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diff --git a/node_modules/elliptic/README.md b/node_modules/elliptic/README.md new file mode 100644 index 0000000..96219e5 --- /dev/null +++ b/node_modules/elliptic/README.md @@ -0,0 +1,238 @@ +# Elliptic [](http://travis-ci.org/indutny/elliptic) [](https://coveralls.io/github/indutny/elliptic?branch=master) [](https://codeclimate.com/github/indutny/elliptic) + +[](https://saucelabs.com/u/gh-indutny-elliptic) + +Fast elliptic-curve cryptography in a plain javascript implementation. + +NOTE: Please take a look at http://safecurves.cr.yp.to/ before choosing a curve +for your cryptography operations. + +## Incentive + +ECC is much slower than regular RSA cryptography, the JS implementations are +even more slower. + +## Benchmarks + +```bash +$ node benchmarks/index.js +Benchmarking: sign +elliptic#sign x 262 ops/sec ±0.51% (177 runs sampled) +eccjs#sign x 55.91 ops/sec ±0.90% (144 runs sampled) +------------------------ +Fastest is elliptic#sign +======================== +Benchmarking: verify +elliptic#verify x 113 ops/sec ±0.50% (166 runs sampled) +eccjs#verify x 48.56 ops/sec ±0.36% (125 runs sampled) +------------------------ +Fastest is elliptic#verify +======================== +Benchmarking: gen +elliptic#gen x 294 ops/sec ±0.43% (176 runs sampled) +eccjs#gen x 62.25 ops/sec ±0.63% (129 runs sampled) +------------------------ +Fastest is elliptic#gen +======================== +Benchmarking: ecdh +elliptic#ecdh x 136 ops/sec ±0.85% (156 runs sampled) +------------------------ +Fastest is elliptic#ecdh +======================== +``` + +## API + +### ECDSA + +```javascript +var EC = require('elliptic').ec; + +// Create and initialize EC context +// (better do it once and reuse it) +var ec = new EC('secp256k1'); + +// Generate keys +var key = ec.genKeyPair(); + +// Sign the message's hash (input must be an array, or a hex-string) +var msgHash = [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ]; +var signature = key.sign(msgHash); + +// Export DER encoded signature in Array +var derSign = signature.toDER(); + +// Verify signature +console.log(key.verify(msgHash, derSign)); + +// CHECK WITH NO PRIVATE KEY + +var pubPoint = key.getPublic(); +var x = pubPoint.getX(); +var y = pubPoint.getY(); + +// Public Key MUST be either: +// 1) '04' + hex string of x + hex string of y; or +// 2) object with two hex string properties (x and y); or +// 3) object with two buffer properties (x and y) +var pub = pubPoint.encode('hex'); // case 1 +var pub = { x: x.toString('hex'), y: y.toString('hex') }; // case 2 +var pub = { x: x.toBuffer(), y: y.toBuffer() }; // case 3 +var pub = { x: x.toArrayLike(Buffer), y: y.toArrayLike(Buffer) }; // case 3 + +// Import public key +var key = ec.keyFromPublic(pub, 'hex'); + +// Signature MUST be either: +// 1) DER-encoded signature as hex-string; or +// 2) DER-encoded signature as buffer; or +// 3) object with two hex-string properties (r and s); or +// 4) object with two buffer properties (r and s) + +var signature = '3046022100...'; // case 1 +var signature = new Buffer('...'); // case 2 +var signature = { r: 'b1fc...', s: '9c42...' }; // case 3 + +// Verify signature +console.log(key.verify(msgHash, signature)); +``` + +### EdDSA + +```javascript +var EdDSA = require('elliptic').eddsa; + +// Create and initialize EdDSA context +// (better do it once and reuse it) +var ec = new EdDSA('ed25519'); + +// Create key pair from secret +var key = ec.keyFromSecret('693e3c...'); // hex string, array or Buffer + +// Sign the message's hash (input must be an array, or a hex-string) +var msgHash = [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ]; +var signature = key.sign(msgHash).toHex(); + +// Verify signature +console.log(key.verify(msgHash, signature)); + +// CHECK WITH NO PRIVATE KEY + +// Import public key +var pub = '0a1af638...'; +var key = ec.keyFromPublic(pub, 'hex'); + +// Verify signature +var signature = '70bed1...'; +console.log(key.verify(msgHash, signature)); +``` + +### ECDH + +```javascript +var EC = require('elliptic').ec; +var ec = new EC('curve25519'); + +// Generate keys +var key1 = ec.genKeyPair(); +var key2 = ec.genKeyPair(); + +var shared1 = key1.derive(key2.getPublic()); +var shared2 = key2.derive(key1.getPublic()); + +console.log('Both shared secrets are BN instances'); +console.log(shared1.toString(16)); +console.log(shared2.toString(16)); +``` + +three and more members: +```javascript +var EC = require('elliptic').ec; +var ec = new EC('curve25519'); + +var A = ec.genKeyPair(); +var B = ec.genKeyPair(); +var C = ec.genKeyPair(); + +var AB = A.getPublic().mul(B.getPrivate()) +var BC = B.getPublic().mul(C.getPrivate()) +var CA = C.getPublic().mul(A.getPrivate()) + +var ABC = AB.mul(C.getPrivate()) +var BCA = BC.mul(A.getPrivate()) +var CAB = CA.mul(B.getPrivate()) + +console.log(ABC.getX().toString(16)) +console.log(BCA.getX().toString(16)) +console.log(CAB.getX().toString(16)) +``` + +NOTE: `.derive()` returns a [BN][1] instance. + +## Supported curves + +Elliptic.js support following curve types: + +* Short Weierstrass +* Montgomery +* Edwards +* Twisted Edwards + +Following curve 'presets' are embedded into the library: + +* `secp256k1` +* `p192` +* `p224` +* `p256` +* `p384` +* `p521` +* `curve25519` +* `ed25519` + +NOTE: That `curve25519` could not be used for ECDSA, use `ed25519` instead. + +### Implementation details + +ECDSA is using deterministic `k` value generation as per [RFC6979][0]. Most of +the curve operations are performed on non-affine coordinates (either projective +or extended), various windowing techniques are used for different cases. + +All operations are performed in reduction context using [bn.js][1], hashing is +provided by [hash.js][2] + +### Related projects + +* [eccrypto][3]: isomorphic implementation of ECDSA, ECDH and ECIES for both + browserify and node (uses `elliptic` for browser and [secp256k1-node][4] for + node) + +#### LICENSE + +This software is licensed under the MIT License. + +Copyright Fedor Indutny, 2014. + +Permission is hereby granted, free of charge, to any person obtaining a +copy of this software and associated documentation files (the +"Software"), to deal in the Software without restriction, including +without limitation the rights to use, copy, modify, merge, publish, +distribute, sublicense, and/or sell copies of the Software, and to permit +persons to whom the Software is furnished to do so, subject to the +following conditions: + +The above copyright notice and this permission notice shall be included +in all copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS +OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF +MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN +NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, +DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR +OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE +USE OR OTHER DEALINGS IN THE SOFTWARE. + +[0]: http://tools.ietf.org/html/rfc6979 +[1]: https://github.com/indutny/bn.js +[2]: https://github.com/indutny/hash.js +[3]: https://github.com/bitchan/eccrypto +[4]: https://github.com/wanderer/secp256k1-node diff --git a/node_modules/elliptic/lib/elliptic.js b/node_modules/elliptic/lib/elliptic.js new file mode 100644 index 0000000..dfe2fe7 --- /dev/null +++ b/node_modules/elliptic/lib/elliptic.js @@ -0,0 +1,13 @@ +'use strict'; + +var elliptic = exports; + +elliptic.version = require('../package.json').version; +elliptic.utils = require('./elliptic/utils'); +elliptic.rand = require('brorand'); +elliptic.curve = require('./elliptic/curve'); +elliptic.curves = require('./elliptic/curves'); + +// Protocols +elliptic.ec = require('./elliptic/ec'); +elliptic.eddsa = require('./elliptic/eddsa'); diff --git a/node_modules/elliptic/lib/elliptic/curve/base.js b/node_modules/elliptic/lib/elliptic/curve/base.js new file mode 100644 index 0000000..83ffe9f --- /dev/null +++ b/node_modules/elliptic/lib/elliptic/curve/base.js @@ -0,0 +1,376 @@ +'use strict'; + +var BN = require('bn.js'); +var utils = require('../utils'); +var getNAF = utils.getNAF; +var getJSF = utils.getJSF; +var assert = utils.assert; + +function BaseCurve(type, conf) { + this.type = type; + this.p = new BN(conf.p, 16); + + // Use Montgomery, when there is no fast reduction for the prime + this.red = conf.prime ? BN.red(conf.prime) : BN.mont(this.p); + + // Useful for many curves + this.zero = new BN(0).toRed(this.red); + this.one = new BN(1).toRed(this.red); + this.two = new BN(2).toRed(this.red); + + // Curve configuration, optional + this.n = conf.n && new BN(conf.n, 16); + this.g = conf.g && this.pointFromJSON(conf.g, conf.gRed); + + // Temporary arrays + this._wnafT1 = new Array(4); + this._wnafT2 = new Array(4); + this._wnafT3 = new Array(4); + this._wnafT4 = new Array(4); + + this._bitLength = this.n ? this.n.bitLength() : 0; + + // Generalized Greg Maxwell's trick + var adjustCount = this.n && this.p.div(this.n); + if (!adjustCount || adjustCount.cmpn(100) > 0) { + this.redN = null; + } else { + this._maxwellTrick = true; + this.redN = this.n.toRed(this.red); + } +} +module.exports = BaseCurve; + +BaseCurve.prototype.point = function point() { + throw new Error('Not implemented'); +}; + +BaseCurve.prototype.validate = function validate() { + throw new Error('Not implemented'); +}; + +BaseCurve.prototype._fixedNafMul = function _fixedNafMul(p, k) { + assert(p.precomputed); + var doubles = p._getDoubles(); + + var naf = getNAF(k, 1, this._bitLength); + var I = (1 << (doubles.step + 1)) - (doubles.step % 2 === 0 ? 2 : 1); + I /= 3; + + // Translate into more windowed form + var repr = []; + for (var j = 0; j < naf.length; j += doubles.step) { + var nafW = 0; + for (var k = j + doubles.step - 1; k >= j; k--) + nafW = (nafW << 1) + naf[k]; + repr.push(nafW); + } + + var a = this.jpoint(null, null, null); + var b = this.jpoint(null, null, null); + for (var i = I; i > 0; i--) { + for (var j = 0; j < repr.length; j++) { + var nafW = repr[j]; + if (nafW === i) + b = b.mixedAdd(doubles.points[j]); + else if (nafW === -i) + b = b.mixedAdd(doubles.points[j].neg()); + } + a = a.add(b); + } + return a.toP(); +}; + +BaseCurve.prototype._wnafMul = function _wnafMul(p, k) { + var w = 4; + + // Precompute window + var nafPoints = p._getNAFPoints(w); + w = nafPoints.wnd; + var wnd = nafPoints.points; + + // Get NAF form + var naf = getNAF(k, w, this._bitLength); + + // Add `this`*(N+1) for every w-NAF index + var acc = this.jpoint(null, null, null); + for (var i = naf.length - 1; i >= 0; i--) { + // Count zeroes + for (var k = 0; i >= 0 && naf[i] === 0; i--) + k++; + if (i >= 0) + k++; + acc = acc.dblp(k); + + if (i < 0) + break; + var z = naf[i]; + assert(z !== 0); + if (p.type === 'affine') { + // J +- P + if (z > 0) + acc = acc.mixedAdd(wnd[(z - 1) >> 1]); + else + acc = acc.mixedAdd(wnd[(-z - 1) >> 1].neg()); + } else { + // J +- J + if (z > 0) + acc = acc.add(wnd[(z - 1) >> 1]); + else + acc = acc.add(wnd[(-z - 1) >> 1].neg()); + } + } + return p.type === 'affine' ? acc.toP() : acc; +}; + +BaseCurve.prototype._wnafMulAdd = function _wnafMulAdd(defW, + points, + coeffs, + len, + jacobianResult) { + var wndWidth = this._wnafT1; + var wnd = this._wnafT2; + var naf = this._wnafT3; + + // Fill all arrays + var max = 0; + for (var i = 0; i < len; i++) { + var p = points[i]; + var nafPoints = p._getNAFPoints(defW); + wndWidth[i] = nafPoints.wnd; + wnd[i] = nafPoints.points; + } + + // Comb small window NAFs + for (var i = len - 1; i >= 1; i -= 2) { + var a = i - 1; + var b = i; + if (wndWidth[a] !== 1 || wndWidth[b] !== 1) { + naf[a] = getNAF(coeffs[a], wndWidth[a], this._bitLength); + naf[b] = getNAF(coeffs[b], wndWidth[b], this._bitLength); + max = Math.max(naf[a].length, max); + max = Math.max(naf[b].length, max); + continue; + } + + var comb = [ + points[a], /* 1 */ + null, /* 3 */ + null, /* 5 */ + points[b] /* 7 */ + ]; + + // Try to avoid Projective points, if possible + if (points[a].y.cmp(points[b].y) === 0) { + comb[1] = points[a].add(points[b]); + comb[2] = points[a].toJ().mixedAdd(points[b].neg()); + } else if (points[a].y.cmp(points[b].y.redNeg()) === 0) { + comb[1] = points[a].toJ().mixedAdd(points[b]); + comb[2] = points[a].add(points[b].neg()); + } else { + comb[1] = points[a].toJ().mixedAdd(points[b]); + comb[2] = points[a].toJ().mixedAdd(points[b].neg()); + } + + var index = [ + -3, /* -1 -1 */ + -1, /* -1 0 */ + -5, /* -1 1 */ + -7, /* 0 -1 */ + 0, /* 0 0 */ + 7, /* 0 1 */ + 5, /* 1 -1 */ + 1, /* 1 0 */ + 3 /* 1 1 */ + ]; + + var jsf = getJSF(coeffs[a], coeffs[b]); + max = Math.max(jsf[0].length, max); + naf[a] = new Array(max); + naf[b] = new Array(max); + for (var j = 0; j < max; j++) { + var ja = jsf[0][j] | 0; + var jb = jsf[1][j] | 0; + + naf[a][j] = index[(ja + 1) * 3 + (jb + 1)]; + naf[b][j] = 0; + wnd[a] = comb; + } + } + + var acc = this.jpoint(null, null, null); + var tmp = this._wnafT4; + for (var i = max; i >= 0; i--) { + var k = 0; + + while (i >= 0) { + var zero = true; + for (var j = 0; j < len; j++) { + tmp[j] = naf[j][i] | 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 (var j = 0; j < len; j++) { + var z = tmp[j]; + var 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 (var 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; +}; diff --git a/node_modules/elliptic/lib/elliptic/curve/edwards.js b/node_modules/elliptic/lib/elliptic/curve/edwards.js new file mode 100644 index 0000000..1c53fe9 --- /dev/null +++ b/node_modules/elliptic/lib/elliptic/curve/edwards.js @@ -0,0 +1,432 @@ +'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; + if (this.curve.twisted) { + // E = a * C + var 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 + var h = this.z.redSqr(); + // J = F - 2 * H + var 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 + var e = c.redAdd(d); + // H = (c * Z1)^2 + var h = this.curve._mulC(this.z).redSqr(); + // J = E - 2 * H + var 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; diff --git a/node_modules/elliptic/lib/elliptic/curve/index.js b/node_modules/elliptic/lib/elliptic/curve/index.js new file mode 100644 index 0000000..c589281 --- /dev/null +++ b/node_modules/elliptic/lib/elliptic/curve/index.js @@ -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'); diff --git a/node_modules/elliptic/lib/elliptic/curve/mont.js b/node_modules/elliptic/lib/elliptic/curve/mont.js new file mode 100644 index 0000000..4b9f80f --- /dev/null +++ b/node_modules/elliptic/lib/elliptic/curve/mont.js @@ -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(); +}; diff --git a/node_modules/elliptic/lib/elliptic/curve/short.js b/node_modules/elliptic/lib/elliptic/curve/short.js new file mode 100644 index 0000000..b263ecf --- /dev/null +++ b/node_modules/elliptic/lib/elliptic/curve/short.js @@ -0,0 +1,937 @@ +'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(); + + if (this.curve.zeroA || this.curve.threeA) { + var r = this; + for (var 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 (var 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; +}; diff --git a/node_modules/elliptic/lib/elliptic/curves.js b/node_modules/elliptic/lib/elliptic/curves.js new file mode 100644 index 0000000..63d8655 --- /dev/null +++ b/node_modules/elliptic/lib/elliptic/curves.js @@ -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 + ] +}); diff --git a/node_modules/elliptic/lib/elliptic/ec/index.js b/node_modules/elliptic/lib/elliptic/ec/index.js new file mode 100644 index 0000000..0f1d8ce --- /dev/null +++ b/node_modules/elliptic/lib/elliptic/ec/index.js @@ -0,0 +1,241 @@ +'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(curves.hasOwnProperty(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)); + do { + var priv = new BN(drbg.generate(bytes)); + if (priv.cmp(ns2) > 0) + continue; + + priv.iaddn(1); + return this.keyFromPrivate(priv); + } while (true); +}; + +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; true; 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); + + if (!this.curve._maxwellTrick) { + var 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 + + var 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'); +}; diff --git a/node_modules/elliptic/lib/elliptic/ec/key.js b/node_modules/elliptic/lib/elliptic/ec/key.js new file mode 100644 index 0000000..4a56d69 --- /dev/null +++ b/node_modules/elliptic/lib/elliptic/ec/key.js @@ -0,0 +1,118 @@ +'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) { + 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()) + ' >'; +}; diff --git a/node_modules/elliptic/lib/elliptic/ec/signature.js b/node_modules/elliptic/lib/elliptic/ec/signature.js new file mode 100644 index 0000000..539df6a --- /dev/null +++ b/node_modules/elliptic/lib/elliptic/ec/signature.js @@ -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); +}; diff --git a/node_modules/elliptic/lib/elliptic/eddsa/index.js b/node_modules/elliptic/lib/elliptic/eddsa/index.js new file mode 100644 index 0000000..f82fa35 --- /dev/null +++ b/node_modules/elliptic/lib/elliptic/eddsa/index.js @@ -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); + + var 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; +}; diff --git a/node_modules/elliptic/lib/elliptic/eddsa/key.js b/node_modules/elliptic/lib/elliptic/eddsa/key.js new file mode 100644 index 0000000..a00028f --- /dev/null +++ b/node_modules/elliptic/lib/elliptic/eddsa/key.js @@ -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; diff --git a/node_modules/elliptic/lib/elliptic/eddsa/signature.js b/node_modules/elliptic/lib/elliptic/eddsa/signature.js new file mode 100644 index 0000000..17b96d7 --- /dev/null +++ b/node_modules/elliptic/lib/elliptic/eddsa/signature.js @@ -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; diff --git a/node_modules/elliptic/lib/elliptic/precomputed/secp256k1.js b/node_modules/elliptic/lib/elliptic/precomputed/secp256k1.js new file mode 100644 index 0000000..e4c91e5 --- /dev/null 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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; + 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 { + var 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 { + var 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; + diff --git a/node_modules/elliptic/node_modules/bn.js/README.md b/node_modules/elliptic/node_modules/bn.js/README.md new file mode 100644 index 0000000..370f06d --- /dev/null +++ b/node_modules/elliptic/node_modules/bn.js/README.md @@ -0,0 +1,221 @@ +# <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. + +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. + +[0]: https://en.wikipedia.org/wiki/Montgomery_modular_multiplication +[1]: https://en.wikipedia.org/wiki/Mersenne_prime diff --git a/node_modules/elliptic/node_modules/bn.js/lib/bn.js b/node_modules/elliptic/node_modules/bn.js/lib/bn.js new file mode 100644 index 0000000..855dfa6 --- /dev/null +++ b/node_modules/elliptic/node_modules/bn.js/lib/bn.js @@ -0,0 +1,3433 @@ +(function (module, exports) { + 'use strict'; + + // Utils + function assert (val, msg) { + if (!val) throw new Error(msg || 'Assertion failed'); + } + + // Could use `inherits` module, but don't want to move from single file + // architecture yet. + function inherits (ctor, superCtor) { + ctor.super_ = superCtor; + var TempCtor = function () {}; + TempCtor.prototype = superCtor.prototype; + ctor.prototype = new TempCtor(); + ctor.prototype.constructor = ctor; + } + + // BN + + function BN (number, base, endian) { + if (BN.isBN(number)) { + return number; + } + + this.negative = 0; + this.words = null; + this.length = 0; + + // Reduction context + this.red = null; + + if (number !== null) { + if (base === 'le' || base === 'be') { + endian = base; + base = 10; + } + + this._init(number || 0, base || 10, endian || 'be'); + } + } + if (typeof module === 'object') { + module.exports = BN; + } else { + exports.BN = BN; + } + + BN.BN = BN; + BN.wordSize = 26; + + var Buffer; + try { + Buffer = require('buffer').Buffer; + } catch (e) { + } + + BN.isBN = function isBN (num) { + if (num instanceof BN) { + return true; + } + + return num !== null && typeof num === 'object' && + num.constructor.wordSize === BN.wordSize && Array.isArray(num.words); + }; + + BN.max = function max (left, right) { + if (left.cmp(right) > 0) return left; + return right; + }; + + BN.min = function min (left, right) { + if (left.cmp(right) < 0) return left; + return right; + }; + + BN.prototype._init = function init (number, base, endian) { + if (typeof number === 'number') { + return this._initNumber(number, base, endian); + } + + if (typeof number === 'object') { + return this._initArray(number, base, endian); + } + + if (base === 'hex') { + base = 16; + } + assert(base === (base | 0) && base >= 2 && base <= 36); + + number = number.toString().replace(/\s+/g, ''); + var start = 0; + if (number[0] === '-') { + start++; + } + + if (base === 16) { + this._parseHex(number, start); + } else { + this._parseBase(number, base, start); + } + + if (number[0] === '-') { + this.negative = 1; + } + + this.strip(); + + if (endian !== 'le') return; + + this._initArray(this.toArray(), base, endian); + }; + + BN.prototype._initNumber = function _initNumber (number, base, endian) { + if (number < 0) { + this.negative = 1; + number = -number; + } + if (number < 0x4000000) { + this.words = [ number & 0x3ffffff ]; + this.length = 1; + } else if (number < 0x10000000000000) { + this.words = [ + number & 0x3ffffff, + (number / 0x4000000) & 0x3ffffff + ]; + this.length = 2; + } else { + assert(number < 0x20000000000000); // 2 ^ 53 (unsafe) + this.words = [ + number & 0x3ffffff, + (number / 0x4000000) & 0x3ffffff, + 1 + ]; + this.length = 3; + } + + if (endian !== 'le') return; + + // Reverse the bytes + this._initArray(this.toArray(), base, endian); + }; + + BN.prototype._initArray = function _initArray (number, base, endian) { + // Perhaps a Uint8Array + assert(typeof number.length === 'number'); + if (number.length <= 0) { + this.words = [ 0 ]; + this.length = 1; + return this; + } + + this.length = Math.ceil(number.length / 3); + this.words = new Array(this.length); + for (var i = 0; i < this.length; i++) { + this.words[i] = 0; + } + + var j, w; + var off = 0; + if (endian === 'be') { + for (i = number.length - 1, j = 0; i >= 0; i -= 3) { + w = number[i] | (number[i - 1] << 8) | (number[i - 2] << 16); + this.words[j] |= (w << off) & 0x3ffffff; + this.words[j + 1] = (w >>> (26 - off)) & 0x3ffffff; + off += 24; + if (off >= 26) { + off -= 26; + j++; + } + } + } else if (endian === 'le') { + for (i = 0, j = 0; i < number.length; i += 3) { + w = number[i] | (number[i + 1] << 8) | (number[i + 2] << 16); + this.words[j] |= (w << off) & 0x3ffffff; + this.words[j + 1] = (w >>> (26 - off)) & 0x3ffffff; + off += 24; + if (off >= 26) { + off -= 26; + j++; + } + } + } + return this.strip(); + }; + + function parseHex (str, start, end) { + var r = 0; + var len = Math.min(str.length, end); + for (var i = start; i < len; i++) { + var c = str.charCodeAt(i) - 48; + + r <<= 4; + + // 'a' - 'f' + if (c >= 49 && c <= 54) { + r |= c - 49 + 0xa; + + // 'A' - 'F' + } else if (c >= 17 && c <= 22) { + r |= c - 17 + 0xa; + + // '0' - '9' + } else { + r |= c & 0xf; + } + } + return r; + } + + BN.prototype._parseHex = function _parseHex (number, start) { + // Create possibly bigger array to ensure that it fits the number + this.length = Math.ceil((number.length - start) / 6); + this.words = new Array(this.length); + for (var i = 0; i < this.length; i++) { + this.words[i] = 0; + } + + var j, w; + // Scan 24-bit chunks and add them to the number + var off = 0; + for (i = number.length - 6, j = 0; i >= start; i -= 6) { + w = parseHex(number, i, i + 6); + this.words[j] |= (w << off) & 0x3ffffff; + // NOTE: `0x3fffff` is intentional here, 26bits max shift + 24bit hex limb + this.words[j + 1] |= w >>> (26 - off) & 0x3fffff; + off += 24; + if (off >= 26) { + off -= 26; + j++; + } + } + if (i + 6 !== start) { + w = parseHex(number, start, i + 6); + this.words[j] |= (w << off) & 0x3ffffff; + this.words[j + 1] |= w >>> (26 - off) & 0x3fffff; + } + this.strip(); + }; + + function parseBase (str, start, end, mul) { + var r = 0; + var len = Math.min(str.length, end); + for (var i = start; i < len; i++) { + var c = str.charCodeAt(i) - 48; + + r *= mul; + + // 'a' + if (c >= 49) { + r += c - 49 + 0xa; + + // 'A' + } else if (c >= 17) { + r += c - 17 + 0xa; + + // '0' - '9' + } else { + r += c; + } + } + return r; + } + + BN.prototype._parseBase = function _parseBase (number, base, start) { + // Initialize as zero + this.words = [ 0 ]; + this.length = 1; + + // Find length of limb in base + for (var limbLen = 0, limbPow = 1; limbPow <= 0x3ffffff; limbPow *= base) { + limbLen++; + } + limbLen--; + limbPow = (limbPow / base) | 0; + + var total = number.length - start; + var mod = total % limbLen; + var end = Math.min(total, total - mod) + start; + + var word = 0; + for (var i = start; i < end; i += limbLen) { + word = parseBase(number, i, i + limbLen, base); + + this.imuln(limbPow); + if (this.words[0] + word < 0x4000000) { + this.words[0] += word; + } else { + this._iaddn(word); + } + } + + if (mod !== 0) { + var pow = 1; + word = parseBase(number, i, number.length, base); + + for (i = 0; i < mod; i++) { + pow *= base; + } + + this.imuln(pow); + if (this.words[0] + word < 0x4000000) { + this.words[0] += word; + } else { + this._iaddn(word); + } + } + }; + + BN.prototype.copy = function copy (dest) { + dest.words = new Array(this.length); + for (var i = 0; i < this.length; i++) { + dest.words[i] = this.words[i]; + } + dest.length = this.length; + dest.negative = this.negative; + dest.red = this.red; + }; + + BN.prototype.clone = function clone () { + var r = new BN(null); + this.copy(r); + return r; + }; + + BN.prototype._expand = function _expand (size) { + while (this.length < size) { + this.words[this.length++] = 0; + } + return this; + }; + + // Remove leading `0` from `this` + BN.prototype.strip = function strip () { + while (this.length > 1 && this.words[this.length - 1] === 0) { + this.length--; + } + return this._normSign(); + }; + + BN.prototype._normSign = function _normSign () { + // -0 = 0 + if (this.length === 1 && this.words[0] === 0) { + this.negative = 0; + } + return this; + }; + + BN.prototype.inspect = function inspect () { + return (this.red ? '<BN-R: ' : '<BN: ') + this.toString(16) + '>'; + }; + + /* + + var zeros = []; + var groupSizes = []; + var groupBases = []; + + var s = ''; + var i = -1; + while (++i < BN.wordSize) { + zeros[i] = s; + s += '0'; + } + groupSizes[0] = 0; + groupSizes[1] = 0; + groupBases[0] = 0; + groupBases[1] = 0; + var base = 2 - 1; + while (++base < 36 + 1) { + var groupSize = 0; + var groupBase = 1; + while (groupBase < (1 << BN.wordSize) / base) { + groupBase *= base; + groupSize += 1; + } + groupSizes[base] = groupSize; + groupBases[base] = groupBase; + } + + */ + + var zeros = [ + '', + '0', + '00', + '000', + '0000', + '00000', + '000000', + '0000000', + '00000000', + '000000000', + '0000000000', + '00000000000', + '000000000000', + '0000000000000', + '00000000000000', + '000000000000000', + '0000000000000000', + '00000000000000000', + '000000000000000000', + '0000000000000000000', + '00000000000000000000', + '000000000000000000000', + '0000000000000000000000', + '00000000000000000000000', + '000000000000000000000000', + '0000000000000000000000000' + ]; + + var groupSizes = [ + 0, 0, + 25, 16, 12, 11, 10, 9, 8, + 8, 7, 7, 7, 7, 6, 6, + 6, 6, 6, 6, 6, 5, 5, + 5, 5, 5, 5, 5, 5, 5, + 5, 5, 5, 5, 5, 5, 5 + ]; + + var groupBases = [ + 0, 0, + 33554432, 43046721, 16777216, 48828125, 60466176, 40353607, 16777216, + 43046721, 10000000, 19487171, 35831808, 62748517, 7529536, 11390625, + 16777216, 24137569, 34012224, 47045881, 64000000, 4084101, 5153632, + 6436343, 7962624, 9765625, 11881376, 14348907, 17210368, 20511149, + 24300000, 28629151, 33554432, 39135393, 45435424, 52521875, 60466176 + ]; + + BN.prototype.toString = function toString (base, padding) { + base = base || 10; + padding = padding | 0 || 1; + + var out; + if (base === 16 || base === 'hex') { + out = ''; + var off = 0; + var carry = 0; + for (var i = 0; i < this.length; i++) { + var w = this.words[i]; + var word = (((w << off) | carry) & 0xffffff).toString(16); + carry = (w >>> (24 - off)) & 0xffffff; + if (carry !== 0 || i !== this.length - 1) { + out = zeros[6 - word.length] + word + out; + } else { + out = word + out; + } + off += 2; + if (off >= 26) { + off -= 26; + i--; + } + } + if (carry !== 0) { + out = carry.toString(16) + out; + } + while (out.length % padding !== 0) { + out = '0' + out; + } + if (this.negative !== 0) { + out = '-' + out; + } + return out; + } + + if (base === (base | 0) && base >= 2 && base <= 36) { + // var groupSize = Math.floor(BN.wordSize * Math.LN2 / Math.log(base)); + var groupSize = groupSizes[base]; + // var groupBase = Math.pow(base, groupSize); + var groupBase = groupBases[base]; + out = ''; + var c = this.clone(); + c.negative = 0; + while (!c.isZero()) { + var r = c.modn(groupBase).toString(base); + c = c.idivn(groupBase); + + if (!c.isZero()) { + out = zeros[groupSize - r.length] + r + out; + } else { + out = r + out; + } + } + if (this.isZero()) { + out = '0' + out; + } + while (out.length % padding !== 0) { + out = '0' + out; + } + if (this.negative !== 0) { + out = '-' + out; + } + return out; + } + + assert(false, 'Base should be between 2 and 36'); + }; + + BN.prototype.toNumber = function toNumber () { + var ret = this.words[0]; + if (this.length === 2) { + ret += this.words[1] * 0x4000000; + } else if (this.length === 3 && this.words[2] === 0x01) { + // NOTE: at this stage it is known that the top bit is set + ret += 0x10000000000000 + (this.words[1] * 0x4000000); + } else if (this.length > 2) { + assert(false, 'Number can only safely store up to 53 bits'); + } + return (this.negative !== 0) ? -ret : ret; + }; + + BN.prototype.toJSON = function toJSON () { + return this.toString(16); + }; + + BN.prototype.toBuffer = function toBuffer (endian, length) { + assert(typeof Buffer !== 'undefined'); + return this.toArrayLike(Buffer, endian, length); + }; + + BN.prototype.toArray = function toArray (endian, length) { + return this.toArrayLike(Array, endian, length); + }; + + BN.prototype.toArrayLike = function toArrayLike (ArrayType, endian, length) { + var byteLength = this.byteLength(); + var reqLength = length || Math.max(1, byteLength); + assert(byteLength <= reqLength, 'byte array longer than desired length'); + assert(reqLength > 0, 'Requested array length <= 0'); + + this.strip(); + var littleEndian = endian === 'le'; + var res = new ArrayType(reqLength); + + var b, i; + var q = this.clone(); + if (!littleEndian) { + // Assume big-endian + for (i = 0; i < reqLength - byteLength; i++) { + res[i] = 0; + } + + for (i = 0; !q.isZero(); i++) { + b = q.andln(0xff); + q.iushrn(8); + + res[reqLength - i - 1] = b; + } + } else { + for (i = 0; !q.isZero(); i++) { + b = q.andln(0xff); + q.iushrn(8); + + res[i] = b; + } + + for (; i < reqLength; i++) { + res[i] = 0; + } + } + + return res; + }; + + if (Math.clz32) { + BN.prototype._countBits = function _countBits (w) { + return 32 - Math.clz32(w); + }; + } else { + BN.prototype._countBits = function _countBits (w) { + var t = w; + var r = 0; + if (t >= 0x1000) { + r += 13; + t >>>= 13; + } + if (t >= 0x40) { + r += 7; + t >>>= 7; + } + if (t >= 0x8) { + r += 4; + t >>>= 4; + } + if (t >= 0x02) { + r += 2; + t >>>= 2; + } + return r + t; + }; + } + + BN.prototype._zeroBits = function _zeroBits (w) { + // Short-cut + if (w === 0) return 26; + + var t = w; + var r = 0; + if ((t & 0x1fff) === 0) { + r += 13; + t >>>= 13; + } + if ((t & 0x7f) === 0) { + r += 7; + t >>>= 7; + } + if ((t & 0xf) === 0) { + r += 4; + t >>>= 4; + } + if ((t & 0x3) === 0) { + r += 2; + t >>>= 2; + } + if ((t & 0x1) === 0) { + r++; + } + return r; + }; + + // Return number of used bits in a BN + BN.prototype.bitLength = function bitLength () { + var w = this.words[this.length - 1]; + var hi = this._countBits(w); + return (this.length - 1) * 26 + hi; + }; + + function toBitArray (num) { + var w = new Array(num.bitLength()); + + for (var bit = 0; bit < w.length; bit++) { + var off = (bit / 26) | 0; + var wbit = bit % 26; + + w[bit] = (num.words[off] & (1 << wbit)) >>> wbit; + } + + return w; + } + + // Number of trailing zero bits + BN.prototype.zeroBits = function zeroBits () { + if (this.isZero()) return 0; + + var r = 0; + for (var i = 0; i < this.length; i++) { + var b = this._zeroBits(this.words[i]); + r += b; + if (b !== 26) break; + } + return r; + }; + + BN.prototype.byteLength = function byteLength () { + return Math.ceil(this.bitLength() / 8); + }; + + BN.prototype.toTwos = function toTwos (width) { + if (this.negative !== 0) { + return this.abs().inotn(width).iaddn(1); + } + return this.clone(); + }; + + BN.prototype.fromTwos = function fromTwos (width) { + if (this.testn(width - 1)) { + return this.notn(width).iaddn(1).ineg(); + } + return this.clone(); + }; + + BN.prototype.isNeg = function isNeg () { + return this.negative !== 0; + }; + + // Return negative clone of `this` + BN.prototype.neg = function neg () { + return this.clone().ineg(); + }; + + BN.prototype.ineg = function ineg () { + if (!this.isZero()) { + this.negative ^= 1; + } + + return this; + }; + + // Or `num` with `this` in-place + BN.prototype.iuor = function iuor (num) { + while (this.length < num.length) { + this.words[this.length++] = 0; + } + + for (var i = 0; i < num.length; i++) { + this.words[i] = this.words[i] | num.words[i]; + } + + return this.strip(); + }; + + BN.prototype.ior = function ior (num) { + assert((this.negative | num.negative) === 0); + return this.iuor(num); + }; + + // Or `num` with `this` + BN.prototype.or = function or (num) { + if (this.length > num.length) return this.clone().ior(num); + return num.clone().ior(this); + }; + + BN.prototype.uor = function uor (num) { + if (this.length > num.length) return this.clone().iuor(num); + return num.clone().iuor(this); + }; + + // And `num` with `this` in-place + BN.prototype.iuand = function iuand (num) { + // b = min-length(num, this) + var b; + if (this.length > num.length) { + b = num; + } else { + b = this; + } + + for (var i = 0; i < b.length; i++) { + this.words[i] = this.words[i] & num.words[i]; + } + + this.length = b.length; + + return this.strip(); + }; + + BN.prototype.iand = function iand (num) { + assert((this.negative | num.negative) === 0); + return this.iuand(num); + }; + + // And `num` with `this` + BN.prototype.and = function and (num) { + if (this.length > num.length) return this.clone().iand(num); + return num.clone().iand(this); + }; + + BN.prototype.uand = function uand (num) { + if (this.length > num.length) return this.clone().iuand(num); + return num.clone().iuand(this); + }; + + // Xor `num` with `this` in-place + BN.prototype.iuxor = function iuxor (num) { + // a.length > b.length + var a; + var b; + if (this.length > num.length) { + a = this; + b = num; + } else { + a = num; + b = this; + } + + for (var i = 0; i < b.length; i++) { + this.words[i] = a.words[i] ^ b.words[i]; + } + + if (this !== a) { + for (; i < a.length; i++) { + this.words[i] = a.words[i]; + } + } + + this.length = a.length; + + return this.strip(); + }; + + BN.prototype.ixor = function ixor (num) { + assert((this.negative | num.negative) === 0); + return this.iuxor(num); + }; + + // Xor `num` with `this` + BN.prototype.xor = function xor (num) { + if (this.length > num.length) return this.clone().ixor(num); + return num.clone().ixor(this); + }; + + BN.prototype.uxor = function uxor (num) { + if (this.length > num.length) return this.clone().iuxor(num); + return num.clone().iuxor(this); + }; + + // Not ``this`` with ``width`` bitwidth + BN.prototype.inotn = function inotn (width) { + assert(typeof width === 'number' && width >= 0); + + var bytesNeeded = Math.ceil(width / 26) | 0; + var bitsLeft = width % 26; + + // Extend the buffer with leading zeroes + this._expand(bytesNeeded); + + if (bitsLeft > 0) { + bytesNeeded--; + } + + // Handle complete words + for (var i = 0; i < bytesNeeded; i++) { + this.words[i] = ~this.words[i] & 0x3ffffff; + } + + // Handle the residue + if (bitsLeft > 0) { + this.words[i] = ~this.words[i] & (0x3ffffff >> (26 - bitsLeft)); + } + + // And remove leading zeroes + return this.strip(); + }; + + BN.prototype.notn = function notn (width) { + return this.clone().inotn(width); + }; + + // Set `bit` of `this` + BN.prototype.setn = function setn (bit, val) { + assert(typeof bit === 'number' && bit >= 0); + + var off = (bit / 26) | 0; + var wbit = bit % 26; + + this._expand(off + 1); + + if (val) { + this.words[off] = this.words[off] | (1 << wbit); + } else { + this.words[off] = this.words[off] & ~(1 << wbit); + } + + return this.strip(); + }; + + // Add `num` to `this` in-place + BN.prototype.iadd = function iadd (num) { + var r; + + // negative + positive + if (this.negative !== 0 && num.negative === 0) { + this.negative = 0; + r = this.isub(num); + this.negative ^= 1; + return this._normSign(); + + // positive + negative + } else if (this.negative === 0 && num.negative !== 0) { + num.negative = 0; + r = this.isub(num); + num.negative = 1; + return r._normSign(); + } + + // a.length > b.length + var a, b; + if (this.length > num.length) { + a = this; + b = num; + } else { + a = num; + b = this; + } + + var carry = 0; + for (var i = 0; i < b.length; i++) { + r = (a.words[i] | 0) + (b.words[i] | 0) + carry; + this.words[i] = r & 0x3ffffff; + carry = r >>> 26; + } + for (; carry !== 0 && i < a.length; i++) { + r = (a.words[i] | 0) + carry; + this.words[i] = r & 0x3ffffff; + carry = r >>> 26; + } + + this.length = a.length; + if (carry !== 0) { + this.words[this.length] = carry; + this.length++; + // Copy the rest of the words + } else if (a !== this) { + for (; i < a.length; i++) { + this.words[i] = a.words[i]; + } + } + + return this; + }; + + // Add `num` to `this` + BN.prototype.add = function add (num) { + var res; + if (num.negative !== 0 && this.negative === 0) { + num.negative = 0; + res = this.sub(num); + num.negative ^= 1; + return res; + } else if (num.negative === 0 && this.negative !== 0) { + this.negative = 0; + res = num.sub(this); + this.negative = 1; + return res; + } + + if (this.length > num.length) return this.clone().iadd(num); + + return num.clone().iadd(this); + }; + + // Subtract `num` from `this` in-place + BN.prototype.isub = function isub (num) { + // this - (-num) = this + num + if (num.negative !== 0) { + num.negative = 0; + var r = this.iadd(num); + num.negative = 1; + return r._normSign(); + + // -this - num = -(this + num) + } else if (this.negative !== 0) { + this.negative = 0; + this.iadd(num); + this.negative = 1; + return this._normSign(); + } + + // At this point both numbers are positive + var cmp = this.cmp(num); + + // Optimization - zeroify + if (cmp === 0) { + this.negative = 0; + this.length = 1; + this.words[0] = 0; + return this; + } + + // a > b + var a, b; + if (cmp > 0) { + a = this; + b = num; + } else { + a = num; + b = this; + } + + var carry = 0; + for (var i = 0; i < b.length; i++) { + r = (a.words[i] | 0) - (b.words[i] | 0) + carry; + carry = r >> 26; + this.words[i] = r & 0x3ffffff; + } + for (; carry !== 0 && i < a.length; i++) { + r = (a.words[i] | 0) + carry; + carry = r >> 26; + this.words[i] = r & 0x3ffffff; + } + + // Copy rest of the words + if (carry === 0 && i < a.length && a !== this) { + for (; i < a.length; i++) { + this.words[i] = a.words[i]; + } + } + + this.length = Math.max(this.length, i); + + if (a !== this) { + this.negative = 1; + } + + return this.strip(); + }; + + // Subtract `num` from `this` + BN.prototype.sub = function sub (num) { + return this.clone().isub(num); + }; + + function smallMulTo (self, num, out) { + out.negative = num.negative ^ self.negative; + var len = (self.length + num.length) | 0; + out.length = len; + len = (len - 1) | 0; + + // Peel one iteration (compiler can't do it, because of code complexity) + var a = self.words[0] | 0; + var b = num.words[0] | 0; + var r = a * b; + + var lo = r & 0x3ffffff; + var carry = (r / 0x4000000) | 0; + out.words[0] = lo; + + for (var k = 1; k < len; k++) { + // Sum all words with the same `i + j = k` and accumulate `ncarry`, + // note that ncarry could be >= 0x3ffffff + var ncarry = carry >>> 26; + var rword = carry & 0x3ffffff; + var maxJ = Math.min(k, num.length - 1); + for (var j = Math.max(0, k - self.length + 1); j <= maxJ; j++) { + var i = (k - j) | 0; + a = self.words[i] | 0; + b = num.words[j] | 0; + r = a * b + rword; + ncarry += (r / 0x4000000) | 0; + rword = r & 0x3ffffff; + } + out.words[k] = rword | 0; + carry = ncarry | 0; + } + if (carry !== 0) { + out.words[k] = carry | 0; + } else { + out.length--; + } + + return out.strip(); + } + + // TODO(indutny): it may be reasonable to omit it for users who don't need + // to work with 256-bit numbers, otherwise it gives 20% improvement for 256-bit + // multiplication (like elliptic secp256k1). + var comb10MulTo = function comb10MulTo (self, num, out) { + var a = self.words; + var b = num.words; + var o = out.words; + var c = 0; + var lo; + var mid; + var hi; + var a0 = a[0] | 0; + var al0 = a0 & 0x1fff; + var ah0 = a0 >>> 13; + var a1 = a[1] | 0; + var al1 = a1 & 0x1fff; + var ah1 = a1 >>> 13; + var a2 = a[2] | 0; + var al2 = a2 & 0x1fff; + var ah2 = a2 >>> 13; + var a3 = a[3] | 0; + var al3 = a3 & 0x1fff; + var ah3 = a3 >>> 13; + var a4 = a[4] | 0; + var al4 = a4 & 0x1fff; + var ah4 = a4 >>> 13; + var a5 = a[5] | 0; + var al5 = a5 & 0x1fff; + var ah5 = a5 >>> 13; + var a6 = a[6] | 0; + var al6 = a6 & 0x1fff; + var ah6 = a6 >>> 13; + var a7 = a[7] | 0; + var al7 = a7 & 0x1fff; + var ah7 = a7 >>> 13; + var a8 = a[8] | 0; + var al8 = a8 & 0x1fff; + var ah8 = a8 >>> 13; + var a9 = a[9] | 0; + var al9 = a9 & 0x1fff; + var ah9 = a9 >>> 13; + var b0 = b[0] | 0; + var bl0 = b0 & 0x1fff; + var bh0 = b0 >>> 13; + var b1 = b[1] | 0; + var bl1 = b1 & 0x1fff; + var bh1 = b1 >>> 13; + var b2 = b[2] | 0; + var bl2 = b2 & 0x1fff; + var bh2 = b2 >>> 13; + var b3 = b[3] | 0; + var bl3 = b3 & 0x1fff; + var bh3 = b3 >>> 13; + var b4 = b[4] | 0; + var bl4 = b4 & 0x1fff; + var bh4 = b4 >>> 13; + var b5 = b[5] | 0; + var bl5 = b5 & 0x1fff; + var bh5 = b5 >>> 13; + var b6 = b[6] | 0; + var bl6 = b6 & 0x1fff; + var bh6 = b6 >>> 13; + var b7 = b[7] | 0; + var bl7 = b7 & 0x1fff; + var bh7 = b7 >>> 13; + var b8 = b[8] | 0; + var bl8 = b8 & 0x1fff; + var bh8 = b8 >>> 13; + var b9 = b[9] | 0; + var bl9 = b9 & 0x1fff; + var bh9 = b9 >>> 13; + + out.negative = self.negative ^ num.negative; + out.length = 19; + /* k = 0 */ + lo = Math.imul(al0, bl0); + mid = Math.imul(al0, bh0); + mid = (mid + Math.imul(ah0, bl0)) | 0; + hi = Math.imul(ah0, bh0); + var w0 = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0; + c = (((hi + (mid >>> 13)) | 0) + (w0 >>> 26)) | 0; + w0 &= 0x3ffffff; + /* k = 1 */ + lo = Math.imul(al1, bl0); + mid = Math.imul(al1, bh0); + mid = (mid + Math.imul(ah1, bl0)) | 0; + hi = Math.imul(ah1, bh0); + lo = (lo + Math.imul(al0, bl1)) | 0; + mid = (mid + Math.imul(al0, bh1)) | 0; + mid = (mid + Math.imul(ah0, bl1)) | 0; + hi = (hi + Math.imul(ah0, bh1)) | 0; + var w1 = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0; + c = (((hi + (mid >>> 13)) | 0) + (w1 >>> 26)) | 0; + w1 &= 0x3ffffff; + /* k = 2 */ + lo = Math.imul(al2, bl0); + mid = Math.imul(al2, bh0); + mid = (mid + Math.imul(ah2, bl0)) | 0; + hi = Math.imul(ah2, bh0); + lo = (lo + Math.imul(al1, bl1)) | 0; + mid = (mid + Math.imul(al1, bh1)) | 0; + mid = (mid + Math.imul(ah1, bl1)) | 0; + hi = (hi + Math.imul(ah1, bh1)) | 0; + lo = (lo + Math.imul(al0, bl2)) | 0; + mid = (mid + Math.imul(al0, bh2)) | 0; + mid = (mid + Math.imul(ah0, bl2)) | 0; + hi = (hi + Math.imul(ah0, bh2)) | 0; + var w2 = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0; + c = (((hi + (mid >>> 13)) | 0) + (w2 >>> 26)) | 0; + w2 &= 0x3ffffff; + /* k = 3 */ + lo = Math.imul(al3, bl0); + mid = Math.imul(al3, bh0); + mid = (mid + Math.imul(ah3, bl0)) | 0; + hi = Math.imul(ah3, bh0); + lo = (lo + Math.imul(al2, bl1)) | 0; + mid = (mid + Math.imul(al2, bh1)) | 0; + mid = (mid + Math.imul(ah2, bl1)) | 0; + hi = (hi + Math.imul(ah2, bh1)) | 0; + lo = (lo + Math.imul(al1, bl2)) | 0; + mid = (mid + Math.imul(al1, bh2)) | 0; + mid = (mid + Math.imul(ah1, bl2)) | 0; + hi = (hi + Math.imul(ah1, bh2)) | 0; + lo = (lo + Math.imul(al0, bl3)) | 0; + mid = (mid + Math.imul(al0, bh3)) | 0; + mid = (mid + Math.imul(ah0, bl3)) | 0; + hi = (hi + Math.imul(ah0, bh3)) | 0; + var w3 = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0; + c = (((hi + (mid >>> 13)) | 0) + (w3 >>> 26)) | 0; + w3 &= 0x3ffffff; + /* k = 4 */ + lo = Math.imul(al4, bl0); + mid = Math.imul(al4, bh0); + mid = (mid + Math.imul(ah4, bl0)) | 0; + hi = Math.imul(ah4, bh0); + lo = (lo + Math.imul(al3, bl1)) | 0; + mid = (mid + Math.imul(al3, bh1)) | 0; + mid = (mid + Math.imul(ah3, bl1)) | 0; + hi = (hi + Math.imul(ah3, bh1)) | 0; + lo = (lo + Math.imul(al2, bl2)) | 0; + mid = (mid + Math.imul(al2, bh2)) | 0; + mid = (mid + Math.imul(ah2, bl2)) | 0; + hi = (hi + Math.imul(ah2, bh2)) | 0; + lo = (lo + Math.imul(al1, bl3)) | 0; + mid = (mid + Math.imul(al1, bh3)) | 0; + mid = (mid + Math.imul(ah1, bl3)) | 0; + hi = (hi + Math.imul(ah1, bh3)) | 0; + lo = (lo + Math.imul(al0, bl4)) | 0; + mid = (mid + Math.imul(al0, bh4)) | 0; + mid = (mid + Math.imul(ah0, bl4)) | 0; + hi = (hi + Math.imul(ah0, bh4)) | 0; + var w4 = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0; + c = (((hi + (mid >>> 13)) | 0) + (w4 >>> 26)) | 0; + w4 &= 0x3ffffff; + /* k = 5 */ + lo = Math.imul(al5, bl0); + mid = Math.imul(al5, bh0); + mid = (mid + Math.imul(ah5, bl0)) | 0; + hi = Math.imul(ah5, bh0); + lo = (lo + Math.imul(al4, bl1)) | 0; + mid = (mid + Math.imul(al4, bh1)) | 0; + mid = (mid + Math.imul(ah4, bl1)) | 0; + hi = (hi + Math.imul(ah4, bh1)) | 0; + lo = (lo + Math.imul(al3, bl2)) | 0; + mid = (mid + Math.imul(al3, bh2)) | 0; + mid = (mid + Math.imul(ah3, bl2)) | 0; + hi = (hi + Math.imul(ah3, bh2)) | 0; + lo = (lo + Math.imul(al2, bl3)) | 0; + mid = (mid + Math.imul(al2, bh3)) | 0; + mid = (mid + Math.imul(ah2, bl3)) | 0; + hi = (hi + Math.imul(ah2, bh3)) | 0; + lo = (lo + Math.imul(al1, bl4)) | 0; + mid = (mid + Math.imul(al1, bh4)) | 0; + mid = (mid + Math.imul(ah1, bl4)) | 0; + hi = (hi + Math.imul(ah1, bh4)) | 0; + lo = (lo + Math.imul(al0, bl5)) | 0; + mid = (mid + Math.imul(al0, bh5)) | 0; + mid = (mid + Math.imul(ah0, bl5)) | 0; + hi = (hi + Math.imul(ah0, bh5)) | 0; + var w5 = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0; + c = (((hi + (mid >>> 13)) | 0) + (w5 >>> 26)) | 0; + w5 &= 0x3ffffff; + /* k = 6 */ + lo = Math.imul(al6, bl0); + mid = Math.imul(al6, bh0); + mid = (mid + Math.imul(ah6, bl0)) | 0; + hi = Math.imul(ah6, bh0); + lo = (lo + Math.imul(al5, bl1)) | 0; + mid = (mid + Math.imul(al5, bh1)) | 0; + mid = (mid + Math.imul(ah5, bl1)) | 0; + hi = (hi + Math.imul(ah5, bh1)) | 0; + lo = (lo + Math.imul(al4, bl2)) | 0; + mid = (mid + Math.imul(al4, bh2)) | 0; + mid = (mid + Math.imul(ah4, bl2)) | 0; + hi = (hi + Math.imul(ah4, bh2)) | 0; + lo = (lo + Math.imul(al3, bl3)) | 0; + mid = (mid + Math.imul(al3, bh3)) | 0; + mid = (mid + Math.imul(ah3, bl3)) | 0; + hi = (hi + Math.imul(ah3, bh3)) | 0; + lo = (lo + Math.imul(al2, bl4)) | 0; + mid = (mid + Math.imul(al2, bh4)) | 0; + mid = (mid + Math.imul(ah2, bl4)) | 0; + hi = (hi + Math.imul(ah2, bh4)) | 0; + lo = (lo + Math.imul(al1, bl5)) | 0; + mid = (mid + Math.imul(al1, bh5)) | 0; + mid = (mid + Math.imul(ah1, bl5)) | 0; + hi = (hi + Math.imul(ah1, bh5)) | 0; + lo = (lo + Math.imul(al0, bl6)) | 0; + mid = (mid + Math.imul(al0, bh6)) | 0; + mid = (mid + Math.imul(ah0, bl6)) | 0; + hi = (hi + Math.imul(ah0, bh6)) | 0; + var w6 = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0; + c = (((hi + (mid >>> 13)) | 0) + (w6 >>> 26)) | 0; + w6 &= 0x3ffffff; + /* k = 7 */ + lo = Math.imul(al7, bl0); + mid = Math.imul(al7, bh0); + mid = (mid + Math.imul(ah7, bl0)) | 0; + hi = Math.imul(ah7, bh0); + lo = (lo + Math.imul(al6, bl1)) | 0; + mid = (mid + Math.imul(al6, bh1)) | 0; + mid = (mid + Math.imul(ah6, bl1)) | 0; + hi = (hi + Math.imul(ah6, bh1)) | 0; + lo = (lo + Math.imul(al5, bl2)) | 0; + mid = (mid + Math.imul(al5, bh2)) | 0; + mid = (mid + Math.imul(ah5, bl2)) | 0; + hi = (hi + Math.imul(ah5, bh2)) | 0; + lo = (lo + Math.imul(al4, bl3)) | 0; + mid = (mid + Math.imul(al4, bh3)) | 0; + mid = (mid + Math.imul(ah4, bl3)) | 0; + hi = (hi + Math.imul(ah4, bh3)) | 0; + lo = (lo + Math.imul(al3, bl4)) | 0; + mid = (mid + Math.imul(al3, bh4)) | 0; + mid = (mid + Math.imul(ah3, bl4)) | 0; + hi = (hi + Math.imul(ah3, bh4)) | 0; + lo = (lo + Math.imul(al2, bl5)) | 0; + mid = (mid + Math.imul(al2, bh5)) | 0; + mid = (mid + Math.imul(ah2, bl5)) | 0; + hi = (hi + Math.imul(ah2, bh5)) | 0; + lo = (lo + Math.imul(al1, bl6)) | 0; + mid = (mid + Math.imul(al1, bh6)) | 0; + mid = (mid + Math.imul(ah1, bl6)) | 0; + hi = (hi + Math.imul(ah1, bh6)) | 0; + lo = (lo + Math.imul(al0, bl7)) | 0; + mid = (mid + Math.imul(al0, bh7)) | 0; + mid = (mid + Math.imul(ah0, bl7)) | 0; + hi = (hi + Math.imul(ah0, bh7)) | 0; + var w7 = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0; + c = (((hi + (mid >>> 13)) | 0) + (w7 >>> 26)) | 0; + w7 &= 0x3ffffff; + /* k = 8 */ + lo = Math.imul(al8, bl0); + mid = Math.imul(al8, bh0); + mid = (mid + Math.imul(ah8, bl0)) | 0; + hi = Math.imul(ah8, bh0); + lo = (lo + Math.imul(al7, bl1)) | 0; + mid = (mid + Math.imul(al7, bh1)) | 0; + mid = (mid + Math.imul(ah7, bl1)) | 0; + hi = (hi + Math.imul(ah7, bh1)) | 0; + lo = (lo + Math.imul(al6, bl2)) | 0; + mid = (mid + Math.imul(al6, bh2)) | 0; + mid = (mid + Math.imul(ah6, bl2)) | 0; + hi = (hi + Math.imul(ah6, bh2)) | 0; + lo = (lo + Math.imul(al5, bl3)) | 0; + mid = (mid + Math.imul(al5, bh3)) | 0; + mid = (mid + Math.imul(ah5, bl3)) | 0; + hi = (hi + Math.imul(ah5, bh3)) | 0; + lo = (lo + Math.imul(al4, bl4)) | 0; + mid = (mid + Math.imul(al4, bh4)) | 0; + mid = (mid + Math.imul(ah4, bl4)) | 0; + hi = (hi + Math.imul(ah4, bh4)) | 0; + lo = (lo + Math.imul(al3, bl5)) | 0; + mid = (mid + Math.imul(al3, bh5)) | 0; + mid = (mid + Math.imul(ah3, bl5)) | 0; + hi = (hi + Math.imul(ah3, bh5)) | 0; + lo = (lo + Math.imul(al2, bl6)) | 0; + mid = (mid + Math.imul(al2, bh6)) | 0; + mid = (mid + Math.imul(ah2, bl6)) | 0; + hi = (hi + Math.imul(ah2, bh6)) | 0; + lo = (lo + Math.imul(al1, bl7)) | 0; + mid = (mid + Math.imul(al1, bh7)) | 0; + mid = (mid + Math.imul(ah1, bl7)) | 0; + hi = (hi + Math.imul(ah1, bh7)) | 0; + lo = (lo + Math.imul(al0, bl8)) | 0; + mid = (mid + Math.imul(al0, bh8)) | 0; + mid = (mid + Math.imul(ah0, bl8)) | 0; + hi = (hi + Math.imul(ah0, bh8)) | 0; + var w8 = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0; + c = (((hi + (mid >>> 13)) | 0) + (w8 >>> 26)) | 0; + w8 &= 0x3ffffff; + /* k = 9 */ + lo = Math.imul(al9, bl0); + mid = Math.imul(al9, bh0); + mid = (mid + Math.imul(ah9, bl0)) | 0; + hi = Math.imul(ah9, bh0); + lo = (lo + Math.imul(al8, bl1)) | 0; + mid = (mid + Math.imul(al8, bh1)) | 0; + mid = (mid + Math.imul(ah8, bl1)) | 0; + hi = (hi + Math.imul(ah8, bh1)) | 0; + lo = (lo + Math.imul(al7, bl2)) | 0; + mid = (mid + Math.imul(al7, bh2)) | 0; + mid = (mid + Math.imul(ah7, bl2)) | 0; + hi = (hi + Math.imul(ah7, bh2)) | 0; + lo = (lo + Math.imul(al6, bl3)) | 0; + mid = (mid + Math.imul(al6, bh3)) | 0; + mid = (mid + Math.imul(ah6, bl3)) | 0; + hi = (hi + Math.imul(ah6, bh3)) | 0; + lo = (lo + Math.imul(al5, bl4)) | 0; + mid = (mid + Math.imul(al5, bh4)) | 0; + mid = (mid + Math.imul(ah5, bl4)) | 0; + hi = (hi + Math.imul(ah5, bh4)) | 0; + lo = (lo + Math.imul(al4, bl5)) | 0; + mid = (mid + Math.imul(al4, bh5)) | 0; + mid = (mid + Math.imul(ah4, bl5)) | 0; + hi = (hi + Math.imul(ah4, bh5)) | 0; + lo = (lo + Math.imul(al3, bl6)) | 0; + mid = (mid + Math.imul(al3, bh6)) | 0; + mid = (mid + Math.imul(ah3, bl6)) | 0; + hi = (hi + Math.imul(ah3, bh6)) | 0; + lo = (lo + Math.imul(al2, bl7)) | 0; + mid = (mid + Math.imul(al2, bh7)) | 0; + mid = (mid + Math.imul(ah2, bl7)) | 0; + hi = (hi + Math.imul(ah2, bh7)) | 0; + lo = (lo + Math.imul(al1, bl8)) | 0; + mid = (mid + Math.imul(al1, bh8)) | 0; + mid = (mid + Math.imul(ah1, bl8)) | 0; + hi = (hi + Math.imul(ah1, bh8)) | 0; + lo = (lo + Math.imul(al0, bl9)) | 0; + mid = (mid + Math.imul(al0, bh9)) | 0; + mid = (mid + Math.imul(ah0, bl9)) | 0; + hi = (hi + Math.imul(ah0, bh9)) | 0; + var w9 = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0; + c = (((hi + (mid >>> 13)) | 0) + (w9 >>> 26)) | 0; + w9 &= 0x3ffffff; + /* k = 10 */ + lo = Math.imul(al9, bl1); + mid = Math.imul(al9, bh1); + mid = (mid + Math.imul(ah9, bl1)) | 0; + hi = Math.imul(ah9, bh1); + lo = (lo + Math.imul(al8, bl2)) | 0; + mid = (mid + Math.imul(al8, bh2)) | 0; + mid = (mid + Math.imul(ah8, bl2)) | 0; + hi = (hi + Math.imul(ah8, bh2)) | 0; + lo = (lo + Math.imul(al7, bl3)) | 0; + mid = (mid + Math.imul(al7, bh3)) | 0; + mid = (mid + Math.imul(ah7, bl3)) | 0; + hi = (hi + Math.imul(ah7, bh3)) | 0; + lo = (lo + Math.imul(al6, bl4)) | 0; + mid = (mid + Math.imul(al6, bh4)) | 0; + mid = (mid + Math.imul(ah6, bl4)) | 0; + hi = (hi + Math.imul(ah6, bh4)) | 0; + lo = (lo + Math.imul(al5, bl5)) | 0; + mid = (mid + Math.imul(al5, bh5)) | 0; + mid = (mid + Math.imul(ah5, bl5)) | 0; + hi = (hi + Math.imul(ah5, bh5)) | 0; + lo = (lo + Math.imul(al4, bl6)) | 0; + mid = (mid + Math.imul(al4, bh6)) | 0; + mid = (mid + Math.imul(ah4, bl6)) | 0; + hi = (hi + Math.imul(ah4, bh6)) | 0; + lo = (lo + Math.imul(al3, bl7)) | 0; + mid = (mid + Math.imul(al3, bh7)) | 0; + mid = (mid + Math.imul(ah3, bl7)) | 0; + hi = (hi + Math.imul(ah3, bh7)) | 0; + lo = (lo + Math.imul(al2, bl8)) | 0; + mid = (mid + Math.imul(al2, bh8)) | 0; + mid = (mid + Math.imul(ah2, bl8)) | 0; + hi = (hi + Math.imul(ah2, bh8)) | 0; + lo = (lo + Math.imul(al1, bl9)) | 0; + mid = (mid + Math.imul(al1, bh9)) | 0; + mid = (mid + Math.imul(ah1, bl9)) | 0; + hi = (hi + Math.imul(ah1, bh9)) | 0; + var w10 = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0; + c = (((hi + (mid >>> 13)) | 0) + (w10 >>> 26)) | 0; + w10 &= 0x3ffffff; + /* k = 11 */ + lo = Math.imul(al9, bl2); + mid = Math.imul(al9, bh2); + mid = (mid + Math.imul(ah9, bl2)) | 0; + hi = Math.imul(ah9, bh2); + lo = (lo + Math.imul(al8, bl3)) | 0; + mid = (mid + Math.imul(al8, bh3)) | 0; + mid = (mid + Math.imul(ah8, bl3)) | 0; + hi = (hi + Math.imul(ah8, bh3)) | 0; + lo = (lo + Math.imul(al7, bl4)) | 0; + mid = (mid + Math.imul(al7, bh4)) | 0; + mid = (mid + Math.imul(ah7, bl4)) | 0; + hi = (hi + Math.imul(ah7, bh4)) | 0; + lo = (lo + Math.imul(al6, bl5)) | 0; + mid = (mid + Math.imul(al6, bh5)) | 0; + mid = (mid + Math.imul(ah6, bl5)) | 0; + hi = (hi + Math.imul(ah6, bh5)) | 0; + lo = (lo + Math.imul(al5, bl6)) | 0; + mid = (mid + Math.imul(al5, bh6)) | 0; + mid = (mid + Math.imul(ah5, bl6)) | 0; + hi = (hi + Math.imul(ah5, bh6)) | 0; + lo = (lo + Math.imul(al4, bl7)) | 0; + mid = (mid + Math.imul(al4, bh7)) | 0; + mid = (mid + Math.imul(ah4, bl7)) | 0; + hi = (hi + Math.imul(ah4, bh7)) | 0; + lo = (lo + Math.imul(al3, bl8)) | 0; + mid = (mid + Math.imul(al3, bh8)) | 0; + mid = (mid + Math.imul(ah3, bl8)) | 0; + hi = (hi + Math.imul(ah3, bh8)) | 0; + lo = (lo + Math.imul(al2, bl9)) | 0; + mid = (mid + Math.imul(al2, bh9)) | 0; + mid = (mid + Math.imul(ah2, bl9)) | 0; + hi = (hi + Math.imul(ah2, bh9)) | 0; + var w11 = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0; + c = (((hi + (mid >>> 13)) | 0) + (w11 >>> 26)) | 0; + w11 &= 0x3ffffff; + /* k = 12 */ + lo = Math.imul(al9, bl3); + mid = Math.imul(al9, bh3); + mid = (mid + Math.imul(ah9, bl3)) | 0; + hi = Math.imul(ah9, bh3); + lo = (lo + Math.imul(al8, bl4)) | 0; + mid = (mid + Math.imul(al8, bh4)) | 0; + mid = (mid + Math.imul(ah8, bl4)) | 0; + hi = (hi + Math.imul(ah8, bh4)) | 0; + lo = (lo + Math.imul(al7, bl5)) | 0; + mid = (mid + Math.imul(al7, bh5)) | 0; + mid = (mid + Math.imul(ah7, bl5)) | 0; + hi = (hi + Math.imul(ah7, bh5)) | 0; + lo = (lo + Math.imul(al6, bl6)) | 0; + mid = (mid + Math.imul(al6, bh6)) | 0; + mid = (mid + Math.imul(ah6, bl6)) | 0; + hi = (hi + Math.imul(ah6, bh6)) | 0; + lo = (lo + Math.imul(al5, bl7)) | 0; + mid = (mid + Math.imul(al5, bh7)) | 0; + mid = (mid + Math.imul(ah5, bl7)) | 0; + hi = (hi + Math.imul(ah5, bh7)) | 0; + lo = (lo + Math.imul(al4, bl8)) | 0; + mid = (mid + Math.imul(al4, bh8)) | 0; + mid = (mid + Math.imul(ah4, bl8)) | 0; + hi = (hi + Math.imul(ah4, bh8)) | 0; + lo = (lo + Math.imul(al3, bl9)) | 0; + mid = (mid + Math.imul(al3, bh9)) | 0; + mid = (mid + Math.imul(ah3, bl9)) | 0; + hi = (hi + Math.imul(ah3, bh9)) | 0; + var w12 = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0; + c = (((hi + (mid >>> 13)) | 0) + (w12 >>> 26)) | 0; + w12 &= 0x3ffffff; + /* k = 13 */ + lo = Math.imul(al9, bl4); + mid = Math.imul(al9, bh4); + mid = (mid + Math.imul(ah9, bl4)) | 0; + hi = Math.imul(ah9, bh4); + lo = (lo + Math.imul(al8, bl5)) | 0; + mid = (mid + Math.imul(al8, bh5)) | 0; + mid = (mid + Math.imul(ah8, bl5)) | 0; + hi = (hi + Math.imul(ah8, bh5)) | 0; + lo = (lo + Math.imul(al7, bl6)) | 0; + mid = (mid + Math.imul(al7, bh6)) | 0; + mid = (mid + Math.imul(ah7, bl6)) | 0; + hi = (hi + Math.imul(ah7, bh6)) | 0; + lo = (lo + Math.imul(al6, bl7)) | 0; + mid = (mid + Math.imul(al6, bh7)) | 0; + mid = (mid + Math.imul(ah6, bl7)) | 0; + hi = (hi + Math.imul(ah6, bh7)) | 0; + lo = (lo + Math.imul(al5, bl8)) | 0; + mid = (mid + Math.imul(al5, bh8)) | 0; + mid = (mid + Math.imul(ah5, bl8)) | 0; + hi = (hi + Math.imul(ah5, bh8)) | 0; + lo = (lo + Math.imul(al4, bl9)) | 0; + mid = (mid + Math.imul(al4, bh9)) | 0; + mid = (mid + Math.imul(ah4, bl9)) | 0; + hi = (hi + Math.imul(ah4, bh9)) | 0; + var w13 = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0; + c = (((hi + (mid >>> 13)) | 0) + (w13 >>> 26)) | 0; + w13 &= 0x3ffffff; + /* k = 14 */ + lo = Math.imul(al9, bl5); + mid = Math.imul(al9, bh5); + mid = (mid + Math.imul(ah9, bl5)) | 0; + hi = Math.imul(ah9, bh5); + lo = (lo + Math.imul(al8, bl6)) | 0; + mid = (mid + Math.imul(al8, bh6)) | 0; + mid = (mid + Math.imul(ah8, bl6)) | 0; + hi = (hi + Math.imul(ah8, bh6)) | 0; + lo = (lo + Math.imul(al7, bl7)) | 0; + mid = (mid + Math.imul(al7, bh7)) | 0; + mid = (mid + Math.imul(ah7, bl7)) | 0; + hi = (hi + Math.imul(ah7, bh7)) | 0; + lo = (lo + Math.imul(al6, bl8)) | 0; + mid = (mid + Math.imul(al6, bh8)) | 0; + mid = (mid + Math.imul(ah6, bl8)) | 0; + hi = (hi + Math.imul(ah6, bh8)) | 0; + lo = (lo + Math.imul(al5, bl9)) | 0; + mid = (mid + Math.imul(al5, bh9)) | 0; + mid = (mid + Math.imul(ah5, bl9)) | 0; + hi = (hi + Math.imul(ah5, bh9)) | 0; + var w14 = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0; + c = (((hi + (mid >>> 13)) | 0) + (w14 >>> 26)) | 0; + w14 &= 0x3ffffff; + /* k = 15 */ + lo = Math.imul(al9, bl6); + mid = Math.imul(al9, bh6); + mid = (mid + Math.imul(ah9, bl6)) | 0; + hi = Math.imul(ah9, bh6); + lo = (lo + Math.imul(al8, bl7)) | 0; + mid = (mid + Math.imul(al8, bh7)) | 0; + mid = (mid + Math.imul(ah8, bl7)) | 0; + hi = (hi + Math.imul(ah8, bh7)) | 0; + lo = (lo + Math.imul(al7, bl8)) | 0; + mid = (mid + Math.imul(al7, bh8)) | 0; + mid = (mid + Math.imul(ah7, bl8)) | 0; + hi = (hi + Math.imul(ah7, bh8)) | 0; + lo = (lo + Math.imul(al6, bl9)) | 0; + mid = (mid + Math.imul(al6, bh9)) | 0; + mid = (mid + Math.imul(ah6, bl9)) | 0; + hi = (hi + Math.imul(ah6, bh9)) | 0; + var w15 = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0; + c = (((hi + (mid >>> 13)) | 0) + (w15 >>> 26)) | 0; + w15 &= 0x3ffffff; + /* k = 16 */ + lo = Math.imul(al9, bl7); + mid = Math.imul(al9, bh7); + mid = (mid + Math.imul(ah9, bl7)) | 0; + hi = Math.imul(ah9, bh7); + lo = (lo + Math.imul(al8, bl8)) | 0; + mid = (mid + Math.imul(al8, bh8)) | 0; + mid = (mid + Math.imul(ah8, bl8)) | 0; + hi = (hi + Math.imul(ah8, bh8)) | 0; + lo = (lo + Math.imul(al7, bl9)) | 0; + mid = (mid + Math.imul(al7, bh9)) | 0; + mid = (mid + Math.imul(ah7, bl9)) | 0; + hi = (hi + Math.imul(ah7, bh9)) | 0; + var w16 = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0; + c = (((hi + (mid >>> 13)) | 0) + (w16 >>> 26)) | 0; + w16 &= 0x3ffffff; + /* k = 17 */ + lo = Math.imul(al9, bl8); + mid = Math.imul(al9, bh8); + mid = (mid + Math.imul(ah9, bl8)) | 0; + hi = Math.imul(ah9, bh8); + lo = (lo + Math.imul(al8, bl9)) | 0; + mid = (mid + Math.imul(al8, bh9)) | 0; + mid = (mid + Math.imul(ah8, bl9)) | 0; + hi = (hi + Math.imul(ah8, bh9)) | 0; + var w17 = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0; + c = (((hi + (mid >>> 13)) | 0) + (w17 >>> 26)) | 0; + w17 &= 0x3ffffff; + /* k = 18 */ + lo = Math.imul(al9, bl9); + mid = Math.imul(al9, bh9); + mid = (mid + Math.imul(ah9, bl9)) | 0; + hi = Math.imul(ah9, bh9); + var w18 = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0; + c = (((hi + (mid >>> 13)) | 0) + (w18 >>> 26)) | 0; + w18 &= 0x3ffffff; + o[0] = w0; + o[1] = w1; + o[2] = w2; + o[3] = w3; + o[4] = w4; + o[5] = w5; + o[6] = w6; + o[7] = w7; + o[8] = w8; + o[9] = w9; + o[10] = w10; + o[11] = w11; + o[12] = w12; + o[13] = w13; + o[14] = w14; + o[15] = w15; + o[16] = w16; + o[17] = w17; + o[18] = w18; + if (c !== 0) { + o[19] = c; + out.length++; + } + return out; + }; + + // Polyfill comb + if (!Math.imul) { + comb10MulTo = smallMulTo; + } + + function bigMulTo (self, num, out) { + out.negative = num.negative ^ self.negative; + out.length = self.length + num.length; + + var carry = 0; + var hncarry = 0; + for (var k = 0; k < out.length - 1; k++) { + // Sum all words with the same `i + j = k` and accumulate `ncarry`, + // note that ncarry could be >= 0x3ffffff + var ncarry = hncarry; + hncarry = 0; + var rword = carry & 0x3ffffff; + var maxJ = Math.min(k, num.length - 1); + for (var j = Math.max(0, k - self.length + 1); j <= maxJ; j++) { + var i = k - j; + var a = self.words[i] | 0; + var b = num.words[j] | 0; + var r = a * b; + + var lo = r & 0x3ffffff; + ncarry = (ncarry + ((r / 0x4000000) | 0)) | 0; + lo = (lo + rword) | 0; + rword = lo & 0x3ffffff; + ncarry = (ncarry + (lo >>> 26)) | 0; + + hncarry += ncarry >>> 26; + ncarry &= 0x3ffffff; + } + out.words[k] = rword; + carry = ncarry; + ncarry = hncarry; + } + if (carry !== 0) { + out.words[k] = carry; + } else { + out.length--; + } + + return out.strip(); + } + + function jumboMulTo (self, num, out) { + var fftm = new FFTM(); + return fftm.mulp(self, num, out); + } + + BN.prototype.mulTo = function mulTo (num, out) { + var res; + var len = this.length + num.length; + if (this.length === 10 && num.length === 10) { + res = comb10MulTo(this, num, out); + } else if (len < 63) { + res = smallMulTo(this, num, out); + } else if (len < 1024) { + res = bigMulTo(this, num, out); + } else { + res = jumboMulTo(this, num, out); + } + + return res; + }; + + // Cooley-Tukey algorithm for FFT + // slightly revisited to rely on looping instead of recursion + + function FFTM (x, y) { + this.x = x; + this.y = y; + } + + FFTM.prototype.makeRBT = function makeRBT (N) { + var t = new Array(N); + var l = BN.prototype._countBits(N) - 1; + for (var i = 0; i < N; i++) { + t[i] = this.revBin(i, l, N); + } + + return t; + }; + + // Returns binary-reversed representation of `x` + FFTM.prototype.revBin = function revBin (x, l, N) { + if (x === 0 || x === N - 1) return x; + + var rb = 0; + for (var i = 0; i < l; i++) { + rb |= (x & 1) << (l - i - 1); + x >>= 1; + } + + return rb; + }; + + // Performs "tweedling" phase, therefore 'emulating' + // behaviour of the recursive algorithm + FFTM.prototype.permute = function permute (rbt, rws, iws, rtws, itws, N) { + for (var i = 0; i < N; i++) { + rtws[i] = rws[rbt[i]]; + itws[i] = iws[rbt[i]]; + } + }; + + FFTM.prototype.transform = function transform (rws, iws, rtws, itws, N, rbt) { + this.permute(rbt, rws, iws, rtws, itws, N); + + for (var s = 1; s < N; s <<= 1) { + var l = s << 1; + + var rtwdf = Math.cos(2 * Math.PI / l); + var itwdf = Math.sin(2 * Math.PI / l); + + for (var p = 0; p < N; p += l) { + var rtwdf_ = rtwdf; + var itwdf_ = itwdf; + + for (var j = 0; j < s; j++) { + var re = rtws[p + j]; + var ie = itws[p + j]; + + var ro = rtws[p + j + s]; + var io = itws[p + j + s]; + + var rx = rtwdf_ * ro - itwdf_ * io; + + io = rtwdf_ * io + itwdf_ * ro; + ro = rx; + + rtws[p + j] = re + ro; + itws[p + j] = ie + io; + + rtws[p + j + s] = re - ro; + itws[p + j + s] = ie - io; + + /* jshint maxdepth : false */ + if (j !== l) { + rx = rtwdf * rtwdf_ - itwdf * itwdf_; + + itwdf_ = rtwdf * itwdf_ + itwdf * rtwdf_; + rtwdf_ = rx; + } + } + } + } + }; + + FFTM.prototype.guessLen13b = function guessLen13b (n, m) { + var N = Math.max(m, n) | 1; + var odd = N & 1; + var i = 0; + for (N = N / 2 | 0; N; N = N >>> 1) { + i++; + } + + return 1 << i + 1 + odd; + }; + + FFTM.prototype.conjugate = function conjugate (rws, iws, N) { + if (N <= 1) return; + + for (var i = 0; i < N / 2; i++) { + var t = rws[i]; + + rws[i] = rws[N - i - 1]; + rws[N - i - 1] = t; + + t = iws[i]; + + iws[i] = -iws[N - i - 1]; + iws[N - i - 1] = -t; + } + }; + + FFTM.prototype.normalize13b = function normalize13b (ws, N) { + var carry = 0; + for (var i = 0; i < N / 2; i++) { + var w = Math.round(ws[2 * i + 1] / N) * 0x2000 + + Math.round(ws[2 * i] / N) + + carry; + + ws[i] = w & 0x3ffffff; + + if (w < 0x4000000) { + carry = 0; + } else { + carry = w / 0x4000000 | 0; + } + } + + return ws; + }; + + FFTM.prototype.convert13b = function convert13b (ws, len, rws, N) { + var carry = 0; + for (var i = 0; i < len; i++) { + carry = carry + (ws[i] | 0); + + rws[2 * i] = carry & 0x1fff; carry = carry >>> 13; + rws[2 * i + 1] = carry & 0x1fff; carry = carry >>> 13; + } + + // Pad with zeroes + for (i = 2 * len; i < N; ++i) { + rws[i] = 0; + } + + assert(carry === 0); + assert((carry & ~0x1fff) === 0); + }; + + FFTM.prototype.stub = function stub (N) { + var ph = new Array(N); + for (var i = 0; i < N; i++) { + ph[i] = 0; + } + + return ph; + }; + + FFTM.prototype.mulp = function mulp (x, y, out) { + var N = 2 * this.guessLen13b(x.length, y.length); + + var rbt = this.makeRBT(N); + + var _ = this.stub(N); + + var rws = new Array(N); + var rwst = new Array(N); + var iwst = new Array(N); + + var nrws = new Array(N); + var nrwst = new Array(N); + var niwst = new Array(N); + + var rmws = out.words; + rmws.length = N; + + this.convert13b(x.words, x.length, rws, N); + this.convert13b(y.words, y.length, nrws, N); + + this.transform(rws, _, rwst, iwst, N, rbt); + this.transform(nrws, _, nrwst, niwst, N, rbt); + + for (var i = 0; i < N; i++) { + var rx = rwst[i] * nrwst[i] - iwst[i] * niwst[i]; + iwst[i] = rwst[i] * niwst[i] + iwst[i] * nrwst[i]; + rwst[i] = rx; + } + + this.conjugate(rwst, iwst, N); + this.transform(rwst, iwst, rmws, _, N, rbt); + this.conjugate(rmws, _, N); + this.normalize13b(rmws, N); + + out.negative = x.negative ^ y.negative; + out.length = x.length + y.length; + return out.strip(); + }; + + // Multiply `this` by `num` + BN.prototype.mul = function mul (num) { + var out = new BN(null); + out.words = new Array(this.length + num.length); + return this.mulTo(num, out); + }; + + // Multiply employing FFT + BN.prototype.mulf = function mulf (num) { + var out = new BN(null); + out.words = new Array(this.length + num.length); + return jumboMulTo(this, num, out); + }; + + // In-place Multiplication + BN.prototype.imul = function imul (num) { + return this.clone().mulTo(num, this); + }; + + BN.prototype.imuln = function imuln (num) { + assert(typeof num === 'number'); + assert(num < 0x4000000); + + // Carry + var carry = 0; + for (var i = 0; i < this.length; i++) { + var w = (this.words[i] | 0) * num; + var lo = (w & 0x3ffffff) + (carry & 0x3ffffff); + carry >>= 26; + carry += (w / 0x4000000) | 0; + // NOTE: lo is 27bit maximum + carry += lo >>> 26; + this.words[i] = lo & 0x3ffffff; + } + + if (carry !== 0) { + this.words[i] = carry; + this.length++; + } + + return this; + }; + + BN.prototype.muln = function muln (num) { + return this.clone().imuln(num); + }; + + // `this` * `this` + BN.prototype.sqr = function sqr () { + return this.mul(this); + }; + + // `this` * `this` in-place + BN.prototype.isqr = function isqr () { + return this.imul(this.clone()); + }; + + // Math.pow(`this`, `num`) + BN.prototype.pow = function pow (num) { + var w = toBitArray(num); + if (w.length === 0) return new BN(1); + + // Skip leading zeroes + var res = this; + for (var i = 0; i < w.length; i++, res = res.sqr()) { + if (w[i] !== 0) break; + } + + if (++i < w.length) { + for (var q = res.sqr(); i < w.length; i++, q = q.sqr()) { + if (w[i] === 0) continue; + + res = res.mul(q); + } + } + + return res; + }; + + // Shift-left in-place + BN.prototype.iushln = function iushln (bits) { + assert(typeof bits === 'number' && bits >= 0); + var r = bits % 26; + var s = (bits - r) / 26; + var carryMask = (0x3ffffff >>> (26 - r)) << (26 - r); + var i; + + if (r !== 0) { + var carry = 0; + + for (i = 0; i < this.length; i++) { + var newCarry = this.words[i] & carryMask; + var c = ((this.words[i] | 0) - newCarry) << r; + this.words[i] = c | carry; + carry = newCarry >>> (26 - r); + } + + if (carry) { + this.words[i] = carry; + this.length++; + } + } + + if (s !== 0) { + for (i = this.length - 1; i >= 0; i--) { + this.words[i + s] = this.words[i]; + } + + for (i = 0; i < s; i++) { + this.words[i] = 0; + } + + this.length += s; + } + + return this.strip(); + }; + + BN.prototype.ishln = function ishln (bits) { + // TODO(indutny): implement me + assert(this.negative === 0); + return this.iushln(bits); + }; + + // Shift-right in-place + // NOTE: `hint` is a lowest bit before trailing zeroes + // NOTE: if `extended` is present - it will be filled with destroyed bits + BN.prototype.iushrn = function iushrn (bits, hint, extended) { + assert(typeof bits === 'number' && bits >= 0); + var h; + if (hint) { + h = (hint - (hint % 26)) / 26; + } else { + h = 0; + } + + var r = bits % 26; + var s = Math.min((bits - r) / 26, this.length); + var mask = 0x3ffffff ^ ((0x3ffffff >>> r) << r); + var maskedWords = extended; + + h -= s; + h = Math.max(0, h); + + // Extended mode, copy masked part + if (maskedWords) { + for (var i = 0; i < s; i++) { + maskedWords.words[i] = this.words[i]; + } + maskedWords.length = s; + } + + if (s === 0) { + // No-op, we should not move anything at all + } else if (this.length > s) { + this.length -= s; + for (i = 0; i < this.length; i++) { + this.words[i] = this.words[i + s]; + } + } else { + this.words[0] = 0; + this.length = 1; + } + + var carry = 0; + for (i = this.length - 1; i >= 0 && (carry !== 0 || i >= h); i--) { + var word = this.words[i] | 0; + this.words[i] = (carry << (26 - r)) | (word >>> r); + carry = word & mask; + } + + // Push carried bits as a mask + if (maskedWords && carry !== 0) { + maskedWords.words[maskedWords.length++] = carry; + } + + if (this.length === 0) { + this.words[0] = 0; + this.length = 1; + } + + return this.strip(); + }; + + BN.prototype.ishrn = function ishrn (bits, hint, extended) { + // TODO(indutny): implement me + assert(this.negative === 0); + return this.iushrn(bits, hint, extended); + }; + + // Shift-left + BN.prototype.shln = function shln (bits) { + return this.clone().ishln(bits); + }; + + BN.prototype.ushln = function ushln (bits) { + return this.clone().iushln(bits); + }; + + // Shift-right + BN.prototype.shrn = function shrn (bits) { + return this.clone().ishrn(bits); + }; + + BN.prototype.ushrn = function ushrn (bits) { + return this.clone().iushrn(bits); + }; + + // Test if n bit is set + BN.prototype.testn = function testn (bit) { + assert(typeof bit === 'number' && bit >= 0); + var r = bit % 26; + var s = (bit - r) / 26; + var q = 1 << r; + + // Fast case: bit is much higher than all existing words + if (this.length <= s) return false; + + // Check bit and return + var w = this.words[s]; + + return !!(w & q); + }; + + // Return only lowers bits of number (in-place) + BN.prototype.imaskn = function imaskn (bits) { + assert(typeof bits === 'number' && bits >= 0); + var r = bits % 26; + var s = (bits - r) / 26; + + assert(this.negative === 0, 'imaskn works only with positive numbers'); + + if (this.length <= s) { + return this; + } + + if (r !== 0) { + s++; + } + this.length = Math.min(s, this.length); + + if (r !== 0) { + var mask = 0x3ffffff ^ ((0x3ffffff >>> r) << r); + this.words[this.length - 1] &= mask; + } + + return this.strip(); + }; + + // Return only lowers bits of number + BN.prototype.maskn = function maskn (bits) { + return this.clone().imaskn(bits); + }; + + // Add plain number `num` to `this` + BN.prototype.iaddn = function iaddn (num) { + assert(typeof num === 'number'); + assert(num < 0x4000000); + if (num < 0) return this.isubn(-num); + + // Possible sign change + if (this.negative !== 0) { + if (this.length === 1 && (this.words[0] | 0) < num) { + this.words[0] = num - (this.words[0] | 0); + this.negative = 0; + return this; + } + + this.negative = 0; + this.isubn(num); + this.negative = 1; + return this; + } + + // Add without checks + return this._iaddn(num); + }; + + BN.prototype._iaddn = function _iaddn (num) { + this.words[0] += num; + + // Carry + for (var i = 0; i < this.length && this.words[i] >= 0x4000000; i++) { + this.words[i] -= 0x4000000; + if (i === this.length - 1) { + this.words[i + 1] = 1; + } else { + this.words[i + 1]++; + } + } + this.length = Math.max(this.length, i + 1); + + return this; + }; + + // Subtract plain number `num` from `this` + BN.prototype.isubn = function isubn (num) { + assert(typeof num === 'number'); + assert(num < 0x4000000); + if (num < 0) return this.iaddn(-num); + + if (this.negative !== 0) { + this.negative = 0; + this.iaddn(num); + this.negative = 1; + return this; + } + + this.words[0] -= num; + + if (this.length === 1 && this.words[0] < 0) { + this.words[0] = -this.words[0]; + this.negative = 1; + } else { + // Carry + for (var i = 0; i < this.length && this.words[i] < 0; i++) { + this.words[i] += 0x4000000; + this.words[i + 1] -= 1; + } + } + + return this.strip(); + }; + + BN.prototype.addn = function addn (num) { + return this.clone().iaddn(num); + }; + + BN.prototype.subn = function subn (num) { + return this.clone().isubn(num); + }; + + BN.prototype.iabs = function iabs () { + this.negative = 0; + + return this; + }; + + BN.prototype.abs = function abs () { + return this.clone().iabs(); + }; + + BN.prototype._ishlnsubmul = function _ishlnsubmul (num, mul, shift) { + var len = num.length + shift; + var i; + + this._expand(len); + + var w; + var carry = 0; + for (i = 0; i < num.length; i++) { + w = (this.words[i + shift] | 0) + carry; + var right = (num.words[i] | 0) * mul; + w -= right & 0x3ffffff; + carry = (w >> 26) - ((right / 0x4000000) | 0); + this.words[i + shift] = w & 0x3ffffff; + } + for (; i < this.length - shift; i++) { + w = (this.words[i + shift] | 0) + carry; + carry = w >> 26; + this.words[i + shift] = w & 0x3ffffff; + } + + if (carry === 0) return this.strip(); + + // Subtraction overflow + assert(carry === -1); + carry = 0; + for (i = 0; i < this.length; i++) { + w = -(this.words[i] | 0) + carry; + carry = w >> 26; + this.words[i] = w & 0x3ffffff; + } + this.negative = 1; + + return this.strip(); + }; + + BN.prototype._wordDiv = function _wordDiv (num, mode) { + var shift = this.length - num.length; + + var a = this.clone(); + var b = num; + + // Normalize + var bhi = b.words[b.length - 1] | 0; + var bhiBits = this._countBits(bhi); + shift = 26 - bhiBits; + if (shift !== 0) { + b = b.ushln(shift); + a.iushln(shift); + bhi = b.words[b.length - 1] | 0; + } + + // Initialize quotient + var m = a.length - b.length; + var q; + + if (mode !== 'mod') { + q = new BN(null); + q.length = m + 1; + q.words = new Array(q.length); + for (var i = 0; i < q.length; i++) { + q.words[i] = 0; + } + } + + var diff = a.clone()._ishlnsubmul(b, 1, m); + if (diff.negative === 0) { + a = diff; + if (q) { + q.words[m] = 1; + } + } + + for (var j = m - 1; j >= 0; j--) { + var qj = (a.words[b.length + j] | 0) * 0x4000000 + + (a.words[b.length + j - 1] | 0); + + // NOTE: (qj / bhi) is (0x3ffffff * 0x4000000 + 0x3ffffff) / 0x2000000 max + // (0x7ffffff) + qj = Math.min((qj / bhi) | 0, 0x3ffffff); + + a._ishlnsubmul(b, qj, j); + while (a.negative !== 0) { + qj--; + a.negative = 0; + a._ishlnsubmul(b, 1, j); + if (!a.isZero()) { + a.negative ^= 1; + } + } + if (q) { + q.words[j] = qj; + } + } + if (q) { + q.strip(); + } + a.strip(); + + // Denormalize + if (mode !== 'div' && shift !== 0) { + a.iushrn(shift); + } + + return { + div: q || null, + mod: a + }; + }; + + // NOTE: 1) `mode` can be set to `mod` to request mod only, + // to `div` to request div only, or be absent to + // request both div & mod + // 2) `positive` is true if unsigned mod is requested + BN.prototype.divmod = function divmod (num, mode, positive) { + assert(!num.isZero()); + + if (this.isZero()) { + return { + div: new BN(0), + mod: new BN(0) + }; + } + + var div, mod, res; + if (this.negative !== 0 && num.negative === 0) { + res = this.neg().divmod(num, mode); + + if (mode !== 'mod') { + div = res.div.neg(); + } + + if (mode !== 'div') { + mod = res.mod.neg(); + if (positive && mod.negative !== 0) { + mod.iadd(num); + } + } + + return { + div: div, + mod: mod + }; + } + + if (this.negative === 0 && num.negative !== 0) { + res = this.divmod(num.neg(), mode); + + if (mode !== 'mod') { + div = res.div.neg(); + } + + return { + div: div, + mod: res.mod + }; + } + + if ((this.negative & num.negative) !== 0) { + res = this.neg().divmod(num.neg(), mode); + + if (mode !== 'div') { + mod = res.mod.neg(); + if (positive && mod.negative !== 0) { + mod.isub(num); + } + } + + return { + div: res.div, + mod: mod + }; + } + + // Both numbers are positive at this point + + // Strip both numbers to approximate shift value + if (num.length > this.length || this.cmp(num) < 0) { + return { + div: new BN(0), + mod: this + }; + } + + // Very short reduction + if (num.length === 1) { + if (mode === 'div') { + return { + div: this.divn(num.words[0]), + mod: null + }; + } + + if (mode === 'mod') { + return { + div: null, + mod: new BN(this.modn(num.words[0])) + }; + } + + return { + div: this.divn(num.words[0]), + mod: new BN(this.modn(num.words[0])) + }; + } + + return this._wordDiv(num, mode); + }; + + // Find `this` / `num` + BN.prototype.div = function div (num) { + return this.divmod(num, 'div', false).div; + }; + + // Find `this` % `num` + BN.prototype.mod = function mod (num) { + return this.divmod(num, 'mod', false).mod; + }; + + BN.prototype.umod = function umod (num) { + return this.divmod(num, 'mod', true).mod; + }; + + // Find Round(`this` / `num`) + BN.prototype.divRound = function divRound (num) { + var dm = this.divmod(num); + + // Fast case - exact division + if (dm.mod.isZero()) return dm.div; + + var mod = dm.div.negative !== 0 ? dm.mod.isub(num) : dm.mod; + + var half = num.ushrn(1); + var r2 = num.andln(1); + var cmp = mod.cmp(half); + + // Round down + if (cmp < 0 || r2 === 1 && cmp === 0) return dm.div; + + // Round up + return dm.div.negative !== 0 ? dm.div.isubn(1) : dm.div.iaddn(1); + }; + + BN.prototype.modn = function modn (num) { + assert(num <= 0x3ffffff); + var p = (1 << 26) % num; + + var acc = 0; + for (var i = this.length - 1; i >= 0; i--) { + acc = (p * acc + (this.words[i] | 0)) % num; + } + + return acc; + }; + + // In-place division by number + BN.prototype.idivn = function idivn (num) { + assert(num <= 0x3ffffff); + + var carry = 0; + for (var i = this.length - 1; i >= 0; i--) { + var w = (this.words[i] | 0) + carry * 0x4000000; + this.words[i] = (w / num) | 0; + carry = w % num; + } + + return this.strip(); + }; + + BN.prototype.divn = function divn (num) { + return this.clone().idivn(num); + }; + + BN.prototype.egcd = function egcd (p) { + assert(p.negative === 0); + assert(!p.isZero()); + + var x = this; + var y = p.clone(); + + if (x.negative !== 0) { + x = x.umod(p); + } else { + x = x.clone(); + } + + // A * x + B * y = x + var A = new BN(1); + var B = new BN(0); + + // C * x + D * y = y + var C = new BN(0); + var D = new BN(1); + + var g = 0; + + while (x.isEven() && y.isEven()) { + x.iushrn(1); + y.iushrn(1); + ++g; + } + + var yp = y.clone(); + var xp = x.clone(); + + while (!x.isZero()) { + for (var i = 0, im = 1; (x.words[0] & im) === 0 && i < 26; ++i, im <<= 1); + if (i > 0) { + x.iushrn(i); + while (i-- > 0) { + if (A.isOdd() || B.isOdd()) { + A.iadd(yp); + B.isub(xp); + } + + A.iushrn(1); + B.iushrn(1); + } + } + + for (var j = 0, jm = 1; (y.words[0] & jm) === 0 && j < 26; ++j, jm <<= 1); + if (j > 0) { + y.iushrn(j); + while (j-- > 0) { + if (C.isOdd() || D.isOdd()) { + C.iadd(yp); + D.isub(xp); + } + + C.iushrn(1); + D.iushrn(1); + } + } + + if (x.cmp(y) >= 0) { + x.isub(y); + A.isub(C); + B.isub(D); + } else { + y.isub(x); + C.isub(A); + D.isub(B); + } + } + + return { + a: C, + b: D, + gcd: y.iushln(g) + }; + }; + + // This is reduced incarnation of the binary EEA + // above, designated to invert members of the + // _prime_ fields F(p) at a maximal speed + BN.prototype._invmp = function _invmp (p) { + assert(p.negative === 0); + assert(!p.isZero()); + + var a = this; + var b = p.clone(); + + if (a.negative !== 0) { + a = a.umod(p); + } else { + a = a.clone(); + } + + var x1 = new BN(1); + var x2 = new BN(0); + + var delta = b.clone(); + + while (a.cmpn(1) > 0 && b.cmpn(1) > 0) { + for (var i = 0, im = 1; (a.words[0] & im) === 0 && i < 26; ++i, im <<= 1); + if (i > 0) { + a.iushrn(i); + while (i-- > 0) { + if (x1.isOdd()) { + x1.iadd(delta); + } + + x1.iushrn(1); + } + } + + for (var j = 0, jm = 1; (b.words[0] & jm) === 0 && j < 26; ++j, jm <<= 1); + if (j > 0) { + b.iushrn(j); + while (j-- > 0) { + if (x2.isOdd()) { + x2.iadd(delta); + } + + x2.iushrn(1); + } + } + + if (a.cmp(b) >= 0) { + a.isub(b); + x1.isub(x2); + } else { + b.isub(a); + x2.isub(x1); + } + } + + var res; + if (a.cmpn(1) === 0) { + res = x1; + } else { + res = x2; + } + + if (res.cmpn(0) < 0) { + res.iadd(p); + } + + return res; + }; + + BN.prototype.gcd = function gcd (num) { + if (this.isZero()) return num.abs(); + if (num.isZero()) return this.abs(); + + var a = this.clone(); + var b = num.clone(); + a.negative = 0; + b.negative = 0; + + // Remove common factor of two + for (var shift = 0; a.isEven() && b.isEven(); shift++) { + a.iushrn(1); + b.iushrn(1); + } + + do { + while (a.isEven()) { + a.iushrn(1); + } + while (b.isEven()) { + b.iushrn(1); + } + + var r = a.cmp(b); + if (r < 0) { + // Swap `a` and `b` to make `a` always bigger than `b` + var t = a; + a = b; + b = t; + } else if (r === 0 || b.cmpn(1) === 0) { + break; + } + + a.isub(b); + } while (true); + + return b.iushln(shift); + }; + + // Invert number in the field F(num) + BN.prototype.invm = function invm (num) { + return this.egcd(num).a.umod(num); + }; + + BN.prototype.isEven = function isEven () { + return (this.words[0] & 1) === 0; + }; + + BN.prototype.isOdd = function isOdd () { + return (this.words[0] & 1) === 1; + }; + + // And first word and num + BN.prototype.andln = function andln (num) { + return this.words[0] & num; + }; + + // Increment at the bit position in-line + BN.prototype.bincn = function bincn (bit) { + assert(typeof bit === 'number'); + var r = bit % 26; + var s = (bit - r) / 26; + var q = 1 << r; + + // Fast case: bit is much higher than all existing words + if (this.length <= s) { + this._expand(s + 1); + this.words[s] |= q; + return this; + } + + // Add bit and propagate, if needed + var carry = q; + for (var i = s; carry !== 0 && i < this.length; i++) { + var w = this.words[i] | 0; + w += carry; + carry = w >>> 26; + w &= 0x3ffffff; + this.words[i] = w; + } + if (carry !== 0) { + this.words[i] = carry; + this.length++; + } + return this; + }; + + BN.prototype.isZero = function isZero () { + return this.length === 1 && this.words[0] === 0; + }; + + BN.prototype.cmpn = function cmpn (num) { + var negative = num < 0; + + if (this.negative !== 0 && !negative) return -1; + if (this.negative === 0 && negative) return 1; + + this.strip(); + + var res; + if (this.length > 1) { + res = 1; + } else { + if (negative) { + num = -num; + } + + assert(num <= 0x3ffffff, 'Number is too big'); + + var w = this.words[0] | 0; + res = w === num ? 0 : w < num ? -1 : 1; + } + if (this.negative !== 0) return -res | 0; + return res; + }; + + // Compare two numbers and return: + // 1 - if `this` > `num` + // 0 - if `this` == `num` + // -1 - if `this` < `num` + BN.prototype.cmp = function cmp (num) { + if (this.negative !== 0 && num.negative === 0) return -1; + if (this.negative === 0 && num.negative !== 0) return 1; + + var res = this.ucmp(num); + if (this.negative !== 0) return -res | 0; + return res; + }; + + // Unsigned comparison + BN.prototype.ucmp = function ucmp (num) { + // At this point both numbers have the same sign + if (this.length > num.length) return 1; + if (this.length < num.length) return -1; + + var res = 0; + for (var i = this.length - 1; i >= 0; i--) { + var a = this.words[i] | 0; + var b = num.words[i] | 0; + + if (a === b) continue; + if (a < b) { + res = -1; + } else if (a > b) { + res = 1; + } + break; + } + return res; + }; + + BN.prototype.gtn = function gtn (num) { + return this.cmpn(num) === 1; + }; + + BN.prototype.gt = function gt (num) { + return this.cmp(num) === 1; + }; + + BN.prototype.gten = function gten (num) { + return this.cmpn(num) >= 0; + }; + + BN.prototype.gte = function gte (num) { + return this.cmp(num) >= 0; + }; + + BN.prototype.ltn = function ltn (num) { + return this.cmpn(num) === -1; + }; + + BN.prototype.lt = function lt (num) { + return this.cmp(num) === -1; + }; + + BN.prototype.lten = function lten (num) { + return this.cmpn(num) <= 0; + }; + + BN.prototype.lte = function lte (num) { + return this.cmp(num) <= 0; + }; + + BN.prototype.eqn = function eqn (num) { + return this.cmpn(num) === 0; + }; + + BN.prototype.eq = function eq (num) { + return this.cmp(num) === 0; + }; + + // + // A reduce context, could be using montgomery or something better, depending + // on the `m` itself. + // + BN.red = function red (num) { + return new Red(num); + }; + + BN.prototype.toRed = function toRed (ctx) { + assert(!this.red, 'Already a number in reduction context'); + assert(this.negative === 0, 'red works only with positives'); + return ctx.convertTo(this)._forceRed(ctx); + }; + + BN.prototype.fromRed = function fromRed () { + assert(this.red, 'fromRed works only with numbers in reduction context'); + return this.red.convertFrom(this); + }; + + BN.prototype._forceRed = function _forceRed (ctx) { + this.red = ctx; + return this; + }; + + BN.prototype.forceRed = function forceRed (ctx) { + assert(!this.red, 'Already a number in reduction context'); + return this._forceRed(ctx); + }; + + BN.prototype.redAdd = function redAdd (num) { + assert(this.red, 'redAdd works only with red numbers'); + return this.red.add(this, num); + }; + + BN.prototype.redIAdd = function redIAdd (num) { + assert(this.red, 'redIAdd works only with red numbers'); + return this.red.iadd(this, num); + }; + + BN.prototype.redSub = function redSub (num) { + assert(this.red, 'redSub works only with red numbers'); + return this.red.sub(this, num); + }; + + BN.prototype.redISub = function redISub (num) { + assert(this.red, 'redISub works only with red numbers'); + return this.red.isub(this, num); + }; + + BN.prototype.redShl = function redShl (num) { + assert(this.red, 'redShl works only with red numbers'); + return this.red.shl(this, num); + }; + + BN.prototype.redMul = function redMul (num) { + assert(this.red, 'redMul works only with red numbers'); + this.red._verify2(this, num); + return this.red.mul(this, num); + }; + + BN.prototype.redIMul = function redIMul (num) { + assert(this.red, 'redMul works only with red numbers'); + this.red._verify2(this, num); + return this.red.imul(this, num); + }; + + BN.prototype.redSqr = function redSqr () { + assert(this.red, 'redSqr works only with red numbers'); + this.red._verify1(this); + return this.red.sqr(this); + }; + + BN.prototype.redISqr = function redISqr () { + assert(this.red, 'redISqr works only with red numbers'); + this.red._verify1(this); + return this.red.isqr(this); + }; + + // Square root over p + BN.prototype.redSqrt = function redSqrt () { + assert(this.red, 'redSqrt works only with red numbers'); + this.red._verify1(this); + return this.red.sqrt(this); + }; + + BN.prototype.redInvm = function redInvm () { + assert(this.red, 'redInvm works only with red numbers'); + this.red._verify1(this); + return this.red.invm(this); + }; + + // Return negative clone of `this` % `red modulo` + BN.prototype.redNeg = function redNeg () { + assert(this.red, 'redNeg works only with red numbers'); + this.red._verify1(this); + return this.red.neg(this); + }; + + BN.prototype.redPow = function redPow (num) { + assert(this.red && !num.red, 'redPow(normalNum)'); + this.red._verify1(this); + return this.red.pow(this, num); + }; + + // Prime numbers with efficient reduction + var primes = { + k256: null, + p224: null, + p192: null, + p25519: null + }; + + // Pseudo-Mersenne prime + function MPrime (name, p) { + // P = 2 ^ N - K + this.name = name; + this.p = new BN(p, 16); + this.n = this.p.bitLength(); + this.k = new BN(1).iushln(this.n).isub(this.p); + + this.tmp = this._tmp(); + } + + MPrime.prototype._tmp = function _tmp () { + var tmp = new BN(null); + tmp.words = new Array(Math.ceil(this.n / 13)); + return tmp; + }; + + MPrime.prototype.ireduce = function ireduce (num) { + // Assumes that `num` is less than `P^2` + // num = HI * (2 ^ N - K) + HI * K + LO = HI * K + LO (mod P) + var r = num; + var rlen; + + do { + this.split(r, this.tmp); + r = this.imulK(r); + r = r.iadd(this.tmp); + rlen = r.bitLength(); + } while (rlen > this.n); + + var cmp = rlen < this.n ? -1 : r.ucmp(this.p); + if (cmp === 0) { + r.words[0] = 0; + r.length = 1; + } else if (cmp > 0) { + r.isub(this.p); + } else { + if (r.strip !== undefined) { + // r is BN v4 instance + r.strip(); + } else { + // r is BN v5 instance + r._strip(); + } + } + + return r; + }; + + MPrime.prototype.split = function split (input, out) { + input.iushrn(this.n, 0, out); + }; + + MPrime.prototype.imulK = function imulK (num) { + return num.imul(this.k); + }; + + function K256 () { + MPrime.call( + this, + 'k256', + 'ffffffff ffffffff ffffffff ffffffff ffffffff ffffffff fffffffe fffffc2f'); + } + inherits(K256, MPrime); + + K256.prototype.split = function split (input, output) { + // 256 = 9 * 26 + 22 + var mask = 0x3fffff; + + var outLen = Math.min(input.length, 9); + for (var i = 0; i < outLen; i++) { + output.words[i] = input.words[i]; + } + output.length = outLen; + + if (input.length <= 9) { + input.words[0] = 0; + input.length = 1; + return; + } + + // Shift by 9 limbs + var prev = input.words[9]; + output.words[output.length++] = prev & mask; + + for (i = 10; i < input.length; i++) { + var next = input.words[i] | 0; + input.words[i - 10] = ((next & mask) << 4) | (prev >>> 22); + prev = next; + } + prev >>>= 22; + input.words[i - 10] = prev; + if (prev === 0 && input.length > 10) { + input.length -= 10; + } else { + input.length -= 9; + } + }; + + K256.prototype.imulK = function imulK (num) { + // K = 0x1000003d1 = [ 0x40, 0x3d1 ] + num.words[num.length] = 0; + num.words[num.length + 1] = 0; + num.length += 2; + + // bounded at: 0x40 * 0x3ffffff + 0x3d0 = 0x100000390 + var lo = 0; + for (var i = 0; i < num.length; i++) { + var w = num.words[i] | 0; + lo += w * 0x3d1; + num.words[i] = lo & 0x3ffffff; + lo = w * 0x40 + ((lo / 0x4000000) | 0); + } + + // Fast length reduction + if (num.words[num.length - 1] === 0) { + num.length--; + if (num.words[num.length - 1] === 0) { + num.length--; + } + } + return num; + }; + + function P224 () { + MPrime.call( + this, + 'p224', + 'ffffffff ffffffff ffffffff ffffffff 00000000 00000000 00000001'); + } + inherits(P224, MPrime); + + function P192 () { + MPrime.call( + this, + 'p192', + 'ffffffff ffffffff ffffffff fffffffe ffffffff ffffffff'); + } + inherits(P192, MPrime); + + function P25519 () { + // 2 ^ 255 - 19 + MPrime.call( + this, + '25519', + '7fffffffffffffff ffffffffffffffff ffffffffffffffff ffffffffffffffed'); + } + inherits(P25519, MPrime); + + P25519.prototype.imulK = function imulK (num) { + // K = 0x13 + var carry = 0; + for (var i = 0; i < num.length; i++) { + var hi = (num.words[i] | 0) * 0x13 + carry; + var lo = hi & 0x3ffffff; + hi >>>= 26; + + num.words[i] = lo; + carry = hi; + } + if (carry !== 0) { + num.words[num.length++] = carry; + } + return num; + }; + + // Exported mostly for testing purposes, use plain name instead + BN._prime = function prime (name) { + // Cached version of prime + if (primes[name]) return primes[name]; + + var prime; + if (name === 'k256') { + prime = new K256(); + } else if (name === 'p224') { + prime = new P224(); + } else if (name === 'p192') { + prime = new P192(); + } else if (name === 'p25519') { + prime = new P25519(); + } else { + throw new Error('Unknown prime ' + name); + } + primes[name] = prime; + + return prime; + }; + + // + // Base reduction engine + // + function Red (m) { + if (typeof m === 'string') { + var prime = BN._prime(m); + this.m = prime.p; + this.prime = prime; + } else { + assert(m.gtn(1), 'modulus must be greater than 1'); + this.m = m; + this.prime = null; + } + } + + Red.prototype._verify1 = function _verify1 (a) { + assert(a.negative === 0, 'red works only with positives'); + assert(a.red, 'red works only with red numbers'); + }; + + Red.prototype._verify2 = function _verify2 (a, b) { + assert((a.negative | b.negative) === 0, 'red works only with positives'); + assert(a.red && a.red === b.red, + 'red works only with red numbers'); + }; + + Red.prototype.imod = function imod (a) { + if (this.prime) return this.prime.ireduce(a)._forceRed(this); + return a.umod(this.m)._forceRed(this); + }; + + Red.prototype.neg = function neg (a) { + if (a.isZero()) { + return a.clone(); + } + + return this.m.sub(a)._forceRed(this); + }; + + Red.prototype.add = function add (a, b) { + this._verify2(a, b); + + var res = a.add(b); + if (res.cmp(this.m) >= 0) { + res.isub(this.m); + } + return res._forceRed(this); + }; + + Red.prototype.iadd = function iadd (a, b) { + this._verify2(a, b); + + var res = a.iadd(b); + if (res.cmp(this.m) >= 0) { + res.isub(this.m); + } + return res; + }; + + Red.prototype.sub = function sub (a, b) { + this._verify2(a, b); + + var res = a.sub(b); + if (res.cmpn(0) < 0) { + res.iadd(this.m); + } + return res._forceRed(this); + }; + + Red.prototype.isub = function isub (a, b) { + this._verify2(a, b); + + var res = a.isub(b); + if (res.cmpn(0) < 0) { + res.iadd(this.m); + } + return res; + }; + + Red.prototype.shl = function shl (a, num) { + this._verify1(a); + return this.imod(a.ushln(num)); + }; + + Red.prototype.imul = function imul (a, b) { + this._verify2(a, b); + return this.imod(a.imul(b)); + }; + + Red.prototype.mul = function mul (a, b) { + this._verify2(a, b); + return this.imod(a.mul(b)); + }; + + Red.prototype.isqr = function isqr (a) { + return this.imul(a, a.clone()); + }; + + Red.prototype.sqr = function sqr (a) { + return this.mul(a, a); + }; + + Red.prototype.sqrt = function sqrt (a) { + if (a.isZero()) return a.clone(); + + var mod3 = this.m.andln(3); + assert(mod3 % 2 === 1); + + // Fast case + if (mod3 === 3) { + var pow = this.m.add(new BN(1)).iushrn(2); + return this.pow(a, pow); + } + + // Tonelli-Shanks algorithm (Totally unoptimized and slow) + // + // Find Q and S, that Q * 2 ^ S = (P - 1) + var q = this.m.subn(1); + var s = 0; + while (!q.isZero() && q.andln(1) === 0) { + s++; + q.iushrn(1); + } + assert(!q.isZero()); + + var one = new BN(1).toRed(this); + var nOne = one.redNeg(); + + // Find quadratic non-residue + // NOTE: Max is such because of generalized Riemann hypothesis. + var lpow = this.m.subn(1).iushrn(1); + var z = this.m.bitLength(); + z = new BN(2 * z * z).toRed(this); + + while (this.pow(z, lpow).cmp(nOne) !== 0) { + z.redIAdd(nOne); + } + + var c = this.pow(z, q); + var r = this.pow(a, q.addn(1).iushrn(1)); + var t = this.pow(a, q); + var m = s; + while (t.cmp(one) !== 0) { + var tmp = t; + for (var i = 0; tmp.cmp(one) !== 0; i++) { + tmp = tmp.redSqr(); + } + assert(i < m); + var b = this.pow(c, new BN(1).iushln(m - i - 1)); + + r = r.redMul(b); + c = b.redSqr(); + t = t.redMul(c); + m = i; + } + + return r; + }; + + Red.prototype.invm = function invm (a) { + var inv = a._invmp(this.m); + if (inv.negative !== 0) { + inv.negative = 0; + return this.imod(inv).redNeg(); + } else { + return this.imod(inv); + } + }; + + Red.prototype.pow = function pow (a, num) { + if (num.isZero()) return new BN(1).toRed(this); + if (num.cmpn(1) === 0) return a.clone(); + + var windowSize = 4; + var wnd = new Array(1 << windowSize); + wnd[0] = new BN(1).toRed(this); + wnd[1] = a; + for (var i = 2; i < wnd.length; i++) { + wnd[i] = this.mul(wnd[i - 1], a); + } + + var res = wnd[0]; + var current = 0; + var currentLen = 0; + var start = num.bitLength() % 26; + if (start === 0) { + start = 26; + } + + for (i = num.length - 1; i >= 0; i--) { + var word = num.words[i]; + for (var j = start - 1; j >= 0; j--) { + var bit = (word >> j) & 1; + if (res !== wnd[0]) { + res = this.sqr(res); + } + + if (bit === 0 && current === 0) { + currentLen = 0; + continue; + } + + current <<= 1; + current |= bit; + currentLen++; + if (currentLen !== windowSize && (i !== 0 || j !== 0)) continue; + + res = this.mul(res, wnd[current]); + currentLen = 0; + current = 0; + } + start = 26; + } + + return res; + }; + + Red.prototype.convertTo = function convertTo (num) { + var r = num.umod(this.m); + + return r === num ? r.clone() : r; + }; + + Red.prototype.convertFrom = function convertFrom (num) { + var res = num.clone(); + res.red = null; + return res; + }; + + // + // Montgomery method engine + // + + BN.mont = function mont (num) { + return new Mont(num); + }; + + function Mont (m) { + Red.call(this, m); + + this.shift = this.m.bitLength(); + if (this.shift % 26 !== 0) { + this.shift += 26 - (this.shift % 26); + } + + this.r = new BN(1).iushln(this.shift); + this.r2 = this.imod(this.r.sqr()); + this.rinv = this.r._invmp(this.m); + + this.minv = this.rinv.mul(this.r).isubn(1).div(this.m); + this.minv = this.minv.umod(this.r); + this.minv = this.r.sub(this.minv); + } + inherits(Mont, Red); + + Mont.prototype.convertTo = function convertTo (num) { + return this.imod(num.ushln(this.shift)); + }; + + Mont.prototype.convertFrom = function convertFrom (num) { + var r = this.imod(num.mul(this.rinv)); + r.red = null; + return r; + }; + + Mont.prototype.imul = function imul (a, b) { + if (a.isZero() || b.isZero()) { + a.words[0] = 0; + a.length = 1; + return a; + } + + var t = a.imul(b); + var c = t.maskn(this.shift).mul(this.minv).imaskn(this.shift).mul(this.m); + var u = t.isub(c).iushrn(this.shift); + var res = u; + + if (u.cmp(this.m) >= 0) { + res = u.isub(this.m); + } else if (u.cmpn(0) < 0) { + res = u.iadd(this.m); + } + + return res._forceRed(this); + }; + + Mont.prototype.mul = function mul (a, b) { + if (a.isZero() || b.isZero()) return new BN(0)._forceRed(this); + + var t = a.mul(b); + var c = t.maskn(this.shift).mul(this.minv).imaskn(this.shift).mul(this.m); + var u = t.isub(c).iushrn(this.shift); + var res = u; + if (u.cmp(this.m) >= 0) { + res = u.isub(this.m); + } else if (u.cmpn(0) < 0) { + res = u.iadd(this.m); + } + + return res._forceRed(this); + }; + + Mont.prototype.invm = function invm (a) { + // (AR)^-1 * R^2 = (A^-1 * R^-1) * R^2 = A^-1 * R + var res = this.imod(a._invmp(this.m).mul(this.r2)); + return res._forceRed(this); + }; +})(typeof module === 'undefined' || module, this); diff --git a/node_modules/elliptic/node_modules/bn.js/package.json b/node_modules/elliptic/node_modules/bn.js/package.json new file mode 100644 index 0000000..5e7465f --- /dev/null +++ b/node_modules/elliptic/node_modules/bn.js/package.json @@ -0,0 +1,64 @@ +{ + "_from": "bn.js@^4.4.0", + "_id": "bn.js@4.11.9", + "_inBundle": false, + "_integrity": "sha512-E6QoYqCKZfgatHTdHzs1RRKP7ip4vvm+EyRUeE2RF0NblwVvb0p6jSVeNTOFxPn26QXN2o6SMfNxKp6kU8zQaw==", + "_location": "/elliptic/bn.js", + "_phantomChildren": {}, + "_requested": { + "type": "range", + "registry": true, + "raw": "bn.js@^4.4.0", + "name": "bn.js", + "escapedName": "bn.js", + "rawSpec": "^4.4.0", + "saveSpec": null, + "fetchSpec": "^4.4.0" + }, + "_requiredBy": [ + "/elliptic" + ], + "_resolved": "https://registry.npmjs.org/bn.js/-/bn.js-4.11.9.tgz", + "_shasum": "26d556829458f9d1e81fc48952493d0ba3507828", + "_spec": "bn.js@^4.4.0", + "_where": "/home/pruss/Dev/3-minute-website/node_modules/elliptic", + "author": { + "name": "Fedor Indutny", + "email": "fedor@indutny.com" + }, + "browser": { + "buffer": false + }, + "bugs": { + "url": "https://github.com/indutny/bn.js/issues" + }, + "bundleDependencies": false, + "deprecated": false, + "description": "Big number implementation in pure javascript", + "devDependencies": { + "istanbul": "^0.3.5", + "mocha": "^2.1.0", + "semistandard": "^7.0.4" + }, + "homepage": "https://github.com/indutny/bn.js", + "keywords": [ + "BN", + "BigNum", + "Big number", + "Modulo", + "Montgomery" + ], + "license": "MIT", + "main": "lib/bn.js", + "name": "bn.js", + "repository": { + "type": "git", + "url": "git+ssh://git@github.com/indutny/bn.js.git" + }, + "scripts": { + "lint": "semistandard", + "test": "npm run lint && npm run unit", + "unit": "mocha --reporter=spec test/*-test.js" + }, + "version": "4.11.9" +} diff --git a/node_modules/elliptic/node_modules/bn.js/util/genCombMulTo.js b/node_modules/elliptic/node_modules/bn.js/util/genCombMulTo.js new file mode 100644 index 0000000..8b456c7 --- /dev/null +++ b/node_modules/elliptic/node_modules/bn.js/util/genCombMulTo.js @@ -0,0 +1,65 @@ +'use strict'; + +// NOTE: This could be potentionally used to generate loop-less multiplications +function genCombMulTo (alen, blen) { + var len = alen + blen - 1; + var src = [ + 'var a = self.words;', + 'var b = num.words;', + 'var o = out.words;', + 'var c = 0;', + 'var lo;', + 'var mid;', + 'var hi;' + ]; + for (var i = 0; i < alen; i++) { + src.push('var a' + i + ' = a[' + i + '] | 0;'); + src.push('var al' + i + ' = a' + i + ' & 0x1fff;'); + src.push('var ah' + i + ' = a' + i + ' >>> 13;'); + } + for (i = 0; i < blen; i++) { + src.push('var b' + i + ' = b[' + i + '] | 0;'); + src.push('var bl' + i + ' = b' + i + ' & 0x1fff;'); + src.push('var bh' + i + ' = b' + i + ' >>> 13;'); + } + src.push(''); + src.push('out.negative = self.negative ^ num.negative;'); + src.push('out.length = ' + len + ';'); + + for (var k = 0; k < len; k++) { + var minJ = Math.max(0, k - alen + 1); + var maxJ = Math.min(k, blen - 1); + + src.push('\/* k = ' + k + ' *\/'); + src.push('var w' + k + ' = c;'); + src.push('c = 0;'); + for (var j = minJ; j <= maxJ; j++) { + i = k - j; + + src.push('lo = Math.imul(al' + i + ', bl' + j + ');'); + src.push('mid = Math.imul(al' + i + ', bh' + j + ');'); + src.push('mid = (mid + Math.imul(ah' + i + ', bl' + j + ')) | 0;'); + src.push('hi = Math.imul(ah' + i + ', bh' + j + ');'); + + src.push('w' + k + ' = (w' + k + ' + lo) | 0;'); + src.push('w' + k + ' = (w' + k + ' + ((mid & 0x1fff) << 13)) | 0;'); + src.push('c = (c + hi) | 0;'); + src.push('c = (c + (mid >>> 13)) | 0;'); + src.push('c = (c + (w' + k + ' >>> 26)) | 0;'); + src.push('w' + k + ' &= 0x3ffffff;'); + } + } + // Store in separate step for better memory access + for (k = 0; k < len; k++) { + src.push('o[' + k + '] = w' + k + ';'); + } + src.push('if (c !== 0) {', + ' o[' + k + '] = c;', + ' out.length++;', + '}', + 'return out;'); + + return src.join('\n'); +} + +console.log(genCombMulTo(10, 10)); diff --git a/node_modules/elliptic/node_modules/bn.js/util/genCombMulTo10.js b/node_modules/elliptic/node_modules/bn.js/util/genCombMulTo10.js new file mode 100644 index 0000000..cf2e6e8 --- /dev/null +++ b/node_modules/elliptic/node_modules/bn.js/util/genCombMulTo10.js @@ -0,0 +1,65 @@ +'use strict'; + +function genCombMulTo (alen, blen) { + var len = alen + blen - 1; + var src = [ + 'var a = self.words;', + 'var b = num.words;', + 'var o = out.words;', + 'var c = 0;', + 'var lo;', + 'var mid;', + 'var hi;' + ]; + for (var i = 0; i < alen; i++) { + src.push('var a' + i + ' = a[' + i + '] | 0;'); + src.push('var al' + i + ' = a' + i + ' & 0x1fff;'); + src.push('var ah' + i + ' = a' + i + ' >>> 13;'); + } + for (i = 0; i < blen; i++) { + src.push('var b' + i + ' = b[' + i + '] | 0;'); + src.push('var bl' + i + ' = b' + i + ' & 0x1fff;'); + src.push('var bh' + i + ' = b' + i + ' >>> 13;'); + } + src.push(''); + src.push('out.negative = self.negative ^ num.negative;'); + src.push('out.length = ' + len + ';'); + + for (var k = 0; k < len; k++) { + var minJ = Math.max(0, k - alen + 1); + var maxJ = Math.min(k, blen - 1); + + src.push('\/* k = ' + k + ' *\/'); + src.push('lo = Math.imul(al' + (k - minJ) + ', bl' + minJ + ');'); + src.push('mid = Math.imul(al' + (k - minJ) + ', bh' + minJ + ');'); + src.push( + 'mid = (mid + Math.imul(ah' + (k - minJ) + ', bl' + minJ + ')) | 0;'); + src.push('hi = Math.imul(ah' + (k - minJ) + ', bh' + minJ + ');'); + + for (var j = minJ + 1; j <= maxJ; j++) { + i = k - j; + + src.push('lo = (lo + Math.imul(al' + i + ', bl' + j + ')) | 0;'); + src.push('mid = (mid + Math.imul(al' + i + ', bh' + j + ')) | 0;'); + src.push('mid = (mid + Math.imul(ah' + i + ', bl' + j + ')) | 0;'); + src.push('hi = (hi + Math.imul(ah' + i + ', bh' + j + ')) | 0;'); + } + + src.push('var w' + k + ' = (((c + lo) | 0) + ((mid & 0x1fff) << 13)) | 0;'); + src.push('c = (((hi + (mid >>> 13)) | 0) + (w' + k + ' >>> 26)) | 0;'); + src.push('w' + k + ' &= 0x3ffffff;'); + } + // Store in separate step for better memory access + for (k = 0; k < len; k++) { + src.push('o[' + k + '] = w' + k + ';'); + } + src.push('if (c !== 0) {', + ' o[' + k + '] = c;', + ' out.length++;', + '}', + 'return out;'); + + return src.join('\n'); +} + +console.log(genCombMulTo(10, 10)); diff --git a/node_modules/elliptic/package.json b/node_modules/elliptic/package.json new file mode 100644 index 0000000..f360e5c --- /dev/null +++ b/node_modules/elliptic/package.json @@ -0,0 +1,87 @@ +{ + "_from": "elliptic@^6.5.3", + "_id": "elliptic@6.5.3", + "_inBundle": false, + "_integrity": "sha512-IMqzv5wNQf+E6aHeIqATs0tOLeOTwj1QKbRcS3jBbYkl5oLAserA8yJTT7/VyHUYG91PRmPyeQDObKLPpeS4dw==", + "_location": "/elliptic", + "_phantomChildren": {}, + "_requested": { + "type": "range", + "registry": true, + "raw": "elliptic@^6.5.3", + "name": "elliptic", + "escapedName": "elliptic", + "rawSpec": "^6.5.3", + "saveSpec": null, + "fetchSpec": "^6.5.3" + }, + "_requiredBy": [ + "/browserify-sign", + "/create-ecdh" + ], + "_resolved": "https://registry.npmjs.org/elliptic/-/elliptic-6.5.3.tgz", + "_shasum": "cb59eb2efdaf73a0bd78ccd7015a62ad6e0f93d6", + "_spec": "elliptic@^6.5.3", + "_where": "/home/pruss/Dev/3-minute-website/node_modules/browserify-sign", + "author": { + "name": "Fedor Indutny", + "email": "fedor@indutny.com" + }, + "bugs": { + "url": "https://github.com/indutny/elliptic/issues" + }, + "bundleDependencies": false, + "dependencies": { + "bn.js": "^4.4.0", + "brorand": "^1.0.1", + "hash.js": "^1.0.0", + "hmac-drbg": "^1.0.0", + "inherits": "^2.0.1", + "minimalistic-assert": "^1.0.0", + "minimalistic-crypto-utils": "^1.0.0" + }, + "deprecated": false, + "description": "EC cryptography", + "devDependencies": { + "brfs": "^1.4.3", + "coveralls": "^3.0.8", + "grunt": "^1.0.4", + "grunt-browserify": "^5.0.0", + "grunt-cli": "^1.2.0", + "grunt-contrib-connect": "^1.0.0", + "grunt-contrib-copy": "^1.0.0", + "grunt-contrib-uglify": "^1.0.1", + "grunt-mocha-istanbul": "^3.0.1", + "grunt-saucelabs": "^9.0.1", + "istanbul": "^0.4.2", + "jscs": "^3.0.7", + "jshint": "^2.10.3", + "mocha": "^6.2.2" + }, + "files": [ + "lib" + ], + "homepage": "https://github.com/indutny/elliptic", + "keywords": [ + "EC", + "Elliptic", + "curve", + "Cryptography" + ], + "license": "MIT", + "main": "lib/elliptic.js", + "name": "elliptic", + "repository": { + "type": "git", + "url": "git+ssh://git@github.com/indutny/elliptic.git" + }, + "scripts": { + "jscs": "jscs benchmarks/*.js lib/*.js lib/**/*.js lib/**/**/*.js test/index.js", + "jshint": "jscs benchmarks/*.js lib/*.js lib/**/*.js lib/**/**/*.js test/index.js", + "lint": "npm run jscs && npm run jshint", + "test": "npm run lint && npm run unit", + "unit": "istanbul test _mocha --reporter=spec test/index.js", + "version": "grunt dist && git add dist/" + }, + "version": "6.5.3" +} |