Related papers: A Finite-Automaton Based Stream Cipher As a Quasig…

In this paper, we characterize completely the structure of Clifford semigroups of matrices over an arbitrary field. It is shown that a semigroups of matrices of finite order is a Clifford semigroup if and only if it is isomorphic to a…

We announce an atlas of subgroup lattices of almost simple groups and present two algorithms that were used to produce the atlas.

Quantum encryption is a well studied problem for both classical and quantum information. However, little is known about quantum encryption schemes which enable the user, under different keys, to learn different functions of the plaintext,…

For quantum computer circuits, it is proposed that they have, besides the presently used compact graphs, an expanded system of subgraphs, in line with the quantum mechanics superposition axiom. The representation of each process by these…

In this paper we model a class of stream and block ciphers as systems of (ordinary) explicit difference equations over a finite field. We call this class "difference ciphers" and we show that ciphers of application interest, as for example…

We call an affine algebraic supergroup quasireductive if its underlying algebraic group is reductive. We obtain some results about the structure and representations of reductive supergroups.

Quantum-mechanical devices have the potential to transform cryptography. Most research in this area has focused either on the information-theoretic advantages of quantum protocols or on the security of classical cryptographic schemes…

We consider an application to the discrete log problem using completely regular semigroups which may provide a more secure symmetric cryptosystem than the classic system based on groups. In particular we describe a scheme that would appear…

The multiplier representation of the generalized symmetry group of a quasiperiodic flow on the n-torus defines, for each subgroup of the multiplier group of the flow, a group invariant of the smooth conjugacy class of that flow. This group…

In this paper, we study algorithmic problems for automaton semigroups and automaton groups related to freeness and finiteness. In the course of this study, we also exhibit some connections between the algebraic structure of automaton…

Privacy amplification is the key step to guarantee the security of quantum communication. The existing security proofs require accumulating a large number of raw key bits for privacy amplification. This is similar to block ciphers in…

We describe the infinite dihedral group as automaton group. We collect basic results and give full proofs in details for all statements.

We show that an automaton group or semigroup is infinite if and only if it admits an $\omega$-word (i. e. a right-infinite word) with an infinite orbit, which solves an open problem communicated to us by Ievgen V. Bondarenko. In fact, we…

We consider distributions on $\mathbb{R}$ that can be written as the sum of a non-zero discrete distribution and an absolutely continuous distribution. We show that such a distribution is quasi-infinitely divisible if and only if its…

We show that one can define and effectively compute Stallings graphs for quasi-convex subgroups of automatic groups (\textit{e.g.} hyperbolic groups or right-angled Artin groups). These Stallings graphs are finite labeled graphs, which are…

We develop a new framework for analysing finite connected, oriented graphs of valency 4, which admit a vertex-transitive and edge-transitive group of automorphisms preserving the edge orientation. We identify a sub-family of "basic" graphs…

This is Chapter 24 in the "AutoMathA" handbook. Finite automata have been used effectively in recent years to define infinite groups. The two main lines of research have as their most representative objects the class of automatic groups…

Recently, several cryptosystems have been proposed based semidirect products of various algebraic structures. Efficient attacks against several of them have already been given, along with a very general attack. The purpose of this note is…

We survey mathematical properties of quasicrystals, first from the point of view of harmonic analysis, then from the point of view of morphic and automatic sequences. Nous proposons un tour d'horizon de propri\'et\'es math\'ematiques des…

We investigate the class of quasitrivial semigroups and provide various characterizations of the subclass of quasitrivial and commutative semigroups as well as the subclass of quasitrivial and order-preserving semigroups. We also determine…