We define a translation based cipher over arbitrary finite field and we study properties of the permutation group generated by the round functions of such cipher. We show under which cryptographic hypothesis this group is primitive. Moreover, a minor strengthening of our hypothesis lets us prove that such group is the symmetric group or the alternating group for characteristic p bigger or equal to 2; in particular we improve a previous result
Aragona, R., Caranti, A., DALLA VOLTA, F., Sala, M. (2014). On the group generated by the round encryptions of translation based ciphers over arbitrary finite fields. FINITE FIELDS AND THEIR APPLICATIONS, 25, 293-305 [10.1016/j.ffa.2013.10.005].
On the group generated by the round encryptions of translation based ciphers over arbitrary finite fields
DALLA VOLTA, FRANCESCA;
2014
Abstract
We define a translation based cipher over arbitrary finite field and we study properties of the permutation group generated by the round functions of such cipher. We show under which cryptographic hypothesis this group is primitive. Moreover, a minor strengthening of our hypothesis lets us prove that such group is the symmetric group or the alternating group for characteristic p bigger or equal to 2; in particular we improve a previous result
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