public List <BigInteger> PolyMulMod(BigInteger p, List <BigInteger> a, List <BigInteger> b)
{
int i, j, k, m = a.Count - 1, n = b.Count - 1, q = m + n;
BigInteger ai = 0, bj = 0, sum = 0;
List <BigInteger> c = new List <BigInteger>();
for (k = 0; k <= q; k++)
{
sum = 0;
for (i = 0; i <= k; i++)
{
j = k - i;
if (i > m)
{
ai = 0;
}
else
{
ai = a[i];
}
if (j > n)
{
bj = 0;
}
else
{
bj = b[j];
}
sum = Maths.AddMod(sum, Maths.MulMod(ai, bj, p), p);
}
c.Add(sum);
}
return(c);
}
public BigInteger Weierstrass(BigInteger x)
{
BigInteger t3 = BigInteger.ModPow(x, 3, p);
BigInteger t1 = Maths.MulMod(a, x, p);
BigInteger t2 = Maths.AddMod(t3, t1, p);
return(Maths.AddMod(t2, b, p));
}
private BigInteger Horner(BigInteger p, BigInteger x, List <BigInteger> P)
{
BigInteger s = P[P.Count - 1], t = 0;
for (int i = P.Count - 2; i >= 0; i--)
{
t = Maths.MulMod(s, x, p);
s = Maths.AddMod(t, P[i], p);
}
return(s);
}
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 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);
}
}
}