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On the primitivity of PRESENT and other lightweight ciphers (1611.01346v2)
Published 4 Nov 2016 in math.GR, cs.CR, cs.IT, and math.IT
Abstract: We provide two sufficient conditions to guarantee that the round functions of a translation based cipher generate a primitive group. Furthermore, under the same hypotheses, and assuming that a round of the cipher is strongly proper and consists of m-bit S-Boxes, with m = 3; 4 or 5, we prove that such a group is the alternating group. As an immediate consequence, we deduce that the round functions of some lightweight translation based ciphers, such as the PRESENT cipher, generate the alternating group.