In this paper, we describe a new contribution that uses the optimization problem to create a new version of the Diffie-Hellman key exchange (DHKE). The proposed version depended on the optimized discrete logarithm functions (ODLFs) that are given as a new definition in this work. A graphical method considers a fundamental tool to compute a shared secret key (SSK) in the proposed optimized Diffie-Hellman key exchange (ODHKE). The ODHKE is a more secure protocol for computing the SSK in comparison with the original DHKE.