Group-based Cryptography PDF Download

Author: Alexei Myasnikov
Publisher: Springer Science & Business Media
ISBN: 3764388277
Category : Mathematics
Languages : en
Pages : 192

View

Book Description
Covering relations between three different areas of mathematics and theoretical computer science, this book explores how non-commutative (infinite) groups, which are typically studied in combinatorial group theory, can be used in public key cryptography.

Author: Alexei Myasnikov
Publisher: Springer Science & Business Media
ISBN: 3764388269
Category : Language Arts & Disciplines
Languages : en
Pages : 192

View

Book Description
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: María Isabel González Vasco
Publisher: MDPI
ISBN: 3039288024
Category : Mathematics
Languages : en
Pages : 164

View

Book Description
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: Steven D. Galbraith
Publisher: Cambridge University Press
ISBN: 1107013925
Category : Computers
Languages : en
Pages : 631

View

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

Author: Yvo Desmedt
Publisher: Springer Science & Business Media
ISBN: 354000324X
Category : Business & Economics
Languages : en
Pages : 378

View

Book Description
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: Carl Pomerance
Publisher: Springer
ISBN: 3540481842
Category : Computers
Languages : en
Pages : 458

View

Book Description
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: Tsuyoshi Takagi
Publisher: Springer Nature
ISBN: 981155191X
Category : Technology & Engineering
Languages : en
Pages : 275

View

Book Description
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: Nadia El Mrabet
Publisher: CRC Press
ISBN: 1498729517
Category : Computers
Languages : en
Pages : 410

View

Book Description
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: Khairol Amali Bin Ahmad
Publisher: Springer Nature
ISBN: 3030608905
Category : Technology & Engineering
Languages : en
Pages : 311

View

Book Description
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.

Author: David Wong
Publisher: Simon and Schuster
ISBN: 1638350841
Category : Computers
Languages : en
Pages : 398

View

Book Description
"A staggeringly comprehensive review of the state of modern cryptography. Essential for anyone getting up to speed in information security." - Thomas Doylend, Green Rocket Security An all-practical guide to the cryptography behind common tools and protocols that will help you make excellent security choices for your systems and applications. In Real-World Cryptography, you will find: Best practices for using cryptography Diagrams and explanations of cryptographic algorithms Implementing digital signatures and zero-knowledge proofs Specialized hardware for attacks and highly adversarial environments Identifying and fixing bad practices Choosing the right cryptographic tool for any problem Real-World Cryptography reveals the cryptographic techniques that drive the security of web APIs, registering and logging in users, and even the blockchain. You’ll learn how these techniques power modern security, and how to apply them to your own projects. Alongside modern methods, the book also anticipates the future of cryptography, diving into emerging and cutting-edge advances such as cryptocurrencies, and post-quantum cryptography. All techniques are fully illustrated with diagrams and examples so you can easily see how to put them into practice. Purchase of the print book includes a free eBook in PDF, Kindle, and ePub formats from Manning Publications. About the technology Cryptography is the essential foundation of IT security. To stay ahead of the bad actors attacking your systems, you need to understand the tools, frameworks, and protocols that protect your networks and applications. This book introduces authentication, encryption, signatures, secret-keeping, and other cryptography concepts in plain language and beautiful illustrations. About the book Real-World Cryptography teaches practical techniques for day-to-day work as a developer, sysadmin, or security practitioner. There’s no complex math or jargon: Modern cryptography methods are explored through clever graphics and real-world use cases. You’ll learn building blocks like hash functions and signatures; cryptographic protocols like HTTPS and secure messaging; and cutting-edge advances like post-quantum cryptography and cryptocurrencies. This book is a joy to read—and it might just save your bacon the next time you’re targeted by an adversary after your data. What's inside Implementing digital signatures and zero-knowledge proofs Specialized hardware for attacks and highly adversarial environments Identifying and fixing bad practices Choosing the right cryptographic tool for any problem About the reader For cryptography beginners with no previous experience in the field. About the author David Wong is a cryptography engineer. He is an active contributor to internet standards including Transport Layer Security. Table of Contents PART 1 PRIMITIVES: THE INGREDIENTS OF CRYPTOGRAPHY 1 Introduction 2 Hash functions 3 Message authentication codes 4 Authenticated encryption 5 Key exchanges 6 Asymmetric encryption and hybrid encryption 7 Signatures and zero-knowledge proofs 8 Randomness and secrets PART 2 PROTOCOLS: THE RECIPES OF CRYPTOGRAPHY 9 Secure transport 10 End-to-end encryption 11 User authentication 12 Crypto as in cryptocurrency? 13 Hardware cryptography 14 Post-quantum cryptography 15 Is this it? Next-generation cryptography 16 When and where cryptography fails