ec2.js

// Extension of Elliptic Curve implementation JSBN
// to support compression and decompression of EC
// points.
// Ported loosely from BouncyCastle's Java EC code
// like the original JSBN.

// Requires jsbn.js, jsbn2.js, rng.js and ec.js
// http://www-cs-students.stanford.edu/~tjw/jsbn/


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 ];
}