In this project, Extended Access Control on the electronic passport was designed to overcome limited computing resources. Today, experts are looking for safer ways to identify and authenticate authenticity. One of the most successful of these ways is the use of biometrics. In this project, in order to reduce the volume of computing, the Fast Exponential method has also been added to Diffie- Hellman, as well as to enhance the security of the proposed research protocol and reduce the success rate of attacks such as a man-in-the-middle attack to steal information, from fingerprint to extract some of the required parameters of the Diffie-Hellman method (parameters q and g) is used. To this end, three different scenarios were raised. The results of the simulation showed that the proposed method reduces the computational load of the classical Diffie-Hellman method and, therefore, reduces the run-time. Also, the results showed that the first scenario is better than the other two scenarios in terms of both runtime and computational load.