Wave-Shaped Round Functions and Primitive Groups

TL;DR

This paper introduces wave ciphers, a new family of block ciphers using wave functions with non-invertible layers in Feistel structures, enhancing non-linearity and security against certain algebraic attacks.

Contribution

The work proposes wave ciphers with non-invertible layers, enabling the use of injective APN S-boxes and analyzing their security against group-theoretical attacks.

Findings

Wave ciphers incorporate wave functions with non-invertible layers.

They enable the use of injective APN S-boxes for enhanced non-linearity.

The security analysis shows how to prevent imprimitivity in the generated group.

Abstract

Round functions used as building blocks for iterated block ciphers, both in the case of Substitution-Permutation Networks and Feistel Networks, are often obtained as the composition of different layers which provide confusion and diffusion, and key additions. The bijectivity of any encryption function, crucial in order to make the decryption possible, is guaranteed by the use of invertible layers or by the Feistel structure. In this work a new family of ciphers, called wave ciphers, is introduced. In wave ciphers, round functions feature wave functions, which are vectorial Boolean functions obtained as the composition of non-invertible layers, where the confusion layer enlarges the message which returns to its original size after the diffusion layer is applied. This is motivated by the fact that relaxing the requirement that all the layers are invertible allows to consider more functions which are optimal with regard to non-linearity. In particular it allows to consider injective APN S-boxes. In order to guarantee efficient decryption we propose to use wave functions in Feistel Networks. With regard to security, the immunity from some group-theoretical attacks is investigated. In particular, it is shown how to avoid that the group generated by the round functions acts imprimitively, which represent a serious flaw for the cipher.