We propose a variation of the Diffie and Hellman key distribution scheme for which we can prove that decryption of a single key requires the ability to factor a number that is the product of two large primes. The practical advantage of such a scheme is that it will still be secure if the cryptanalyst knows a very fast algorithm for either factoring or computing discrete logarithms, but not for both. Using these keys in the ElGamal public-key cryptosystem provides a scheme for which the decryption of a message requires the ability to factor the modulus and break the original Diffie and Hellman scheme.