Ejemplo n.º 1
0
        protected FpCurve(BigInteger q, BigInteger r, ECFieldElement a, ECFieldElement b, BigInteger order, BigInteger cofactor)
            : base(q)
        {
            this.m_q = q;
            this.m_r = r;
            this.m_infinity = new FpPoint(this, null, null);

            this.m_a = a;
            this.m_b = b;
            this.m_order = order;
            this.m_cofactor = cofactor;
            this.m_coord = FP_DEFAULT_COORDS;
        }
Ejemplo n.º 2
0
        public static ECKey RecoverFromSignature(int recId, ECDSASignature sig, byte[] message, bool compressed)
        {
            if(recId < 0)
                throw new ArgumentException("recId should be positive");
            if(sig.R.SignValue < 0)
                throw new ArgumentException("r should be positive");
            if(sig.S.SignValue < 0)
                throw new ArgumentException("s should be positive");
            if(message == null)
                throw new ArgumentNullException("message");

            var curve = ECKey.CreateCurve();

            // 1.0 For j from 0 to h   (h == recId here and the loop is outside this function)
            //   1.1 Let x = r + jn

            var n = curve.N;
            var i = BitcoinKit.BouncyCastle.Math.BigInteger.ValueOf((long)recId / 2);
            var x = sig.R.Add(i.Multiply(n));

            //   1.2. Convert the integer x to an octet string X of length mlen using the conversion routine
            //        specified in Section 2.3.7, where mlen = ⌈(log2 p)/8⌉ or mlen = ⌈m/8⌉.
            //   1.3. Convert the octet string (16 set binary digits)||X to an elliptic curve point R using the
            //        conversion routine specified in Section 2.3.4. If this conversion routine outputs “invalid”, then
            //        do another iteration of Step 1.
            //
            // More concisely, what these points mean is to use X as a compressed public key.
            var prime = ((FpCurve)curve.Curve).Q;
            if(x.CompareTo(prime) >= 0)
            {
                return null;
            }

            // Compressed keys require you to know an extra bit of data about the y-coord as there are two possibilities.
            // So it's encoded in the recId.
            ECPoint R = DecompressKey(x, (recId & 1) == 1);
            //   1.4. If nR != point at infinity, then do another iteration of Step 1 (callers responsibility).

            if(!R.Multiply(n).IsInfinity)
                return null;

            //   1.5. Compute e from M using Steps 2 and 3 of ECDSA signature verification.
            var e = new BitcoinKit.BouncyCastle.Math.BigInteger(1, message);
            //   1.6. For k from 1 to 2 do the following.   (loop is outside this function via iterating recId)
            //   1.6.1. Compute a candidate public key as:
            //               Q = mi(r) * (sR - eG)
            //
            // Where mi(x) is the modular multiplicative inverse. We transform this into the following:
            //               Q = (mi(r) * s ** R) + (mi(r) * -e ** G)
            // Where -e is the modular additive inverse of e, that is z such that z + e = 0 (mod n). In the above equation
            // ** is point multiplication and + is point addition (the EC group operator).
            //
            // We can find the additive inverse by subtracting e from zero then taking the mod. For example the additive
            // inverse of 3 modulo 11 is 8 because 3 + 8 mod 11 = 0, and -3 mod 11 = 8.

            var eInv = BitcoinKit.BouncyCastle.Math.BigInteger.Zero.Subtract(e).Mod(n);
            var rInv = sig.R.ModInverse(n);
            var srInv = rInv.Multiply(sig.S).Mod(n);
            var eInvrInv = rInv.Multiply(eInv).Mod(n);
            var q = (FpPoint)ECAlgorithms.SumOfTwoMultiplies(curve.G, eInvrInv, R, srInv);
            if(compressed)
            {
                q = new FpPoint(curve.Curve, q.X, q.Y, true);
            }
            return new ECKey(q.GetEncoded(), false);
        }
Ejemplo n.º 3
0
        public FpCurve(BigInteger q, BigInteger a, BigInteger b, BigInteger order, BigInteger cofactor)
            : base(q)
        {
            this.m_q = q;
            this.m_r = FpFieldElement.CalculateResidue(q);
            this.m_infinity = new FpPoint(this, null, null);

            this.m_a = FromBigInteger(a);
            this.m_b = FromBigInteger(b);
            this.m_order = order;
            this.m_cofactor = cofactor;
            this.m_coord = FP_DEFAULT_COORDS;
        }