private static BigInteger ModPowMonty(BigInteger b, BigInteger e, BigInteger m, bool convert)
{
int n = m.magnitude.Length;
int powR = 32 * n;
bool smallMontyModulus = m.BitLength + 2 <= powR;
uint mDash = (uint)m.GetMQuote();
// tmp = this * R mod m
if (convert)
{
b = b.ShiftLeft(powR).Remainder(m);
}
int[] yAccum = new int[n + 1];
int[] zVal = b.magnitude;
Debug.Assert(zVal.Length <= n);
if (zVal.Length < n)
{
int[] tmp = new int[n];
zVal.CopyTo(tmp, n - zVal.Length);
zVal = tmp;
}
// Sliding window from MSW to LSW
int extraBits = 0;
// Filter the common case of small RSA exponents with few bits set
if (e.magnitude.Length > 1 || e.BitCount > 2)
{
int expLength = e.BitLength;
while (expLength > ExpWindowThresholds[extraBits])
{
++extraBits;
}
}
int numPowers = 1 << extraBits;
int[][] oddPowers = new int[numPowers][];
oddPowers[0] = zVal;
int[] zSquared = Arrays.Clone(zVal);
SquareMonty(yAccum, zSquared, m.magnitude, mDash, smallMontyModulus);
for (int i = 1; i < numPowers; ++i)
{
oddPowers[i] = Arrays.Clone(oddPowers[i - 1]);
MultiplyMonty(yAccum, oddPowers[i], zSquared, m.magnitude, mDash, smallMontyModulus);
}
int[] windowList = GetWindowList(e.magnitude, extraBits);
Debug.Assert(windowList.Length > 1);
int window = windowList[0];
int mult = window & 0xFF, lastZeroes = window >> 8;
int[] yVal;
if (mult == 1)
{
yVal = zSquared;
--lastZeroes;
}
else
{
yVal = Arrays.Clone(oddPowers[mult >> 1]);
}
int windowPos = 1;
while ((window = windowList[windowPos++]) != -1)
{
mult = window & 0xFF;
int bits = lastZeroes + BitLengthTable[mult];
for (int j = 0; j < bits; ++j)
{
SquareMonty(yAccum, yVal, m.magnitude, mDash, smallMontyModulus);
}
MultiplyMonty(yAccum, yVal, oddPowers[mult >> 1], m.magnitude, mDash, smallMontyModulus);
lastZeroes = window >> 8;
}
for (int i = 0; i < lastZeroes; ++i)
{
SquareMonty(yAccum, yVal, m.magnitude, mDash, smallMontyModulus);
}
if (convert)
{
// Return y * R^(-1) mod m
MontgomeryReduce(yVal, m.magnitude, mDash);
}
else if (smallMontyModulus && CompareTo(0, yVal, 0, m.magnitude) >= 0)
{
Subtract(0, yVal, 0, m.magnitude);
}
return new BigInteger(1, yVal, true);
}
/*
* Finds a pair of prime BigInteger's {p, q: p = 2q + 1}
*
* (see: Handbook of Applied Cryptography 4.86)
*/
internal static BigInteger[] GenerateSafePrimes(int size, int certainty, SecureRandom random)
{
BigInteger p, q;
int qLength = size - 1;
int minWeight = size >> 2;
if (size <= 32)
{
for (;;)
{
q = new BigInteger(qLength, 2, random);
p = q.ShiftLeft(1).Add(BigInteger.One);
if (!p.IsProbablePrime(certainty))
continue;
if (certainty > 2 && !q.IsProbablePrime(certainty - 2))
continue;
break;
}
}
else
{
// Note: Modified from Java version for speed
for (;;)
{
q = new BigInteger(qLength, 0, random);
retry:
for (int i = 0; i < primeLists.Length; ++i)
{
int test = q.Remainder(BigPrimeProducts[i]).IntValue;
if (i == 0)
{
int rem3 = test % 3;
if (rem3 != 2)
{
int diff = 2 * rem3 + 2;
q = q.Add(BigInteger.ValueOf(diff));
test = (test + diff) % primeProducts[i];
}
}
int[] primeList = primeLists[i];
for (int j = 0; j < primeList.Length; ++j)
{
int prime = primeList[j];
int qRem = test % prime;
if (qRem == 0 || qRem == (prime >> 1))
{
q = q.Add(Six);
goto retry;
}
}
}
if (q.BitLength != qLength)
continue;
if (!q.RabinMillerTest(2, random))
continue;
p = q.ShiftLeft(1).Add(BigInteger.One);
if (!p.RabinMillerTest(certainty, random))
continue;
if (certainty > 2 && !q.RabinMillerTest(certainty - 2, random))
continue;
/*
* Require a minimum weight of the NAF representation, since low-weight primes may be
* weak against a version of the number-field-sieve for the discrete-logarithm-problem.
*
* See "The number field sieve for integers of low weight", Oliver Schirokauer.
*/
if (WNafUtilities.GetNafWeight(p) < minWeight)
continue;
break;
}
}
return new BigInteger[] { p, q };
}
public BigInteger Multiply(
BigInteger val)
{
if (val == this)
return Square();
if ((sign & val.sign) == 0)
return Zero;
if (val.QuickPow2Check()) // val is power of two
{
BigInteger result = this.ShiftLeft(val.Abs().BitLength - 1);
return val.sign > 0 ? result : result.Negate();
}
if (this.QuickPow2Check()) // this is power of two
{
BigInteger result = val.ShiftLeft(this.Abs().BitLength - 1);
return this.sign > 0 ? result : result.Negate();
}
int resLength = magnitude.Length + val.magnitude.Length;
int[] res = new int[resLength];
Multiply(res, this.magnitude, val.magnitude);
int resSign = sign ^ val.sign ^ 1;
return new BigInteger(resSign, res, true);
}
