--- /dev/null
+// Basic Javascript Elliptic Curve implementation
+// Ported loosely from BouncyCastle's Java EC code
+// Only Fp curves implemented for now
+
+// Requires jsbn.js and jsbn2.js
+var BigInteger = require('jsbn').BigInteger
+var Barrett = BigInteger.prototype.Barrett
+
+// ----------------
+// ECFieldElementFp
+
+// constructor
+function ECFieldElementFp(q,x) {
+ 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));
+}
+
+function feFpToBigInteger() {
+ return this.x;
+}
+
+function feFpNegate() {
+ 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));
+}
+
+function feFpSubtract(b) {
+ 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));
+}
+
+function feFpSquare() {
+ 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));
+}
+
+ECFieldElementFp.prototype.equals = feFpEquals;
+ECFieldElementFp.prototype.toBigInteger = feFpToBigInteger;
+ECFieldElementFp.prototype.negate = feFpNegate;
+ECFieldElementFp.prototype.add = feFpAdd;
+ECFieldElementFp.prototype.subtract = feFpSubtract;
+ECFieldElementFp.prototype.multiply = feFpMultiply;
+ECFieldElementFp.prototype.square = feFpSquare;
+ECFieldElementFp.prototype.divide = feFpDivide;
+
+// ----------------
+// ECPointFp
+
+// 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
+}
+
+function pointFpGetX() {
+ if(this.zinv == null) {
+ this.zinv = this.z.modInverse(this.curve.q);
+ }
+ var r = this.x.toBigInteger().multiply(this.zinv);
+ this.curve.reduce(r);
+ return this.curve.fromBigInteger(r);
+}
+
+function pointFpGetY() {
+ if(this.zinv == null) {
+ this.zinv = this.z.modInverse(this.curve.q);
+ }
+ var r = this.y.toBigInteger().multiply(this.zinv);
+ this.curve.reduce(r);
+ return this.curve.fromBigInteger(r);
+}
+
+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.equals(BigInteger.ZERO)) 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.equals(BigInteger.ZERO);
+}
+
+function pointFpIsInfinity() {
+ if((this.x == null) && (this.y == null)) return true;
+ return this.z.equals(BigInteger.ZERO) && !this.y.toBigInteger().equals(BigInteger.ZERO);
+}
+
+function pointFpNegate() {
+ 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;
+
+ // u = Y2 * Z1 - Y1 * Z2
+ var u = b.y.toBigInteger().multiply(this.z).subtract(this.y.toBigInteger().multiply(b.z)).mod(this.curve.q);
+ // v = X2 * Z1 - X1 * Z2
+ var v = b.x.toBigInteger().multiply(this.z).subtract(this.x.toBigInteger().multiply(b.z)).mod(this.curve.q);
+
+ if(BigInteger.ZERO.equals(v)) {
+ if(BigInteger.ZERO.equals(u)) {
+ return this.twice(); // this == b, so double
+ }
+ return this.curve.getInfinity(); // this = -b, so infinity
+ }
+
+ var THREE = new BigInteger("3");
+ var x1 = this.x.toBigInteger();
+ var y1 = this.y.toBigInteger();
+ var x2 = b.x.toBigInteger();
+ var y2 = b.y.toBigInteger();
+
+ 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);
+
+ 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();
+
+ // TODO: optimized handling of constants
+ var THREE = new BigInteger("3");
+ 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();
+
+ // w = 3 * x1^2 + a * z1^2
+ var w = x1.square().multiply(THREE);
+ if(!BigInteger.ZERO.equals(a)) {
+ w = w.add(this.z.square().multiply(a));
+ }
+ w = w.mod(this.curve.q);
+ //this.curve.reduce(w);
+ // 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.square().multiply(w)).mod(this.curve.q);
+ // z3 = 8 * (y1 * z1)^3
+ var z3 = y1z1.square().multiply(y1z1).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();
+
+ var e = k;
+ var h = e.multiply(new BigInteger("3"));
+
+ var neg = this.negate();
+ var R = this;
+
+ var i;
+ for(i = h.bitLength() - 2; i > 0; --i) {
+ R = R.twice();
+
+ var hBit = h.testBit(i);
+ var eBit = e.testBit(i);
+
+ if (hBit != eBit) {
+ R = R.add(hBit ? this : neg);
+ }
+ }
+
+ return R;
+}
+
+// Compute this*j + x*k (simultaneous multiplication)
+function pointFpMultiplyTwo(j,x,k) {
+ var i;
+ if(j.bitLength() > k.bitLength())
+ i = j.bitLength() - 1;
+ else
+ i = k.bitLength() - 1;
+
+ var R = this.curve.getInfinity();
+ var both = this.add(x);
+ while(i >= 0) {
+ R = R.twice();
+ if(j.testBit(i)) {
+ if(k.testBit(i)) {
+ R = R.add(both);
+ }
+ else {
+ R = R.add(this);
+ }
+ }
+ else {
+ if(k.testBit(i)) {
+ R = R.add(x);
+ }
+ }
+ --i;
+ }
+
+ return R;
+}
+
+ECPointFp.prototype.getX = pointFpGetX;
+ECPointFp.prototype.getY = pointFpGetY;
+ECPointFp.prototype.equals = pointFpEquals;
+ECPointFp.prototype.isInfinity = pointFpIsInfinity;
+ECPointFp.prototype.negate = pointFpNegate;
+ECPointFp.prototype.add = pointFpAdd;
+ECPointFp.prototype.twice = pointFpTwice;
+ECPointFp.prototype.multiply = pointFpMultiply;
+ECPointFp.prototype.multiplyTwo = pointFpMultiplyTwo;
+
+// ----------------
+// ECCurveFp
+
+// 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.reducer = new Barrett(this.q);
+}
+
+function curveFpGetQ() {
+ return this.q;
+}
+
+function curveFpGetA() {
+ return this.a;
+}
+
+function curveFpGetB() {
+ 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));
+}
+
+function curveFpGetInfinity() {
+ return this.infinity;
+}
+
+function curveFpFromBigInteger(x) {
+ return new ECFieldElementFp(this.q, x);
+}
+
+function curveReduce(x) {
+ this.reducer.reduce(x);
+}
+
+// for now, work with hex strings because they're easier in JS
+function curveFpDecodePointHex(s) {
+ switch(parseInt(s.substr(0,2), 16)) { // first byte
+ case 0:
+ return this.infinity;
+ case 2:
+ case 3:
+ // point compression not supported yet
+ return null;
+ case 4:
+ case 6:
+ case 7:
+ var len = (s.length - 2) / 2;
+ var xHex = s.substr(2, len);
+ var yHex = s.substr(len+2, len);
+
+ return new ECPointFp(this,
+ this.fromBigInteger(new BigInteger(xHex, 16)),
+ this.fromBigInteger(new BigInteger(yHex, 16)));
+
+ default: // unsupported
+ return null;
+ }
+}
+
+function curveFpEncodePointHex(p) {
+ if (p.isInfinity()) return "00";
+ var xHex = p.getX().toBigInteger().toString(16);
+ var yHex = p.getY().toBigInteger().toString(16);
+ var oLen = this.getQ().toString(16).length;
+ if ((oLen % 2) != 0) oLen++;
+ while (xHex.length < oLen) {
+ xHex = "0" + xHex;
+ }
+ while (yHex.length < oLen) {
+ yHex = "0" + yHex;
+ }
+ return "04" + xHex + yHex;
+}
+
+ECCurveFp.prototype.getQ = curveFpGetQ;
+ECCurveFp.prototype.getA = curveFpGetA;
+ECCurveFp.prototype.getB = curveFpGetB;
+ECCurveFp.prototype.equals = curveFpEquals;
+ECCurveFp.prototype.getInfinity = curveFpGetInfinity;
+ECCurveFp.prototype.fromBigInteger = curveFpFromBigInteger;
+ECCurveFp.prototype.reduce = curveReduce;
+//ECCurveFp.prototype.decodePointHex = curveFpDecodePointHex;
+ECCurveFp.prototype.encodePointHex = curveFpEncodePointHex;
+
+// from: https://github.com/kaielvin/jsbn-ec-point-compression
+ECCurveFp.prototype.decodePointHex = function(s)
+{
+ var yIsEven;
+ switch(parseInt(s.substr(0,2), 16)) { // first byte
+ case 0:
+ return this.infinity;
+ case 2:
+ yIsEven = false;
+ case 3:
+ if(yIsEven == undefined) yIsEven = true;
+ var len = s.length - 2;
+ var xHex = s.substr(2, len);
+ var x = this.fromBigInteger(new BigInteger(xHex,16));
+ var alpha = x.multiply(x.square().add(this.getA())).add(this.getB());
+ var beta = alpha.sqrt();
+
+ if (beta == null) throw "Invalid point compression";
+
+ var betaValue = beta.toBigInteger();
+ if (betaValue.testBit(0) != yIsEven)
+ {
+ // Use the other root
+ beta = this.fromBigInteger(this.getQ().subtract(betaValue));
+ }
+ return new ECPointFp(this,x,beta);
+ case 4:
+ case 6:
+ case 7:
+ var len = (s.length - 2) / 2;
+ var xHex = s.substr(2, len);
+ var yHex = s.substr(len+2, len);
+
+ return new ECPointFp(this,
+ this.fromBigInteger(new BigInteger(xHex, 16)),
+ this.fromBigInteger(new BigInteger(yHex, 16)));
+
+ default: // unsupported
+ return null;
+ }
+}
+ECCurveFp.prototype.encodeCompressedPointHex = function(p)
+{
+ if (p.isInfinity()) return "00";
+ var xHex = p.getX().toBigInteger().toString(16);
+ var oLen = this.getQ().toString(16).length;
+ if ((oLen % 2) != 0) oLen++;
+ while (xHex.length < oLen)
+ xHex = "0" + xHex;
+ var yPrefix;
+ if(p.getY().toBigInteger().isEven()) yPrefix = "02";
+ else yPrefix = "03";
+
+ return yPrefix + xHex;
+}
+
+
+ECFieldElementFp.prototype.getR = function()
+{
+ if(this.r != undefined) return this.r;
+
+ this.r = null;
+ var bitLength = this.q.bitLength();
+ if (bitLength > 128)
+ {
+ var firstWord = this.q.shiftRight(bitLength - 64);
+ if (firstWord.intValue() == -1)
+ {
+ this.r = BigInteger.ONE.shiftLeft(bitLength).subtract(this.q);
+ }
+ }
+ return this.r;
+}
+ECFieldElementFp.prototype.modMult = function(x1,x2)
+{
+ return this.modReduce(x1.multiply(x2));
+}
+ECFieldElementFp.prototype.modReduce = function(x)
+{
+ if (this.getR() != null)
+ {
+ var qLen = q.bitLength();
+ while (x.bitLength() > (qLen + 1))
+ {
+ var u = x.shiftRight(qLen);
+ var v = x.subtract(u.shiftLeft(qLen));
+ if (!this.getR().equals(BigInteger.ONE))
+ {
+ u = u.multiply(this.getR());
+ }
+ x = u.add(v);
+ }
+ while (x.compareTo(q) >= 0)
+ {
+ x = x.subtract(q);
+ }
+ }
+ else
+ {
+ x = x.mod(q);
+ }
+ return x;
+}
+ECFieldElementFp.prototype.sqrt = function()
+{
+ if (!this.q.testBit(0)) throw "unsupported";
+
+ // p mod 4 == 3
+ if (this.q.testBit(1))
+ {
+ var z = new ECFieldElementFp(this.q,this.x.modPow(this.q.shiftRight(2).add(BigInteger.ONE),this.q));
+ return z.square().equals(this) ? z : null;
+ }
+
+ // p mod 4 == 1
+ var qMinusOne = this.q.subtract(BigInteger.ONE);
+
+ var legendreExponent = qMinusOne.shiftRight(1);
+ if (!(this.x.modPow(legendreExponent, this.q).equals(BigInteger.ONE)))
+ {
+ return null;
+ }
+
+ var u = qMinusOne.shiftRight(2);
+ var k = u.shiftLeft(1).add(BigInteger.ONE);
+
+ var Q = this.x;
+ var fourQ = modDouble(modDouble(Q));
+
+ var U, V;
+ do
+ {
+ var P;
+ do
+ {
+ P = new BigInteger(this.q.bitLength(), new SecureRandom());
+ }
+ while (P.compareTo(this.q) >= 0
+ || !(P.multiply(P).subtract(fourQ).modPow(legendreExponent, this.q).equals(qMinusOne)));
+
+ var result = this.lucasSequence(P, Q, k);
+ U = result[0];
+ V = result[1];
+
+ if (this.modMult(V, V).equals(fourQ))
+ {
+ // Integer division by 2, mod q
+ if (V.testBit(0))
+ {
+ V = V.add(q);
+ }
+
+ V = V.shiftRight(1);
+
+ return new ECFieldElementFp(q,V);
+ }
+ }
+ while (U.equals(BigInteger.ONE) || U.equals(qMinusOne));
+
+ return null;
+}
+ECFieldElementFp.prototype.lucasSequence = function(P,Q,k)
+{
+ var n = k.bitLength();
+ var s = k.getLowestSetBit();
+
+ var Uh = BigInteger.ONE;
+ var Vl = BigInteger.TWO;
+ var Vh = P;
+ var Ql = BigInteger.ONE;
+ var Qh = BigInteger.ONE;
+
+ for (var j = n - 1; j >= s + 1; --j)
+ {
+ Ql = this.modMult(Ql, Qh);
+
+ if (k.testBit(j))
+ {
+ Qh = this.modMult(Ql, Q);
+ Uh = this.modMult(Uh, Vh);
+ Vl = this.modReduce(Vh.multiply(Vl).subtract(P.multiply(Ql)));
+ Vh = this.modReduce(Vh.multiply(Vh).subtract(Qh.shiftLeft(1)));
+ }
+ else
+ {
+ Qh = Ql;
+ Uh = this.modReduce(Uh.multiply(Vl).subtract(Ql));
+ Vh = this.modReduce(Vh.multiply(Vl).subtract(P.multiply(Ql)));
+ Vl = this.modReduce(Vl.multiply(Vl).subtract(Ql.shiftLeft(1)));
+ }
+ }
+
+ Ql = this.modMult(Ql, Qh);
+ Qh = this.modMult(Ql, Q);
+ Uh = this.modReduce(Uh.multiply(Vl).subtract(Ql));
+ Vl = this.modReduce(Vh.multiply(Vl).subtract(P.multiply(Ql)));
+ Ql = this.modMult(Ql, Qh);
+
+ for (var j = 1; j <= s; ++j)
+ {
+ Uh = this.modMult(Uh, Vl);
+ Vl = this.modReduce(Vl.multiply(Vl).subtract(Ql.shiftLeft(1)));
+ Ql = this.modMult(Ql, Ql);
+ }
+
+ return [ Uh, Vl ];
+}
+
+var exports = {
+ ECCurveFp: ECCurveFp,
+ ECPointFp: ECPointFp,
+ ECFieldElementFp: ECFieldElementFp
+}
+
+module.exports = exports
Code Review / simantics / district.git / blobdiff