private unsafe BigInteger OddModTwoPow (BigInteger exp)
{
uint [] wkspace = new uint [mod.length << 1 + 1];
BigInteger resultNum = Montgomery.ToMont ((BigInteger)2, this.mod);
resultNum = new BigInteger (resultNum, mod.length << 1 +1);
uint mPrime = Montgomery.Inverse (mod.data [0]);
//
// TODO: eat small bits, the ones we can do with no modular reduction
//
uint pos = (uint)exp.BitCount () - 2;
do {
Kernel.SquarePositive (resultNum, ref wkspace);
resultNum = Montgomery.Reduce (resultNum, mod, mPrime);
if (exp.TestBit (pos)) {
//
// resultNum = (resultNum * 2) % mod
//
fixed (uint* u = resultNum.data) {
//
// Double
//
uint* uu = u;
uint* uuE = u + resultNum.length;
uint x, carry = 0;
while (uu < uuE) {
x = *uu;
*uu = (x << 1) | carry;
carry = x >> (32 - 1);
uu++;
}
// subtraction inlined because we know it is square
if (carry != 0 || resultNum >= mod) {
fixed (uint* s = mod.data) {
uu = u;
uint c = 0;
uint* ss = s;
do {
uint a = *ss++;
if (((a += c) < c) | ((* (uu++) -= a) > ~a))
c = 1;
else
c = 0;
} while (uu < uuE);
}
}
}
}
} while (pos-- > 0);
resultNum = 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;
}
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);
}
// the value of tempNum is required in the last loop
if (pos < totalBits - 1) {
Kernel.SquarePositive (tempNum, ref wkspace);
Montgomery.Reduce (tempNum, mod, mPrime);
}
}
Montgomery.Reduce (resultNum, mod, mPrime);
return resultNum;
}
public BigInteger Pow(BigInteger a, BigInteger k)
{
var b = new BigInteger(1);
if (k == 0)
return b;
BigInteger A = a;
if (k.TestBit(0))
b = a;
for (int i = 1; i < k.BitCount(); i++)
{
A = Multiply(A, A);
if (k.TestBit(i))
b = Multiply(A, b);
}
return b;
}