private BigInteger OddPow(BigInteger b, BigInteger exp)
{
BigInteger resultNum = new BigInteger(Montgomery.ToMont(1, mod), mod.length << 1);
BigInteger tempNum = new BigInteger(Montgomery.ToMont(b, mod), mod.length << 1); // ensures (tempNum * tempNum) < b^ (2k)
uint mPrime = Montgomery.Inverse(mod.data[0]);
uint totalBits = (uint)exp.BitCount();
uint[] wkspace = new uint[mod.length << 1];
// perform squaring and multiply exponentiation
for (uint pos = 0; pos < totalBits; pos++)
{
if (exp.TestBit(pos))
{
Array.Clear(wkspace, 0, wkspace.Length);
Kernel.Multiply(resultNum.data, 0, resultNum.length, tempNum.data, 0, tempNum.length, wkspace, 0);
resultNum.length += tempNum.length;
uint[] t = wkspace;
wkspace = resultNum.data;
resultNum.data = t;
Montgomery.Reduce(resultNum, mod, mPrime);
}
Kernel.SquarePositive(tempNum, ref wkspace);
Montgomery.Reduce(tempNum, mod, mPrime);
}
Montgomery.Reduce(resultNum, mod, mPrime);
return resultNum;
}
private unsafe BigInteger EvenPow(uint b, BigInteger exp)
{
exp.Normalize();
uint[] wkspace = new uint[mod.length << 1 + 1];
BigInteger resultNum = new BigInteger((BigInteger)b, mod.length << 1 + 1);
uint pos = (uint)exp.BitCount() - 2;
//
// We know that the first itr will make the val b
//
do
{
//
// r = r ^ 2 % m
//
Kernel.SquarePositive(resultNum, ref wkspace);
if (!(resultNum.length < mod.length))
BarrettReduction(resultNum);
if (exp.TestBit(pos))
{
//
// r = r * b % m
//
// TODO: Is Unsafe really speeding things up?
fixed (uint* u = resultNum.data)
{
uint i = 0;
ulong mc = 0;
do
{
mc += (ulong)u[i] * (ulong)b;
u[i] = (uint)mc;
mc >>= 32;
} while (++i < resultNum.length);
if (resultNum.length < mod.length)
{
if (mc != 0)
{
u[i] = (uint)mc;
resultNum.length++;
while (resultNum >= mod)
Kernel.MinusEq(resultNum, mod);
}
}
else if (mc != 0)
{
//
// First, we estimate the quotient by dividing
// the first part of each of the numbers. Then
// we correct this, if necessary, with a subtraction.
//
uint cc = (uint)mc;
// We would rather have this estimate overshoot,
// so we add one to the divisor
uint divEstimate = (uint)((((ulong)cc << 32) | (ulong)u[i - 1]) /
(mod.data[mod.length - 1] + 1));
uint t;
i = 0;
mc = 0;
do
{
mc += (ulong)mod.data[i] * (ulong)divEstimate;
t = u[i];
u[i] -= (uint)mc;
mc >>= 32;
if (u[i] > t) mc++;
i++;
} while (i < resultNum.length);
cc -= (uint)mc;
if (cc != 0)
{
uint sc = 0, j = 0;
uint[] s = mod.data;
do
{
uint a = s[j];
if (((a += sc) < sc) | ((u[j] -= a) > ~a)) sc = 1;
else sc = 0;
j++;
} while (j < resultNum.length);
cc -= sc;
}
while (resultNum >= mod)
Kernel.MinusEq(resultNum, mod);
}
else
{
while (resultNum >= mod)
Kernel.MinusEq(resultNum, mod);
}
}
}
} while (pos-- > 0);
return resultNum;
}
public BigInteger EvenPow(BigInteger b, BigInteger exp)
{
BigInteger resultNum = new BigInteger((BigInteger)1, mod.length << 1);
BigInteger tempNum = new BigInteger(b % mod, mod.length << 1); // ensures (tempNum * tempNum) < b^ (2k)
uint totalBits = (uint)exp.BitCount();
uint[] wkspace = new uint[mod.length << 1];
// perform squaring and multiply exponentiation
for (uint pos = 0; pos < totalBits; pos++)
{
if (exp.TestBit(pos))
{
Array.Clear(wkspace, 0, wkspace.Length);
Kernel.Multiply(resultNum.data, 0, resultNum.length, tempNum.data, 0, tempNum.length, wkspace, 0);
resultNum.length += tempNum.length;
uint[] t = wkspace;
wkspace = resultNum.data;
resultNum.data = t;
BarrettReduction(resultNum);
}
Kernel.SquarePositive(tempNum, ref wkspace);
BarrettReduction(tempNum);
if (tempNum == 1)
{
return resultNum;
}
}
return resultNum;
}