The prime factorization problem forms the basis for most public key cryptographic algorithms, including RSA, PGP, and GPG. So, that eliminates all three of those – RSA, PGP, and GPG – as the answer. The elliptic curve cryptosystem (ECC) does not depend upon the prime factorization problem. The security of ECC depends upon the difficulty of finding the discrete logarithm of a random elliptic curve element with respect to a publicly known base point. That makes it our correct answer!