Changed alot of things.

node_modules/ecc-jsbn/lib/ec.js

@@ -0,0 +1,561 @@
+// 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