public void GenerateRandomCurve()
{
// 1 - generowanie liczby pierwszej przystającej do 3 modulo 4
p = PrimeHelper.GenerateRandomPrimeForElipticCurve(primeSize);
pMinus1 = BigInteger.Subtract(p, BigInteger.One);
while (true)
{
// 2 - losowanie a, b, chi
a = PrimeHelper.GenerateRandom(RandomGenerator.Next(2, primeSize - 1));
b = PrimeHelper.GenerateRandom(RandomGenerator.Next(2, primeSize - 1));
// 2.1 - jeśli delta przystaje do 0 to skok do punktu 2
delta = CalculateDelta(a, b);
if (delta.Mod(p) != 0)
{
// Krzywa gotowa, można szukać punktu należącego do krzywej
break;
}
}
Console.WriteLine($"p:\t{p}");
Console.WriteLine($"a:\t{a}");
Console.WriteLine($"b:\t{b}");
Console.WriteLine($"delta:\t{delta}");
}
public Point GenerateRandomPointOnCurve()
{
BigInteger x, y, f, legendreFP;
while (true)
{
x = PrimeHelper.GenerateRandom(RandomGenerator.Next(2, primeSize - 1));
f = CalculateF(a, b, x, p);
legendreFP = CalculateLegendreSymbol(f, p);
if (legendreFP == BigInteger.One)
{
y = BigInteger.ModPow(f, (p + 1) / 4, p);
BigInteger left, right;
left = BigInteger.ModPow(y, 2, p);
right = (BigInteger.Pow(x, 3) + a * x + b).Mod(p);
bool test = left == right;
if (test)
{
break;
}
}
}
return(new Point(x, y, a, p));
}
static void Main(string[] args)
{
ElipticCurve elipticCurve = new ElipticCurve(256);
elipticCurve.GenerateRandomCurve();
Point randomPoint = elipticCurve.GenerateRandomPointOnCurve();
BigInteger nA = PrimeHelper.GenerateRandom(64);
BigInteger nB = PrimeHelper.GenerateRandom(64);
Point qA = elipticCurve.ScalarMultiplication(randomPoint, nA);
Point qB = elipticCurve.ScalarMultiplication(randomPoint, nB);
if (qA == qB)
{
Console.WriteLine("Ok");
}
else
{
Console.WriteLine("Nie ok");
}
Console.ReadKey();
}
public Point ScalarMultiplication(Point P, BigInteger n)
{
// 1)
Point Q = P;
// 2)
string binaryString = PrimeHelper.BigintegerToBinaryString(n);
Point R = binaryString[0] == '0'
? Point.NeutralElement(P.a, P.p)
: P;
// 3)
for (int i = 1; i < binaryString.Length; i++)
{
Q = Q + Q;
if (binaryString[i] == '1')
{
R = R + Q;
}
}
return(R);
}
