Shapeless quasigroups derived by Feistel orthomorphisms

Abstract

Shapeless quasigroups are needed for cryptography purposes. In this paper, we construct shapeless quasigroups by the diagonal method from orthomorphisms over abelian groups. We use generalizations of Feistel networks as orthomorphisms. We introduce parameters into several types of Extended Feistel networks and Generalized Feistel-non linear feedback shift registers and, by suitable choice of the parameter values, different shapeless quasigroup can be used in every application.