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.
['Riccardo Aragona', 'A. Caranti', 'F. Dalla Volta', 'Massimiliano Sala']
On the group generated by the round functions of translation based ciphers over arbitrary finite fields