Computing in Finite Fields

The mathematical apparatus of Galois field theory is used in coding theory, cryptography, stochastic informatics. The paper considers algorithms for multiplying field elements, while paying attention to both table multiplication and multiplication "on the fly"; algorithms for calculating multiplicative inversion. The solution to the problem of finding primitive elements of the field GF (pn) is discussed. The questions of extension of finite fields are considered. Numerical examples of the operation of all considered algorithms are given.