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Edit File: curves.js

'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;

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,
  ],
});

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