Related papers: Imprimitive permutations groups generated by the r…
The group generated by the round functions of a block ciphers is a widely investigated problem. We identify a large class of block ciphers for which such group is easily guaranteed to be primitive. Our class includes the AES and the…
In a previous paper, we had proved that the permutation group generated by the round functions of an AES-like cipher is primitive. Here we apply the O'Nan Scott classification of primitive groups to prove that this group is the alternating…
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,…
The algebraic structure of the group generated by the encryption functions of a block cipher depends on the key schedule algorithm used for generating the round keys. For such a reason, in general, studying this group does not appear to be…
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…
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…
In symmetric cryptography, the round functions used as building blocks for iterated block ciphers are often obtained as the composition of different layers providing confusion and diffusion. The study of the conditions on such layers which…
S. S. Magliveras et al. have described symmetric and public key cryptosystems based on logarithmic signatures (also known as group bases) for finite permutation groups. In this paper we show that if $G$ is a nontrivial finite group which is…
The key-scheduling algorithm in the AES is the component responsible for selecting from the master key the sequence of round keys to be xor-ed to the partially encrypted state at each iteration. We consider here the group $\Gamma$ generated…
We provide conditions under which the set of Rijndael functions considered as permutations of the state space and based on operations of the finite field $\GF (p^k)$ ($p\geq 2$ a prime number) is not closed under functional composition.…
We provide a new property, called Non-Type-Preserving, for a mixing layer which guarantees protection against algebraic attacks based on the imprimitivity of the group generated by the round functions. Our main result is to present…
Various descending chains of subgroups of a finite permutation group can be used to define a sequence of `basic' permutation groups that are analogues of composition factors for abstract finite groups. Primitive groups have been the…
A block cipher is intended to be computationally indistinguishable from a random permutation of appropriate domain and range. But what are the properties of a random permutation? By the aid of exponential and ordinary generating functions,…
We provide sufficient conditions to guarantee that a translation based cipher is not vulnerable with respect to the partition-based trapdoor. This trapdoor has been introduced, recently, by Bannier et al. (2016) and it generalizes that…
We study permutation groups of given minimal degree without the classical primitivity assumption. We provide sharp upper bounds on the order of a permutation group of minimal degree m and on the number of its elements of any given support.…
We study the quantum security of key-alternating ciphers (KAC), a natural multi-round generalization of the Even--Mansour construction. KAC abstracts the round structure of practical block ciphers as public permutations interleaved with key…
In this article we look into characterizing primitive groups in the following way. Given a primitive group we single out a subset of its generators such that these generators alone (the so-called primitive generators) imply the group is…
A transitive permutation group is semiprimitive if each of its normal subgroups is transitive or semiregular. Interest in this class of groups is motivated by two sources: problems arising in universal algebra related to collapsing monoids…
Two fundamental ways to represent a group are as permutations and as matrices. In this paper, we study linear representations of groups that intertwine with a permutation representation. Recently, D'Alconzo and Di Scala investigated how…
Cryptographic systems are derived using units in group rings. Combinations of types of units in group rings give units not of any particular type. This includes cases of taking powers of units and products of such powers and adds the…