Related papers: MOR Cryptosystem and classical Chevalley groups in…

In this article, we propose a method to construct self orthogonal matrix, orthogonal matrix and anti orthogonal matrix over the finite field. Orthogonal matrices has numerous applications in cryptography, so here we demonstrate the…

In this paper, we identify many important properties and develop criteria for the existence of subquasigroups in finite quasigroups. Based on these results, we propose an effective method that concludes the nonexistence of subquasigroup of…

Several cryptographic protocols constructed based on less-known algorithmic problems, such as those in non-commutative groups, group rings, semigroups, etc., which claim quantum security, have been broken through classical reduction methods…

An improved design of a cryptosystem based on small Ree groups is proposed. We have changed the encryption algorithm and propose to use a logarithmic signature for the entire Ree group. This approach improves security against sequential key…

We describe the rings of invariants for the finite orthogonal groups of plus type in odd characteristic acting on the defining representations. We also describe the invariants of the corresponding Sylow subgroups in the defining…

Polycyclic groups are natural generalizations of cyclic groups but with more complicated algorithmic properties. They are finitely presented and the word, conjugacy, and isomorphism decision problems are all solvable in these groups.…

Ab-initio studies of strongly interacting bosonic and fermionic systems is greatly facilitated by efficient Monte Carlo algorithms. This article emphasizes this requirement, and outlines the ideas behind the construction of the cluster…

The paper proposes a new and systematic approach to the so-called black box group methods in computational group theory. As the starting point of our programme, we construct Frobenius maps on black box groups of untwisted Lie type in odd…

Here is a more detailed description of the algorithm proposed in [1]. This algorithm simultaneously uses two cryptographic procedures: encryption using a generalization of the Markovski algorithm [2] and encryption using a system of…

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…

In this paper we consider cryptographic applications of the arithmetic on the hyperoctahedral group. On an appropriate subgroup of the latter, we particularly propose to construct public key cryptosystems based on the discrete logarithm.…

As a special type of factorization of finite groups, logarithmic signature (LS) is used as the main component of cryptographic keys for secret key cryptosystems such as PGM and public key cryptosystems like MST1, MST2 and MST3. An LS with…

In this paper we consider several classical and novel algorithmic problems for right-angled Artin groups, some of which are closely related to graph theoretic problems, and study their computational complexity. We study these problems with…

We present a new algorithm for constructing a Chevalley basis for any Chevalley Lie algebra over a finite field. This is a necessary component for some constructive recognition algorithms of exceptional quasisimple groups of Lie type. When…

The paper analyzes a new public key cryptosystem whose security is based on a matrix version of the discrete logarithm problem over an elliptic curve. It is shown that the complexity of solving the underlying problem for the proposed system…

Let f be an arbitrary positive integer valued function. The goal of this note is to show that one can construct a finitely generated group in which the discrete log problem is polynomially equivalent to computing the function f. In…

The combinative applications of one-way coupled map lattice (OCML) and some simple algebraic operations have demonstrated to be able to construct the best known chaotic cryptosystem with high practical security, fast encryption speed, and…

We establish a theorem concerning the commuting scheme in characteristic p. As a significant application of this theorem, we derive an explicit lower bound for the characteristic p, ensuring the validity of the higher-dimensional Chevalley…

We present a uniform methodology for computing with finitely generated matrix groups over any infinite field. As one application, we completely solve the problem of deciding finiteness in this class of groups. We also present an algorithm…

This book describes some computational methods to deal with modular characters of finite groups. It is the theoretical background of the MOC system of the same authors. This system was, and is still used, to compute the modular character…