On the group generated by the round functions of translation based ciphers over arbitrary finite fields

Abstract

We define a translation based cipher over an arbitrary finite field, and study the permutation group generated by the round functions of such a cipher. We show that under certain cryptographic assumptions this group is primitive. Moreover, a minor strengthening of our assumptions allows us to prove that such a group is the symmetric or the alternating group; this improves upon a previous result for the case of characteristic two.

Extensive revision, including fixing a mistake concerning the blocks of imprimitivity

Cited by in corpus (5)

• The group generated by the round functions of a GOST-like cipher
• On the primitivity of PRESENT and other lightweight ciphers
• On differential uniformity of maps that may hide an algebraic trapdoor
• On weak differential uniformity of vectorial Boolean functions as a cryptographic criterion
• A note on an infeasible linearization of some block ciphers