SOME CLASSES OF POLYNOMIALS OVER FINITE FIELDS

Abstract

Mathematics and cryptography have a long history together. Almost all the modern crypto systems use the notions either from number theory or from nite elds in some way or the other. This thesis is devoted to the study of some mathematical problems arising from cyptography. More precisely, we study cryptographic properties of some classes of polynomials over nite elds. Substitution boxes (S-boxes) play a very crucial role in the design of secure cryptographic primitives such as block ciphers. Di erential attack, introduced by Biham and Shamir [4] in 1991, is one of the most e cient attacks on the S-boxes used in the block ciphers. To quantify the degree of security of a S-box against the di erential attacks, Nyberg [45] in 1993 introduced the notion of di erential uniformity. In 2020, Ellingsen et. al generalized the notion of di erential uniformity and introduced the concept of c-di erential uniformity.