Related papers: Group theory in cryptography

This article presets a review of the achievements rapidly developing field of cryptography - public-key cryptography based on the lattice theory. Paper contains the necessary basic concepts and the major problems of the lattice theory, as…

GroupMath is a Mathematica package which performs several calculations related to semi-simple Lie algebras and the permutation groups, both of which are important in particle physics as well as in other areas of research.

This is a first step guide to the theory of cluster algebras. We especially focus on basic notions, techniques, and results concerning seeds, cluster patterns, and cluster algebras.

In this research work, security concepts are formalized in steganography, and the common paradigms based on information theory are replaced by another ones inspired from cryptography, more practicable are closer than what is usually done in…

We give a review of some known published applications of quasigroups in cryptology.

A new proposal for group key exchange is introduced which proves to be both efficient and secure and compares favorably with state of the art protocols.

This is an account of the theory of inverse semigroups, assuming only that the reader knows the basics of semigroup theory.

This paper introduces a completely new approach to encryption based on group theoretic quantum framework. Quantum cryptography has essentially focused only on key distribution and proceeded with classical encryption algorithm with the…

The purpose of this paper is to present a systematic exposition of the main results obtained in the studies carried out in groupoid theory. Key words and phrases: groupoid, topological groupoid, Lie groupoid, group-groupoid, vector…

Quantum cryptography is the art and science of exploiting quantum mechanical effects in order to perform cryptographic tasks. While the most well-known example of this discipline is quantum key distribution (QKD), there exist many other…

In the last decade, a number of public key cryptosystems based on com- binatorial group theoretic problems in braid groups have been proposed. We survey these cryptosystems and some known attacks on them. This survey includes: Basic facts…

In this talk we introduce several topics in combinatorial number theory which are related to groups; the topics include combinatorial aspects of covers of groups by cosets, and also restricted sumsets and zero-sum problems on abelian…

In a previous paper we generalized the definition of a multilinear map to arbitrary groups and introduced two multiparty key-exchange protocols using nilpotent groups. In this paper we have a closer look at the protocols and will address…

This is a survey paper based on my talk at the Workshop on Orbifolds and String Theory, the goal of which was to explain the role of groupoids and their classifying spaces as a foundation for the theory of orbifolds.

This paper provides a preparatory introduction to torsors, written with a view toward later applications in the author's work. Rather than aiming at a comprehensive survey, the exposition focuses on those aspects of torsors that are most…

Cryptography is the science of using mathematics to encrypt and decrypt data. Cryptography enables you to store sensitive information or transmit it across insecure networks so that it cannot be read by anyone except the intended recipient.…

We propose a new cryptosystem based on polycyclic groups. The cryptosystem is based on the fact that the word problem can be solved effectively in polycyclic groups, while the known solutions to the conjugacy problem are far less efficient.

This paper summarizes basic properties of PPTs and shows that each PPT belongs to one of six different classes. Mapping an ordered sequence of PPTs into a corresponding sequence of these six classes makes it possible to use them in…

Game theory is an established branch of mathematics that offers a rich set of mathematical tools for multi-person strategic decision making that can be used to model the interactions of decision makers in security problems who compete for…

These notes form an introduction to Lie algebras and group theory. Most of the material can be found in many works by various authors given in the list of references. The reader is referred to such works for more detail.