A Course In Mathematical Cryptography

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A Course in Mathematical Cryptography

Author : Gilbert Baumslag
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 311038616X
Total Pages : 476 pages
Book Rating : 4.1/5 (13 download)

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Book Synopsis A Course in Mathematical Cryptography by : Gilbert Baumslag

Download or read book A Course in Mathematical Cryptography written by Gilbert Baumslag and published by Walter de Gruyter GmbH & Co KG. This book was released on 2015-06-16 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cryptography has become essential as bank transactions, credit card infor-mation, contracts, and sensitive medical information are sent through inse-cure channels. This book is concerned with the mathematical, especially algebraic, aspects of cryptography. It grew out of many courses presented by the authors over the past twenty years at various universities and covers a wide range of topics in mathematical cryptography. It is primarily geared towards graduate students and advanced undergraduates in mathematics and computer science, but may also be of interest to researchers in the area. Besides the classical methods of symmetric and private key encryption, the book treats the mathematics of cryptographic protocols and several unique topics such as Group-Based Cryptography Gröbner Basis Methods in Cryptography Lattice-Based Cryptography

An Introduction to Mathematical Cryptography

Author : Jeffrey Hoffstein
Publisher : Springer
ISBN 13 : 1493917110
Total Pages : 549 pages
Book Rating : 4.4/5 (939 download)

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Book Synopsis An Introduction to Mathematical Cryptography by : Jeffrey Hoffstein

Download or read book An Introduction to Mathematical Cryptography written by Jeffrey Hoffstein and published by Springer. This book was released on 2014-09-11 with total page 549 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained introduction to modern cryptography emphasizes the mathematics behind the theory of public key cryptosystems and digital signature schemes. The book focuses on these key topics while developing the mathematical tools needed for the construction and security analysis of diverse cryptosystems. Only basic linear algebra is required of the reader; techniques from algebra, number theory, and probability are introduced and developed as required. This text provides an ideal introduction for mathematics and computer science students to the mathematical foundations of modern cryptography. The book includes an extensive bibliography and index; supplementary materials are available online. The book covers a variety of topics that are considered central to mathematical cryptography. Key topics include: classical cryptographic constructions, such as Diffie–Hellmann key exchange, discrete logarithm-based cryptosystems, the RSA cryptosystem, and digital signatures; fundamental mathematical tools for cryptography, including primality testing, factorization algorithms, probability theory, information theory, and collision algorithms; an in-depth treatment of important cryptographic innovations, such as elliptic curves, elliptic curve and pairing-based cryptography, lattices, lattice-based cryptography, and the NTRU cryptosystem. The second edition of An Introduction to Mathematical Cryptography includes a significant revision of the material on digital signatures, including an earlier introduction to RSA, Elgamal, and DSA signatures, and new material on lattice-based signatures and rejection sampling. Many sections have been rewritten or expanded for clarity, especially in the chapters on information theory, elliptic curves, and lattices, and the chapter of additional topics has been expanded to include sections on digital cash and homomorphic encryption. Numerous new exercises have been included.

A Course in Cryptography

Author : Heiko Knospe
Publisher : American Mathematical Soc.
ISBN 13 : 1470450550
Total Pages : 344 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis A Course in Cryptography by : Heiko Knospe

Download or read book A Course in Cryptography written by Heiko Knospe and published by American Mathematical Soc.. This book was released on 2019-09-27 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a compact course in modern cryptography. The mathematical foundations in algebra, number theory and probability are presented with a focus on their cryptographic applications. The text provides rigorous definitions and follows the provable security approach. The most relevant cryptographic schemes are covered, including block ciphers, stream ciphers, hash functions, message authentication codes, public-key encryption, key establishment, digital signatures and elliptic curves. The current developments in post-quantum cryptography are also explored, with separate chapters on quantum computing, lattice-based and code-based cryptosystems. Many examples, figures and exercises, as well as SageMath (Python) computer code, help the reader to understand the concepts and applications of modern cryptography. A special focus is on algebraic structures, which are used in many cryptographic constructions and also in post-quantum systems. The essential mathematics and the modern approach to cryptography and security prepare the reader for more advanced studies. The text requires only a first-year course in mathematics (calculus and linear algebra) and is also accessible to computer scientists and engineers. This book is suitable as a textbook for undergraduate and graduate courses in cryptography as well as for self-study.

A Course in Number Theory and Cryptography

Author : Neal Koblitz
Publisher : Springer Science & Business Media
ISBN 13 : 1441985921
Total Pages : 245 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis A Course in Number Theory and Cryptography by : Neal Koblitz

Download or read book A Course in Number Theory and Cryptography written by Neal Koblitz and published by Springer Science & Business Media. This book was released on 2012-09-05 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a substantially revised and updated introduction to arithmetic topics, both ancient and modern, that have been at the centre of interest in applications of number theory, particularly in cryptography. As such, no background in algebra or number theory is assumed, and the book begins with a discussion of the basic number theory that is needed. The approach taken is algorithmic, emphasising estimates of the efficiency of the techniques that arise from the theory, and one special feature is the inclusion of recent applications of the theory of elliptic curves. Extensive exercises and careful answers are an integral part all of the chapters.

Mathematics of Public Key Cryptography

Author : Steven D. Galbraith
Publisher : Cambridge University Press
ISBN 13 : 1107013925
Total Pages : 631 pages
Book Rating : 4.1/5 (7 download)

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Book Synopsis Mathematics of Public Key Cryptography by : Steven D. Galbraith

Download or read book Mathematics of Public Key Cryptography written by Steven D. Galbraith and published by Cambridge University Press. This book was released on 2012-03-15 with total page 631 pages. Available in PDF, EPUB and Kindle. Book excerpt: This advanced graduate textbook gives an authoritative and insightful description of the major ideas and techniques of public key cryptography.

Mathematical Modelling for Next-Generation Cryptography

Author : Tsuyoshi Takagi
Publisher : Springer
ISBN 13 : 9811050651
Total Pages : 363 pages
Book Rating : 4.8/5 (11 download)

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Book Synopsis Mathematical Modelling for Next-Generation Cryptography by : Tsuyoshi Takagi

Download or read book Mathematical Modelling for Next-Generation Cryptography written by Tsuyoshi Takagi and published by Springer. This book was released on 2017-07-25 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the mathematical background underlying security modeling in the context of next-generation cryptography. By introducing new mathematical results in order to strengthen information security, while simultaneously presenting fresh insights and developing the respective areas of mathematics, it is the first-ever book to focus on areas that have not yet been fully exploited for cryptographic applications such as representation theory and mathematical physics, among others. Recent advances in cryptanalysis, brought about in particular by quantum computation and physical attacks on cryptographic devices, such as side-channel analysis or power analysis, have revealed the growing security risks for state-of-the-art cryptographic schemes. To address these risks, high-performance, next-generation cryptosystems must be studied, which requires the further development of the mathematical background of modern cryptography. More specifically, in order to avoid the security risks posed by adversaries with advanced attack capabilities, cryptosystems must be upgraded, which in turn relies on a wide range of mathematical theories. This book is suitable for use in an advanced graduate course in mathematical cryptography, while also offering a valuable reference guide for experts.

Understanding Cryptography

Author : Christof Paar
Publisher : Springer Science & Business Media
ISBN 13 : 3642041019
Total Pages : 382 pages
Book Rating : 4.6/5 (42 download)

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Book Synopsis Understanding Cryptography by : Christof Paar

Download or read book Understanding Cryptography written by Christof Paar and published by Springer Science & Business Media. This book was released on 2009-11-27 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cryptography is now ubiquitous – moving beyond the traditional environments, such as government communications and banking systems, we see cryptographic techniques realized in Web browsers, e-mail programs, cell phones, manufacturing systems, embedded software, smart buildings, cars, and even medical implants. Today's designers need a comprehensive understanding of applied cryptography. After an introduction to cryptography and data security, the authors explain the main techniques in modern cryptography, with chapters addressing stream ciphers, the Data Encryption Standard (DES) and 3DES, the Advanced Encryption Standard (AES), block ciphers, the RSA cryptosystem, public-key cryptosystems based on the discrete logarithm problem, elliptic-curve cryptography (ECC), digital signatures, hash functions, Message Authentication Codes (MACs), and methods for key establishment, including certificates and public-key infrastructure (PKI). Throughout the book, the authors focus on communicating the essentials and keeping the mathematics to a minimum, and they move quickly from explaining the foundations to describing practical implementations, including recent topics such as lightweight ciphers for RFIDs and mobile devices, and current key-length recommendations. The authors have considerable experience teaching applied cryptography to engineering and computer science students and to professionals, and they make extensive use of examples, problems, and chapter reviews, while the book’s website offers slides, projects and links to further resources. This is a suitable textbook for graduate and advanced undergraduate courses and also for self-study by engineers.

Serious Cryptography

Author : Jean-Philippe Aumasson
Publisher : No Starch Press
ISBN 13 : 1593278268
Total Pages : 313 pages
Book Rating : 4.5/5 (932 download)

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Book Synopsis Serious Cryptography by : Jean-Philippe Aumasson

Download or read book Serious Cryptography written by Jean-Philippe Aumasson and published by No Starch Press. This book was released on 2017-11-06 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: This practical guide to modern encryption breaks down the fundamental mathematical concepts at the heart of cryptography without shying away from meaty discussions of how they work. You’ll learn about authenticated encryption, secure randomness, hash functions, block ciphers, and public-key techniques such as RSA and elliptic curve cryptography. You’ll also learn: - Key concepts in cryptography, such as computational security, attacker models, and forward secrecy - The strengths and limitations of the TLS protocol behind HTTPS secure websites - Quantum computation and post-quantum cryptography - About various vulnerabilities by examining numerous code examples and use cases - How to choose the best algorithm or protocol and ask vendors the right questions Each chapter includes a discussion of common implementation mistakes using real-world examples and details what could go wrong and how to avoid these pitfalls. Whether you’re a seasoned practitioner or a beginner looking to dive into the field, Serious Cryptography will provide a complete survey of modern encryption and its applications.

The Mathematics of Encryption

Author : Margaret Cozzens
Publisher : American Mathematical Soc.
ISBN 13 : 0821883216
Total Pages : 355 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis The Mathematics of Encryption by : Margaret Cozzens

Download or read book The Mathematics of Encryption written by Margaret Cozzens and published by American Mathematical Soc.. This book was released on 2013-09-05 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: How quickly can you compute the remainder when dividing by 120143? Why would you even want to compute this? And what does this have to do with cryptography? Modern cryptography lies at the intersection of mathematics and computer sciences, involving number theory, algebra, computational complexity, fast algorithms, and even quantum mechanics. Many people think of codes in terms of spies, but in the information age, highly mathematical codes are used every day by almost everyone, whether at the bank ATM, at the grocery checkout, or at the keyboard when you access your email or purchase products online. This book provides a historical and mathematical tour of cryptography, from classical ciphers to quantum cryptography. The authors introduce just enough mathematics to explore modern encryption methods, with nothing more than basic algebra and some elementary number theory being necessary. Complete expositions are given of the classical ciphers and the attacks on them, along with a detailed description of the famous Enigma system. The public-key system RSA is described, including a complete mathematical proof that it works. Numerous related topics are covered, such as efficiencies of algorithms, detecting and correcting errors, primality testing and digital signatures. The topics and exposition are carefully chosen to highlight mathematical thinking and problem solving. Each chapter ends with a collection of problems, ranging from straightforward applications to more challenging problems that introduce advanced topics. Unlike many books in the field, this book is aimed at a general liberal arts student, but without losing mathematical completeness.

Algebraic Aspects of Cryptography

Author : Neal Koblitz
Publisher : Springer Science & Business Media
ISBN 13 : 3662036428
Total Pages : 214 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Algebraic Aspects of Cryptography by : Neal Koblitz

Download or read book Algebraic Aspects of Cryptography written by Neal Koblitz and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "This is a textbook in cryptography with emphasis on algebraic methods. It is supported by many exercises (with answers) making it appropriate for a course in mathematics or computer science. [...] Overall, this is an excellent expository text, and will be very useful to both the student and researcher." Mathematical Reviews

Introduction to Cryptography

Author : Johannes Buchmann
Publisher : Springer Science & Business Media
ISBN 13 : 1441990038
Total Pages : 342 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis Introduction to Cryptography by : Johannes Buchmann

Download or read book Introduction to Cryptography written by Johannes Buchmann and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explains the basic methods of modern cryptography. It is written for readers with only basic mathematical knowledge who are interested in modern cryptographic algorithms and their mathematical foundation. Several exercises are included following each chapter. From the reviews: "Gives a clear and systematic introduction into the subject whose popularity is ever increasing, and can be recommended to all who would like to learn about cryptography." --ZENTRALBLATT MATH

Fundamentals of Cryptography

Author : Duncan Buell
Publisher : Springer Nature
ISBN 13 : 3030734927
Total Pages : 279 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis Fundamentals of Cryptography by : Duncan Buell

Download or read book Fundamentals of Cryptography written by Duncan Buell and published by Springer Nature. This book was released on 2021-07-17 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cryptography, as done in this century, is heavily mathematical. But it also has roots in what is computationally feasible. This unique textbook text balances the theorems of mathematics against the feasibility of computation. Cryptography is something one actually “does”, not a mathematical game one proves theorems about. There is deep math; there are some theorems that must be proved; and there is a need to recognize the brilliant work done by those who focus on theory. But at the level of an undergraduate course, the emphasis should be first on knowing and understanding the algorithms and how to implement them, and also to be aware that the algorithms must be implemented carefully to avoid the “easy” ways to break the cryptography. This text covers the algorithmic foundations and is complemented by core mathematics and arithmetic.

BigNum Math

Author : Tom St Denis
Publisher : Elsevier
ISBN 13 : 0080488382
Total Pages : 316 pages
Book Rating : 4.0/5 (84 download)

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Book Synopsis BigNum Math by : Tom St Denis

Download or read book BigNum Math written by Tom St Denis and published by Elsevier. This book was released on 2006-08-18 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: Implementing cryptography requires integers of significant magnitude to resist cryptanalytic attacks. Modern programming languages only provide support for integers which are relatively small and single precision. The purpose of this text is to instruct the reader regarding how to implement efficient multiple precision algorithms.Bignum math is the backbone of modern computer security algorithms. It is the ability to work with hundred-digit numbers efficiently using techniques that are both elegant and occasionally bizarre. This book introduces the reader to the concept of bignum algorithms and proceeds to build an entire library of functionality from the ground up. Through the use of theory, pseudo-code and actual fielded C source code the book explains each and every algorithm that goes into a modern bignum library. Excellent for the student as a learning tool and practitioner as a reference alike BigNum Math is for anyone with a background in computer science who has taken introductory level mathematic courses. The text is for students learning mathematics and cryptography as well as the practioner who needs a reference for any of the algorithms documented within.* Complete coverage of Karatsuba Multiplication, the Barrett Algorithm, Toom-Cook 3-Way Multiplication, and More * Tom St Denis is the developer of the industry standard cryptographic suite of tools called LibTom. * This book provides step-by-step exercises to enforce concepts

Introduction to Modern Cryptography

Author : Jonathan Katz
Publisher : CRC Press
ISBN 13 : 1351133012
Total Pages : 435 pages
Book Rating : 4.3/5 (511 download)

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Book Synopsis Introduction to Modern Cryptography by : Jonathan Katz

Download or read book Introduction to Modern Cryptography written by Jonathan Katz and published by CRC Press. This book was released on 2020-12-21 with total page 435 pages. Available in PDF, EPUB and Kindle. Book excerpt: Now the most used texbook for introductory cryptography courses in both mathematics and computer science, the Third Edition builds upon previous editions by offering several new sections, topics, and exercises. The authors present the core principles of modern cryptography, with emphasis on formal definitions, rigorous proofs of security.

Handbook of Applied Cryptography

Author : Alfred J. Menezes
Publisher : CRC Press
ISBN 13 : 0429881320
Total Pages : 810 pages
Book Rating : 4.4/5 (298 download)

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Book Synopsis Handbook of Applied Cryptography by : Alfred J. Menezes

Download or read book Handbook of Applied Cryptography written by Alfred J. Menezes and published by CRC Press. This book was released on 2018-12-07 with total page 810 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cryptography, in particular public-key cryptography, has emerged in the last 20 years as an important discipline that is not only the subject of an enormous amount of research, but provides the foundation for information security in many applications. Standards are emerging to meet the demands for cryptographic protection in most areas of data communications. Public-key cryptographic techniques are now in widespread use, especially in the financial services industry, in the public sector, and by individuals for their personal privacy, such as in electronic mail. This Handbook will serve as a valuable reference for the novice as well as for the expert who needs a wider scope of coverage within the area of cryptography. It is a necessary and timely guide for professionals who practice the art of cryptography. The Handbook of Applied Cryptography provides a treatment that is multifunctional: It serves as an introduction to the more practical aspects of both conventional and public-key cryptography It is a valuable source of the latest techniques and algorithms for the serious practitioner It provides an integrated treatment of the field, while still presenting each major topic as a self-contained unit It provides a mathematical treatment to accompany practical discussions It contains enough abstraction to be a valuable reference for theoreticians while containing enough detail to actually allow implementation of the algorithms discussed Now in its third printing, this is the definitive cryptography reference that the novice as well as experienced developers, designers, researchers, engineers, computer scientists, and mathematicians alike will use.

Introduction to Cryptography

Author : Hans Delfs
Publisher : Springer Science & Business Media
ISBN 13 : 3540492445
Total Pages : 372 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Introduction to Cryptography by : Hans Delfs

Download or read book Introduction to Cryptography written by Hans Delfs and published by Springer Science & Business Media. This book was released on 2007-05-31 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: Due to the rapid growth of digital communication and electronic data exchange, information security has become a crucial issue in industry, business, and administration. Modern cryptography provides essential techniques for securing information and protecting data. In the first part, this book covers the key concepts of cryptography on an undergraduate level, from encryption and digital signatures to cryptographic protocols. Essential techniques are demonstrated in protocols for key exchange, user identification, electronic elections and digital cash. In the second part, more advanced topics are addressed, such as the bit security of one-way functions and computationally perfect pseudorandom bit generators. The security of cryptographic schemes is a central topic. Typical examples of provably secure encryption and signature schemes and their security proofs are given. Though particular attention is given to the mathematical foundations, no special background in mathematics is presumed. The necessary algebra, number theory and probability theory are included in the appendix. Each chapter closes with a collection of exercises. The second edition contains corrections, revisions and new material, including a complete description of the AES, an extended section on cryptographic hash functions, a new section on random oracle proofs, and a new section on public-key encryption schemes that are provably secure against adaptively-chosen-ciphertext attacks.

Cryptography

Author : Simon Rubinstein-Salzedo
Publisher : Springer
ISBN 13 : 3319948180
Total Pages : 259 pages
Book Rating : 4.3/5 (199 download)

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Book Synopsis Cryptography by : Simon Rubinstein-Salzedo

Download or read book Cryptography written by Simon Rubinstein-Salzedo and published by Springer. This book was released on 2018-09-27 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text introduces cryptography, from its earliest roots to cryptosystems used today for secure online communication. Beginning with classical ciphers and their cryptanalysis, this book proceeds to focus on modern public key cryptosystems such as Diffie-Hellman, ElGamal, RSA, and elliptic curve cryptography with an analysis of vulnerabilities of these systems and underlying mathematical issues such as factorization algorithms. Specialized topics such as zero knowledge proofs, cryptographic voting, coding theory, and new research are covered in the final section of this book. Aimed at undergraduate students, this book contains a large selection of problems, ranging from straightforward to difficult, and can be used as a textbook for classes as well as self-study. Requiring only a solid grounding in basic mathematics, this book will also appeal to advanced high school students and amateur mathematicians interested in this fascinating and topical subject.