|
|
@ -10,12 +10,12 @@ var THREE = BigInteger.valueOf(3) |
|
|
|
|
|
|
|
function ECFieldElementFp(q,x) { |
|
|
|
this.x = x; |
|
|
|
// TODO if(x.compareTo(q) >= 0) error
|
|
|
|
// TODO if (x.compareTo(q) >= 0) error
|
|
|
|
this.q = q; |
|
|
|
} |
|
|
|
|
|
|
|
function feFpEquals(other) { |
|
|
|
if(other == this) return true; |
|
|
|
if (other == this) return true; |
|
|
|
return (this.q.equals(other.q) && this.x.equals(other.x)); |
|
|
|
} |
|
|
|
|
|
|
@ -66,7 +66,7 @@ function ECPointFp(curve,x,y,z) { |
|
|
|
this.y = y; |
|
|
|
// Projective coordinates: either zinv == null or z * zinv == 1
|
|
|
|
// z and zinv are just BigIntegers, not fieldElements
|
|
|
|
if(z == null) { |
|
|
|
if (z == null) { |
|
|
|
this.z = BigInteger.ONE; |
|
|
|
} |
|
|
|
else { |
|
|
@ -77,23 +77,24 @@ function ECPointFp(curve,x,y,z) { |
|
|
|
} |
|
|
|
|
|
|
|
function pointFpGetX() { |
|
|
|
if(this.zinv == null) { |
|
|
|
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) { |
|
|
|
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(); |
|
|
|
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); |
|
|
@ -113,8 +114,8 @@ function pointFpNegate() { |
|
|
|
} |
|
|
|
|
|
|
|
function pointFpAdd(b) { |
|
|
|
if(this.isInfinity()) return b; |
|
|
|
if(b.isInfinity()) return this; |
|
|
|
if (this.isInfinity()) return b; |
|
|
|
if (b.isInfinity()) return this; |
|
|
|
|
|
|
|
var x1 = this.x.toBigInteger() |
|
|
|
var y1 = this.y.toBigInteger() |
|
|
@ -126,10 +127,11 @@ function pointFpAdd(b) { |
|
|
|
// 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) { |
|
|
|
if (v.signum() === 0) { |
|
|
|
if (u.signum() === 0) { |
|
|
|
return this.twice(); // this == b, so double
|
|
|
|
} |
|
|
|
|
|
|
|
return this.curve.getInfinity(); // this = -b, so infinity
|
|
|
|
} |
|
|
|
|
|
|
@ -149,8 +151,8 @@ function pointFpAdd(b) { |
|
|
|
} |
|
|
|
|
|
|
|
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(); |
|
|
@ -161,9 +163,11 @@ function pointFpTwice() { |
|
|
|
|
|
|
|
// w = 3 * x1^2 + a * z1^2
|
|
|
|
var w = x1.square().multiply(THREE); |
|
|
|
if(a.signum() !== 0) { |
|
|
|
|
|
|
|
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); |
|
|
@ -178,8 +182,8 @@ function pointFpTwice() { |
|
|
|
// 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) |
|
|
@ -205,7 +209,8 @@ function pointFpMultiply(k) { |
|
|
|
// 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); |
|
|
|
} |
|
|
|
} |
|
|
@ -267,7 +272,7 @@ function curveFpGetB() { |
|
|
|
} |
|
|
|
|
|
|
|
function curveFpEquals(other) { |
|
|
|
if(other == this) return true; |
|
|
|
if (other == this) return true; |
|
|
|
return(this.q.equals(other.q) && this.a.equals(other.a) && this.b.equals(other.b)); |
|
|
|
} |
|
|
|
|
|
|
@ -410,6 +415,5 @@ ECPointFp.prototype.validate = function () { |
|
|
|
return true; |
|
|
|
}; |
|
|
|
|
|
|
|
|
|
|
|
module.exports = ECCurveFp; |
|
|
|
module.exports.ECPointFp = ECPointFp; |
|
|
|