Interactions Between Group Theory Symmetry And Cryptology

Author : María Isabel González Vasco
Publisher : MDPI
Page : 164 pages
File Size : 45,8 Mb
Release : 2020-04-22
Category : Mathematics
ISBN : 9783039288021

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Interactions between Group Theory, Symmetry and Cryptology by María Isabel González Vasco Pdf

Cryptography lies at the heart of most technologies deployed today for secure communications. At the same time, mathematics lies at the heart of cryptography, as cryptographic constructions are based on algebraic scenarios ruled by group or number theoretical laws. Understanding the involved algebraic structures is, thus, essential to design robust cryptographic schemes. This Special Issue is concerned with the interplay between group theory, symmetry and cryptography. The book highlights four exciting areas of research in which these fields intertwine: post-quantum cryptography, coding theory, computational group theory and symmetric cryptography. The articles presented demonstrate the relevance of rigorously analyzing the computational hardness of the mathematical problems used as a base for cryptographic constructions. For instance, decoding problems related to algebraic codes and rewriting problems in non-abelian groups are explored with cryptographic applications in mind. New results on the algebraic properties or symmetric cryptographic tools are also presented, moving ahead in the understanding of their security properties. In addition, post-quantum constructions for digital signatures and key exchange are explored in this Special Issue, exemplifying how (and how not) group theory may be used for developing robust cryptographic tools to withstand quantum attacks.

Author : María Isabel González Vasco
Publisher : Unknown
Page : 164 pages
File Size : 53,6 Mb
Release : 2020
Category : Mathematics
ISBN : 3039288032

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Interactions between Group Theory, Symmetry and Cryptology by María Isabel González Vasco Pdf

Cryptography lies at the heart of most technologies deployed today for secure communications. At the same time, mathematics lies at the heart of cryptography, as cryptographic constructions are based on algebraic scenarios ruled by group or number theoretical laws. Understanding the involved algebraic structures is, thus, essential to design robust cryptographic schemes. This Special Issue is concerned with the interplay between group theory, symmetry and cryptography. The book highlights four exciting areas of research in which these fields intertwine: post-quantum cryptography, coding theory, computational group theory and symmetric cryptography. The articles presented demonstrate the relevance of rigorously analyzing the computational hardness of the mathematical problems used as a base for cryptographic constructions. For instance, decoding problems related to algebraic codes and rewriting problems in non-abelian groups are explored with cryptographic applications in mind. New results on the algebraic properties or symmetric cryptographic tools are also presented, moving ahead in the understanding of their security properties. In addition, post-quantum constructions for digital signatures and key exchange are explored in this Special Issue, exemplifying how (and how not) group theory may be used for developing robust cryptographic tools to withstand quantum attacks.

Author : Alexei G. Myasnikov,Vladimir Shpilrain,Alexander Ushakov
Publisher : American Mathematical Soc.
Page : 402 pages
File Size : 44,8 Mb
Release : 2011
Category : Computers
ISBN : 9780821853603

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Non-commutative Cryptography and Complexity of Group-theoretic Problems by Alexei G. Myasnikov,Vladimir Shpilrain,Alexander Ushakov Pdf

Examines the relationship between three different areas of mathematics and theoretical computer science: combinatorial group theory, cryptography, and complexity theory. It explores how non-commutative (infinite) groups can be used in public key cryptography. It also shows that there is remarkable feedback from cryptography to combinatorial group theory because some of the problems motivated by cryptography appear to be new to group theory.

Author : Hamid Krim,A. Ben Hamza
Publisher : Cambridge University Press
Page : 299 pages
File Size : 51,6 Mb
Release : 2015-06-18
Category : Computers
ISBN : 9781107033900

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Geometric Methods in Signal and Image Analysis by Hamid Krim,A. Ben Hamza Pdf

A comprehensive guide to modern geometric methods for signal and image analysis, from basic principles to state-of-the-art concepts and applications.

Author : N.B. Singh
Publisher : N.B. Singh
Page : 130 pages
File Size : 44,5 Mb
Release : 2024-06-23
Category : Mathematics
ISBN : 8210379456XXX

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Abstract Algebra: Group Theory by N.B. Singh Pdf

Author : Kazuo Iwama,Yasuhito Kawano,Mio Murao
Publisher : Springer
Page : 153 pages
File Size : 41,7 Mb
Release : 2013-01-05
Category : Computers
ISBN : 9783642356568

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Theory of Quantum Computation, Communication, and Cryptography by Kazuo Iwama,Yasuhito Kawano,Mio Murao Pdf

This book constitutes revised selected papers from the 7th Conference on Theory of Quantum Computation, Communication, and Cryptography, TQC 2012, held in Tokyo, Japan, in May 2012. The 12 papers presented were carefully reviewed and selected for inclusion in this book. They contain original research on the rapidly growing, interdisciplinary field of quantum computation, communication and cryptography. Topics addressed are such as quantum algorithms, quantum computation models, quantum complexity theory, simulation of quantum systems, quantum programming languages, quantum cryptography, quantum communication, quantum estimation, quantum measurement, quantum tomography, completely positive maps, decoherence, quantum noise, quantum coding theory, fault-tolerant quantum computing, entanglement theory, and quantum teleportation.

Author : Juan A. Garay,Akira Otsuka
Publisher : Springer
Page : 538 pages
File Size : 47,5 Mb
Release : 2009-11-23
Category : Computers
ISBN : 9783642104336

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Cryptology and Network Security by Juan A. Garay,Akira Otsuka Pdf

This book constitutes the refereed proceedings of the 8th International Conference on Cryptology and Network Security, CANS 2009, held in Kanazawa, Japan, in December 2009. The 32 revised full papers presented together with 3 invited talks were carefully reviewed and selected from 109 submissions. The papers are organized in topical sections on cryptographic protocols and schemes; cryptanalysis; wireless and sensor security; network security; privacy and anonymity; functional and searchable encryption; authentication; block cipher design; and algebraic and number-theoretic schemes.

Author : Raf Cluckers,Johannes Nicaise,Julien Sebag
Publisher : Cambridge University Press
Page : 347 pages
File Size : 44,5 Mb
Release : 2011-09-22
Category : Mathematics
ISBN : 9781139499798

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Motivic Integration and its Interactions with Model Theory and Non-Archimedean Geometry: Volume 1 by Raf Cluckers,Johannes Nicaise,Julien Sebag Pdf

Assembles different theories of motivic integration for the first time, providing all of the necessary background for graduate students and researchers from algebraic geometry, model theory and number theory. In a rapidly-evolving area of research, this volume and Volume 2, which unite the several viewpoints and applications, will prove invaluable.

Author : Glenn Cunningham
Publisher : Scientific e-Resources
Page : 316 pages
File Size : 49,6 Mb
Release : 2019-07-07
Category : Electronic
ISBN : 9781839473852

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High Energy Physics by Glenn Cunningham Pdf

Particle physics (also high energy physics) is the branch of physics that studies the nature of the particles that constitute matter and radiation. Although the word "e;particle"e; can refer to various types of very small objects "e;particle physics"e; usually investigates the irreducibly smallest detectable particles and the fundamental interactions necessary to explain their behaviour. By our current understanding, these elementary particles are excitations of the quantum fields that also govern their interactions. The currently dominant theory explaining these fundamental particles and fields, along with their dynamics, is called the Standard Model. Thus, modern particle physics generally investigates the Standard Model and its various possible extensions, e.g. to the newest "e;known"e; particle, the Higgs boson, or even to the oldest known force field, gravity. Written in a clear pedagogic style by active researchers, this book will prepare a beginner to work in the field and at the same time will also provide useful reference material for active researchers.

Author : Volker Diekert,Manfred Kufleitner,Gerhard Rosenberger,Ulrich Hertrampf
Publisher : Walter de Gruyter GmbH & Co KG
Page : 354 pages
File Size : 42,9 Mb
Release : 2016-05-24
Category : Mathematics
ISBN : 9783110413335

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Discrete Algebraic Methods by Volker Diekert,Manfred Kufleitner,Gerhard Rosenberger,Ulrich Hertrampf Pdf

The idea behind this book is to provide the mathematical foundations for assessing modern developments in the Information Age. It deepens and complements the basic concepts, but it also considers instructive and more advanced topics. The treatise starts with a general chapter on algebraic structures; this part provides all the necessary knowledge for the rest of the book. The next chapter gives a concise overview of cryptography. Chapter 3 on number theoretic algorithms is important for developping cryptosystems, Chapter 4 presents the deterministic primality test of Agrawal, Kayal, and Saxena. The account to elliptic curves again focuses on cryptographic applications and algorithms. With combinatorics on words and automata theory, the reader is introduced to two areas of theoretical computer science where semigroups play a fundamental role.The last chapter is devoted to combinatorial group theory and its connections to automata. Contents: Algebraic structures Cryptography Number theoretic algorithms Polynomial time primality test Elliptic curves Combinatorics on words Automata Discrete infinite groups

Author : Benjamin Fine
Publisher : World Scientific
Page : 253 pages
File Size : 50,9 Mb
Release : 2008
Category : Mathematics
ISBN : 9789812793416

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Aspects of Infinite Groups by Benjamin Fine Pdf

This book is a festschrift in honor of Professor Anthony Gaglione''s sixtieth birthday. This volume presents an excellent mix of research and expository articles on various aspects of infinite group theory. The papers give a broad overview of present research in infinite group theory in general, and combinatorial group theory and non-Abelian group-based cryptography in particular. They also pinpoint the interactions between combinatorial group theory and mathematical logic, especially model theory.

Author : Lewis Bowen,R. I. Grigorchuk,Yaroslav Vorobets
Publisher : American Mathematical Soc.
Page : 280 pages
File Size : 52,8 Mb
Release : 2012
Category : Mathematics
ISBN : 9780821869222

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Dynamical Systems and Group Actions by Lewis Bowen,R. I. Grigorchuk,Yaroslav Vorobets Pdf

This volume contains cutting-edge research from leading experts in ergodic theory, dynamical systems and group actions. A large part of the volume addresses various aspects of ergodic theory of general group actions including local entropy theory, universal minimal spaces, minimal models and rank one transformations. Other papers deal with interval exchange transformations, hyperbolic dynamics, transfer operators, amenable actions and group actions on graphs.

Author : Eike Kiltz,Vinod Vaikuntanathan
Publisher : Springer Nature
Page : 813 pages
File Size : 46,8 Mb
Release : 2022-12-21
Category : Computers
ISBN : 9783031223655

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Theory of Cryptography by Eike Kiltz,Vinod Vaikuntanathan Pdf

The three-volume set LNCS 13747, LNCS 13748 and LNCS 13749 constitutes the refereed proceedings of the 20th International Conference on Theory of Cryptography, TCC 2022, held in Chicago, IL, USA, in November 2022. The total of 60 full papers presented in this three-volume set was carefully reviewed and selected from 139 submissions. They cover topics on post-quantum cryptography; interactive proofs; quantum cryptography; secret-sharing and applications; succinct proofs; identity-based encryption and functional encryption; attribute-based encryption and functional encryption; encryption; multi-party computation; protocols: key agreement and commitments; theory: sampling and friends; lattices; anonymity, verfiability and robustness; ORAM, OT and PIR; and theory.

Author : David R. Kohel,Robert Rolland
Publisher : American Mathematical Soc.
Page : 178 pages
File Size : 52,7 Mb
Release : 2010
Category : Computers
ISBN : 9780821849552

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Arithmetic, Geometry, Cryptography and Coding Theory 2009 by David R. Kohel,Robert Rolland Pdf

This volume contains the proceedings of the 12th conference on Arithmetic, Geometry, Cryptography and Coding Theory, held in Marseille, France from March 30 to April 3, 2009, as well as the first Geocrypt conference, held in Pointe-a-Pitre, Guadeloupe from April 27 to May 1, 2009, and the European Science Foundation exploratory workshop on Curves, Coding Theory, and Cryptography, held in Marseille, France from March 25 to 29, 2009. The articles contained in this volume come from three related symposia organized by the group Arithmetique et Theorie de l'Information in Marseille. The topics cover arithmetic properties of curves and higher dimensional varieties with applications to codes and cryptography.

Author : Vladimir Shpilrain
Publisher : American Mathematical Soc.
Page : 188 pages
File Size : 43,6 Mb
Release : 2004-10-14
Category : Cryptography
ISBN : 0821856952

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Group Theory, Statistics, and Cryptography by Vladimir Shpilrain Pdf

This volume consists of contributions by speakers at the AMS Special Session on Combinatorial and Statistical Group Theory held at New York University. Readers will find a variety of contributions, including survey papers on applications of group theory in cryptography, research papers on various aspects of statistical group theory, and papers on more traditional combinatorial group theory. The book is suitable for graduate students and research mathematicians interested in group theory and its applications to cryptography.