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Author : Steven D. Galbraith
Publisher : Cambridge University Press
Page : 631 pages
File Size : 45,5 Mb
Release : 2012-03-15
Category : Computers
ISBN : 9781107013926
This advanced graduate textbook gives an authoritative and insightful description of the major ideas and techniques of public key cryptography.
Author : Xiaoyun Wang,Guangwu Xu,Mingqiang Wang,Xianmeng Meng
Publisher : CRC Press
Page : 236 pages
File Size : 48,7 Mb
Release : 2015-10-22
Category : Computers
ISBN : 9781498702249
In Mathematical Foundations of Public Key Cryptography, the authors integrate the results of more than 20 years of research and teaching experience to help students bridge the gap between math theory and crypto practice. The book provides a theoretical structure of fundamental number theory and algebra knowledge supporting public-key cryptography.R
Author : Jeffrey Hoffstein,Jill Pipher,Joseph H. Silverman
Publisher : Springer
Page : 538 pages
File Size : 52,9 Mb
Release : 2014-09-11
Category : Mathematics
ISBN : 9781493917112
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.
Author : Richard A. Mollin
Publisher : CRC Press
Page : 304 pages
File Size : 42,9 Mb
Release : 2002-11-12
Category : Mathematics
ISBN : 9781420035247
Although much literature exists on the subject of RSA and public-key cryptography, until now there has been no single source that reveals recent developments in the area at an accessible level. Acclaimed author Richard A. Mollin brings together all of the relevant information available on public-key cryptography (PKC), from RSA to the latest applications of PKC, including electronic cash, secret broadcasting, secret balloting systems, various banking and payment protocols, high security logins, smart cards, and biometrics. Moreover, he covers public-key infrastructure (PKI) and its various security applications. Throughout the book, Mollin gives a human face to cryptography by including nearly 40 biographies of the individuals who helped develop cryptographic concepts. He includes a number of illustrative and motivating examples, as well as optional topics that go beyond the basics, such as Lenstra's elliptic curve method and the number field sieve. From history and basic concepts to future trends and emerging applications, this book provides a rigorous and detailed treatment of public-key cryptography. Accessible to anyone from the senior undergraduate to the research scientist, RSA and Public-Key Cryptography offers challenging and inspirational material for all readers.
Author : Kazimierz Alster,Jerzy Urbanowicz,Hugh C. Williams
Publisher : Walter de Gruyter
Page : 345 pages
File Size : 46,8 Mb
Release : 2011-06-24
Category : Mathematics
ISBN : 9783110881035
The Proceedings contain twenty selected, refereed contributions arising from the International Conference on Public-Key Cryptography and Computational Number Theory held in Warsaw, Poland, on September 11-15, 2000. The conference, attended by eightyfive mathematicians from eleven countries, was organized by the Stefan Banach International Mathematical Center. This volume contains articles from leading experts in the world on cryptography and computational number theory, providing an account of the state of research in a wide variety of topics related to the conference theme. It is dedicated to the memory of the Polish mathematicians Marian Rejewski (1905-1980), Jerzy Róøycki (1909-1942) and Henryk Zygalski (1907-1978), who deciphered the military version of the famous Enigma in December 1932 January 1933. A noteworthy feature of the volume is a foreword written by Andrew Odlyzko on the progress in cryptography from Enigma time until now.
Author : Jintai Ding,Albrecht Petzoldt,Dieter S. Schmidt
Publisher : Springer Nature
Page : 253 pages
File Size : 51,5 Mb
Release : 2020-09-30
Category : Computers
ISBN : 9781071609873
This book discusses the current research concerning public key cryptosystems. It begins with an introduction to the basic concepts of multivariate cryptography and the history of this field. The authors provide a detailed description and security analysis of the most important multivariate public key schemes, including the four multivariate signature schemes participating as second round candidates in the NIST standardization process for post-quantum cryptosystems. Furthermore, this book covers the Simple Matrix encryption scheme, which is currently the most promising multivariate public key encryption scheme. This book also covers the current state of security analysis methods for Multivariate Public Key Cryptosystems including the algorithms and theory of solving systems of multivariate polynomial equations over finite fields. Through the book’s website, interested readers can find source code to the algorithms handled in this book. In 1994, Dr. Peter Shor from Bell Laboratories proposed a quantum algorithm solving the Integer Factorization and the Discrete Logarithm problem in polynomial time, thus making all of the currently used public key cryptosystems, such as RSA and ECC insecure. Therefore, there is an urgent need for alternative public key schemes which are resistant against quantum computer attacks. Researchers worldwide, as well as companies and governmental organizations have put a tremendous effort into the development of post-quantum public key cryptosystems to meet this challenge. One of the most promising candidates for this are Multivariate Public Key Cryptosystems (MPKCs). The public key of an MPKC is a set of multivariate polynomials over a small finite field. Especially for digital signatures, numerous well-studied multivariate schemes offering very short signatures and high efficiency exist. The fact that these schemes work over small finite fields, makes them suitable not only for interconnected computer systems, but also for small devices with limited resources, which are used in ubiquitous computing. This book gives a systematic introduction into the field of Multivariate Public Key Cryptosystems (MPKC), and presents the most promising multivariate schemes for digital signatures and encryption. Although, this book was written more from a computational perspective, the authors try to provide the necessary mathematical background. Therefore, this book is suitable for a broad audience. This would include researchers working in either computer science or mathematics interested in this exciting new field, or as a secondary textbook for a course in MPKC suitable for beginning graduate students in mathematics or computer science. Information security experts in industry, computer scientists and mathematicians would also find this book valuable as a guide for understanding the basic mathematical structures necessary to implement multivariate cryptosystems for practical applications.
Author : Arto Salomaa
Publisher : Springer Science & Business Media
Page : 282 pages
File Size : 48,8 Mb
Release : 2013-04-17
Category : Computers
ISBN : 9783662032695
Cryptography, secret writing, is enjoying a scientific renaissance following the seminal discovery in 1977 of public-key cryptography and applications in computers and communications. This book gives a broad overview of public-key cryptography - its essence and advantages, various public-key cryptosystems, and protocols - as well as a comprehensive introduction to classical cryptography and cryptoanalysis. The second edition has been revised and enlarged especially in its treatment of cryptographic protocols. From a review of the first edition: "This is a comprehensive review ... there can be no doubt that this will be accepted as a standard text. At the same time, it is clearly and entertainingly written ... and can certainly stand alone." Alex M. Andrew, Kybernetes, March 1992
Author : Song Y. Yan
Publisher : Springer Science & Business Media
Page : 249 pages
File Size : 48,6 Mb
Release : 2013-06-29
Category : Computers
ISBN : 9781475738162
Primality Testing and Integer Factorization in Public-Key Cryptography introduces various algorithms for primality testing and integer factorization, with their applications in public-key cryptography and information security. More specifically, this book explores basic concepts and results in number theory in Chapter 1. Chapter 2 discusses various algorithms for primality testing and prime number generation, with an emphasis on the Miller-Rabin probabilistic test, the Goldwasser-Kilian and Atkin-Morain elliptic curve tests, and the Agrawal-Kayal-Saxena deterministic test for primality. Chapter 3 introduces various algorithms, particularly the Elliptic Curve Method (ECM), the Quadratic Sieve (QS) and the Number Field Sieve (NFS) for integer factorization. This chapter also discusses some other computational problems that are related to factoring, such as the square root problem, the discrete logarithm problem and the quadratic residuosity problem.
Author : Abhijit Das,C. E. Veni Madhavan
Publisher : Pearson Education India
Page : 588 pages
File Size : 43,7 Mb
Release : 2009
Category : Computers
ISBN : 8131708322
Public-key Cryptography provides a comprehensive coverage of the mathematical tools required for understanding the techniques of public-key cryptography and cryptanalysis. Key topics covered in the book include common cryptographic primitives and symmetric techniques, quantum cryptography, complexity theory, and practical cryptanalytic techniques such as side-channel attacks and backdoor attacks.Organized into eight chapters and supplemented with four appendices, this book is designed to be a self-sufficient resource for all students, teachers and researchers interested in the field of cryptography.
Author : Alexei Myasnikov,Vladimir Shpilrain,Alexander Ushakov
Publisher : Springer Science & Business Media
Page : 183 pages
File Size : 45,7 Mb
Release : 2008-11-04
Category : Mathematics
ISBN : 9783764388270
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 : Gilbert Baumslag,Benjamin Fine,Martin Kreuzer,Gerhard Rosenberger
Publisher : Walter de Gruyter GmbH & Co KG
Page : 389 pages
File Size : 50,5 Mb
Release : 2015-06-16
Category : Computers
ISBN : 9783110386165
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 : Paul B. Garrett,Daniel Lieman
Publisher : American Mathematical Soc.
Page : 194 pages
File Size : 49,9 Mb
Release : 2005
Category : Computers
ISBN : 9780821833650
This collection of articles grew out of an expository and tutorial conference on public-key cryptography, held at the Joint Mathematics Meetings (Baltimore). The book provides an introduction and survey on public-key cryptography for those with considerable mathematical maturity and general mathematical knowledge. Its goal is to bring visibility to the cryptographic issues that fall outside the scope of standard mathematics. These mathematical expositions are intended for experienced mathematicians who are not well acquainted with the subject. The book is suitable for graduate students, researchers, and engineers interested in mathematical aspects and applications of public-key cryptography.
Author : Neal Koblitz
Publisher : Springer Science & Business Media
Page : 184 pages
File Size : 53,5 Mb
Release : 2000-03-31
Category : Business & Economics
ISBN : 0792378024
Dept. of Mathematics, University of Washington, Seattle, USA This book brings together in one place important contributions and up-to-date research results in this fast moving area. Reprinted from Designs, Codes and Cryptography, 19:2/3.
Author : Alfred J. Menezes,Paul C. van Oorschot,Scott A. Vanstone
Publisher : CRC Press
Page : 810 pages
File Size : 55,7 Mb
Release : 2018-12-07
Category : Mathematics
ISBN : 9780429881329
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.
Author : Margaret Cozzens, Steven J. Miller
Publisher : American Mathematical Soc.
Page : 355 pages
File Size : 47,5 Mb
Release : 2013-09-05
Category : Business & Economics
ISBN : 9780821883211
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.
