Group Based Cryptography

Author : Alexei Myasnikov,Vladimir Shpilrain,Alexander Ushakov
Publisher : Springer Science & Business Media
Page : 192 pages
File Size : 47,9 Mb
Release : 2008-07-17
Category : Language Arts & Disciplines
ISBN : 9783764388263

Get Book

Group-based Cryptography by Alexei Myasnikov,Vladimir Shpilrain,Alexander Ushakov Pdf

This book is about relations between three different areas of mathematics and theoretical computer science: combinatorial group theory, cryptography, and complexity theory. It is explored how non-commutative (infinite) groups, which are typically studied in combinatorial group theory, can be used in public key cryptography. It is also shown that there is a remarkable feedback from cryptography to combinatorial group theory because some of the problems motivated by cryptography appear to be new to group theory, and they open many interesting research avenues within group theory. Then, complexity theory, notably generic-case complexity of algorithms, is employed for cryptanalysis of various cryptographic protocols based on infinite groups, and the ideas and machinery from the theory of generic-case complexity are used to study asymptotically dominant properties of some infinite groups that have been applied in public key cryptography so far. Its elementary exposition makes the book accessible to graduate as well as undergraduate students in mathematics or computer science.

Author : Maria Isabel Gonzalez Vasco,Rainer Steinwandt
Publisher : CRC Press
Page : 244 pages
File Size : 41,6 Mb
Release : 2015-04-01
Category : Computers
ISBN : 9781584888376

Get Book

Group Theoretic Cryptography by Maria Isabel Gonzalez Vasco,Rainer Steinwandt Pdf

Group theory appears to be a promising source of hard computational problems for deploying new cryptographic constructions. This reference focuses on the specifics of using groups, including in particular non-Abelian groups, in the field of cryptography. It provides an introduction to cryptography with emphasis on the group theoretic perspective, making it one of the first books to use this approach. The authors provide the needed cryptographic and group theoretic concepts, full proofs of essential theorems, and formal security evaluations of the cryptographic schemes presented. They also provide references for further reading and exercises at the end of each chapter.

Author : María Isabel González Vasco
Publisher : MDPI
Page : 164 pages
File Size : 43,5 Mb
Release : 2020-04-22
Category : Mathematics
ISBN : 9783039288021

Get Book

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 : Nadia El Mrabet,Marc Joye
Publisher : CRC Press
Page : 410 pages
File Size : 54,7 Mb
Release : 2017-01-06
Category : Computers
ISBN : 9781498729512

Get Book

Guide to Pairing-Based Cryptography by Nadia El Mrabet,Marc Joye Pdf

This book is devoted to efficient pairing computations and implementations, useful tools for cryptographers working on topics like identity-based cryptography and the simplification of existing protocols like signature schemes. As well as exploring the basic mathematical background of finite fields and elliptic curves, Guide to Pairing-Based Cryptography offers an overview of the most recent developments in optimizations for pairing implementation. Each chapter includes a presentation of the problem it discusses, the mathematical formulation, a discussion of implementation issues, solutions accompanied by code or pseudocode, several numerical results, and references to further reading and notes. Intended as a self-contained handbook, this book is an invaluable resource for computer scientists, applied mathematicians and security professionals interested in cryptography.

Author : Steven D. Galbraith
Publisher : Cambridge University Press
Page : 631 pages
File Size : 53,9 Mb
Release : 2012-03-15
Category : Computers
ISBN : 9781107013926

Get Book

Mathematics of Public Key Cryptography by Steven D. Galbraith Pdf

This advanced graduate textbook gives an authoritative and insightful description of the major ideas and techniques of public key cryptography.

Author : Delaram Kahrobaei,Ramón Flores,Marialaura Noce,Maggie E. Habeeb,Christopher Battarbee
Publisher : Unknown
Page : 0 pages
File Size : 49,5 Mb
Release : 2024
Category : Business & Economics
ISBN : 1470474697

Get Book

Applications of Group Theory in Cryptography by Delaram Kahrobaei,Ramón Flores,Marialaura Noce,Maggie E. Habeeb,Christopher Battarbee Pdf

Author : Tsuyoshi Takagi,Masato Wakayama,Keisuke Tanaka,Noboru Kunihiro,Kazufumi Kimoto,Yasuhiko Ikematsu
Publisher : Springer Nature
Page : 275 pages
File Size : 47,6 Mb
Release : 2020-10-22
Category : Technology & Engineering
ISBN : 9789811551918

Get Book

International Symposium on Mathematics, Quantum Theory, and Cryptography by Tsuyoshi Takagi,Masato Wakayama,Keisuke Tanaka,Noboru Kunihiro,Kazufumi Kimoto,Yasuhiko Ikematsu Pdf

This open access book presents selected papers from International Symposium on Mathematics, Quantum Theory, and Cryptography (MQC), which was held on September 25-27, 2019 in Fukuoka, Japan. The international symposium MQC addresses the mathematics and quantum theory underlying secure modeling of the post quantum cryptography including e.g. mathematical study of the light-matter interaction models as well as quantum computing. The security of the most widely used RSA cryptosystem is based on the difficulty of factoring large integers. However, in 1994 Shor proposed a quantum polynomial time algorithm for factoring integers, and the RSA cryptosystem is no longer secure in the quantum computing model. This vulnerability has prompted research into post-quantum cryptography using alternative mathematical problems that are secure in the era of quantum computers. In this regard, the National Institute of Standards and Technology (NIST) began to standardize post-quantum cryptography in 2016. This book is suitable for postgraduate students in mathematics and computer science, as well as for experts in industry working on post-quantum cryptography.

Author : Gilbert Baumslag,Benjamin Fine,Martin Kreuzer,Gerhard Rosenberger
Publisher : Walter de Gruyter GmbH & Co KG
Page : 389 pages
File Size : 40,7 Mb
Release : 2015-06-16
Category : Computers
ISBN : 9783110386165

Get Book

A Course in Mathematical Cryptography by Gilbert Baumslag,Benjamin Fine,Martin Kreuzer,Gerhard Rosenberger Pdf

The subject of this book is mathematical cryptography. By this we mean the mathematics involved in cryptographic protocols. As the field has expanded, using both commutative and noncommutative algebraic objects as cryptographic platforms, a book describing and explaining all these mathematical methods is of immeasurable value.

Author : Martin Kreuzer
Publisher : American Mathematical Soc.
Page : 190 pages
File Size : 42,5 Mb
Release : 2006
Category : Algebra
ISBN : 9780821840375

Get Book

Algebraic Methods in Cryptography by Martin Kreuzer Pdf

The book consists of contributions related mostly to public-key cryptography, including the design of new cryptographic primitives as well as cryptanalysis of previously suggested schemes. Most papers are original research papers in the area that can be loosely defined as ``non-commutative cryptography''; this means that groups (or other algebraic structures) which are used as platforms are non-commutative.

Author : Yvo Desmedt
Publisher : Springer Science & Business Media
Page : 378 pages
File Size : 47,6 Mb
Release : 2002-12-13
Category : Business & Economics
ISBN : 9783540003243

Get Book

Public Key Cryptography - PKC 2003 by Yvo Desmedt Pdf

This book constitutes the refereed proceedings of the 6th International Workshop on Practice and Theory in Public Key Cryptosystems, PKC 2003, held in Miami, Florida, USA in January 2003. The 26 revised full papers presented were carefully reviewed and selected from 105 submissions. The papers are organized in topical sections on Diffie-Hellman based schemes, threshold cryptography, reduction proofs, broadcast and tracing, digital signatures, specialized multiparty cryptography, cryptanalysis, elliptic curves: implementation attacks, implementation and hardware issues, new public key schemes, and elliptic curves: general issues.

Author : Henri Gilbert
Publisher : Springer
Page : 706 pages
File Size : 43,7 Mb
Release : 2010-05-29
Category : Computers
ISBN : 9783642131905

Get Book

Advances in Cryptology – EUROCRYPT 2010 by Henri Gilbert Pdf

These are the proceedings of Eurocrypt 2010, the 29th in the series of Eu- pean conferences on the Theory and Application of Cryptographic Techniques. The conference was sponsored by the International Association for Cryptologic Research and held on the French Riviera, May 30–June 3, 2010. A total of 191 papers were received of which 188 were retained as valid submissions. These were each assigned to at least three Program Committee members and a total of 606 review reports were produced. The printed record of the reviews and extensive online discussions that followed would be almost as voluminous as these proceedings. In the end 35 submissions were accepted with twosubmissionpairsbeingmergedtogive33paperspresentedattheconference. The ?nal papers in these proceedings were not subject to a second review before publication and the authors are responsible for their contents. The ProgramCommittee, listed on the next page, deservesparticular thanks for all their hard work, their outstanding expertise, and their constant c- mitment to all aspects of the evaluation process. These thanks are of course extended to the very many external reviewers who took the time to help out during the evaluation process.It was also a greatpleasure to honor and welcome Moti Yung who gave the 2010 IACR Distinguished Lecture.

Author : Tsuyoshi Takagi
Publisher : Springer Science & Business Media
Page : 418 pages
File Size : 55,8 Mb
Release : 2007-06-21
Category : Computers
ISBN : 9783540734888

Get Book

Pairing-Based Cryptography - Pairing 2007 by Tsuyoshi Takagi Pdf

Pairing-based cryptography is at the very leading edge of the current wave in computer cryptography. That makes this book all the more relevant, being as it is the refereed proceedings of the First International Conference on Pairing-Based Cryptography, Pairing 2007, held in Tokyo, Japan in 2007. The 18 revised full papers presented together were carefully reviewed and selected from 86 submissions. The papers are organized in topical sections including those on applications, and certificateless public key encryption.

Author : Mariana Durcheva
Publisher : Cambridge Scholars Publishing
Page : 132 pages
File Size : 44,6 Mb
Release : 2019-11-12
Category : Mathematics
ISBN : 9781527543317

Get Book

Semirings as Building Blocks in Cryptography by Mariana Durcheva Pdf

Semirings as an algebraic structure have been known since 1934, but remained unapplied for mathematical purposes for a long time. It has only been in the past decade that they have been used in cryptography. The advantage of (additively) idempotent semirings is that the additive operation does not have an inverse, which can help in preventing the breakage of a cryptosystem. This book describes a number of cryptographic protocols, as well as the hard mathematical problems on which their security is based. It will appeal to cryptographers and specialists in applied algebra.

Author : Carl Pomerance
Publisher : Springer
Page : 458 pages
File Size : 42,7 Mb
Release : 2003-05-16
Category : Computers
ISBN : 9783540481843

Get Book

Advances in Cryptology - CRYPTO '87 by Carl Pomerance Pdf

Zero-knowledge interactive proofsystems are a new technique which can be used as a cryptographic tool for designing provably secure protocols. Goldwasser, Micali, and Rackoff originally suggested this technique for controlling the knowledge released in an interactive proof of membership in a language, and for classification of languages [19]. In this approach, knowledge is defined in terms of complexity to convey knowledge if it gives a computational advantage to the receiver, theory, and a message is said for example by giving him the result of an intractable computation. The formal model of interacting machines is described in [19, 15, 171. A proof-system (for a language L) is an interactive protocol by which one user, the prover, attempts to convince another user, the verifier, that a given input x is in L. We assume that the verifier is a probabilistic machine which is limited to expected polynomial-time computation, while the prover is an unlimited probabilistic machine. (In cryptographic applications the prover has some trapdoor information, or knows the cleartext of a publicly known ciphertext) A correct proof-system must have the following properties: If XE L, the prover will convince the verifier to accept the pmf with very high probability. If XP L no prover, no matter what program it follows, is able to convince the verifier to accept the proof, except with vanishingly small probability.

Author : Khairol Amali Bin Ahmad,Khaleel Ahmad,Uma N. Dulhare
Publisher : Springer Nature
Page : 311 pages
File Size : 48,5 Mb
Release : 2021-06-12
Category : Technology & Engineering
ISBN : 9783030608903

Get Book

Functional Encryption by Khairol Amali Bin Ahmad,Khaleel Ahmad,Uma N. Dulhare Pdf

This book provides awareness of methods used for functional encryption in the academic and professional communities. The book covers functional encryption algorithms and its modern applications in developing secure systems via entity authentication, message authentication, software security, cyber security, hardware security, Internet of Thing (IoT), cloud security, smart card technology, CAPTCHA, digital signature, and digital watermarking. This book is organized into fifteen chapters; topics include foundations of functional encryption, impact of group theory in cryptosystems, elliptic curve cryptography, XTR algorithm, pairing based cryptography, NTRU algorithms, ring units, cocks IBE schemes, Boneh-Franklin IBE, Sakai-Kasahara IBE, hierarchical identity based encryption, attribute based Encryption, extensions of IBE and related primitives, and digital signatures. Explains the latest functional encryption algorithms in a simple way with examples; Includes applications of functional encryption in information security, application security, and network security; Relevant to academics, research scholars, software developers, etc.