FM / curve

/var/www/flurhymez/node_modules/elliptic/lib/elliptic/curve/

/var/www/flurhymez/node_modules/elliptic/lib/elliptic/curve

Name	Size	Mode	Actions
base.js	9202	0644	edit dl rm
edwards.js	10908	0644	edit dl rm
index.js	173	0644	edit dl rm
mont.js	4581	0644	edit dl rm
short.js	22969	0644	edit dl rm

Edit: /var/www/flurhymez/node_modules/elliptic/lib/elliptic/curve/edwards.js (10908B)

'use strict';

var utils = require('../utils');
var BN = require('bn.js');
var inherits = require('inherits');
var Base = require('./base');

var assert = utils.assert;

function EdwardsCurve(conf) {
  // NOTE: Important as we are creating point in Base.call()
  this.twisted = (conf.a | 0) !== 1;
  this.mOneA = this.twisted && (conf.a | 0) === -1;
  this.extended = this.mOneA;

Base.call(this, 'edwards', conf);

this.a = new BN(conf.a, 16).umod(this.red.m);
  this.a = this.a.toRed(this.red);
  this.c = new BN(conf.c, 16).toRed(this.red);
  this.c2 = this.c.redSqr();
  this.d = new BN(conf.d, 16).toRed(this.red);
  this.dd = this.d.redAdd(this.d);

assert(!this.twisted || this.c.fromRed().cmpn(1) === 0);
  this.oneC = (conf.c | 0) === 1;
}
inherits(EdwardsCurve, Base);
module.exports = EdwardsCurve;

EdwardsCurve.prototype._mulA = function _mulA(num) {
  if (this.mOneA)
    return num.redNeg();
  else
    return this.a.redMul(num);
};

EdwardsCurve.prototype._mulC = function _mulC(num) {
  if (this.oneC)
    return num;
  else
    return this.c.redMul(num);
};

// Just for compatibility with Short curve
EdwardsCurve.prototype.jpoint = function jpoint(x, y, z, t) {
  return this.point(x, y, z, t);
};

EdwardsCurve.prototype.pointFromX = function pointFromX(x, odd) {
  x = new BN(x, 16);
  if (!x.red)
    x = x.toRed(this.red);

var x2 = x.redSqr();
  var rhs = this.c2.redSub(this.a.redMul(x2));
  var lhs = this.one.redSub(this.c2.redMul(this.d).redMul(x2));

var y2 = rhs.redMul(lhs.redInvm());
  var y = y2.redSqrt();
  if (y.redSqr().redSub(y2).cmp(this.zero) !== 0)
    throw new Error('invalid point');

var isOdd = y.fromRed().isOdd();
  if (odd && !isOdd || !odd && isOdd)
    y = y.redNeg();

return this.point(x, y);
};

EdwardsCurve.prototype.pointFromY = function pointFromY(y, odd) {
  y = new BN(y, 16);
  if (!y.red)
    y = y.toRed(this.red);

// x^2 = (y^2 - c^2) / (c^2 d y^2 - a)
  var y2 = y.redSqr();
  var lhs = y2.redSub(this.c2);
  var rhs = y2.redMul(this.d).redMul(this.c2).redSub(this.a);
  var x2 = lhs.redMul(rhs.redInvm());

if (x2.cmp(this.zero) === 0) {
    if (odd)
      throw new Error('invalid point');
    else
      return this.point(this.zero, y);
  }

var x = x2.redSqrt();
  if (x.redSqr().redSub(x2).cmp(this.zero) !== 0)
    throw new Error('invalid point');

if (x.fromRed().isOdd() !== odd)
    x = x.redNeg();

return this.point(x, y);
};

EdwardsCurve.prototype.validate = function validate(point) {
  if (point.isInfinity())
    return true;

// Curve: A * X^2 + Y^2 = C^2 * (1 + D * X^2 * Y^2)
  point.normalize();

var x2 = point.x.redSqr();
  var y2 = point.y.redSqr();
  var lhs = x2.redMul(this.a).redAdd(y2);
  var rhs = this.c2.redMul(this.one.redAdd(this.d.redMul(x2).redMul(y2)));

return lhs.cmp(rhs) === 0;
};

function Point(curve, x, y, z, t) {
  Base.BasePoint.call(this, curve, 'projective');
  if (x === null && y === null && z === null) {
    this.x = this.curve.zero;
    this.y = this.curve.one;
    this.z = this.curve.one;
    this.t = this.curve.zero;
    this.zOne = true;
  } else {
    this.x = new BN(x, 16);
    this.y = new BN(y, 16);
    this.z = z ? new BN(z, 16) : this.curve.one;
    this.t = t && new BN(t, 16);
    if (!this.x.red)
      this.x = this.x.toRed(this.curve.red);
    if (!this.y.red)
      this.y = this.y.toRed(this.curve.red);
    if (!this.z.red)
      this.z = this.z.toRed(this.curve.red);
    if (this.t && !this.t.red)
      this.t = this.t.toRed(this.curve.red);
    this.zOne = this.z === this.curve.one;

// Use extended coordinates
    if (this.curve.extended && !this.t) {
      this.t = this.x.redMul(this.y);
      if (!this.zOne)
        this.t = this.t.redMul(this.z.redInvm());
    }
  }
}
inherits(Point, Base.BasePoint);

EdwardsCurve.prototype.pointFromJSON = function pointFromJSON(obj) {
  return Point.fromJSON(this, obj);
};

EdwardsCurve.prototype.point = function point(x, y, z, t) {
  return new Point(this, x, y, z, t);
};

Point.fromJSON = function fromJSON(curve, obj) {
  return new Point(curve, obj[0], obj[1], obj[2]);
};

Point.prototype.inspect = function inspect() {
  if (this.isInfinity())
    return '<EC Point Infinity>';
  return '<EC Point x: ' + this.x.fromRed().toString(16, 2) +
      ' y: ' + this.y.fromRed().toString(16, 2) +
      ' z: ' + this.z.fromRed().toString(16, 2) + '>';
};

Point.prototype.isInfinity = function isInfinity() {
  // XXX This code assumes that zero is always zero in red
  return this.x.cmpn(0) === 0 &&
    (this.y.cmp(this.z) === 0 ||
    (this.zOne && this.y.cmp(this.curve.c) === 0));
};

Point.prototype._extDbl = function _extDbl() {
  // hyperelliptic.org/EFD/g1p/auto-twisted-extended-1.html
  //     #doubling-dbl-2008-hwcd
  // 4M + 4S

// A = X1^2
  var a = this.x.redSqr();
  // B = Y1^2
  var b = this.y.redSqr();
  // C = 2 * Z1^2
  var c = this.z.redSqr();
  c = c.redIAdd(c);
  // D = a * A
  var d = this.curve._mulA(a);
  // E = (X1 + Y1)^2 - A - B
  var e = this.x.redAdd(this.y).redSqr().redISub(a).redISub(b);
  // G = D + B
  var g = d.redAdd(b);
  // F = G - C
  var f = g.redSub(c);
  // H = D - B
  var h = d.redSub(b);
  // X3 = E * F
  var nx = e.redMul(f);
  // Y3 = G * H
  var ny = g.redMul(h);
  // T3 = E * H
  var nt = e.redMul(h);
  // Z3 = F * G
  var nz = f.redMul(g);
  return this.curve.point(nx, ny, nz, nt);
};

Point.prototype._projDbl = function _projDbl() {
  // hyperelliptic.org/EFD/g1p/auto-twisted-projective.html
  //     #doubling-dbl-2008-bbjlp
  //     #doubling-dbl-2007-bl
  // and others
  // Generally 3M + 4S or 2M + 4S

// B = (X1 + Y1)^2
  var b = this.x.redAdd(this.y).redSqr();
  // C = X1^2
  var c = this.x.redSqr();
  // D = Y1^2
  var d = this.y.redSqr();

var nx;
  var ny;
  var nz;
  var e;
  var h;
  var j;
  if (this.curve.twisted) {
    // E = a * C
    e = this.curve._mulA(c);
    // F = E + D
    var f = e.redAdd(d);
    if (this.zOne) {
      // X3 = (B - C - D) * (F - 2)
      nx = b.redSub(c).redSub(d).redMul(f.redSub(this.curve.two));
      // Y3 = F * (E - D)
      ny = f.redMul(e.redSub(d));
      // Z3 = F^2 - 2 * F
      nz = f.redSqr().redSub(f).redSub(f);
    } else {
      // H = Z1^2
      h = this.z.redSqr();
      // J = F - 2 * H
      j = f.redSub(h).redISub(h);
      // X3 = (B-C-D)*J
      nx = b.redSub(c).redISub(d).redMul(j);
      // Y3 = F * (E - D)
      ny = f.redMul(e.redSub(d));
      // Z3 = F * J
      nz = f.redMul(j);
    }
  } else {
    // E = C + D
    e = c.redAdd(d);
    // H = (c * Z1)^2
    h = this.curve._mulC(this.z).redSqr();
    // J = E - 2 * H
    j = e.redSub(h).redSub(h);
    // X3 = c * (B - E) * J
    nx = this.curve._mulC(b.redISub(e)).redMul(j);
    // Y3 = c * E * (C - D)
    ny = this.curve._mulC(e).redMul(c.redISub(d));
    // Z3 = E * J
    nz = e.redMul(j);
  }
  return this.curve.point(nx, ny, nz);
};

Point.prototype.dbl = function dbl() {
  if (this.isInfinity())
    return this;

// Double in extended coordinates
  if (this.curve.extended)
    return this._extDbl();
  else
    return this._projDbl();
};

Point.prototype._extAdd = function _extAdd(p) {
  // hyperelliptic.org/EFD/g1p/auto-twisted-extended-1.html
  //     #addition-add-2008-hwcd-3
  // 8M

// A = (Y1 - X1) * (Y2 - X2)
  var a = this.y.redSub(this.x).redMul(p.y.redSub(p.x));
  // B = (Y1 + X1) * (Y2 + X2)
  var b = this.y.redAdd(this.x).redMul(p.y.redAdd(p.x));
  // C = T1 * k * T2
  var c = this.t.redMul(this.curve.dd).redMul(p.t);
  // D = Z1 * 2 * Z2
  var d = this.z.redMul(p.z.redAdd(p.z));
  // E = B - A
  var e = b.redSub(a);
  // F = D - C
  var f = d.redSub(c);
  // G = D + C
  var g = d.redAdd(c);
  // H = B + A
  var h = b.redAdd(a);
  // X3 = E * F
  var nx = e.redMul(f);
  // Y3 = G * H
  var ny = g.redMul(h);
  // T3 = E * H
  var nt = e.redMul(h);
  // Z3 = F * G
  var nz = f.redMul(g);
  return this.curve.point(nx, ny, nz, nt);
};

Point.prototype._projAdd = function _projAdd(p) {
  // hyperelliptic.org/EFD/g1p/auto-twisted-projective.html
  //     #addition-add-2008-bbjlp
  //     #addition-add-2007-bl
  // 10M + 1S

// A = Z1 * Z2
  var a = this.z.redMul(p.z);
  // B = A^2
  var b = a.redSqr();
  // C = X1 * X2
  var c = this.x.redMul(p.x);
  // D = Y1 * Y2
  var d = this.y.redMul(p.y);
  // E = d * C * D
  var e = this.curve.d.redMul(c).redMul(d);
  // F = B - E
  var f = b.redSub(e);
  // G = B + E
  var g = b.redAdd(e);
  // X3 = A * F * ((X1 + Y1) * (X2 + Y2) - C - D)
  var tmp = this.x.redAdd(this.y).redMul(p.x.redAdd(p.y)).redISub(c).redISub(d);
  var nx = a.redMul(f).redMul(tmp);
  var ny;
  var nz;
  if (this.curve.twisted) {
    // Y3 = A * G * (D - a * C)
    ny = a.redMul(g).redMul(d.redSub(this.curve._mulA(c)));
    // Z3 = F * G
    nz = f.redMul(g);
  } else {
    // Y3 = A * G * (D - C)
    ny = a.redMul(g).redMul(d.redSub(c));
    // Z3 = c * F * G
    nz = this.curve._mulC(f).redMul(g);
  }
  return this.curve.point(nx, ny, nz);
};

Point.prototype.add = function add(p) {
  if (this.isInfinity())
    return p;
  if (p.isInfinity())
    return this;

if (this.curve.extended)
    return this._extAdd(p);
  else
    return this._projAdd(p);
};

Point.prototype.mul = function mul(k) {
  if (this._hasDoubles(k))
    return this.curve._fixedNafMul(this, k);
  else
    return this.curve._wnafMul(this, k);
};

Point.prototype.mulAdd = function mulAdd(k1, p, k2) {
  return this.curve._wnafMulAdd(1, [ this, p ], [ k1, k2 ], 2, false);
};

Point.prototype.jmulAdd = function jmulAdd(k1, p, k2) {
  return this.curve._wnafMulAdd(1, [ this, p ], [ k1, k2 ], 2, true);
};

Point.prototype.normalize = function normalize() {
  if (this.zOne)
    return this;

// Normalize coordinates
  var zi = this.z.redInvm();
  this.x = this.x.redMul(zi);
  this.y = this.y.redMul(zi);
  if (this.t)
    this.t = this.t.redMul(zi);
  this.z = this.curve.one;
  this.zOne = true;
  return this;
};

Point.prototype.neg = function neg() {
  return this.curve.point(this.x.redNeg(),
    this.y,
    this.z,
    this.t && this.t.redNeg());
};

Point.prototype.getX = function getX() {
  this.normalize();
  return this.x.fromRed();
};

Point.prototype.getY = function getY() {
  this.normalize();
  return this.y.fromRed();
};

Point.prototype.eq = function eq(other) {
  return this === other ||
         this.getX().cmp(other.getX()) === 0 &&
         this.getY().cmp(other.getY()) === 0;
};

Point.prototype.eqXToP = function eqXToP(x) {
  var rx = x.toRed(this.curve.red).redMul(this.z);
  if (this.x.cmp(rx) === 0)
    return true;

var xc = x.clone();
  var t = this.curve.redN.redMul(this.z);
  for (;;) {
    xc.iadd(this.curve.n);
    if (xc.cmp(this.curve.p) >= 0)
      return false;

rx.redIAdd(t);
    if (this.x.cmp(rx) === 0)
      return true;
  }
};

// Compatibility with BaseCurve
Point.prototype.toP = Point.prototype.normalize;
Point.prototype.mixedAdd = Point.prototype.add;

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