private static BigInteger Pow2ModPow(BigInteger X, BigInteger Y, int N)
{
// PRE: (base > 0), (exponent > 0) and (j > 0)
BigInteger res = BigInteger.One;
BigInteger e = Y.Copy();
BigInteger baseMod2toN = X.Copy();
BigInteger res2;
// If 'base' is odd then it's coprime with 2^j and phi(2^j) = 2^(j-1);
// so we can reduce reduce the exponent (mod 2^(j-1)).
if (X.TestBit(0))
{
InplaceModPow2(e, N - 1);
}
InplaceModPow2(baseMod2toN, N);
for (int i = e.BitLength - 1; i >= 0; i--)
{
res2 = res.Copy();
InplaceModPow2(res2, N);
res = res.Multiply(res2);
if (BitLevel.TestBit(e, i))
{
res = res.Multiply(baseMod2toN);
InplaceModPow2(res, N);
}
}
InplaceModPow2(res, N);
return(res);
}
private static BigInteger SlidingWindow(BigInteger X2, BigInteger A2, BigInteger Exponent, BigInteger Modulus, int N2)
{
// Implements the Montgomery modular exponentiation based in The sliding windows algorithm and the Mongomery Reduction
// ar.org.fitc.ref "A. Menezes,P. van Oorschot, S. Vanstone - Handbook of Applied Cryptography"
BigInteger[] pows = new BigInteger[8];
BigInteger res = X2;
int lowexp;
BigInteger x3;
int acc3;
// fill odd low pows of a2
pows[0] = A2;
x3 = MonPro(A2, A2, Modulus, N2);
for (int i = 1; i <= 7; i++)
{
pows[i] = MonPro(pows[i - 1], x3, Modulus, N2);
}
for (int i = Exponent.BitLength - 1; i >= 0; i--)
{
if (BitLevel.TestBit(Exponent, i))
{
lowexp = 1;
acc3 = i;
for (int j = System.Math.Max(i - 3, 0); j <= i - 1; j++)
{
if (BitLevel.TestBit(Exponent, j))
{
if (j < acc3)
{
acc3 = j;
lowexp = (lowexp << (i - j)) ^ 1;
}
else
{
lowexp = lowexp ^ (1 << (j - acc3));
}
}
}
for (int j = acc3; j <= i; j++)
{
res = MonPro(res, res, Modulus, N2);
}
res = MonPro(pows[(lowexp - 1) >> 1], res, Modulus, N2);
i = acc3;
}
else
{
res = MonPro(res, res, Modulus, N2);
}
}
return(res);
}
private static BigInteger SquareAndMultiply(BigInteger X2, BigInteger A2, BigInteger Exponent, BigInteger Modulus, int N2)
{
BigInteger res = X2;
for (int i = Exponent.BitLength - 1; i >= 0; i--)
{
res = MonPro(res, res, Modulus, N2);
if (BitLevel.TestBit(Exponent, i))
{
res = MonPro(res, A2, Modulus, N2);
}
}
return(res);
}
private static BigInteger ModPow2Inverse(BigInteger X, int N)
{
// PRE: (x > 0), (x is odd), and (n > 0)
BigInteger y = new BigInteger(1, new int[1 << N]);
y.m_numberLength = 1;
y.m_digits[0] = 1;
y.m_sign = 1;
for (int i = 1; i < N; i++)
{
if (BitLevel.TestBit(X.Multiply(y), i))
{
// Adding 2^i to y (setting the i-th bit)
y.m_digits[i >> 5] |= (1 << (i & 31));
}
}
return(y);
}
