On the primitivity of PRESENT and other lightweight ciphers
This provides a theoretical security guarantee for lightweight ciphers used in resource-constrained devices, but it is incremental as it builds on existing mathematical frameworks.
The paper tackled the problem of determining the algebraic primitivity of round functions in lightweight ciphers like PRESENT, proving that under certain conditions, these functions generate the alternating group.
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.