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elliptic.js
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elliptic.js
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(function(f){if(typeof exports==="object"&&typeof module!=="undefined"){module.exports=f()}else if(typeof define==="function"&&define.amd){define([],f)}else{var g;if(typeof window!=="undefined"){g=window}else if(typeof global!=="undefined"){g=global}else if(typeof self!=="undefined"){g=self}else{g=this}g.elliptic = f()}})(function(){var define,module,exports;return (function e(t,n,r){function s(o,u){if(!n[o]){if(!t[o]){var a=typeof require=="function"&&require;if(!u&&a)return a(o,!0);if(i)return i(o,!0);var f=new Error("Cannot find module '"+o+"'");throw f.code="MODULE_NOT_FOUND",f}var l=n[o]={exports:{}};t[o][0].call(l.exports,function(e){var n=t[o][1][e];return s(n?n:e)},l,l.exports,e,t,n,r)}return n[o].exports}var i=typeof require=="function"&&require;for(var o=0;o<r.length;o++)s(r[o]);return s})({1:[function(require,module,exports){
'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');
},{"../package.json":30,"./elliptic/curve":4,"./elliptic/curves":7,"./elliptic/ec":8,"./elliptic/eddsa":11,"./elliptic/utils":15,"brorand":17}],2:[function(require,module,exports){
'use strict';
var BN = require('bn.js');
var elliptic = require('../../elliptic');
var utils = elliptic.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);
// 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);
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);
// 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]);
naf[b] = getNAF(coeffs[b], wndWidth[b]);
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;
};
},{"../../elliptic":1,"bn.js":16}],3:[function(require,module,exports){
'use strict';
var curve = require('../curve');
var elliptic = require('../../elliptic');
var BN = require('bn.js');
var inherits = require('inherits');
var Base = curve.base;
var assert = elliptic.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;
},{"../../elliptic":1,"../curve":4,"bn.js":16,"inherits":27}],4:[function(require,module,exports){
'use strict';
var curve = exports;
curve.base = require('./base');
curve.short = require('./short');
curve.mont = require('./mont');
curve.edwards = require('./edwards');
},{"./base":2,"./edwards":3,"./mont":5,"./short":6}],5:[function(require,module,exports){
'use strict';
var curve = require('../curve');
var BN = require('bn.js');
var inherits = require('inherits');
var Base = curve.base;
var elliptic = require('../../elliptic');
var utils = elliptic.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');