416 lines
9.8 KiB
JavaScript
416 lines
9.8 KiB
JavaScript
// Basic Javascript Elliptic Curve implementation
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// Ported loosely from BouncyCastle's Java EC code
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// Only Fp curves implemented for now
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// Requires jsbn.js and jsbn2.js
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import { BigInteger } from 'jsbn'
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const { Barrett } = BigInteger.prototype
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// Basic Javascript Elliptic Curve implementation
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// Ported loosely from BouncyCastle's Java EC code
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// Only Fp curves implemented for now
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// Requires jsbn.js and jsbn2.js
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// ----------------
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// ECFieldElementFp
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// constructor
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function ECFieldElementFp(q, x) {
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this.x = x
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// TODO if(x.compareTo(q) >= 0) error
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this.q = q
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}
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function feFpEquals(other) {
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if (other == this) return true
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return this.q.equals(other.q) && this.x.equals(other.x)
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}
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function feFpToBigInteger() {
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return this.x
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}
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function feFpNegate() {
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return new ECFieldElementFp(this.q, this.x.negate().mod(this.q))
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}
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function feFpAdd(b) {
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return new ECFieldElementFp(this.q, this.x.add(b.toBigInteger()).mod(this.q))
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}
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function feFpSubtract(b) {
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return new ECFieldElementFp(
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this.q,
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this.x.subtract(b.toBigInteger()).mod(this.q)
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)
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}
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function feFpMultiply(b) {
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return new ECFieldElementFp(
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this.q,
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this.x.multiply(b.toBigInteger()).mod(this.q)
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)
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}
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function feFpSquare() {
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return new ECFieldElementFp(this.q, this.x.square().mod(this.q))
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}
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function feFpDivide(b) {
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return new ECFieldElementFp(
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this.q,
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this.x.multiply(b.toBigInteger().modInverse(this.q)).mod(this.q)
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)
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}
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ECFieldElementFp.prototype.equals = feFpEquals
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ECFieldElementFp.prototype.toBigInteger = feFpToBigInteger
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ECFieldElementFp.prototype.negate = feFpNegate
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ECFieldElementFp.prototype.add = feFpAdd
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ECFieldElementFp.prototype.subtract = feFpSubtract
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ECFieldElementFp.prototype.multiply = feFpMultiply
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ECFieldElementFp.prototype.square = feFpSquare
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ECFieldElementFp.prototype.divide = feFpDivide
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// ----------------
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// ECPointFp
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// constructor
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export function ECPointFp(curve, x, y, z) {
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this.curve = curve
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this.x = x
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this.y = y
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// Projective coordinates: either zinv == null or z * zinv == 1
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// z and zinv are just BigIntegers, not fieldElements
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if (z == null) {
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this.z = BigInteger.ONE
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} else {
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this.z = z
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}
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this.zinv = null
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//TODO: compression flag
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}
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function pointFpGetX() {
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if (this.zinv == null) {
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this.zinv = this.z.modInverse(this.curve.q)
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}
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var r = this.x.toBigInteger().multiply(this.zinv)
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this.curve.reduce(r)
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return this.curve.fromBigInteger(r)
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}
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function pointFpGetY() {
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if (this.zinv == null) {
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this.zinv = this.z.modInverse(this.curve.q)
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}
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var r = this.y.toBigInteger().multiply(this.zinv)
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this.curve.reduce(r)
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return this.curve.fromBigInteger(r)
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}
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function pointFpEquals(other) {
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if (other == this) return true
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if (this.isInfinity()) return other.isInfinity()
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if (other.isInfinity()) return this.isInfinity()
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var u, v
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// u = Y2 * Z1 - Y1 * Z2
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u = other.y
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.toBigInteger()
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.multiply(this.z)
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.subtract(this.y.toBigInteger().multiply(other.z))
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.mod(this.curve.q)
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if (!u.equals(BigInteger.ZERO)) return false
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// v = X2 * Z1 - X1 * Z2
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v = other.x
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.toBigInteger()
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.multiply(this.z)
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.subtract(this.x.toBigInteger().multiply(other.z))
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.mod(this.curve.q)
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return v.equals(BigInteger.ZERO)
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}
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function pointFpIsInfinity() {
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if (this.x == null && this.y == null) return true
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return (
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this.z.equals(BigInteger.ZERO) &&
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!this.y.toBigInteger().equals(BigInteger.ZERO)
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)
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}
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function pointFpNegate() {
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return new ECPointFp(this.curve, this.x, this.y.negate(), this.z)
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}
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function pointFpAdd(b) {
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if (this.isInfinity()) return b
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if (b.isInfinity()) return this
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// u = Y2 * Z1 - Y1 * Z2
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var u = b.y
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.toBigInteger()
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.multiply(this.z)
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.subtract(this.y.toBigInteger().multiply(b.z))
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.mod(this.curve.q)
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// v = X2 * Z1 - X1 * Z2
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var v = b.x
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.toBigInteger()
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.multiply(this.z)
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.subtract(this.x.toBigInteger().multiply(b.z))
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.mod(this.curve.q)
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if (BigInteger.ZERO.equals(v)) {
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if (BigInteger.ZERO.equals(u)) {
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return this.twice() // this == b, so double
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}
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return this.curve.getInfinity() // this = -b, so infinity
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}
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var THREE = new BigInteger('3')
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var x1 = this.x.toBigInteger()
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var y1 = this.y.toBigInteger()
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var x2 = b.x.toBigInteger()
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var y2 = b.y.toBigInteger()
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var v2 = v.square()
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var v3 = v2.multiply(v)
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var x1v2 = x1.multiply(v2)
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var zu2 = u.square().multiply(this.z)
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// x3 = v * (z2 * (z1 * u^2 - 2 * x1 * v^2) - v^3)
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var x3 = zu2
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.subtract(x1v2.shiftLeft(1))
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.multiply(b.z)
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.subtract(v3)
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.multiply(v)
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.mod(this.curve.q)
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// y3 = z2 * (3 * x1 * u * v^2 - y1 * v^3 - z1 * u^3) + u * v^3
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var y3 = x1v2
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.multiply(THREE)
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.multiply(u)
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.subtract(y1.multiply(v3))
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.subtract(zu2.multiply(u))
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.multiply(b.z)
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.add(u.multiply(v3))
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.mod(this.curve.q)
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// z3 = v^3 * z1 * z2
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var z3 = v3.multiply(this.z).multiply(b.z).mod(this.curve.q)
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return new ECPointFp(
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this.curve,
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this.curve.fromBigInteger(x3),
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this.curve.fromBigInteger(y3),
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z3
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)
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}
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function pointFpTwice() {
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if (this.isInfinity()) return this
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if (this.y.toBigInteger().signum() == 0) return this.curve.getInfinity()
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// TODO: optimized handling of constants
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var THREE = new BigInteger('3')
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var x1 = this.x.toBigInteger()
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var y1 = this.y.toBigInteger()
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var y1z1 = y1.multiply(this.z)
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var y1sqz1 = y1z1.multiply(y1).mod(this.curve.q)
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var a = this.curve.a.toBigInteger()
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// w = 3 * x1^2 + a * z1^2
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var w = x1.square().multiply(THREE)
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if (!BigInteger.ZERO.equals(a)) {
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w = w.add(this.z.square().multiply(a))
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}
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w = w.mod(this.curve.q)
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//this.curve.reduce(w);
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// x3 = 2 * y1 * z1 * (w^2 - 8 * x1 * y1^2 * z1)
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var x3 = w
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.square()
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.subtract(x1.shiftLeft(3).multiply(y1sqz1))
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.shiftLeft(1)
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.multiply(y1z1)
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.mod(this.curve.q)
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// y3 = 4 * y1^2 * z1 * (3 * w * x1 - 2 * y1^2 * z1) - w^3
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var y3 = w
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.multiply(THREE)
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.multiply(x1)
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.subtract(y1sqz1.shiftLeft(1))
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.shiftLeft(2)
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.multiply(y1sqz1)
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.subtract(w.square().multiply(w))
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.mod(this.curve.q)
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// z3 = 8 * (y1 * z1)^3
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var z3 = y1z1.square().multiply(y1z1).shiftLeft(3).mod(this.curve.q)
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return new ECPointFp(
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this.curve,
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this.curve.fromBigInteger(x3),
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this.curve.fromBigInteger(y3),
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z3
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)
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}
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// Simple NAF (Non-Adjacent Form) multiplication algorithm
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// TODO: modularize the multiplication algorithm
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function pointFpMultiply(k) {
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if (this.isInfinity()) return this
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if (k.signum() == 0) return this.curve.getInfinity()
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var e = k
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var h = e.multiply(new BigInteger('3'))
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var neg = this.negate()
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var R = this
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var i
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for (i = h.bitLength() - 2; i > 0; --i) {
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R = R.twice()
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var hBit = h.testBit(i)
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var eBit = e.testBit(i)
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if (hBit != eBit) {
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R = R.add(hBit ? this : neg)
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}
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}
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return R
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}
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// Compute this*j + x*k (simultaneous multiplication)
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function pointFpMultiplyTwo(j, x, k) {
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var i
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if (j.bitLength() > k.bitLength()) i = j.bitLength() - 1
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else i = k.bitLength() - 1
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var R = this.curve.getInfinity()
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var both = this.add(x)
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while (i >= 0) {
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R = R.twice()
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if (j.testBit(i)) {
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if (k.testBit(i)) {
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R = R.add(both)
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} else {
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R = R.add(this)
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}
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} else {
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if (k.testBit(i)) {
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R = R.add(x)
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}
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}
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--i
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}
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return R
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}
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ECPointFp.prototype.getX = pointFpGetX
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ECPointFp.prototype.getY = pointFpGetY
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ECPointFp.prototype.equals = pointFpEquals
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ECPointFp.prototype.isInfinity = pointFpIsInfinity
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ECPointFp.prototype.negate = pointFpNegate
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ECPointFp.prototype.add = pointFpAdd
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ECPointFp.prototype.twice = pointFpTwice
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ECPointFp.prototype.multiply = pointFpMultiply
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ECPointFp.prototype.multiplyTwo = pointFpMultiplyTwo
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// ----------------
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// ECCurveFp
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// constructor
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export function ECCurveFp(q, a, b) {
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this.q = q
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this.a = this.fromBigInteger(a)
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this.b = this.fromBigInteger(b)
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this.infinity = new ECPointFp(this, null, null)
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this.reducer = new Barrett(this.q)
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}
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function curveFpGetQ() {
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return this.q
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}
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function curveFpGetA() {
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return this.a
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}
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function curveFpGetB() {
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return this.b
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}
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function curveFpEquals(other) {
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if (other == this) return true
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return (
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this.q.equals(other.q) && this.a.equals(other.a) && this.b.equals(other.b)
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)
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}
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function curveFpGetInfinity() {
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return this.infinity
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}
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function curveFpFromBigInteger(x) {
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return new ECFieldElementFp(this.q, x)
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}
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function curveReduce(x) {
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this.reducer.reduce(x)
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}
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// for now, work with hex strings because they're easier in JS
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function curveFpDecodePointHex(s) {
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switch (
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parseInt(s.substr(0, 2), 16) // first byte
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) {
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case 0:
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return this.infinity
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case 2:
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case 3:
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// point compression not supported yet
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return null
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case 4:
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case 6:
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case 7:
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var len = (s.length - 2) / 2
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var xHex = s.substr(2, len)
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var yHex = s.substr(len + 2, len)
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return new ECPointFp(
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this,
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this.fromBigInteger(new BigInteger(xHex, 16)),
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this.fromBigInteger(new BigInteger(yHex, 16))
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)
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default:
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// unsupported
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return null
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}
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}
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function curveFpEncodePointHex(p) {
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if (p.isInfinity()) return '00'
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var xHex = p.getX().toBigInteger().toString(16)
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var yHex = p.getY().toBigInteger().toString(16)
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var oLen = this.getQ().toString(16).length
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if (oLen % 2 != 0) oLen++
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while (xHex.length < oLen) {
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xHex = '0' + xHex
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}
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while (yHex.length < oLen) {
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yHex = '0' + yHex
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}
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return '04' + xHex + yHex
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}
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ECCurveFp.prototype.getQ = curveFpGetQ
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ECCurveFp.prototype.getA = curveFpGetA
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ECCurveFp.prototype.getB = curveFpGetB
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ECCurveFp.prototype.equals = curveFpEquals
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ECCurveFp.prototype.getInfinity = curveFpGetInfinity
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ECCurveFp.prototype.fromBigInteger = curveFpFromBigInteger
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ECCurveFp.prototype.reduce = curveReduce
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ECCurveFp.prototype.decodePointHex = curveFpDecodePointHex
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ECCurveFp.prototype.encodePointHex = curveFpEncodePointHex
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