On the primitivity of PRESENT and other lightweight ciphers

November 04, 2016 Β· Declared Dead Β· πŸ› arXiv.org

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Authors Riccardo Aragona, Marco Calderini, Antonio Tortora, Maria Tota arXiv ID 1611.01346 Category math.GR Cross-listed cs.CR, cs.IT Citations 16 Venue arXiv.org Last Checked 3 months ago
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.
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