public BlumBlumShub(int bits, Ibasa.Numerics.Random.Generator generator)
{
if (bits < 6)
{
throw new ArgumentException("bits is less than 6.", "bits");
}
var p = GetPrime(bits / 2, generator);
var q = GetPrime(bits / 2, generator);
while (q == p)
{
q = GetPrime(bits / 2, generator);
}
M = p * q;
do
{
var bytes = new byte[((bits + 7) / 8) + 1];
generator.NextBytes(bytes);
bytes[bytes.Length - 1] = 0;
State = new BigInteger(bytes);
} while (State == 0 || State == 1 || State % p == 0 || State % q == 0);
State = BigInteger.ModPow(State, 2, M);
}
public static bool IsProbablyPrime(this BigInteger prime, int certainty, Ibasa.Numerics.Random.Generator random)
{
if (prime == 2 || prime == 3)
{
return(true);
}
if (prime < 2 || prime % 2 == 0)
{
return(false);
}
if (prime <= long.MaxValue)
{
return(IsProbablyPrime((long)prime, certainty, random));
}
int s = 0;
var d = prime - 1;
while (d % 2 == 0)
{
d /= 2;
s += 1;
}
byte[] bytes = new byte[prime.ToByteArray().Length];
for (int i = 0; i < certainty; ++i)
{
BigInteger a;
do
{
random.NextBytes(bytes);
a = new BigInteger(bytes);
} while (a < 2 || a >= prime - 2);
BigInteger x = BigInteger.ModPow(a, d, prime);
if (x != 1 && x != prime - 1)
{
for (int r = 1; r < s; ++r)
{
x = BigInteger.ModPow(x, 2, prime);
if (x == 1)
{
return(false);
}
if (x == prime - 1)
{
break;
}
}
if (x != prime - 1)
{
return(false);
}
}
}
return(true);
}
private static BigInteger GetPrime(int bits, Ibasa.Numerics.Random.Generator generator)
{
BigInteger prime;
do
{
prime = Primes.GetPrime(bits, generator);
} while (prime % 4 != 3);
return(prime);
}
public static BigInteger GetPrime(int bits, Ibasa.Numerics.Random.Generator random)
{
if (bits < 2)
{
throw new ArgumentException("bits is less than two.", "bits");
}
BigInteger pi = 2;
if (bits > 4)
{
pi = pi * 3;
}
if (bits > 6)
{
pi = pi * 5 * 7;
}
if (bits > 8)
{
pi = pi * 11 * 13;
}
if (bits > 10)
{
pi = pi * 17 * 19 * 23 * 29;
}
byte[] bytes = new byte[((bits + 7) / 8) + 1];
var bytemask = (byte)(uint.MaxValue >> (32 - (bits % 8)));
var intmask = BigInteger.Pow(2, bits) - 1;
BigInteger prime;
do
{
do
{
random.NextBytes(bytes);
bytes[bytes.Length - 1] = 0;
bytes[bytes.Length - 2] &= bytemask;
prime = new BigInteger(bytes);
} while (prime.IsEven);
} while (BigInteger.GreatestCommonDivisor(prime, pi) != 1);
while (!prime.IsProbablyPrime(100, random))
{
prime = (prime + pi) & intmask;
}
return(prime);
}
public static bool IsProbablyPrime(this long prime, int certainty, Ibasa.Numerics.Random.Generator random)
{
if (prime == 2 || prime == 3)
{
return(true);
}
if (prime < 2 || prime % 2 == 0)
{
return(false);
}
int s = 0;
var d = prime - 1;
while (d % 2 == 0)
{
d /= 2;
s += 1;
}
for (int i = 0; i < certainty; ++i)
{
long a = random.Next(2, prime - 2);
long x = Ibasa.Numerics.Functions.ModPow(a, d, prime);
if (x != 1 && x != prime - 1)
{
for (int r = 1; r < s; ++r)
{
x = Ibasa.Numerics.Functions.ModPow(x, 2, prime);
if (x == 1)
{
return(false);
}
if (x == prime - 1)
{
break;
}
}
if (x != prime - 1)
{
return(false);
}
}
}
return(true);
}
