//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 * modInverse(dx, 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;
}
//сложение двух точек P1 и P2
public static ECPoint operator +(ECPoint leftPoint, ECPoint rightPoint)
{
ECPoint resultPoint = new ECPoint();
resultPoint.a = leftPoint.a;
resultPoint.b = leftPoint.b;
resultPoint.FieldChar = leftPoint.FieldChar;
BigInteger dy = rightPoint.y - leftPoint.y;
BigInteger dx = rightPoint.x - leftPoint.x;
if (dx < 0)
dx += leftPoint.FieldChar;
if (dy < 0)
dy += leftPoint.FieldChar;
BigInteger m = (dy * modInverse(dx, leftPoint.FieldChar)) % leftPoint.FieldChar;
if (m < 0)
m += leftPoint.FieldChar;
resultPoint.x = (m * m - leftPoint.x - rightPoint.x) % leftPoint.FieldChar;
resultPoint.y = (m * (leftPoint.x - resultPoint.x) - leftPoint.y) % leftPoint.FieldChar;
if (resultPoint.x < 0)
resultPoint.x += leftPoint.FieldChar;
if (resultPoint.y < 0)
resultPoint.y += leftPoint.FieldChar;
return resultPoint;
}
//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;
}
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 SingVer(byte[] H, string sing, ECPoint Q)
{
string Rvector = sing.Substring(0, n.bitCount() / 4);
string Svector = sing.Substring(n.bitCount() / 4, n.bitCount() / 4);
BigInteger r = new BigInteger(Rvector, 16);
BigInteger s = new BigInteger(Svector, 16);
if ((r < 1) || (r > (n - 1)) || (s < 1) || (s > (n - 1)))
return false;
BigInteger alpha = new BigInteger(H);
BigInteger e = alpha % n;
if (e == 0)
e = 1;
BigInteger v = e.modInverse(n);
BigInteger z1 = (s * v) % n;
BigInteger z2 = n + ((-(r * v)) % n);
this.G = GDecompression();
ECPoint A = ECPoint.multiply(z1, G);
ECPoint B = ECPoint.multiply(z2, Q);
ECPoint C = A + B;
BigInteger R = C.x % n;
if (R == r)
return true;
else
return false;
}
//подписываем сообщение
public string SingGen(byte[] h, BigInteger d)
{
BigInteger alpha = new BigInteger(h);
BigInteger e = alpha % n;
if (e == 0)
e = 1;
BigInteger k = new BigInteger();
ECPoint C=new ECPoint();
BigInteger r=new BigInteger();
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;
}
public override string Encrypt(string text)
{
p = new BigInteger("6277101735386680763835789423207666416083908700390324961279", 10);
a = new BigInteger("-3", 10);
b = new BigInteger("64210519e59c80e70fa7e9ab72243049feb8deecc146b9b1", 16);
xG = FromHexStringToByte("03188da80eb03090f67cbf20eb43a18800f4ff0afd82ff1012");
n = new BigInteger("ffffffffffffffffffffffff99def836146bc9b1b4d22831", 16);
BigInteger d = GenPrivateKey(192);
Q = GenPublicKey(d);
GOST hash = new GOST(256);
byte[] H = hash.GetHash(Encoding.Default.GetBytes(text));
signature = GenerateSignature(H, d);
return signature;
}