//умножение точки на число.
public static CECPoint multiply(CECPoint p, BigInteger c)
{
CECPoint res = p;
c = c - 1;
while (c != 0)
{
if ((c % 2) != 0)
{
if ((res.x == p.x) || (res.y == p.y))
{
res = doubling(res);
}
else
{
res = res + p;
}
c = c - 1;
}
c = c / 2;
p = doubling(p);
}
return(res);
}
//восстановление координат Y из координаты X и бита четности Y.
private CECPoint 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;
}
CECPoint G = new CECPoint();
G.a = a;
G.b = b;
G.fieldChar = p;
G.x = Xcord;
G.y = Ycord;
this.G = G;
return(G);
}
//генерация публичного ключа (с помощью секретного).
public CECPoint genPublicKey(BigInteger d)
{
CECPoint G = gDecompression();
CECPoint Q = CECPoint.multiply(G, d);
return(Q);
}
//формирование цифровой подписи.
public string genDS(byte[] h, BigInteger d)
{
BigInteger a = new BigInteger(h);
BigInteger e = a % n;
if (e == 0)
{
e = 1;
}
BigInteger k = new BigInteger();
CECPoint C = new CECPoint();
BigInteger r = new BigInteger();
BigInteger s = new BigInteger();
do
{
do
{
k.genRandomBits(n.bitCount(), new Random());
}while ((k < 0) || (k > n));
C = CECPoint.multiply(G, k);
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);
}
public CECPoint(CECPoint p)
{
a = p.a;
b = p.b;
x = p.x;
y = p.y;
fieldChar = p.fieldChar;
}
//сложение пары точек.
public static CECPoint operator+(CECPoint p1, CECPoint p2)
{
CECPoint res = new CECPoint();
res.a = p1.a;
res.b = p1.b;
res.fieldChar = p1.fieldChar;
BigInteger dx = p2.x - p1.x;
BigInteger dy = p2.y - p1.y;
if (dx < 0)
{
dx += p1.fieldChar;
}
if (dy < 0)
{
dy += p1.fieldChar;
}
BigInteger t = (dy * dx.modInverse(p1.fieldChar)) % p1.fieldChar;
if (t < 0)
{
t += p1.fieldChar;
}
res.x = (t * t - p1.x - p2.x) % p1.fieldChar;
res.y = (t * (p1.x - res.x) - p1.y) % p1.fieldChar;
if (res.x < 0)
{
res.x += p1.fieldChar;
}
if (res.y < 0)
{
res.y += p1.fieldChar;
}
return(res);
}
//проверка цифровой подписи.
public bool verifDS(byte[] H, string sign, CECPoint Q)
{
string Rvector = sign.Substring(0, n.bitCount() / 4);
string Svector = sign.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 a = new BigInteger(H);
BigInteger e = a % 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();
CECPoint A = CECPoint.multiply(G, z1);
CECPoint B = CECPoint.multiply(Q, z2);
CECPoint C = A + B;
BigInteger R = C.x % n;
if (R == r)
{
return(true);
}
else
{
return(false);
}
}
//удвоение точки.
public static CECPoint doubling(CECPoint p)
{
CECPoint res = new CECPoint();
res.a = p.a;
res.b = p.b;
res.fieldChar = p.fieldChar;
BigInteger dx = 2 * p.y;
BigInteger dy = 3 * p.x * p.x + p.a;
if (dx < 0)
{
dx += p.fieldChar;
}
if (dy < 0)
{
dy += p.fieldChar;
}
BigInteger t = (dy * dx.modInverse(p.fieldChar)) % p.fieldChar;
res.x = (t * t - p.x - p.x) % p.fieldChar;
res.y = (t * (p.x - res.x) - p.y) % p.fieldChar;
if (res.x < 0)
{
res.x += p.fieldChar;
}
if (res.y < 0)
{
res.y += p.fieldChar;
}
return(res);
}