public static CurvePoint operator +(CurvePoint p1, CurvePoint p2)
{
CurvePoint res = new CurvePoint();
res.a = p1.a;
res.b = p1.b;
res.mod = p1.mod;
BigInteger dy = p2.y - p1.y;
BigInteger dx = p2.x - p1.x;
if (dx < 0)
{
dx += p1.mod;
}
if (dy < 0)
{
dy += p1.mod;
}
BigInteger alpha = (dy * dx.ModInvert(p1.mod)) % p1.mod;
if (alpha < 0)
{
alpha += p1.mod;
}
res.x = (alpha * alpha - p1.x - p2.x) % p1.mod;
if (res.x < 0)
{
res.x += p1.mod;
}
res.y = (alpha * (p1.x - res.x) - p1.y) % p1.mod;
if (res.y < 0)
{
res.y += p1.mod;
}
return(res);
}
public static CurvePoint operator *(BigInteger x, CurvePoint p)
{
CurvePoint temp = p;
x--;
while (x != 0)
{
if ((x % 2) != 0)
{
if ((temp.x == p.x) || (temp.y == p.y))
{
temp = Double(temp);
}
else
{
temp = temp + p;
}
x--;
}
x /= 2;
p = Double(p);
}
return(temp);
}
public static bool VerifySignature(BigInteger msg, Tuple <BigInteger, BigInteger> signature, CurvePoint G, CurvePoint Q, BigInteger n)
{
BigInteger r = signature.Item1;
BigInteger s = signature.Item2;
if ((r < 1) || (r > (n - 1)) || (s < 1) || (s > (n - 1)))
{
return(false);
}
BigInteger e = msg % n;
if (e < 0)
{
e = -e;
}
if (e == 0)
{
e = 1;
}
BigInteger v = e.ModInvert(n);
BigInteger param1 = (s * v) % n;
BigInteger param2 = n + ((-(r * v)) % n);
CurvePoint A = param1 * G;
CurvePoint B = param2 * Q;
CurvePoint C = A + B;
BigInteger R = C.x % n;
return(R == r);
}
public static Tuple <BigInteger, BigInteger> GetSignature(BigInteger msg, BigInteger d, CurvePoint G, BigInteger n)
{
BigInteger e = msg % n;
if (e < 0)
{
e = -e;
}
if (e == 0)
{
e = 1;
}
CurvePoint C = new CurvePoint();
BigInteger r = BigInteger.Zero;
BigInteger s = BigInteger.Zero;
int length = n.ToByteArray().Length;
BigInteger k = BigInteger.Zero;
do
{
do
{
k = RSA.GetRandomBigInteger(length - 1);
} while ((k < 0) || (k > n));
C = k * G;
r = C.x % n;
s = ((r * d) + (k * e)) % n;
} while ((r == 0) || (s == 0));
return(Tuple.Create(r, s));
}