/*
* Test an integer for primality. This function runs up to 50
* Miller-Rabin rounds, which is a lot of overkill but ensures
* that non-primes will be reliably detected (with overwhelming
* probability) even with maliciously crafted inputs. "Normal"
* non-primes will be detected most of the time at the first
* iteration.
*
* This function is not constant-time.
*/
public static bool IsPrime(byte[] x)
{
x = NormalizeBE(x);
/*
* Handle easy cases:
* 0 is not prime
* small primes (one byte) are known in a constant bit-field
* even numbers (larger than one byte) are non-primes
*/
if (x.Length == 0)
{
return(false);
}
if (x.Length == 1)
{
return(IsSmallPrime(x[0]));
}
if ((x[x.Length - 1] & 0x01) == 0)
{
return(false);
}
/*
* Perform some trial divisions by small primes.
*/
for (int sp = 3; sp < 256; sp += 2)
{
if (!IsSmallPrime(sp))
{
continue;
}
int z = 0;
foreach (byte b in x)
{
z = ((z << 8) + b) % sp;
}
if (z == 0)
{
return(false);
}
}
/*
* Run some Miller-Rabin rounds. We use as basis random
* integers that are one byte smaller than the modulus.
*/
ModInt xm1 = new ModInt(x);
ModInt y = xm1.Dup();
y.Set(1);
xm1.Sub(y);
byte[] e = xm1.Encode();
ModInt a = new ModInt(x);
byte[] buf = new byte[x.Length - 1];
for (int i = 0; i < 50; i++)
{
RNG.GetBytes(buf);
a.Decode(buf);
a.Pow(e);
if (!a.IsOne)
{
return(false);
}
}
return(true);
}