/**
* FIPS 186-4 C.3.2 Enhanced Miller-Rabin Probabilistic Primality Test
*
* Run several iterations of the Miller-Rabin algorithm with randomly-chosen bases. This is an
* alternative to {@link #isMRProbablePrime(BigInteger, SecureRandom, int)} that provides more
* information about a composite candidate, which may be useful when generating or validating
* RSA moduli.
*
* @param candidate
* the {@link BigInteger} instance to test for primality.
* @param random
* the source of randomness to use to choose bases.
* @param iterations
* the number of randomly-chosen bases to perform the test for.
* @return an {@link MROutput} instance that can be further queried for details.
*/
public static MROutput EnhancedMRProbablePrimeTest(BigInteger candidate, SecureRandom random, int iterations)
{
CheckCandidate(candidate, "candidate");
if (random == null)
{
throw new ArgumentNullException("random");
}
if (iterations < 1)
{
throw new ArgumentException("must be > 0", "iterations");
}
if (candidate.BitLength == 2)
{
return(MROutput.ProbablyPrime());
}
if (!candidate.TestBit(0))
{
return(MROutput.ProvablyCompositeWithFactor(Two));
}
BigInteger w = candidate;
BigInteger wSubOne = candidate.Subtract(One);
BigInteger wSubTwo = candidate.Subtract(Two);
int a = wSubOne.GetLowestSetBit();
BigInteger m = wSubOne.ShiftRight(a);
for (int i = 0; i < iterations; ++i)
{
BigInteger b = BigIntegers.CreateRandomInRange(Two, wSubTwo, random);
BigInteger g = b.Gcd(w);
if (g.CompareTo(One) > 0)
{
return(MROutput.ProvablyCompositeWithFactor(g));
}
BigInteger z = b.ModPow(m, w);
if (z.Equals(One) || z.Equals(wSubOne))
{
continue;
}
bool primeToBase = false;
BigInteger x = z;
for (int j = 1; j < a; ++j)
{
z = z.ModPow(Two, w);
if (z.Equals(wSubOne))
{
primeToBase = true;
break;
}
if (z.Equals(One))
{
break;
}
x = z;
}
if (!primeToBase)
{
if (!z.Equals(One))
{
x = z;
z = z.ModPow(Two, w);
if (!z.Equals(One))
{
x = z;
}
}
g = x.Subtract(One).Gcd(w);
if (g.CompareTo(One) > 0)
{
return(MROutput.ProvablyCompositeWithFactor(g));
}
return(MROutput.ProvablyCompositeNotPrimePower());
}
}
return(MROutput.ProbablyPrime());
}
public static MROutput EnhancedMRProbablePrimeTest(BigInteger candidate, SecureRandom random, int iterations)
{
//IL_0013: Unknown result type (might be due to invalid IL or missing references)
//IL_0027: Unknown result type (might be due to invalid IL or missing references)
CheckCandidate(candidate, "candidate");
if (random == null)
{
throw new ArgumentNullException("random");
}
if (iterations < 1)
{
throw new ArgumentException("must be > 0", "iterations");
}
if (candidate.BitLength == 2)
{
return(MROutput.ProbablyPrime());
}
if (!candidate.TestBit(0))
{
return(MROutput.ProvablyCompositeWithFactor(Two));
}
BigInteger bigInteger = candidate.Subtract(One);
BigInteger max = candidate.Subtract(Two);
int lowestSetBit = bigInteger.GetLowestSetBit();
BigInteger e = bigInteger.ShiftRight(lowestSetBit);
for (int i = 0; i < iterations; i++)
{
BigInteger bigInteger2 = BigIntegers.CreateRandomInRange(Two, max, random);
BigInteger bigInteger3 = bigInteger2.Gcd(candidate);
if (bigInteger3.CompareTo(One) > 0)
{
return(MROutput.ProvablyCompositeWithFactor(bigInteger3));
}
BigInteger bigInteger4 = bigInteger2.ModPow(e, candidate);
if (bigInteger4.Equals(One) || bigInteger4.Equals(bigInteger))
{
continue;
}
bool flag = false;
BigInteger bigInteger5 = bigInteger4;
for (int j = 1; j < lowestSetBit; j++)
{
bigInteger4 = bigInteger4.ModPow(Two, candidate);
if (bigInteger4.Equals(bigInteger))
{
flag = true;
break;
}
if (bigInteger4.Equals(One))
{
break;
}
bigInteger5 = bigInteger4;
}
if (flag)
{
continue;
}
if (!bigInteger4.Equals(One))
{
bigInteger5 = bigInteger4;
bigInteger4 = bigInteger4.ModPow(Two, candidate);
if (!bigInteger4.Equals(One))
{
bigInteger5 = bigInteger4;
}
}
bigInteger3 = bigInteger5.Subtract(One).Gcd(candidate);
if (bigInteger3.CompareTo(One) > 0)
{
return(MROutput.ProvablyCompositeWithFactor(bigInteger3));
}
return(MROutput.ProvablyCompositeNotPrimePower());
}
return(MROutput.ProbablyPrime());
}