ec: white space fixes
It is advised to use ?w=0 in comparing this commit.
This commit is contained in:
Daniel Cousens
parent
8a2dcaaaf5
commit
79c7b68d35
1 changed files with 128 additions and 124 deletions
252
src/ec.js
252
src/ec.js
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@ -9,42 +9,42 @@ var BigInteger = require('bigi')
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var THREE = BigInteger.valueOf(3)
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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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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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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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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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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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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(this.q, this.x.subtract(b.toBigInteger()).mod(this.q));
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return new ECFieldElementFp(this.q, this.x.subtract(b.toBigInteger()).mod(this.q));
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}
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function feFpMultiply(b) {
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return new ECFieldElementFp(this.q, this.x.multiply(b.toBigInteger()).mod(this.q));
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return new ECFieldElementFp(this.q, this.x.multiply(b.toBigInteger()).mod(this.q));
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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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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(this.q, this.x.multiply(b.toBigInteger().modInverse(this.q)).mod(this.q));
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return new ECFieldElementFp(this.q, this.x.multiply(b.toBigInteger().modInverse(this.q)).mod(this.q));
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}
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ECFieldElementFp.prototype.equals = feFpEquals;
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@ -61,151 +61,156 @@ ECFieldElementFp.prototype.divide = feFpDivide;
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// constructor
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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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}
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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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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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}
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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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return this.curve.fromBigInteger(this.x.toBigInteger().multiply(this.zinv).mod(this.curve.q));
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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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return this.curve.fromBigInteger(this.x.toBigInteger().multiply(this.zinv).mod(this.curve.q));
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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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return this.curve.fromBigInteger(this.y.toBigInteger().multiply(this.zinv).mod(this.curve.q));
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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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return this.curve.fromBigInteger(this.y.toBigInteger().multiply(this.zinv).mod(this.curve.q));
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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.toBigInteger().multiply(this.z).subtract(this.y.toBigInteger().multiply(other.z)).mod(this.curve.q);
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if (u.signum() !== 0) return false;
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// v = X2 * Z1 - X1 * Z2
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v = other.x.toBigInteger().multiply(this.z).subtract(this.x.toBigInteger().multiply(other.z)).mod(this.curve.q);
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return v.signum() === 0;
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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.toBigInteger().multiply(this.z).subtract(this.y.toBigInteger().multiply(other.z)).mod(this.curve.q);
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if (u.signum() !== 0) return false;
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// v = X2 * Z1 - X1 * Z2
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v = other.x.toBigInteger().multiply(this.z).subtract(this.x.toBigInteger().multiply(other.z)).mod(this.curve.q);
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return v.signum() === 0;
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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 this.z.signum() === 0 && this.y.toBigInteger().signum() !== 0;
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if ((this.x == null) && (this.y == null)) return true;
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return this.z.signum() === 0 && this.y.toBigInteger().signum() !== 0;
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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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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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if (this.isInfinity()) return b;
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if (b.isInfinity()) return this;
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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 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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// u = Y2 * Z1 - Y1 * Z2
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var u = y2.multiply(this.z).subtract(y1.multiply(b.z)).mod(this.curve.q)
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// v = X2 * Z1 - X1 * Z2
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var v = x2.multiply(this.z).subtract(x1.multiply(b.z)).mod(this.curve.q)
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// u = Y2 * Z1 - Y1 * Z2
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var u = y2.multiply(this.z).subtract(y1.multiply(b.z)).mod(this.curve.q)
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// v = X2 * Z1 - X1 * Z2
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var v = x2.multiply(this.z).subtract(x1.multiply(b.z)).mod(this.curve.q)
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if(v.signum() === 0) {
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if(u.signum() === 0) {
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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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if (v.signum() === 0) {
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if (u.signum() === 0) {
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return this.twice(); // this == b, so double
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}
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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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return this.curve.getInfinity(); // this = -b, so infinity
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}
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// x3 = v * (z2 * (z1 * u^2 - 2 * x1 * v^2) - v^3)
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var x3 = zu2.subtract(x1v2.shiftLeft(1)).multiply(b.z).subtract(v3).multiply(v).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.multiply(THREE).multiply(u).subtract(y1.multiply(v3)).subtract(zu2.multiply(u)).multiply(b.z).add(u.multiply(v3)).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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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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return new ECPointFp(this.curve, this.curve.fromBigInteger(x3), this.curve.fromBigInteger(y3), z3);
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// x3 = v * (z2 * (z1 * u^2 - 2 * x1 * v^2) - v^3)
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var x3 = zu2.subtract(x1v2.shiftLeft(1)).multiply(b.z).subtract(v3).multiply(v).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.multiply(THREE).multiply(u).subtract(y1.multiply(v3)).subtract(zu2.multiply(u)).multiply(b.z).add(u.multiply(v3)).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(this.curve, this.curve.fromBigInteger(x3), this.curve.fromBigInteger(y3), z3);
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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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if (this.isInfinity()) return this;
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if (this.y.toBigInteger().signum() === 0) return this.curve.getInfinity();
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var x1 = this.x.toBigInteger();
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var y1 = this.y.toBigInteger();
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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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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(a.signum() !== 0) {
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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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// x3 = 2 * y1 * z1 * (w^2 - 8 * x1 * y1^2 * z1)
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var x3 = w.square().subtract(x1.shiftLeft(3).multiply(y1sqz1)).shiftLeft(1).multiply(y1z1).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.multiply(THREE).multiply(x1).subtract(y1sqz1.shiftLeft(1)).shiftLeft(2).multiply(y1sqz1).subtract(w.pow(3)).mod(this.curve.q);
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// z3 = 8 * (y1 * z1)^3
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var z3 = y1z1.pow(3).shiftLeft(3).mod(this.curve.q);
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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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return new ECPointFp(this.curve, this.curve.fromBigInteger(x3), this.curve.fromBigInteger(y3), z3);
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if (a.signum() !== 0) {
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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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// x3 = 2 * y1 * z1 * (w^2 - 8 * x1 * y1^2 * z1)
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var x3 = w.square().subtract(x1.shiftLeft(3).multiply(y1sqz1)).shiftLeft(1).multiply(y1z1).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.multiply(THREE).multiply(x1).subtract(y1sqz1.shiftLeft(1)).shiftLeft(2).multiply(y1sqz1).subtract(w.pow(3)).mod(this.curve.q);
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// z3 = 8 * (y1 * z1)^3
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var z3 = y1z1.pow(3).shiftLeft(3).mod(this.curve.q);
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return new ECPointFp(this.curve, this.curve.fromBigInteger(x3), this.curve.fromBigInteger(y3), z3);
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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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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(THREE)
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var e = k;
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var h = e.multiply(THREE)
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var neg = this.negate();
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var R = this;
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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 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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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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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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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())
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if (j.bitLength() > k.bitLength())
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i = j.bitLength() - 1;
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else
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i = k.bitLength() - 1;
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@ -214,8 +219,8 @@ function pointFpMultiplyTwo(j,x,k) {
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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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if (j.testBit(i)) {
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if (k.testBit(i)) {
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R = R.add(both);
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}
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else {
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@ -223,7 +228,7 @@ function pointFpMultiplyTwo(j,x,k) {
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}
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}
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else {
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if(k.testBit(i)) {
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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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@ -248,35 +253,35 @@ ECPointFp.prototype.multiplyTwo = pointFpMultiplyTwo;
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// constructor
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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.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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}
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function curveFpGetQ() {
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return this.q;
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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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return this.a;
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}
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function curveFpGetB() {
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return this.b;
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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(this.q.equals(other.q) && this.a.equals(other.a) && this.b.equals(other.b));
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if (other == this) return true;
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return(this.q.equals(other.q) && this.a.equals(other.a) && this.b.equals(other.b));
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}
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function curveFpGetInfinity() {
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return this.infinity;
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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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return new ECFieldElementFp(this.q, x);
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}
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ECCurveFp.prototype.getQ = curveFpGetQ;
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@ -410,6 +415,5 @@ ECPointFp.prototype.validate = function () {
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return true;
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};
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module.exports = ECCurveFp;
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module.exports.ECPointFp = ECPointFp;
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