The chapter considers the cryptographic protocol of B. Chor and R. L. Rivest, in which discrete logarithms of elements of a smooth multiplicative group of a prime field extension are calculated for generating a public key using an arbitrarily chosen random standard basis. Under the assumption of the existence of an optimal normal basis of the first type, a modification of this protocol is considered, which is distinguished by the fact that using known algorithms for transforming bases, discrete algorithmization of elements selected in a random basis is carried out in an optimal normal basis of the first type. This achieves acceleration of the discrete logarithm function, as well as decryption due to the “free” raising to a power multiple of the field characteristics, and the use of an irreducible polynomial that is “convenient” for reduction by modulo, ultimately increasing the information speed of the protocol as a whole.