On the primitivity of PRESENT and other lightweight ciphers
  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. 
Riccardo Aragona, Marco Calderini, Antonio Tortora, Maria Tota
math.GR cs.CR cs.IT math.IT