private void Recurse(BigInteger p, List <BigInteger> A, ref List <BigInteger> root)
{
int count = 0, degreeA = A.Count - 1, degreeB = 0;
BigInteger exp = 0, p1 = p - 1, D = 0, a = 0, b = 0, c = 0, e = 0;
List <BigInteger> B = null, d = null;
List <BigInteger> q = null, r = null, u = null;
exp = p1 / 2;
if (degreeA != 0)
{
if (degreeA == 1)
{
if (A[0] != 0)
{
a = Maths.GetInverse(A[1], p);
b = A[0];
b = -b;
b = Maths.MulMod(b, a, p);
root.Add(b);
}
}
else if (degreeA == 2)
{
a = Maths.MulMod(A[1], A[1], p);
b = Maths.MulMod(A[0], A[2], p);
c = Maths.MulMod(b, 4, p);
D = Maths.SubMod(a, c, p);
e = hcr.SquareRootModPrime(D, p);
BigInteger test = (e * e) % p;
if (e == 1)
{
return;
}
a = Maths.MulMod(A[2], 2, p);
D = Maths.GetInverse(a, p);
if (D == 0)
{
a = -a;
a = Maths.AddMod(a, p, p);
D = Maths.GetInverse(a, p);
}
a = Maths.SubMod(e, A[1], p);
root.Add(Maths.MulMod(a, D, p));
A[1] = -A[1];
e = -e;
a = Maths.AddMod(A[1], e, p);
root.Add(Maths.MulMod(a, D, p));
}
else
{
do
{
count++;
a = hcr.RandomRange(0, p1);
u = new List <BigInteger>();
u.Add(a);
u.Add(1);
PolyPowMod(p, exp, u, A, ref d);
if (d.Count - 1 != 0)
{
d[0] = Maths.SubMod(d[0], 1, p);
B = PolyGCDMod(p, d, A);
if (B.Count == 1 && B[0] == 1)
{
return;
}
degreeB = B.Count - 1;
}
}while (count < 16 && degreeB == 0 || degreeB == degreeA);
if (count == 16)
{
return;
}
Recurse(p, B, ref root);
PolyDivMod(p, A, B, ref q, ref r);
Recurse(p, q, ref root);
}
}
}
public void PolyDivMod(BigInteger p, List <BigInteger> u, List <BigInteger> v, ref List <BigInteger> q, ref List <BigInteger> r)
{
int j, jk, k, nk, m = u.Count - 1, n = v.Count - 1, t, s;
BigInteger a = 0, b = 0, vn = 0, qk = 0;
List <BigInteger> tr = new List <BigInteger>();
r = new List <BigInteger>();
vn = v[n];
if (n == 0)
{
r.Add(0);
q = new List <BigInteger>();
for (int i = 0; i < u.Count; i++)
{
q.Add(Maths.MulMod(u[i], vn, p));
}
return;
}
for (j = 0; j <= m; j++)
{
r.Add(u[j]);
}
if (m < n)
{
q = new List <BigInteger>();
q.Add(0);
}
else
{
t = m - n;
s = n - 1;
q = new List <BigInteger>();
for (k = t; k >= 0; k--)
{
q.Add(0);
}
for (k = t; k >= 0; k--)
{
nk = n + k;
if (k != 0)
{
a = BigInteger.ModPow(vn, k, p);
}
else
{
a = 1;
}
qk = Maths.MulMod(r[nk], a, p);
q[k] = qk;
for (j = nk - 1; j >= 0; j--)
{
jk = j - k;
if (jk >= 0)
{
a = Maths.MulMod(vn, r[j], p);
b = Maths.MulMod(r[nk], v[jk], p);
r[j] = Maths.SubMod(a, b, p);
}
else
{
r[j] = Maths.MulMod(vn, r[j], p);
}
}
}
for (int i = s; i > 0; i--)
{
if (r[i] == 0)
{
s--;
}
else
{
break;
}
}
for (int i = s; i >= 0; i--)
{
tr.Add(r[i]);
}
r = PolyRev(tr);
}
}
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);
}