Primitivity of PRESENT and other lightweight ciphers

Abstract

We provide two sufficient conditions to guarantee that the round functions of a translation-based cipher generate a primitive group. Furthermore, under the same hypotheses, and assuming that a round of the cipher is strongly proper and consists of [Formula: see text]-bit S-Boxes, with [Formula: see text] or [Formula: see text], we prove that such a group is the alternating group. As an immediate consequence, we deduce that the round functions of some lightweight translation-based ciphers, such as the PRESENT cipher, generate the alternating group.