public T Multiply(T other)
{
// Create an extended list which can contain results from both coefficient collections.
List <BigInteger> b = new List <BigInteger>(new BigInteger[(Degree * 2) - 1]);
// Compute each product linearly for every index in our list.
for (int i = 0; i < Coefficients.Count; i++)
{
for (int j = 0; j < other.Coefficients.Count; j++)
{
b[i + j] += Coefficients.ElementAt(i) * other.Coefficients.ElementAt(j);
}
}
for (int exp = Degree - 2; exp >= 0; exp--)
{
BigInteger top = b[b.Count - 1];
b.RemoveAt(b.Count - 1);
for (int i = 0; i < ModulusCoefficients.Count; i++)
{
b[exp + i] -= top * ModulusCoefficients.ElementAt(i);
}
}
// Perform modular division to wrap our coefficients around p.
return(New(b.Select(x => x.Mod(Bn128Curve.P))));
}
public T Inverse()
{
// Define our initial variables and give them their initial assignments.
BigInteger[] newt = new BigInteger[Degree + 1];
newt[0] = 1;
BigInteger[] t = new BigInteger[Degree + 1];
BigInteger[] newr = new BigInteger[Coefficients.Count + 1];
Coefficients.CopyTo(newr, 0);
BigInteger[] r = new BigInteger[ModulusCoefficients.Count + 1];
ModulusCoefficients.CopyTo(r, 0);
r[r.Length - 1] = 1;
// Loop while there are elements which are non-zero.
while (GetDegree(newr) != 0)
{
BigInteger[] quotient = DividePolynomialRounded(r, newr);
Array.Resize(ref quotient, Degree + 1);
BigInteger[] tempt = (BigInteger[])t.Clone();
BigInteger[] tempr = (BigInteger[])r.Clone();
for (int i = 0; i < Degree + 1; i++)
{
for (int j = 0; j < Degree + 1 - i; j++)
{
tempt[i + j] -= newt[i] * quotient[j];
tempr[i + j] -= newr[i] * quotient[j];
}
}
// Perform modulo on tempt
for (int i = 0; i < tempt.Length; i++)
{
tempt[i] = tempt[i].Mod(Bn128Curve.P);
}
// Perform modulo on tempr
for (int i = 0; i < tempr.Length; i++)
{
tempr[i] = tempr[i].Mod(Bn128Curve.P);
}
// Swap state for the next iteration.
(newt, newr, t, r) = (tempt, tempr, newt, newr);
}
// Resize the array to the degree size accordingly, divide and return.
Array.Resize(ref newt, Degree);
return(New(newt).Divide(newr[0]));
}