/// <summary>
/// Computes the inverse mod <c>q</c> from the inverse mod 2.
/// <para>The algorithm is described in <a href="http://www.securityinnovation.com/uploads/Crypto/NTRUTech014.pdf">
/// Almost Inverses and Fast NTRU Key Generation</a>.</para>
/// </summary>
///
/// <param name="Fq">Fq value</param>
/// <param name="Q">Q value</param>
///
/// <returns>The inverse of this polynomial mod q</returns>
private IntegerPolynomial Mod2ToModq(IntegerPolynomial Fq, int Q)
{
if (SystemUtils.Is64Bit() && Q == 2048)
{
LongPolynomial2 thisLong = new LongPolynomial2(this);
LongPolynomial2 FqLong = new LongPolynomial2(Fq);
int v = 2;
while (v < Q)
{
v *= 2;
LongPolynomial2 temp = FqLong.Clone();
temp.Mult2And(v - 1);
FqLong = thisLong.Multiply(FqLong).Multiply(FqLong);
temp.SubAnd(FqLong, v - 1);
FqLong = temp;
}
return FqLong.ToIntegerPolynomial();
}
else
{
int v = 2;
while (v < Q)
{
v *= 2;
IntegerPolynomial temp = Fq.Clone();
temp.Mult2(v);
Fq = Multiply(Fq, v).Multiply(Fq, v);
temp.Subtract(Fq, v);
Fq = temp;
}
return Fq;
}
}
/// <summary>
/// Multiplies the polynomial with another, taking the values mod modulus and the indices mod N
/// </summary>
///
/// <param name="Factor">The polynomial factor</param>
/// <param name="Modulus">The Modulus</param>
///
/// <returns>Multiplied polynomial</returns>
public new IntegerPolynomial Multiply(IntegerPolynomial Factor, int Modulus)
{
// even on 32-bit systems, LongPolynomial5 multiplies faster than IntegerPolynomial
if (Modulus == 2048)
{
IntegerPolynomial poly2Pos = Factor.Clone();
poly2Pos.ModPositive(2048);
LongPolynomial5 poly5 = new LongPolynomial5(poly2Pos);
return poly5.Multiply(this).ToIntegerPolynomial();
}
else
{
return base.Multiply(Factor, Modulus);
}
}