public static int[] CalculateSum(int[] P, int a, int p)
{
int lambda = CalculateLambda(P, a, p);
int x = GCD.Mod(lambda * lambda - P[0] - P[0], p);
int y = GCD.Mod(lambda * (P[0] - x) - P[1], p);
return(new int[] { x, y });
}
public static bool VerifyDigitalSign(int[] digitalSign, int[] G, int q, int d, int a, int p)
{
if (digitalSign[0] <= 1 || digitalSign[1] >= q)
{
return(false);
}
int H = points[alphabeth.IndexOf("м"), 0] % 13; // by task
int w = GCD.ModInverse(digitalSign[1], q);
int u1 = (w * H) % q;
int u2 = (w * digitalSign[0]) % q;
int[] Q = kP(d, G, a, p), u1G = kP(u1, G, a, p), u2Q = kP(u2, Q, a, p);
int v = CalculateSum(u1G, u2Q, p)[0] % q;
return(digitalSign[0] == v);
}
public static int[] CreateDigitalSign(int[] G, int q, int d, int a, int p)
{
Console.WriteLine($"G = ({G[0]}, {G[1]}), d = {d}, q = {q}");
int[] digitalSign = new int[2];
int[] kG;
int k, t;
do
{
do
{
k = random.Next(2, q);
kG = kP(k, G, a, p);
digitalSign[0] = kG[0] % q;
} while (digitalSign[0] <= 1);
t = GCD.ModInverse(k, q);
int H = points[alphabeth.IndexOf("м"), 0] % 13; // by task
digitalSign[1] = (t * (H + d * digitalSign[0])) % q;
} while (digitalSign[1] <= 0);
return(digitalSign);
}
private static int CalculateLambda(int[] P, int[] Q, int p)
{
return(GCD.Mod(GCD.Mod(Q[1] - P[1], p) * GCD.Mod(GCD.ModInverse(Q[0] + GCD.Mod(-P[0], p), p), p), p));
}
private static int CalculateLambda(int[] P, int a, int p)
{
return(GCD.Mod(GCD.Mod(3 * (P[0] * P[0]) + a, p) * GCD.ModInverse(2 * P[1], p), p));
}