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ec: remove semi-colons

hk-custom-address
Daniel Cousens 11 years ago
parent
commit
525b053e39
  1. 281
      src/ec.js

281
src/ec.js

@ -9,113 +9,117 @@ var BigInteger = require('bigi')
var THREE = BigInteger.valueOf(3) var THREE = BigInteger.valueOf(3)
function ECFieldElementFp(q,x) { function ECFieldElementFp(q,x) {
this.x = x; this.x = x
// TODO if (x.compareTo(q) >= 0) error // TODO if (x.compareTo(q) >= 0) error
this.q = q; this.q = q
} }
function feFpEquals(other) { function feFpEquals(other) {
if (other == this) return true; if (other == this) return true
return (this.q.equals(other.q) && this.x.equals(other.x)); return (this.q.equals(other.q) && this.x.equals(other.x))
} }
function feFpToBigInteger() { function feFpToBigInteger() {
return this.x; return this.x
} }
function feFpNegate() { 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) { 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) { 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) { 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() { 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) { 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; ECFieldElementFp.prototype.equals = feFpEquals
ECFieldElementFp.prototype.toBigInteger = feFpToBigInteger; ECFieldElementFp.prototype.toBigInteger = feFpToBigInteger
ECFieldElementFp.prototype.negate = feFpNegate; ECFieldElementFp.prototype.negate = feFpNegate
ECFieldElementFp.prototype.add = feFpAdd; ECFieldElementFp.prototype.add = feFpAdd
ECFieldElementFp.prototype.subtract = feFpSubtract; ECFieldElementFp.prototype.subtract = feFpSubtract
ECFieldElementFp.prototype.multiply = feFpMultiply; ECFieldElementFp.prototype.multiply = feFpMultiply
ECFieldElementFp.prototype.square = feFpSquare; ECFieldElementFp.prototype.square = feFpSquare
ECFieldElementFp.prototype.divide = feFpDivide; ECFieldElementFp.prototype.divide = feFpDivide
// ---------------- // ----------------
// ECPointFp // ECPointFp
// constructor // constructor
function ECPointFp(curve,x,y,z) { function ECPointFp(curve,x,y,z) {
this.curve = curve; this.curve = curve
this.x = x; this.x = x
this.y = y; this.y = y
// Projective coordinates: either zinv == null or z * zinv == 1 // Projective coordinates: either zinv == null or z * zinv == 1
// z and zinv are just BigIntegers, not fieldElements // z and zinv are just BigIntegers, not fieldElements
if (z == null) { if (z == null) {
this.z = BigInteger.ONE; this.z = BigInteger.ONE
}
else { } else {
this.z = z; this.z = z
} }
this.zinv = null; this.zinv = null
//TODO: compression flag //TODO: compression flag
} }
function pointFpGetX() { function pointFpGetX() {
if (this.zinv == null) { if (this.zinv == null) {
this.zinv = this.z.modInverse(this.curve.q); this.zinv = this.z.modInverse(this.curve.q)
} }
return this.curve.fromBigInteger(this.x.toBigInteger().multiply(this.zinv).mod(this.curve.q));
return this.curve.fromBigInteger(this.x.toBigInteger().multiply(this.zinv).mod(this.curve.q))
} }
function pointFpGetY() { function pointFpGetY() {
if (this.zinv == null) { if (this.zinv == null) {
this.zinv = this.z.modInverse(this.curve.q); this.zinv = this.z.modInverse(this.curve.q)
} }
return this.curve.fromBigInteger(this.y.toBigInteger().multiply(this.zinv).mod(this.curve.q));
return this.curve.fromBigInteger(this.y.toBigInteger().multiply(this.zinv).mod(this.curve.q))
} }
function pointFpEquals(other) { function pointFpEquals(other) {
if (other == this) return true; if (other == this) return true
if (this.isInfinity()) return other.isInfinity(); if (this.isInfinity()) return other.isInfinity()
if (other.isInfinity()) return this.isInfinity(); if (other.isInfinity()) return this.isInfinity()
var u, v;
// u = Y2 * Z1 - Y1 * Z2 // u = Y2 * Z1 - Y1 * Z2
u = other.y.toBigInteger().multiply(this.z).subtract(this.y.toBigInteger().multiply(other.z)).mod(this.curve.q); u = other.y.toBigInteger().multiply(this.z).subtract(this.y.toBigInteger().multiply(other.z)).mod(this.curve.q)
if (u.signum() !== 0) return false; if (u.signum() !== 0) return false
// v = X2 * Z1 - X1 * Z2 // v = X2 * Z1 - X1 * Z2
v = other.x.toBigInteger().multiply(this.z).subtract(this.x.toBigInteger().multiply(other.z)).mod(this.curve.q); v = other.x.toBigInteger().multiply(this.z).subtract(this.x.toBigInteger().multiply(other.z)).mod(this.curve.q)
return v.signum() === 0; return v.signum() === 0
} }
function pointFpIsInfinity() { function pointFpIsInfinity() {
if ((this.x == null) && (this.y == null)) return true; if ((this.x == null) && (this.y == null)) return true
return this.z.signum() === 0 && this.y.toBigInteger().signum() !== 0; return this.z.signum() === 0 && this.y.toBigInteger().signum() !== 0
} }
function pointFpNegate() { 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) { function pointFpAdd(b) {
if (this.isInfinity()) return b; if (this.isInfinity()) return b
if (b.isInfinity()) return this; if (b.isInfinity()) return this
var x1 = this.x.toBigInteger() var x1 = this.x.toBigInteger()
var y1 = this.y.toBigInteger() var y1 = this.y.toBigInteger()
@ -129,171 +133,170 @@ function pointFpAdd(b) {
if (v.signum() === 0) { if (v.signum() === 0) {
if (u.signum() === 0) { if (u.signum() === 0) {
return this.twice(); // this == b, so double return this.twice() // this == b, so double
} }
return this.curve.getInfinity(); // this = -b, so infinity return this.curve.getInfinity() // this = -b, so infinity
} }
var v2 = v.square(); var v2 = v.square()
var v3 = v2.multiply(v); var v3 = v2.multiply(v)
var x1v2 = x1.multiply(v2); var x1v2 = x1.multiply(v2)
var zu2 = u.square().multiply(this.z); var zu2 = u.square().multiply(this.z)
// x3 = v * (z2 * (z1 * u^2 - 2 * x1 * v^2) - v^3) // 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); 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 // 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); 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 // z3 = v^3 * z1 * z2
var z3 = v3.multiply(this.z).multiply(b.z).mod(this.curve.q); 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() { function pointFpTwice() {
if (this.isInfinity()) return this; if (this.isInfinity()) return this
if (this.y.toBigInteger().signum() === 0) return this.curve.getInfinity(); if (this.y.toBigInteger().signum() === 0) return this.curve.getInfinity()
var x1 = this.x.toBigInteger(); var x1 = this.x.toBigInteger()
var y1 = this.y.toBigInteger(); var y1 = this.y.toBigInteger()
var y1z1 = y1.multiply(this.z); var y1z1 = y1.multiply(this.z)
var y1sqz1 = y1z1.multiply(y1).mod(this.curve.q); var y1sqz1 = y1z1.multiply(y1).mod(this.curve.q)
var a = this.curve.a.toBigInteger(); var a = this.curve.a.toBigInteger()
// w = 3 * x1^2 + a * z1^2 // w = 3 * x1^2 + a * z1^2
var w = x1.square().multiply(THREE); var w = x1.square().multiply(THREE)
if (a.signum() !== 0) { if (a.signum() !== 0) {
w = w.add(this.z.square().multiply(a)); w = w.add(this.z.square().multiply(a))
} }
w = w.mod(this.curve.q); w = w.mod(this.curve.q)
// x3 = 2 * y1 * z1 * (w^2 - 8 * x1 * y1^2 * z1) // 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); 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 // 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); 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 // z3 = 8 * (y1 * z1)^3
var z3 = y1z1.pow(3).shiftLeft(3).mod(this.curve.q); 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); return new ECPointFp(this.curve, this.curve.fromBigInteger(x3), this.curve.fromBigInteger(y3), z3)
} }
// Simple NAF (Non-Adjacent Form) multiplication algorithm // Simple NAF (Non-Adjacent Form) multiplication algorithm
// TODO: modularize the multiplication algorithm // TODO: modularize the multiplication algorithm
function pointFpMultiply(k) { function pointFpMultiply(k) {
if (this.isInfinity()) return this; if (this.isInfinity()) return this
if (k.signum() === 0) return this.curve.getInfinity() if (k.signum() === 0) return this.curve.getInfinity()
var e = k; var e = k
var h = e.multiply(THREE) var h = e.multiply(THREE)
var neg = this.negate(); var neg = this.negate()
var R = this; var R = this
var i; for (var i = h.bitLength() - 2; i > 0; --i) {
for(i = h.bitLength() - 2; i > 0; --i) { R = R.twice()
R = R.twice();
var hBit = h.testBit(i); var hBit = h.testBit(i)
var eBit = e.testBit(i); var eBit = e.testBit(i)
if (hBit != eBit) { if (hBit != eBit) {
R = R.add(hBit ? this : neg); R = R.add(hBit ? this : neg)
} }
} }
return R; return R
} }
// Compute this*j + x*k (simultaneous multiplication) // Compute this*j + x*k (simultaneous multiplication)
function pointFpMultiplyTwo(j,x,k) { function pointFpMultiplyTwo(j,x,k) {
var i; var i
if (j.bitLength() > k.bitLength()) if (j.bitLength() > k.bitLength())
i = j.bitLength() - 1; i = j.bitLength() - 1
else else
i = k.bitLength() - 1; i = k.bitLength() - 1
var R = this.curve.getInfinity(); var R = this.curve.getInfinity()
var both = this.add(x); var both = this.add(x)
while(i >= 0) { while (i >= 0) {
R = R.twice(); R = R.twice()
if (j.testBit(i)) { if (j.testBit(i)) {
if (k.testBit(i)) { if (k.testBit(i)) {
R = R.add(both); R = R.add(both)
} }
else { else {
R = R.add(this); R = R.add(this)
} }
} }
else { else {
if (k.testBit(i)) { if (k.testBit(i)) {
R = R.add(x); R = R.add(x)
} }
} }
--i; --i
} }
return R; return R
} }
ECPointFp.prototype.getX = pointFpGetX; ECPointFp.prototype.getX = pointFpGetX
ECPointFp.prototype.getY = pointFpGetY; ECPointFp.prototype.getY = pointFpGetY
ECPointFp.prototype.equals = pointFpEquals; ECPointFp.prototype.equals = pointFpEquals
ECPointFp.prototype.isInfinity = pointFpIsInfinity; ECPointFp.prototype.isInfinity = pointFpIsInfinity
ECPointFp.prototype.negate = pointFpNegate; ECPointFp.prototype.negate = pointFpNegate
ECPointFp.prototype.add = pointFpAdd; ECPointFp.prototype.add = pointFpAdd
ECPointFp.prototype.twice = pointFpTwice; ECPointFp.prototype.twice = pointFpTwice
ECPointFp.prototype.multiply = pointFpMultiply; ECPointFp.prototype.multiply = pointFpMultiply
ECPointFp.prototype.multiplyTwo = pointFpMultiplyTwo; ECPointFp.prototype.multiplyTwo = pointFpMultiplyTwo
// ---------------- // ----------------
// ECCurveFp // ECCurveFp
// constructor // constructor
function ECCurveFp(q,a,b) { function ECCurveFp(q,a,b) {
this.q = q; this.q = q
this.a = this.fromBigInteger(a); this.a = this.fromBigInteger(a)
this.b = this.fromBigInteger(b); this.b = this.fromBigInteger(b)
this.infinity = new ECPointFp(this, null, null); this.infinity = new ECPointFp(this, null, null)
} }
function curveFpGetQ() { function curveFpGetQ() {
return this.q; return this.q
} }
function curveFpGetA() { function curveFpGetA() {
return this.a; return this.a
} }
function curveFpGetB() { function curveFpGetB() {
return this.b; return this.b
} }
function curveFpEquals(other) { 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)); return(this.q.equals(other.q) && this.a.equals(other.a) && this.b.equals(other.b))
} }
function curveFpGetInfinity() { function curveFpGetInfinity() {
return this.infinity; return this.infinity
} }
function curveFpFromBigInteger(x) { function curveFpFromBigInteger(x) {
return new ECFieldElementFp(this.q, x); return new ECFieldElementFp(this.q, x)
} }
ECCurveFp.prototype.getQ = curveFpGetQ; ECCurveFp.prototype.getQ = curveFpGetQ
ECCurveFp.prototype.getA = curveFpGetA; ECCurveFp.prototype.getA = curveFpGetA
ECCurveFp.prototype.getB = curveFpGetB; ECCurveFp.prototype.getB = curveFpGetB
ECCurveFp.prototype.equals = curveFpEquals; ECCurveFp.prototype.equals = curveFpEquals
ECCurveFp.prototype.getInfinity = curveFpGetInfinity; ECCurveFp.prototype.getInfinity = curveFpGetInfinity
ECCurveFp.prototype.fromBigInteger = curveFpFromBigInteger; ECCurveFp.prototype.fromBigInteger = curveFpFromBigInteger
ECFieldElementFp.prototype.getByteLength = function () { ECFieldElementFp.prototype.getByteLength = function () {
return Math.floor((this.toBigInteger().bitLength() + 7) / 8); return Math.floor((this.toBigInteger().bitLength() + 7) / 8)
}; }
ECPointFp.prototype.getEncoded = function(compressed) { ECPointFp.prototype.getEncoded = function(compressed) {
var x = this.getX().toBigInteger() var x = this.getX().toBigInteger()
@ -361,20 +364,20 @@ ECPointFp.decodeFrom = function (curve, buffer) {
} }
ECPointFp.prototype.isOnCurve = function () { ECPointFp.prototype.isOnCurve = function () {
var x = this.getX().toBigInteger(); var x = this.getX().toBigInteger()
var y = this.getY().toBigInteger(); var y = this.getY().toBigInteger()
var a = this.curve.getA().toBigInteger(); var a = this.curve.getA().toBigInteger()
var b = this.curve.getB().toBigInteger(); var b = this.curve.getB().toBigInteger()
var p = this.curve.getQ() var p = this.curve.getQ()
var lhs = y.square().mod(p) var lhs = y.square().mod(p)
var rhs = x.pow(3).add(a.multiply(x)).add(b).mod(p) var rhs = x.pow(3).add(a.multiply(x)).add(b).mod(p)
return lhs.equals(rhs); return lhs.equals(rhs)
}; }
ECPointFp.prototype.toString = function () { ECPointFp.prototype.toString = function () {
return '('+this.getX().toBigInteger().toString()+','+ return '('+this.getX().toBigInteger().toString()+','+
this.getY().toBigInteger().toString()+')'; this.getY().toBigInteger().toString()+')'
}; }
/** /**
* Validate an elliptic curve point. * Validate an elliptic curve point.
@ -382,38 +385,38 @@ ECPointFp.prototype.toString = function () {
* See SEC 1, section 3.2.2.1: Elliptic Curve Public Key Validation Primitive * See SEC 1, section 3.2.2.1: Elliptic Curve Public Key Validation Primitive
*/ */
ECPointFp.prototype.validate = function () { ECPointFp.prototype.validate = function () {
var n = this.curve.getQ(); var n = this.curve.getQ()
// Check Q != O // Check Q != O
if (this.isInfinity()) { if (this.isInfinity()) {
throw new Error("Point is at infinity."); throw new Error("Point is at infinity.")
} }
// Check coordinate bounds // Check coordinate bounds
var x = this.getX().toBigInteger(); var x = this.getX().toBigInteger()
var y = this.getY().toBigInteger(); var y = this.getY().toBigInteger()
if (x.compareTo(BigInteger.ONE) < 0 || if (x.compareTo(BigInteger.ONE) < 0 ||
x.compareTo(n.subtract(BigInteger.ONE)) > 0) { x.compareTo(n.subtract(BigInteger.ONE)) > 0) {
throw new Error('x coordinate out of bounds'); throw new Error('x coordinate out of bounds')
} }
if (y.compareTo(BigInteger.ONE) < 0 || if (y.compareTo(BigInteger.ONE) < 0 ||
y.compareTo(n.subtract(BigInteger.ONE)) > 0) { y.compareTo(n.subtract(BigInteger.ONE)) > 0) {
throw new Error('y coordinate out of bounds'); throw new Error('y coordinate out of bounds')
} }
// Check y^2 = x^3 + ax + b (mod n) // Check y^2 = x^3 + ax + b (mod n)
if (!this.isOnCurve()) { if (!this.isOnCurve()) {
throw new Error("Point is not on the curve."); throw new Error("Point is not on the curve.")
} }
// Check nQ = 0 (Q is a scalar multiple of G) // Check nQ = 0 (Q is a scalar multiple of G)
if (this.multiply(n).isInfinity()) { if (this.multiply(n).isInfinity()) {
// TODO: This check doesn't work - fix. // TODO: This check doesn't work - fix.
throw new Error("Point is not a scalar multiple of G."); throw new Error("Point is not a scalar multiple of G.")
} }
return true; return true
}; }
module.exports = ECCurveFp; module.exports = ECCurveFp
module.exports.ECPointFp = ECPointFp; module.exports.ECPointFp = ECPointFp

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