
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|
||||
[
|
||||
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|
||||
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|
||||
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|
||||
[
|
||||
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|
||||
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|
||||
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|
||||
[
|
||||
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|
||||
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|
||||
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|
||||
[
|
||||
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|
||||
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|
||||
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|
||||
[
|
||||
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||||
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|
||||
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|
||||
[
|
||||
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||||
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|
||||
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|
||||
[
|
||||
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||||
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|
||||
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|
||||
[
|
||||
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|
||||
'be52d107bcfa09d8bcb9736a828cfa7fac8db17bf7a76a2c42ad961409018cf7',
|
||||
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|
||||
[
|
||||
'cee31cbf7e34ec379d94fb814d3d775ad954595d1314ba8846959e3e82f74e26',
|
||||
'8fd64a14c06b589c26b947ae2bcf6bfa0149ef0be14ed4d80f448a01c43b1c6d',
|
||||
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|
||||
[
|
||||
'b4f9eaea09b6917619f6ea6a4eb5464efddb58fd45b1ebefcdc1a01d08b47986',
|
||||
'39e5c9925b5a54b07433a4f18c61726f8bb131c012ca542eb24a8ac07200682a',
|
||||
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|
||||
[
|
||||
'd4263dfc3d2df923a0179a48966d30ce84e2515afc3dccc1b77907792ebcc60e',
|
||||
'62dfaf07a0f78feb30e30d6295853ce189e127760ad6cf7fae164e122a208d54',
|
||||
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|
||||
[
|
||||
'48457524820fa65a4f8d35eb6930857c0032acc0a4a2de422233eeda897612c4',
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||||
'25a748ab367979d98733c38a1fa1c2e7dc6cc07db2d60a9ae7a76aaa49bd0f77',
|
||||
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|
||||
[
|
||||
'dfeeef1881101f2cb11644f3a2afdfc2045e19919152923f367a1767c11cceda',
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||||
'ecfb7056cf1de042f9420bab396793c0c390bde74b4bbdff16a83ae09a9a7517',
|
||||
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|
||||
[
|
||||
'6d7ef6b17543f8373c573f44e1f389835d89bcbc6062ced36c82df83b8fae859',
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||||
'cd450ec335438986dfefa10c57fea9bcc521a0959b2d80bbf74b190dca712d10',
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||||
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|
||||
[
|
||||
'e75605d59102a5a2684500d3b991f2e3f3c88b93225547035af25af66e04541f',
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||||
'f5c54754a8f71ee540b9b48728473e314f729ac5308b06938360990e2bfad125',
|
||||
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|
||||
[
|
||||
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||||
'6cb9a8876d9cb8520609af3add26cd20a0a7cd8a9411131ce85f44100099223e',
|
||||
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|
||||
[
|
||||
'13e87b027d8514d35939f2e6892b19922154596941888336dc3563e3b8dba942',
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||||
'fef5a3c68059a6dec5d624114bf1e91aac2b9da568d6abeb2570d55646b8adf1',
|
||||
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|
||||
[
|
||||
'ee163026e9fd6fe017c38f06a5be6fc125424b371ce2708e7bf4491691e5764a',
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||||
'1acb250f255dd61c43d94ccc670d0f58f49ae3fa15b96623e5430da0ad6c62b2',
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||||
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||||
[
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||||
'b268f5ef9ad51e4d78de3a750c2dc89b1e626d43505867999932e5db33af3d80',
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||||
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|
||||
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|
||||
[
|
||||
'ff07f3118a9df035e9fad85eb6c7bfe42b02f01ca99ceea3bf7ffdba93c4750d',
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||||
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||||
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|
||||
[
|
||||
'8d8b9855c7c052a34146fd20ffb658bea4b9f69e0d825ebec16e8c3ce2b526a1',
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||||
'cdb559eedc2d79f926baf44fb84ea4d44bcf50fee51d7ceb30e2e7f463036758',
|
||||
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|
||||
[
|
||||
'52db0b5384dfbf05bfa9d472d7ae26dfe4b851ceca91b1eba54263180da32b63',
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||||
'c3b997d050ee5d423ebaf66a6db9f57b3180c902875679de924b69d84a7b375',
|
||||
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|
||||
[
|
||||
'e62f9490d3d51da6395efd24e80919cc7d0f29c3f3fa48c6fff543becbd43352',
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||||
'6d89ad7ba4876b0b22c2ca280c682862f342c8591f1daf5170e07bfd9ccafa7d',
|
||||
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|
||||
[
|
||||
'7f30ea2476b399b4957509c88f77d0191afa2ff5cb7b14fd6d8e7d65aaab1193',
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||||
'ca5ef7d4b231c94c3b15389a5f6311e9daff7bb67b103e9880ef4bff637acaec',
|
||||
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|
||||
[
|
||||
'5098ff1e1d9f14fb46a210fada6c903fef0fb7b4a1dd1d9ac60a0361800b7a00',
|
||||
'9731141d81fc8f8084d37c6e7542006b3ee1b40d60dfe5362a5b132fd17ddc0',
|
||||
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|
||||
[
|
||||
'32b78c7de9ee512a72895be6b9cbefa6e2f3c4ccce445c96b9f2c81e2778ad58',
|
||||
'ee1849f513df71e32efc3896ee28260c73bb80547ae2275ba497237794c8753c',
|
||||
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|
||||
[
|
||||
'e2cb74fddc8e9fbcd076eef2a7c72b0ce37d50f08269dfc074b581550547a4f7',
|
||||
'd3aa2ed71c9dd2247a62df062736eb0baddea9e36122d2be8641abcb005cc4a4',
|
||||
],
|
||||
[
|
||||
'8438447566d4d7bedadc299496ab357426009a35f235cb141be0d99cd10ae3a8',
|
||||
'c4e1020916980a4da5d01ac5e6ad330734ef0d7906631c4f2390426b2edd791f',
|
||||
],
|
||||
[
|
||||
'4162d488b89402039b584c6fc6c308870587d9c46f660b878ab65c82c711d67e',
|
||||
'67163e903236289f776f22c25fb8a3afc1732f2b84b4e95dbda47ae5a0852649',
|
||||
],
|
||||
[
|
||||
'3fad3fa84caf0f34f0f89bfd2dcf54fc175d767aec3e50684f3ba4a4bf5f683d',
|
||||
'cd1bc7cb6cc407bb2f0ca647c718a730cf71872e7d0d2a53fa20efcdfe61826',
|
||||
],
|
||||
[
|
||||
'674f2600a3007a00568c1a7ce05d0816c1fb84bf1370798f1c69532faeb1a86b',
|
||||
'299d21f9413f33b3edf43b257004580b70db57da0b182259e09eecc69e0d38a5',
|
||||
],
|
||||
[
|
||||
'd32f4da54ade74abb81b815ad1fb3b263d82d6c692714bcff87d29bd5ee9f08f',
|
||||
'f9429e738b8e53b968e99016c059707782e14f4535359d582fc416910b3eea87',
|
||||
],
|
||||
[
|
||||
'30e4e670435385556e593657135845d36fbb6931f72b08cb1ed954f1e3ce3ff6',
|
||||
'462f9bce619898638499350113bbc9b10a878d35da70740dc695a559eb88db7b',
|
||||
],
|
||||
[
|
||||
'be2062003c51cc3004682904330e4dee7f3dcd10b01e580bf1971b04d4cad297',
|
||||
'62188bc49d61e5428573d48a74e1c655b1c61090905682a0d5558ed72dccb9bc',
|
||||
],
|
||||
[
|
||||
'93144423ace3451ed29e0fb9ac2af211cb6e84a601df5993c419859fff5df04a',
|
||||
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|
||||
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|
||||
[
|
||||
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|
||||
'ab8c1e086d04e813744a655b2df8d5f83b3cdc6faa3088c1d3aea1454e3a1d5f',
|
||||
],
|
||||
[
|
||||
'd5e9e1da649d97d89e4868117a465a3a4f8a18de57a140d36b3f2af341a21b52',
|
||||
'4cb04437f391ed73111a13cc1d4dd0db1693465c2240480d8955e8592f27447a',
|
||||
],
|
||||
[
|
||||
'd3ae41047dd7ca065dbf8ed77b992439983005cd72e16d6f996a5316d36966bb',
|
||||
'bd1aeb21ad22ebb22a10f0303417c6d964f8cdd7df0aca614b10dc14d125ac46',
|
||||
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|
||||
[
|
||||
'463e2763d885f958fc66cdd22800f0a487197d0a82e377b49f80af87c897b065',
|
||||
'bfefacdb0e5d0fd7df3a311a94de062b26b80c61fbc97508b79992671ef7ca7f',
|
||||
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|
||||
[
|
||||
'7985fdfd127c0567c6f53ec1bb63ec3158e597c40bfe747c83cddfc910641917',
|
||||
'603c12daf3d9862ef2b25fe1de289aed24ed291e0ec6708703a5bd567f32ed03',
|
||||
],
|
||||
[
|
||||
'74a1ad6b5f76e39db2dd249410eac7f99e74c59cb83d2d0ed5ff1543da7703e9',
|
||||
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|
||||
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|
||||
[
|
||||
'30682a50703375f602d416664ba19b7fc9bab42c72747463a71d0896b22f6da3',
|
||||
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|
||||
],
|
||||
[
|
||||
'9e2158f0d7c0d5f26c3791efefa79597654e7a2b2464f52b1ee6c1347769ef57',
|
||||
'712fcdd1b9053f09003a3481fa7762e9ffd7c8ef35a38509e2fbf2629008373',
|
||||
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|
||||
[
|
||||
'176e26989a43c9cfeba4029c202538c28172e566e3c4fce7322857f3be327d66',
|
||||
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|
||||
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|
||||
[
|
||||
'75d46efea3771e6e68abb89a13ad747ecf1892393dfc4f1b7004788c50374da8',
|
||||
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|
||||
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|
||||
[
|
||||
'809a20c67d64900ffb698c4c825f6d5f2310fb0451c869345b7319f645605721',
|
||||
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|
||||
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|
||||
[
|
||||
'1b38903a43f7f114ed4500b4eac7083fdefece1cf29c63528d563446f972c180',
|
||||
'4036edc931a60ae889353f77fd53de4a2708b26b6f5da72ad3394119daf408f9',
|
||||
],
|
||||
],
|
||||
},
|
||||
};
|
||||
119
web/node_modules/elliptic/lib/elliptic/utils.js
generated
vendored
Normal file
119
web/node_modules/elliptic/lib/elliptic/utils.js
generated
vendored
Normal file
|
|
@ -0,0 +1,119 @@
|
|||
'use strict';
|
||||
|
||||
var utils = exports;
|
||||
var BN = require('bn.js');
|
||||
var minAssert = require('minimalistic-assert');
|
||||
var minUtils = require('minimalistic-crypto-utils');
|
||||
|
||||
utils.assert = minAssert;
|
||||
utils.toArray = minUtils.toArray;
|
||||
utils.zero2 = minUtils.zero2;
|
||||
utils.toHex = minUtils.toHex;
|
||||
utils.encode = minUtils.encode;
|
||||
|
||||
// Represent num in a w-NAF form
|
||||
function getNAF(num, w, bits) {
|
||||
var naf = new Array(Math.max(num.bitLength(), bits) + 1);
|
||||
naf.fill(0);
|
||||
|
||||
var ws = 1 << (w + 1);
|
||||
var k = num.clone();
|
||||
|
||||
for (var i = 0; i < naf.length; i++) {
|
||||
var z;
|
||||
var mod = k.andln(ws - 1);
|
||||
if (k.isOdd()) {
|
||||
if (mod > (ws >> 1) - 1)
|
||||
z = (ws >> 1) - mod;
|
||||
else
|
||||
z = mod;
|
||||
k.isubn(z);
|
||||
} else {
|
||||
z = 0;
|
||||
}
|
||||
|
||||
naf[i] = z;
|
||||
k.iushrn(1);
|
||||
}
|
||||
|
||||
return naf;
|
||||
}
|
||||
utils.getNAF = getNAF;
|
||||
|
||||
// Represent k1, k2 in a Joint Sparse Form
|
||||
function getJSF(k1, k2) {
|
||||
var jsf = [
|
||||
[],
|
||||
[],
|
||||
];
|
||||
|
||||
k1 = k1.clone();
|
||||
k2 = k2.clone();
|
||||
var d1 = 0;
|
||||
var d2 = 0;
|
||||
var m8;
|
||||
while (k1.cmpn(-d1) > 0 || k2.cmpn(-d2) > 0) {
|
||||
// First phase
|
||||
var m14 = (k1.andln(3) + d1) & 3;
|
||||
var m24 = (k2.andln(3) + d2) & 3;
|
||||
if (m14 === 3)
|
||||
m14 = -1;
|
||||
if (m24 === 3)
|
||||
m24 = -1;
|
||||
var u1;
|
||||
if ((m14 & 1) === 0) {
|
||||
u1 = 0;
|
||||
} else {
|
||||
m8 = (k1.andln(7) + d1) & 7;
|
||||
if ((m8 === 3 || m8 === 5) && m24 === 2)
|
||||
u1 = -m14;
|
||||
else
|
||||
u1 = m14;
|
||||
}
|
||||
jsf[0].push(u1);
|
||||
|
||||
var u2;
|
||||
if ((m24 & 1) === 0) {
|
||||
u2 = 0;
|
||||
} else {
|
||||
m8 = (k2.andln(7) + d2) & 7;
|
||||
if ((m8 === 3 || m8 === 5) && m14 === 2)
|
||||
u2 = -m24;
|
||||
else
|
||||
u2 = m24;
|
||||
}
|
||||
jsf[1].push(u2);
|
||||
|
||||
// Second phase
|
||||
if (2 * d1 === u1 + 1)
|
||||
d1 = 1 - d1;
|
||||
if (2 * d2 === u2 + 1)
|
||||
d2 = 1 - d2;
|
||||
k1.iushrn(1);
|
||||
k2.iushrn(1);
|
||||
}
|
||||
|
||||
return jsf;
|
||||
}
|
||||
utils.getJSF = getJSF;
|
||||
|
||||
function cachedProperty(obj, name, computer) {
|
||||
var key = '_' + name;
|
||||
obj.prototype[name] = function cachedProperty() {
|
||||
return this[key] !== undefined ? this[key] :
|
||||
this[key] = computer.call(this);
|
||||
};
|
||||
}
|
||||
utils.cachedProperty = cachedProperty;
|
||||
|
||||
function parseBytes(bytes) {
|
||||
return typeof bytes === 'string' ? utils.toArray(bytes, 'hex') :
|
||||
bytes;
|
||||
}
|
||||
utils.parseBytes = parseBytes;
|
||||
|
||||
function intFromLE(bytes) {
|
||||
return new BN(bytes, 'hex', 'le');
|
||||
}
|
||||
utils.intFromLE = intFromLE;
|
||||
|
||||
19
web/node_modules/elliptic/node_modules/bn.js/LICENSE
generated
vendored
Normal file
19
web/node_modules/elliptic/node_modules/bn.js/LICENSE
generated
vendored
Normal file
|
|
@ -0,0 +1,19 @@
|
|||
Copyright Fedor Indutny, 2015.
|
||||
|
||||
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.
|
||||
200
web/node_modules/elliptic/node_modules/bn.js/README.md
generated
vendored
Normal file
200
web/node_modules/elliptic/node_modules/bn.js/README.md
generated
vendored
Normal file
|
|
@ -0,0 +1,200 @@
|
|||
# <img src="./logo.png" alt="bn.js" width="160" height="160" />
|
||||
|
||||
> BigNum in pure javascript
|
||||
|
||||
[](http://travis-ci.org/indutny/bn.js)
|
||||
|
||||
## Install
|
||||
`npm install --save bn.js`
|
||||
|
||||
## Usage
|
||||
|
||||
```js
|
||||
const BN = require('bn.js');
|
||||
|
||||
var a = new BN('dead', 16);
|
||||
var b = new BN('101010', 2);
|
||||
|
||||
var res = a.add(b);
|
||||
console.log(res.toString(10)); // 57047
|
||||
```
|
||||
|
||||
**Note**: decimals are not supported in this library.
|
||||
|
||||
## Notation
|
||||
|
||||
### Prefixes
|
||||
|
||||
There are several prefixes to instructions that affect the way the work. Here
|
||||
is the list of them in the order of appearance in the function name:
|
||||
|
||||
* `i` - perform operation in-place, storing the result in the host object (on
|
||||
which the method was invoked). Might be used to avoid number allocation costs
|
||||
* `u` - unsigned, ignore the sign of operands when performing operation, or
|
||||
always return positive value. Second case applies to reduction operations
|
||||
like `mod()`. In such cases if the result will be negative - modulo will be
|
||||
added to the result to make it positive
|
||||
|
||||
### Postfixes
|
||||
|
||||
The only available postfix at the moment is:
|
||||
|
||||
* `n` - which means that the argument of the function must be a plain JavaScript
|
||||
Number. Decimals are not supported.
|
||||
|
||||
### Examples
|
||||
|
||||
* `a.iadd(b)` - perform addition on `a` and `b`, storing the result in `a`
|
||||
* `a.umod(b)` - reduce `a` modulo `b`, returning positive value
|
||||
* `a.iushln(13)` - shift bits of `a` left by 13
|
||||
|
||||
## Instructions
|
||||
|
||||
Prefixes/postfixes are put in parens at the of the line. `endian` - could be
|
||||
either `le` (little-endian) or `be` (big-endian).
|
||||
|
||||
### Utilities
|
||||
|
||||
* `a.clone()` - clone number
|
||||
* `a.toString(base, length)` - convert to base-string and pad with zeroes
|
||||
* `a.toNumber()` - convert to Javascript Number (limited to 53 bits)
|
||||
* `a.toJSON()` - convert to JSON compatible hex string (alias of `toString(16)`)
|
||||
* `a.toArray(endian, length)` - convert to byte `Array`, and optionally zero
|
||||
pad to length, throwing if already exceeding
|
||||
* `a.toArrayLike(type, endian, length)` - convert to an instance of `type`,
|
||||
which must behave like an `Array`
|
||||
* `a.toBuffer(endian, length)` - convert to Node.js Buffer (if available). For
|
||||
compatibility with browserify and similar tools, use this instead:
|
||||
`a.toArrayLike(Buffer, endian, length)`
|
||||
* `a.bitLength()` - get number of bits occupied
|
||||
* `a.zeroBits()` - return number of less-significant consequent zero bits
|
||||
(example: `1010000` has 4 zero bits)
|
||||
* `a.byteLength()` - return number of bytes occupied
|
||||
* `a.isNeg()` - true if the number is negative
|
||||
* `a.isEven()` - no comments
|
||||
* `a.isOdd()` - no comments
|
||||
* `a.isZero()` - no comments
|
||||
* `a.cmp(b)` - compare numbers and return `-1` (a `<` b), `0` (a `==` b), or `1` (a `>` b)
|
||||
depending on the comparison result (`ucmp`, `cmpn`)
|
||||
* `a.lt(b)` - `a` less than `b` (`n`)
|
||||
* `a.lte(b)` - `a` less than or equals `b` (`n`)
|
||||
* `a.gt(b)` - `a` greater than `b` (`n`)
|
||||
* `a.gte(b)` - `a` greater than or equals `b` (`n`)
|
||||
* `a.eq(b)` - `a` equals `b` (`n`)
|
||||
* `a.toTwos(width)` - convert to two's complement representation, where `width` is bit width
|
||||
* `a.fromTwos(width)` - convert from two's complement representation, where `width` is the bit width
|
||||
* `BN.isBN(object)` - returns true if the supplied `object` is a BN.js instance
|
||||
|
||||
### Arithmetics
|
||||
|
||||
* `a.neg()` - negate sign (`i`)
|
||||
* `a.abs()` - absolute value (`i`)
|
||||
* `a.add(b)` - addition (`i`, `n`, `in`)
|
||||
* `a.sub(b)` - subtraction (`i`, `n`, `in`)
|
||||
* `a.mul(b)` - multiply (`i`, `n`, `in`)
|
||||
* `a.sqr()` - square (`i`)
|
||||
* `a.pow(b)` - raise `a` to the power of `b`
|
||||
* `a.div(b)` - divide (`divn`, `idivn`)
|
||||
* `a.mod(b)` - reduct (`u`, `n`) (but no `umodn`)
|
||||
* `a.divRound(b)` - rounded division
|
||||
|
||||
### Bit operations
|
||||
|
||||
* `a.or(b)` - or (`i`, `u`, `iu`)
|
||||
* `a.and(b)` - and (`i`, `u`, `iu`, `andln`) (NOTE: `andln` is going to be replaced
|
||||
with `andn` in future)
|
||||
* `a.xor(b)` - xor (`i`, `u`, `iu`)
|
||||
* `a.setn(b)` - set specified bit to `1`
|
||||
* `a.shln(b)` - shift left (`i`, `u`, `iu`)
|
||||
* `a.shrn(b)` - shift right (`i`, `u`, `iu`)
|
||||
* `a.testn(b)` - test if specified bit is set
|
||||
* `a.maskn(b)` - clear bits with indexes higher or equal to `b` (`i`)
|
||||
* `a.bincn(b)` - add `1 << b` to the number
|
||||
* `a.notn(w)` - not (for the width specified by `w`) (`i`)
|
||||
|
||||
### Reduction
|
||||
|
||||
* `a.gcd(b)` - GCD
|
||||
* `a.egcd(b)` - Extended GCD results (`{ a: ..., b: ..., gcd: ... }`)
|
||||
* `a.invm(b)` - inverse `a` modulo `b`
|
||||
|
||||
## Fast reduction
|
||||
|
||||
When doing lots of reductions using the same modulo, it might be beneficial to
|
||||
use some tricks: like [Montgomery multiplication][0], or using special algorithm
|
||||
for [Mersenne Prime][1].
|
||||
|
||||
### Reduction context
|
||||
|
||||
To enable this tricks one should create a reduction context:
|
||||
|
||||
```js
|
||||
var red = BN.red(num);
|
||||
```
|
||||
where `num` is just a BN instance.
|
||||
|
||||
Or:
|
||||
|
||||
```js
|
||||
var red = BN.red(primeName);
|
||||
```
|
||||
|
||||
Where `primeName` is either of these [Mersenne Primes][1]:
|
||||
|
||||
* `'k256'`
|
||||
* `'p224'`
|
||||
* `'p192'`
|
||||
* `'p25519'`
|
||||
|
||||
Or:
|
||||
|
||||
```js
|
||||
var red = BN.mont(num);
|
||||
```
|
||||
|
||||
To reduce numbers with [Montgomery trick][0]. `.mont()` is generally faster than
|
||||
`.red(num)`, but slower than `BN.red(primeName)`.
|
||||
|
||||
### Converting numbers
|
||||
|
||||
Before performing anything in reduction context - numbers should be converted
|
||||
to it. Usually, this means that one should:
|
||||
|
||||
* Convert inputs to reducted ones
|
||||
* Operate on them in reduction context
|
||||
* Convert outputs back from the reduction context
|
||||
|
||||
Here is how one may convert numbers to `red`:
|
||||
|
||||
```js
|
||||
var redA = a.toRed(red);
|
||||
```
|
||||
Where `red` is a reduction context created using instructions above
|
||||
|
||||
Here is how to convert them back:
|
||||
|
||||
```js
|
||||
var a = redA.fromRed();
|
||||
```
|
||||
|
||||
### Red instructions
|
||||
|
||||
Most of the instructions from the very start of this readme have their
|
||||
counterparts in red context:
|
||||
|
||||
* `a.redAdd(b)`, `a.redIAdd(b)`
|
||||
* `a.redSub(b)`, `a.redISub(b)`
|
||||
* `a.redShl(num)`
|
||||
* `a.redMul(b)`, `a.redIMul(b)`
|
||||
* `a.redSqr()`, `a.redISqr()`
|
||||
* `a.redSqrt()` - square root modulo reduction context's prime
|
||||
* `a.redInvm()` - modular inverse of the number
|
||||
* `a.redNeg()`
|
||||
* `a.redPow(b)` - modular exponentiation
|
||||
|
||||
## LICENSE
|
||||
|
||||
This software is licensed under the MIT License.
|
||||
|
||||
[0]: https://en.wikipedia.org/wiki/Montgomery_modular_multiplication
|
||||
[1]: https://en.wikipedia.org/wiki/Mersenne_prime
|
||||
3446
web/node_modules/elliptic/node_modules/bn.js/lib/bn.js
generated
vendored
Normal file
3446
web/node_modules/elliptic/node_modules/bn.js/lib/bn.js
generated
vendored
Normal file
File diff suppressed because it is too large
Load diff
36
web/node_modules/elliptic/node_modules/bn.js/package.json
generated
vendored
Normal file
36
web/node_modules/elliptic/node_modules/bn.js/package.json
generated
vendored
Normal file
|
|
@ -0,0 +1,36 @@
|
|||
{
|
||||
"name": "bn.js",
|
||||
"version": "4.12.0",
|
||||
"description": "Big number implementation in pure javascript",
|
||||
"main": "lib/bn.js",
|
||||
"scripts": {
|
||||
"lint": "semistandard",
|
||||
"unit": "mocha --reporter=spec test/*-test.js",
|
||||
"test": "npm run lint && npm run unit"
|
||||
},
|
||||
"repository": {
|
||||
"type": "git",
|
||||
"url": "git@github.com:indutny/bn.js"
|
||||
},
|
||||
"keywords": [
|
||||
"BN",
|
||||
"BigNum",
|
||||
"Big number",
|
||||
"Modulo",
|
||||
"Montgomery"
|
||||
],
|
||||
"author": "Fedor Indutny <fedor@indutny.com>",
|
||||
"license": "MIT",
|
||||
"bugs": {
|
||||
"url": "https://github.com/indutny/bn.js/issues"
|
||||
},
|
||||
"homepage": "https://github.com/indutny/bn.js",
|
||||
"browser": {
|
||||
"buffer": false
|
||||
},
|
||||
"devDependencies": {
|
||||
"istanbul": "^0.3.5",
|
||||
"mocha": "^2.1.0",
|
||||
"semistandard": "^7.0.4"
|
||||
}
|
||||
}
|
||||
56
web/node_modules/elliptic/package.json
generated
vendored
Normal file
56
web/node_modules/elliptic/package.json
generated
vendored
Normal file
|
|
@ -0,0 +1,56 @@
|
|||
{
|
||||
"name": "elliptic",
|
||||
"version": "6.5.4",
|
||||
"description": "EC cryptography",
|
||||
"main": "lib/elliptic.js",
|
||||
"files": [
|
||||
"lib"
|
||||
],
|
||||
"scripts": {
|
||||
"lint": "eslint lib test",
|
||||
"lint:fix": "npm run lint -- --fix",
|
||||
"unit": "istanbul test _mocha --reporter=spec test/index.js",
|
||||
"test": "npm run lint && npm run unit",
|
||||
"version": "grunt dist && git add dist/"
|
||||
},
|
||||
"repository": {
|
||||
"type": "git",
|
||||
"url": "git@github.com:indutny/elliptic"
|
||||
},
|
||||
"keywords": [
|
||||
"EC",
|
||||
"Elliptic",
|
||||
"curve",
|
||||
"Cryptography"
|
||||
],
|
||||
"author": "Fedor Indutny <fedor@indutny.com>",
|
||||
"license": "MIT",
|
||||
"bugs": {
|
||||
"url": "https://github.com/indutny/elliptic/issues"
|
||||
},
|
||||
"homepage": "https://github.com/indutny/elliptic",
|
||||
"devDependencies": {
|
||||
"brfs": "^2.0.2",
|
||||
"coveralls": "^3.1.0",
|
||||
"eslint": "^7.6.0",
|
||||
"grunt": "^1.2.1",
|
||||
"grunt-browserify": "^5.3.0",
|
||||
"grunt-cli": "^1.3.2",
|
||||
"grunt-contrib-connect": "^3.0.0",
|
||||
"grunt-contrib-copy": "^1.0.0",
|
||||
"grunt-contrib-uglify": "^5.0.0",
|
||||
"grunt-mocha-istanbul": "^5.0.2",
|
||||
"grunt-saucelabs": "^9.0.1",
|
||||
"istanbul": "^0.4.5",
|
||||
"mocha": "^8.0.1"
|
||||
},
|
||||
"dependencies": {
|
||||
"bn.js": "^4.11.9",
|
||||
"brorand": "^1.1.0",
|
||||
"hash.js": "^1.0.0",
|
||||
"hmac-drbg": "^1.0.1",
|
||||
"inherits": "^2.0.4",
|
||||
"minimalistic-assert": "^1.0.1",
|
||||
"minimalistic-crypto-utils": "^1.0.1"
|
||||
}
|
||||
}
|
||||
Loading…
Add table
Add a link
Reference in a new issue