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.
On the group generated by the round functions of translation based ciphers over arbitrary finite fields
Aragona, Riccardo;Caranti, Andrea;Sala, Massimiliano
2014-01-01
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.File in questo prodotto:
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