Integral Cryptanalysis and the Geometric Approach

Recently, we generalized integral cryptanalysis to arbitrary finite field. This generalization was made possible due to the expressiveness of the geometric approach. In this seminar, we will discuss the geometric approach to cryptanalysis and how it can be used to derive a generalized description of integral cryptanalysis, following the recent work "Integral cryptanalysis in characteristic p" by Tim Beyne and myself. Furthermore, we show how integral cryptanalysis can be used to analyze a variety of algebraic properties of ciphers, such as the growth of the degree, density of the algebraic normal form and cubes. We will highlight interesting results from recent work and also look at more classical results from the point of view of integral cryptanalysis in the geometric approach.