Permutation generators of alternating groups

Abstract

The problem of generation of permutations from small ones is especially important from a cryptographic point of view. This work explores the case This work addresses the design of cryptographic systems using elementary permutations, also called modules. These modules have a simple structure and are based on internal smaller permutations. Two cases have been considered. In the first, the modules apply internal permutations only. It has been proved that the composition of modules generates the alternating group for the number of binary inputs bigger than 2. In the second, DES-like modules are considered and it has been shown that for a large enough number of binary inputs, they produce the alternating group, as well.

Support for this project was provided in part by the Australian Research Council under the reference number A48830241 and by TELECOM Australia under the contract number 7027