private BigInteger BabyStepGiantStep(long l, BigInteger t2, BigInteger x, BigInteger y)
{
long W = (long)(Math.Ceiling(Math.Sqrt(0.5 * l)));
BigInteger beta = 0, gamma = 0, k = 0;
BigInteger pmodl = ecs.P % l;
BigInteger ps = ecs.P * ecs.P;
BigInteger Ax = 0, Bx = 0, Ay = 0, By = 0, kmod2 = 0;
BigInteger psil = Maths.Psi((int)l, x, y, ecs.A, ecs.B, ecs.P);
List <ijPair> S = new List <ijPair>();
if (psil == 0)
{
return(-3);
}
EllipticCurve_Point P0 = new EllipticCurve_Point(),
P1 = new EllipticCurve_Point(),
P2 = new EllipticCurve_Point(),
P3 = new EllipticCurve_Point(),
P12 = new EllipticCurve_Point(),
P = new EllipticCurve_Point();
List <EllipticCurve_Point> A = new List <EllipticCurve_Point>();
List <EllipticCurve_Point> B = new List <EllipticCurve_Point>();
P.X = x;
P.Y = y;
P0.X = BigInteger.ModPow(x, ecs.P, psil);
P0.Y = BigInteger.ModPow(y, ecs.P, psil);
P1.X = BigInteger.ModPow(x, ps, psil);
P1.Y = BigInteger.ModPow(y, ps, psil);
ecs.Mult(pmodl, P, ref P2);
if (!ecs.Sum(P1, P2, ref P12))
{
return(-1);
}
if (P12.IsNull)
{
return(0);
}
for (beta = 0; beta < W; beta++)
{
if (!ecs.Mult(beta, P0, ref P3))
{
return(-1);
}
if (!ecs.Sum(P12, P3, ref P3))
{
return(-1);
}
bool found = false;
for (int i = 0; !found && i < A.Count; i++)
{
found = A[i].X == P3.X && A[i].Y == P3.Y;
}
if (!found && !P3.IsNull)
{
A.Add(P3);
}
}
for (gamma = 0; gamma <= W; gamma++)
{
if (!ecs.Mult(gamma * W, P0, ref P3))
{
return(-1);
}
bool found = false;
for (int i = 0; !found && i < B.Count; i++)
{
found = B[i].X == P3.X && B[i].Y == P3.Y;
}
if (!found && !P3.IsNull)
{
B.Add(P3);
}
}
if (A.Count != 0 && B.Count != 0)
{
A.Sort();
B.Sort();
for (int i = 0; i < A.Count; i++)
{
Ax = A[i].X;
for (int j = 0; j < B.Count; j++)
{
Bx = B[j].X;
if (Ax == Bx)
{
ijPair ij = new ijPair();
ij.i = i;
ij.j = j;
S.Add(ij);
}
}
}
if (S.Count == 1)
{
beta = S[0].i;
gamma = S[0].j;
k = beta + gamma * W;
kmod2 = k % 2;
if (t2 == kmod2)
{
Ay = A[(int)beta].Y;
By = B[(int)gamma].Y;
if (Ay == By)
{
return(k);
}
else
{
return(l - k);
}
}
k = beta - gamma * W;
kmod2 = k % 2;
if (kmod2 < 0)
{
kmod2 += 2;
}
if (t2 == kmod2)
{
Ay = A[(int)beta].Y;
By = B[(int)gamma].Y;
if (Ay == By)
{
return(k);
}
else
{
return(l - k);
}
}
}
}
return(-1);
}