bignum & Prime::generate_prime(const integer & length) {
Numbers numbers;
bignum * number = new BigUnsigned( numbers.random(length) );
while ( !primality_test(*number, 4) )
* number = numbers.random( length ); // or sth like: numbers.try_upgrading_to_prime( const bignum & number )
return * number;
}
bool Prime::primality_test(const bignum & n, const integer & accuracy) {
long_integer s = 0;
bignum d(1);
bignum a;
bignum x;
Numbers numbers;
bignum n_minus_one(n - 1);
bignum one(1);
while ( n_minus_one % 2 == 0 ) {
n_minus_one /= 2;
s++;
}
d = n_minus_one;
for(integer k = 0; k < accuracy; k++) {
a = numbers.random(2, n - 1);
x = modexp(a, d, n);
if (x == one || x == n_minus_one) continue;
for(long_integer r = 1; r <= s - 1; r++) {
x = modexp(x, 2, n);
if (x == one) return false;
if (x == n_minus_one) continue;
}
return false;
}
return true; // possibly prime
}