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ec: white space fixes 

It is advised to use ?w=0 in comparing this commit.
hk-custom-address
Daniel Cousens 11 years ago
parent
8a2dcaaaf5
commit
79c7b68d35
1 changed files with 132 additions and 128 deletions
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  1. 260
      src/ec.js

260
src/ec.js
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@ -9,42 +9,42 @@ var BigInteger = require('bigi')
var THREE = BigInteger.valueOf(3)
function ECFieldElementFp(q,x) {
this.x = x;
// TODO if(x.compareTo(q) >= 0) error
this.q = q;
this.x = x;
// TODO if (x.compareTo(q) >= 0) error
this.q = q;
}
function feFpEquals(other) {
if(other == this) return true;
return (this.q.equals(other.q) && this.x.equals(other.x));
if (other == this) return true;
return (this.q.equals(other.q) && this.x.equals(other.x));
}
function feFpToBigInteger() {
return this.x;
return this.x;
}
function feFpNegate() {
return new ECFieldElementFp(this.q, this.x.negate().mod(this.q));
return new ECFieldElementFp(this.q, this.x.negate().mod(this.q));
}
function feFpAdd(b) {
return new ECFieldElementFp(this.q, this.x.add(b.toBigInteger()).mod(this.q));
return new ECFieldElementFp(this.q, this.x.add(b.toBigInteger()).mod(this.q));
}
function feFpSubtract(b) {
return new ECFieldElementFp(this.q, this.x.subtract(b.toBigInteger()).mod(this.q));
return new ECFieldElementFp(this.q, this.x.subtract(b.toBigInteger()).mod(this.q));
}
function feFpMultiply(b) {
return new ECFieldElementFp(this.q, this.x.multiply(b.toBigInteger()).mod(this.q));
return new ECFieldElementFp(this.q, this.x.multiply(b.toBigInteger()).mod(this.q));
}
function feFpSquare() {
return new ECFieldElementFp(this.q, this.x.square().mod(this.q));
return new ECFieldElementFp(this.q, this.x.square().mod(this.q));
}
function feFpDivide(b) {
return new ECFieldElementFp(this.q, this.x.multiply(b.toBigInteger().modInverse(this.q)).mod(this.q));
return new ECFieldElementFp(this.q, this.x.multiply(b.toBigInteger().modInverse(this.q)).mod(this.q));
}
ECFieldElementFp.prototype.equals = feFpEquals;
@ -61,151 +61,156 @@ ECFieldElementFp.prototype.divide = feFpDivide;
// constructor
function ECPointFp(curve,x,y,z) {
this.curve = curve;
this.x = x;
this.y = y;
// Projective coordinates: either zinv == null or z * zinv == 1
// z and zinv are just BigIntegers, not fieldElements
if(z == null) {
this.z = BigInteger.ONE;
}
else {
this.z = z;
}
this.zinv = null;
//TODO: compression flag
this.curve = curve;
this.x = x;
this.y = y;
// Projective coordinates: either zinv == null or z * zinv == 1
// z and zinv are just BigIntegers, not fieldElements
if (z == null) {
this.z = BigInteger.ONE;
}
else {
this.z = z;
}
this.zinv = null;
//TODO: compression flag
}
function pointFpGetX() {
if(this.zinv == null) {
this.zinv = this.z.modInverse(this.curve.q);
}
return this.curve.fromBigInteger(this.x.toBigInteger().multiply(this.zinv).mod(this.curve.q));
if (this.zinv == null) {
this.zinv = this.z.modInverse(this.curve.q);
}
return this.curve.fromBigInteger(this.x.toBigInteger().multiply(this.zinv).mod(this.curve.q));
}
function pointFpGetY() {
if(this.zinv == null) {
this.zinv = this.z.modInverse(this.curve.q);
}
return this.curve.fromBigInteger(this.y.toBigInteger().multiply(this.zinv).mod(this.curve.q));
if (this.zinv == null) {
this.zinv = this.z.modInverse(this.curve.q);
}
return this.curve.fromBigInteger(this.y.toBigInteger().multiply(this.zinv).mod(this.curve.q));
}
function pointFpEquals(other) {
if(other == this) return true;
if(this.isInfinity()) return other.isInfinity();
if(other.isInfinity()) return this.isInfinity();
var u, v;
// u = Y2 * Z1 - Y1 * Z2
u = other.y.toBigInteger().multiply(this.z).subtract(this.y.toBigInteger().multiply(other.z)).mod(this.curve.q);
if (u.signum() !== 0) return false;
// v = X2 * Z1 - X1 * Z2
v = other.x.toBigInteger().multiply(this.z).subtract(this.x.toBigInteger().multiply(other.z)).mod(this.curve.q);
return v.signum() === 0;
if (other == this) return true;
if (this.isInfinity()) return other.isInfinity();
if (other.isInfinity()) return this.isInfinity();
var u, v;
// u = Y2 * Z1 - Y1 * Z2
u = other.y.toBigInteger().multiply(this.z).subtract(this.y.toBigInteger().multiply(other.z)).mod(this.curve.q);
if (u.signum() !== 0) return false;
// v = X2 * Z1 - X1 * Z2
v = other.x.toBigInteger().multiply(this.z).subtract(this.x.toBigInteger().multiply(other.z)).mod(this.curve.q);
return v.signum() === 0;
}
function pointFpIsInfinity() {
if ((this.x == null) && (this.y == null)) return true;
return this.z.signum() === 0 && this.y.toBigInteger().signum() !== 0;
if ((this.x == null) && (this.y == null)) return true;
return this.z.signum() === 0 && this.y.toBigInteger().signum() !== 0;
}
function pointFpNegate() {
return new ECPointFp(this.curve, this.x, this.y.negate(), this.z);
return new ECPointFp(this.curve, this.x, this.y.negate(), this.z);
}
function pointFpAdd(b) {
if(this.isInfinity()) return b;
if(b.isInfinity()) return this;
var x1 = this.x.toBigInteger()
var y1 = this.y.toBigInteger()
var x2 = b.x.toBigInteger()
var y2 = b.y.toBigInteger()
// u = Y2 * Z1 - Y1 * Z2
var u = y2.multiply(this.z).subtract(y1.multiply(b.z)).mod(this.curve.q)
// v = X2 * Z1 - X1 * Z2
var v = x2.multiply(this.z).subtract(x1.multiply(b.z)).mod(this.curve.q)
if(v.signum() === 0) {
if(u.signum() === 0) {
return this.twice(); // this == b, so double
}
return this.curve.getInfinity(); // this = -b, so infinity
}
if (this.isInfinity()) return b;
if (b.isInfinity()) return this;
var x1 = this.x.toBigInteger()
var y1 = this.y.toBigInteger()
var x2 = b.x.toBigInteger()
var y2 = b.y.toBigInteger()
// u = Y2 * Z1 - Y1 * Z2
var u = y2.multiply(this.z).subtract(y1.multiply(b.z)).mod(this.curve.q)
// v = X2 * Z1 - X1 * Z2
var v = x2.multiply(this.z).subtract(x1.multiply(b.z)).mod(this.curve.q)
if (v.signum() === 0) {
if (u.signum() === 0) {
return this.twice(); // this == b, so double
}
return this.curve.getInfinity(); // this = -b, so infinity
}
var v2 = v.square();
var v3 = v2.multiply(v);
var x1v2 = x1.multiply(v2);
var zu2 = u.square().multiply(this.z);
var v2 = v.square();
var v3 = v2.multiply(v);
var x1v2 = x1.multiply(v2);
var zu2 = u.square().multiply(this.z);
// x3 = v * (z2 * (z1 * u^2 - 2 * x1 * v^2) - v^3)
var x3 = zu2.subtract(x1v2.shiftLeft(1)).multiply(b.z).subtract(v3).multiply(v).mod(this.curve.q);
// y3 = z2 * (3 * x1 * u * v^2 - y1 * v^3 - z1 * u^3) + u * v^3
var y3 = x1v2.multiply(THREE).multiply(u).subtract(y1.multiply(v3)).subtract(zu2.multiply(u)).multiply(b.z).add(u.multiply(v3)).mod(this.curve.q);
// z3 = v^3 * z1 * z2
var z3 = v3.multiply(this.z).multiply(b.z).mod(this.curve.q);
// x3 = v * (z2 * (z1 * u^2 - 2 * x1 * v^2) - v^3)
var x3 = zu2.subtract(x1v2.shiftLeft(1)).multiply(b.z).subtract(v3).multiply(v).mod(this.curve.q);
// y3 = z2 * (3 * x1 * u * v^2 - y1 * v^3 - z1 * u^3) + u * v^3
var y3 = x1v2.multiply(THREE).multiply(u).subtract(y1.multiply(v3)).subtract(zu2.multiply(u)).multiply(b.z).add(u.multiply(v3)).mod(this.curve.q);
// z3 = v^3 * z1 * z2
var z3 = v3.multiply(this.z).multiply(b.z).mod(this.curve.q);
return new ECPointFp(this.curve, this.curve.fromBigInteger(x3), this.curve.fromBigInteger(y3), z3);
return new ECPointFp(this.curve, this.curve.fromBigInteger(x3), this.curve.fromBigInteger(y3), z3);
}
function pointFpTwice() {
if(this.isInfinity()) return this;
if(this.y.toBigInteger().signum() === 0) return this.curve.getInfinity();
if (this.isInfinity()) return this;
if (this.y.toBigInteger().signum() === 0) return this.curve.getInfinity();
var x1 = this.x.toBigInteger();
var y1 = this.y.toBigInteger();
var x1 = this.x.toBigInteger();
var y1 = this.y.toBigInteger();
var y1z1 = y1.multiply(this.z);
var y1sqz1 = y1z1.multiply(y1).mod(this.curve.q);
var a = this.curve.a.toBigInteger();
var y1z1 = y1.multiply(this.z);
var y1sqz1 = y1z1.multiply(y1).mod(this.curve.q);
var a = this.curve.a.toBigInteger();
// w = 3 * x1^2 + a * z1^2
var w = x1.square().multiply(THREE);
if(a.signum() !== 0) {
w = w.add(this.z.square().multiply(a));
}
w = w.mod(this.curve.q);
// x3 = 2 * y1 * z1 * (w^2 - 8 * x1 * y1^2 * z1)
var x3 = w.square().subtract(x1.shiftLeft(3).multiply(y1sqz1)).shiftLeft(1).multiply(y1z1).mod(this.curve.q);
// y3 = 4 * y1^2 * z1 * (3 * w * x1 - 2 * y1^2 * z1) - w^3
var y3 = w.multiply(THREE).multiply(x1).subtract(y1sqz1.shiftLeft(1)).shiftLeft(2).multiply(y1sqz1).subtract(w.pow(3)).mod(this.curve.q);
// z3 = 8 * (y1 * z1)^3
var z3 = y1z1.pow(3).shiftLeft(3).mod(this.curve.q);
return new ECPointFp(this.curve, this.curve.fromBigInteger(x3), this.curve.fromBigInteger(y3), z3);
// w = 3 * x1^2 + a * z1^2
var w = x1.square().multiply(THREE);
if (a.signum() !== 0) {
w = w.add(this.z.square().multiply(a));
}
w = w.mod(this.curve.q);
// x3 = 2 * y1 * z1 * (w^2 - 8 * x1 * y1^2 * z1)
var x3 = w.square().subtract(x1.shiftLeft(3).multiply(y1sqz1)).shiftLeft(1).multiply(y1z1).mod(this.curve.q);
// y3 = 4 * y1^2 * z1 * (3 * w * x1 - 2 * y1^2 * z1) - w^3
var y3 = w.multiply(THREE).multiply(x1).subtract(y1sqz1.shiftLeft(1)).shiftLeft(2).multiply(y1sqz1).subtract(w.pow(3)).mod(this.curve.q);
// z3 = 8 * (y1 * z1)^3
var z3 = y1z1.pow(3).shiftLeft(3).mod(this.curve.q);
return new ECPointFp(this.curve, this.curve.fromBigInteger(x3), this.curve.fromBigInteger(y3), z3);
}
// Simple NAF (Non-Adjacent Form) multiplication algorithm
// TODO: modularize the multiplication algorithm
function pointFpMultiply(k) {
if(this.isInfinity()) return this;
if(k.signum() === 0) return this.curve.getInfinity()
if (this.isInfinity()) return this;
if (k.signum() === 0) return this.curve.getInfinity()
var e = k;
var h = e.multiply(THREE)
var e = k;
var h = e.multiply(THREE)
var neg = this.negate();
var R = this;
var neg = this.negate();
var R = this;
var i;
for(i = h.bitLength() - 2; i > 0; --i) {
R = R.twice();
var i;
for(i = h.bitLength() - 2; i > 0; --i) {
R = R.twice();
var hBit = h.testBit(i);
var eBit = e.testBit(i);
var hBit = h.testBit(i);
var eBit = e.testBit(i);
if (hBit != eBit) {
R = R.add(hBit ? this : neg);
}
if (hBit != eBit) {
R = R.add(hBit ? this : neg);
}
}
return R;
return R;
}
// Compute this*j + x*k (simultaneous multiplication)
function pointFpMultiplyTwo(j,x,k) {
var i;
if(j.bitLength() > k.bitLength())
if (j.bitLength() > k.bitLength())
i = j.bitLength() - 1;
else
i = k.bitLength() - 1;
@ -214,8 +219,8 @@ function pointFpMultiplyTwo(j,x,k) {
var both = this.add(x);
while(i >= 0) {
R = R.twice();
if(j.testBit(i)) {
if(k.testBit(i)) {
if (j.testBit(i)) {
if (k.testBit(i)) {
R = R.add(both);
}
else {
@ -223,7 +228,7 @@ function pointFpMultiplyTwo(j,x,k) {
}
}
else {
if(k.testBit(i)) {
if (k.testBit(i)) {
R = R.add(x);
}
}
@ -248,35 +253,35 @@ ECPointFp.prototype.multiplyTwo = pointFpMultiplyTwo;
// constructor
function ECCurveFp(q,a,b) {
this.q = q;
this.a = this.fromBigInteger(a);
this.b = this.fromBigInteger(b);
this.infinity = new ECPointFp(this, null, null);
this.q = q;
this.a = this.fromBigInteger(a);
this.b = this.fromBigInteger(b);
this.infinity = new ECPointFp(this, null, null);
}
function curveFpGetQ() {
return this.q;
return this.q;
}
function curveFpGetA() {
return this.a;
return this.a;
}
function curveFpGetB() {
return this.b;
return this.b;
}
function curveFpEquals(other) {
if(other == this) return true;
return(this.q.equals(other.q) && this.a.equals(other.a) && this.b.equals(other.b));
if (other == this) return true;
return(this.q.equals(other.q) && this.a.equals(other.a) && this.b.equals(other.b));
}
function curveFpGetInfinity() {
return this.infinity;
return this.infinity;
}
function curveFpFromBigInteger(x) {
return new ECFieldElementFp(this.q, x);
return new ECFieldElementFp(this.q, x);
}
ECCurveFp.prototype.getQ = curveFpGetQ;
@ -410,6 +415,5 @@ ECPointFp.prototype.validate = function () {
return true;
};
module.exports = ECCurveFp;
module.exports.ECPointFp = ECPointFp;

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