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;
}
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);
}
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;
}