3 ON THE GROUP GENERATED BY THE ROUND FUNCTIONS OF TRANSLATION BASED CIPHERS OVER ARBITRARY FINITE FIELDS
Riccardo Aragona, A. Caranti, Francesca Dalla Volta, Massimiliano Sala · 2016
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.