Sophie Germain prime
The existence of this algorithm leads to the concept of safe primes, being primes for which "p" − 1 is two times a Sophie Germain prime "q" and thus minimally smooth. These primes are sometimes construed as "safe for cryptographic purposes", but they might be "unsafe" — in current recommendations for cryptographic strong primes ("e.g." ANSI X9.31), it is necessary but not sufficient that "p" − 1 has at least one large prime factor. Most sufficiently large primes are strong; if a prime used for cryptographic purposes turns out to be non-strong, it is much more likely to be through malice than through an accident of random number generation. This terminology is considered obsolete by the cryptography industry: ECM makes safe primes just as easy to factor as non-safe primes, so size is the important factor.