/// <summary>
/// 生成椭圆曲线数字签名
/// </summary>
/// <param name="message">要签名的消息</param>
/// <returns>返回签名的数字编码（r,s）</returns>
public BigInteger[] GenerateSignature(byte[] message)
{
if (privateKey == null)
{
throw new InvalidOperationException();
}
BigInteger e = CalculateE(curve.N, message);
BigInteger d = new BigInteger(privateKey.Reverse().Concat(new byte[1]).ToArray());
BigInteger r, s;
{
do
{
BigInteger k;
do
{
do
{
k = Helper_BigInt.NextBigInteger(curve.N.GetBitLength());
}while (k.Sign == 0 || k.CompareTo(curve.N) >= 0);
ECPoint p = ECPoint.Multiply(curve.G, k);
BigInteger x = p.X.Value;
r = x.Mod(curve.N);
}while (r.Sign == 0);
s = (k.ModInverse(curve.N) * (e + d * r)).Mod(curve.N);
if (s > curve.N / 2)
{
s = curve.N - s;
}
}while (s.Sign == 0);
}
return(new BigInteger[] { r, s });
}
public static UmbralPrivateKey GenRandomPrikey()
{
UmbralPrivateKey k = new UmbralPrivateKey();
k.key = Helper_BigInt.NextBigInteger(k.curve.N.GetBitLength());
return(k);
}
public ECFieldElement Sqrt()
{
if (curve.Q.TestBit(1))
{
ECFieldElement z = new ECFieldElement(BigInteger.ModPow(Value, (curve.Q >> 2) + 1, curve.Q), curve);
return(z.Square().Equals(this) ? z : null);
}
BigInteger qMinusOne = curve.Q - 1;
BigInteger legendreExponent = qMinusOne >> 1;
if (BigInteger.ModPow(Value, legendreExponent, curve.Q) != 1)
{
return(null);
}
BigInteger u = qMinusOne >> 2;
BigInteger k = (u << 1) + 1;
BigInteger Q = this.Value;
BigInteger fourQ = (Q << 2).Mod(curve.Q);
BigInteger U, V;
do
{
BigInteger P;
do
{
P = Helper_BigInt.NextBigIntegerQuick(curve.Q.GetBitLength());
}while (P >= curve.Q || BigInteger.ModPow(P * P - fourQ, legendreExponent, curve.Q) != qMinusOne);
BigInteger[] result = FastLucasSequence(curve.Q, P, Q, k);
U = result[0];
V = result[1];
if ((V * V).Mod(curve.Q) == fourQ)
{
if (V.TestBit(0))
{
V += curve.Q;
}
V >>= 1;
System.Diagnostics.Debug.Assert((V * V).Mod(curve.Q) == Value);
return(new ECFieldElement(V, curve));
}
}while (U.Equals(BigInteger.One) || U.Equals(qMinusOne));
return(null);
}