public static BigInteger SolveDLP(ProjectivePoint P, ProjectivePoint Q)
{
var R = P;
BigInteger a = 1, b = 0;
var R2 = R;
BigInteger a2 = a, b2 = b;
//var MOD = P.E.P;
var MOD = P.E.HasseTheorem();
StepsCount = 1;
for (int i = 1; i < MOD; i++)
{
R = f(P, Q, R, ref a, ref b, MOD);
R2 = f(P, Q, R2, ref a2, ref b2, MOD);
R2 = f(P, Q, R2, ref a2, ref b2, MOD);
if (R == R2)
{
Console.WriteLine(R);
Console.WriteLine(R2);
break;
}
StepsCount++;
}
Console.WriteLine(MOD);
Console.WriteLine(StepsCount);
var dA = a2 - a;
var dB = b - b2;
dA = dA.ModPositive(MOD);
dB = dB.ModPositive(MOD);
var gcd = BigInteger.GreatestCommonDivisor(dB, MOD);
Console.WriteLine(gcd);
GCD = gcd;
if (gcd == 1)
{
BigInteger x = dA * dB.ModInverse(MOD);
return(x.ModPositive(MOD));
}
else
{
var reducedOrder = MOD / gcd;
var x0 = (dB / gcd).ModInverse(reducedOrder);
x0 = x0 * (dA / gcd);
x0 = x0.ModPositive(reducedOrder);
for (BigInteger m = 0; m < gcd; m++)
{
var x = x0 + m * reducedOrder;
if ((x * P) == Q)
{
return(x);
}
}
}
return(-1);
// return (a2 - a) * BigIntegerExtension.ModInverse(b - b2, MOD);
}
private static int chooseSet(ProjectivePoint R)
{
//var x = R.X;
//int countSet = 3;
//return (int)x % countSet;
var y = R.Y;
int countSet = 3;
return((int)y % countSet);
}
public static BigInteger SolveDLP(ProjectivePoint P, ProjectivePoint Q)
{
var startTime = System.Diagnostics.Stopwatch.StartNew();
var x = BabyStepGiantStep.SolveDLP(P, Q);
startTime.Stop();
var resultTime = startTime.Elapsed;
TimeInSec = resultTime.Hours * 3600 + resultTime.Minutes * 60 + resultTime.Seconds + (resultTime.Milliseconds * 1.0) / (1.0 * 100);
ElapsedTime = String.Format("{0:00}:{1:00}:{2:00}.{3:000}", resultTime.Hours, resultTime.Minutes, resultTime.Seconds, resultTime.Milliseconds);
return(x);
}
private static ProjectivePoint f(ProjectivePoint P, ProjectivePoint Q, ProjectivePoint R, ref BigInteger a, ref BigInteger b, BigInteger MOD)
{
int set = chooseSet(R);
if (set == 0)
{
b = (b + 1).ModPositive(MOD);
return(R + Q);
}
else if (set == 1)
{
a = (2 * a).ModPositive(MOD);
b = (2 * b).ModPositive(MOD);
return(2 * R); //ProjectivePoint.Double(R);
}
else
{
a = (a + 1).ModPositive(MOD);
return(R + P);
}
}
//public static BigInteger SolveDLP(AffinePoint P, AffinePoint Q)
//{
// var order = P.E.HasseTheorem();
// var babySteps = new Dictionary<AffinePoint, BigInteger>();
// var m = BigIntegerExtension.Sqrt(order) + 1;
// AffinePoint babyStep;
// for (BigInteger i = 0; i < m; i++)
// {
// babyStep = (i * P.ToProjectivePoint()).ToAffinePoint();
// babySteps.Add(babyStep, i);
// Console.WriteLine(babyStep);
// }
// AffinePoint temp;
// ProjectivePoint giantStep = (m * P.ToProjectivePoint());
// for (BigInteger j = 0; j < m; j++)
// {
// temp = (Q.ToProjectivePoint() - j * giantStep).ToAffinePoint();
// Console.WriteLine(temp);
// BigInteger i = -1;
// try
// {
// i = babySteps[temp];
// }
// catch (KeyNotFoundException e) { }
// if (i != -1)
// return BigIntegerExtension.ModPositive(i + j * m, order);
// }
// return -1;
//}
public static BigInteger SolveDLP(ProjectivePoint P, ProjectivePoint Q)
{
var order = P.E.HasseTheorem();
var babySteps = new Dictionary <AffinePoint, BigInteger>();
var m = BigIntegerExtension.Sqrt(order) + 1;
AffinePoint babyStep;
for (BigInteger i = 0; i <= m; i++)
{
babyStep = (i * P).ToAffinePoint();
babySteps.Add(babyStep, i);
//Console.WriteLine(babyStep);
}
AffinePoint temp;
ProjectivePoint giantStep = (m * P);
//Console.WriteLine();
//Console.WriteLine(giantStep.ToAffinePoint());
//Console.WriteLine();
for (BigInteger j = 0; j <= m; j++)
{
temp = (Q - j * giantStep).ToAffinePoint();
// Console.WriteLine(temp);
BigInteger i = -1;
try
{
i = babySteps[temp];
}
catch (KeyNotFoundException e) { }
if (i != -1)
{
//Console.WriteLine(temp + " dfsd");
return(BigIntegerExtension.ModPositive(i + j * m, order));
}
}
//make modification with m/2 and +-iP
return(-1);
}