Applied Aspects of Number Theory

The article deals with the applied aspects of number theory related to the exponentiation modulo algorithm. This algorithm has found application in the RSA cryptosystem. The method of increasing the level of protection of the asymmetric RSA algorithm is proposed. To increase the level of protection, the RSA algorithm is supplemented by generating the pseudorandom primes with a large modulo. This solution 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. To simulate this process, a reversible one-dimensional cellular automaton is used. This structure corresponds to 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.