The function to generate a safe prime, gen_safe_prime, performs another primality test on the random prime that was just generated.
Specifically, in gen_safe_prime, gen_prime returns a probable prime, but the next check _is_safe_prime(...) && lucas(...) tests again that candidate is a prime. This is already done in gen_prime, so we now only need to check if (candidate - 1)/2 is also prime.
The function to generate a safe prime,
gen_safe_prime, performs another primality test on the random prime that was just generated.Specifically, in gen_safe_prime,
gen_primereturns a probable prime, but the next check_is_safe_prime(...) && lucas(...)tests again thatcandidateis a prime. This is already done ingen_prime, so we now only need to check if(candidate - 1)/2is also prime.