Slovak University of Technology, Bratislava
Faculty of Electrical Engineering and Information Technology
Degree Course: INFORMATICS
Author: Bc. Ján Ťapuška
Diploma thesis: Searching for cryptographically strong S-boxes
Supervisor: Prof. RNDr. Otokar Grošek, PhD.
December 2003

This thesis deals with affine transformations of power permutations in GF(2n) and mappings of these permutations between GF(2n) and GF(2)n. Our aim is to analyze the effect of affine transformations on the cryptographic properties of the permutations.

We split up matrices of affine transformations into classes according to the specific properties of permutations and study distribution of matrices over these classes considering the selection of polynomial basis and degree of power permutation.

Distribution of matrices outlines probabilities for random generation of matrices leading to permutations with best cryptographic properties.

As a part of the thesis, CryptoTool software product has been developed aimed at computing cryptographic properties of Boolean functions and permutations in GF(2)n.