ソフィー・ジェルマン素数
A prime number "p" = 2"q" + 1 is called a "safe prime" if "q" is prime. Thus, "p" = 2"q" + 1 is a safe prime if and only if "q" is a Sophie Germain prime, so finding safe primes and finding Sophie Germain primes are equivalent in computational difficulty. The notion of a safe prime can be strengthened to a strong prime, for which both "p" − 1 and "p" + 1 have large prime factors. Safe and strong primes were useful as the factors of secret keys in the RSA cryptosystem, because they prevent the system being broken by some factorization algorithms such as Pollard's "p" − 1 algorithm. However, with the current factorization technology, the advantage of using safe and strong primes appears to be negligible.