//сложение двух точек P1 и P2
public static ECPoint operator +(ECPoint p1, ECPoint p2)
{
ECPoint p3 = new ECPoint();
p3.a = p1.a;
p3.b = p1.b;
p3.FieldChar = p1.FieldChar;
BigInteger dy = p2.y - p1.y;
BigInteger dx = p2.x - p1.x;
if (dx < 0)
dx += p1.FieldChar;
if (dy < 0)
dy += p1.FieldChar;
BigInteger m = (dy * dx.modInverse(p1.FieldChar)) % p1.FieldChar;
if (m < 0)
m += p1.FieldChar;
p3.x = (m * m - p1.x - p2.x) % p1.FieldChar;
p3.y = (m * (p1.x - p3.x) - p1.y) % p1.FieldChar;
if (p3.x < 0)
p3.x += p1.FieldChar;
if (p3.y < 0)
p3.y += p1.FieldChar;
return p3;
}
//сложение точки P c собой же
public static ECPoint Double(ECPoint p)
{
ECPoint p2 = new ECPoint();
p2.a = p.a;
p2.b = p.b;
p2.FieldChar = p.FieldChar;
BigInteger dy = 3 * p.x * p.x + p.a;
BigInteger dx = 2 * p.y;
if (dx < 0)
dx += p.FieldChar;
if (dy < 0)
dy += p.FieldChar;
BigInteger m = (dy * dx.modInverse(p.FieldChar)) % p.FieldChar;
p2.x = (m * m - p.x - p.x) % p.FieldChar;
p2.y = (m * (p.x - p2.x) - p.y) % p.FieldChar;
if (p2.x < 0)
p2.x += p.FieldChar;
if (p2.y < 0)
p2.y += p.FieldChar;
return p2;
}
public ECPoint(ECPoint p)
{
x = p.x;
y = p.y;
a = p.a;
b = p.b;
FieldChar = p.FieldChar;
}
//Восстанавливаем координату y из координаты x и бита четности y
private ECPoint GDecompression()
{
byte y = xG[0];
byte[] x = new byte[xG.Length - 1];
Array.Copy(xG, 1, x, 0, xG.Length - 1);
BigInteger Xcord = new BigInteger(x);
BigInteger temp = (Xcord * Xcord * Xcord + a * Xcord + b) % p;
BigInteger beta = ModSqrt(temp, p);
BigInteger Ycord = new BigInteger();
if ((beta % 2) == (y % 2))
Ycord = beta;
else
Ycord = p - beta;
ECPoint G = new ECPoint();
G.a = a;
G.b = b;
G.FieldChar = p;
G.x = Xcord;
G.y = Ycord;
this.G = G;
return G;
}
//проверяем подпись
public bool SignVer(byte[] H, string sign, ECPoint Q)
{
string Rvector = sign.Substring(0, n.bitCount() / 4);
string Svector = sign.Substring(n.bitCount() / 4, n.bitCount() / 4);
encr_r = new BigInteger(Rvector, 16);
encr_s = new BigInteger(Svector, 16);
if ((encr_r < 1) || (encr_r > (n - 1)) || (encr_s < 1) || (encr_s > (n - 1)))
return false;
encr_alpha = new BigInteger(H);
encr_e = encr_alpha % n;
if (encr_e == 0)
encr_e = 1;
v = encr_e.modInverse(n);
z1 = (encr_s * v) % n;
z2 = n + ((-(encr_r * v)) % n);
this.G = GDecompression();
A = ECPoint.multiply(z1, G);
B = ECPoint.multiply(z2, Q);
encr_C = A + B;
R = encr_C.x % n;
if (R == encr_r)
return true;
else
return false;
}
//подписываем сообщение
public string SignGen(byte[] h, BigInteger d)
{
alpha = new BigInteger(h);
e = alpha % n;
if (e == 0)
e = 1;
k = new BigInteger();
C = new ECPoint();
r = new BigInteger();
s = new BigInteger();
do
{
do
{
k.genRandomBits(n.bitCount(), new Random());
} while ((k < 0) || (k > n));
C = ECPoint.multiply(k, G);
r = C.x % n;
s = ((r * d) + (k * e)) % n;
} while ((r == 0) || (s == 0));
string Rvector = padding(r.ToHexString(), n.bitCount() / 4);
string Svector = padding(s.ToHexString(), n.bitCount() / 4);
return Rvector + Svector;
}
//умножение точки на число x, по сути своей представляет x сложений точки самой с собой
public static ECPoint multiply(BigInteger x, ECPoint p)
{
ECPoint temp = p;
x = x - 1;
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 - 1;
}
x = x / 2;
p = Double(p);
}
return temp;
}
