The security of Diffie-Hellman relies on the difficulty of the discrete logarithm problem. This project describes attempts to determine what size primes are required for security. In particular, evaluate the secure identification option of the Sun Network File System, which uses Diffie-Hellman algorithm with a prime p of 192 bits. Objectives: To describe the different steps necessary to solve the discrete logarithm problem (DLP). To discuss the state-of-the-art results obtained for the solution of DLP. Present the SUN NFS cryptosystem, and discuss some of its deficiencies. Recommendations in order to have a secure size for the prime number p used in the Diffie-Hellman algorithm.