Related papers: Group theory in cryptography
This is a survey of algorithmic problems in group theory, old and new, motivated by applications to cryptography.
Public-key cryptosystems are suggested based on invariants of groups. We give also an overview of the known cryptosystems which involve groups.
We present a survey of quantum algorithms, primarily for an intended audience of pure mathematicians. We place an emphasis on algorithms involving group theory.
Group theory is a particularly fertile field for the design of practical algorithms. Algorithms have been developed across the various branches of the subject and they find wide application. Because of its relative maturity, computational…
Group Theory has become an invaluable tool in the physics community. Despite numerous introductory books, the subject remains challenging for beginners. Mathematica has emerged as a popular tool for research and education, offering various…
This article is a short introduction to the theory of the groups of points of elliptic curves over finite fields. It is concerned with the elementary theory and practice of elliptic curves cryptography, the new generation of public key…
General cryptographic schemes are presented where keys can be one-time or ephemeral. Processes for key exchange are derived. Public key cryptographic schemes based on the new systems are easily established. Authentication and signature…
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 expository article we present an overview of the current state-of-the-art in post-quantum group-based cryptography. We describe several families of groups that have been proposed as platforms, with special emphasis in polycyclic…
Cryptography is a theory of secret functions. Category theory is a general theory of functions. Cryptography has reached a stage where its structures often take several pages to define, and its formulas sometimes run from page to page.…
In cryptography, encryption is the process of obscuring information to make it unreadable without special knowledge. This is usually done for secrecy, and typically for confidential communications. Encryption can also be used for…
This is a survey of some problems in geometric group theory which I find interesting. The problems are from different areas of group theory. Each section is devoted to problems in one area. It contains an introduction where I give some…
Quantum cryptography can, in principle, provide unconditional security guaranteed by the law of physics only. Here, we survey the theory and practice of the subject and highlight some recent developments.
The theory of finite simple groups is a (rather unexplored) area likely to provide interesting computational problems and modelling tools useful in a cryptographic context. In this note, we review some applications of finite non-abelian…
The paper gives a short account of the contents of "Regular Algebraic K-Theory For Groups" by the author and its connections with other homology and K-theories.
The goal of this chapter is to present a survey of homomorphic encryption techniques and their applications. After a detailed discussion on the introduction and motivation of the chapter, we present some basic concepts of cryptography. The…
Chaotic cryptography describes the use of chaos theory (in particular physical dynamical systems working in chaotic regime as part of communication techniques and computation algorithms) to perform different cryptographic tasks in a…
This book collects the lectures about graph theory and its applications which were given to students of mathematical departments of Moscow State University and Peking University. Graph theory is a very wide field with a lot of applications…
This is a chapter on quantum cryptography for the book "A Multidisciplinary Introduction to Information Security" to be published by CRC Press in 2011/2012. The chapter aims to introduce the topic to undergraduate-level and…
Cryptography is an art and science of secure communication. Here the sender and receiver are guaranteed the security through encryption of their data, with the help of a common key. Both the parties should agree on this key prior to…