The program code deals with the applied aspects of number theory related to the algorithm of exponentiation modulo. This algorithm is used in the RSA cryptosystem. A method of increasing the level of protection of the asymmetric RSA algorithm is proposed, based on the generation of pseudorandom primes with a large module. This generation excludes decomposition into continuous fractions when trying to find the RSA private key. Modeling of the asymmetric cryptosystem is done in the Wolfram Mathematica computer environment. In the simulation process, a reversible one-dimensional cellular automaton is used, implementing rule 15. The work of the cellular automaton is based on the logical operation of the sum modulo two. To assess the vulnerability of the cryptosystem, an attack by Michael Wiener is embedded in the program code.