Abstract. We define a cipher that is an extension of GOST, and study the permutation group generated by its round functions. We show that, under minimal assumptions on the components of the cipher, this group is the alternating group on the plaintext space. This we do by first showing that the group is primitive, and then applying the O'Nan-Scott classification of primitive groups.
We define a translation based cipher over an arbitrary finite field, and study the permutation group generated by the round functions of such a cipher. We show that under certain cryptographic assumptions this group is primitive. Moreover, a minor strengthening of our assumptions allows us to prove that such a group is the symmetric or the alternating group; this improves upon a previous result for the case of characteristic two.
In this paper, we give a characterization of digraphs Q,|Q| ≤ 4 such that the associated Hecke-Kiselman monoid H Q is finite. In general, a necessary condition for H Q to be a finite monoid is that Q is acyclic and its Coxeter components are Dynkin diagram. We show, by constructing examples, that such conditions are not sufficient.Date: June 25, 2018.
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.
In this paper we study the relationships between the elementary abelian regular subgroups and the Sylow 2-subgroups of their normalisers in the symmetric group Sym(F n 2 ), in view of the interest that they have recently raised for their applications in symmetric cryptography.2010 Mathematics Subject Classification. 20B35, 20D20, 94A60.
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