On properties of translation groups in the affine general linear group with applications to cryptography

The affine general linear group acting on a vector space over prime field is well-understood mathematical object. Its elementary abelian regular subgroups have recently drawn attention in applied mathematics thanks to their use cryptography as way hide or detect weaknesses inside block ciphers. This paper focused building convenient representation of elements which suits better the purposes cryptanalyst. Several combinatorial counting formulas and classification conjugacy classes are given well.