Number Theoretic Methods In Cryptology
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Author |
: Jerzy Kaczorowski |
Publisher |
: Springer |
Total Pages |
: 287 |
Release |
: 2018-03-09 |
ISBN-10 |
: 9783319766201 |
ISBN-13 |
: 3319766201 |
Rating |
: 4/5 (01 Downloads) |
Synopsis Number-Theoretic Methods in Cryptology by : Jerzy Kaczorowski
This book constitutes the refereed post-conference proceedings of the First International Conference on Number-Theoretic Methods in Cryptology, NuTMiC 2017, held in Warsaw, Poland, in September 2017.The 15 revised full papers presented in this book together with 3 invited talks were carefully reviewed and selected from 32 initial submissions. The papers are organized in topical sections on elliptic curves in cryptography; public-key cryptography; lattices in cryptography; number theory; pseudorandomness; and algebraic structures and analysis.
Author |
: Igor Shparlinski |
Publisher |
: Birkhäuser |
Total Pages |
: 181 |
Release |
: 2012-12-06 |
ISBN-10 |
: 9783034886642 |
ISBN-13 |
: 3034886640 |
Rating |
: 4/5 (42 Downloads) |
Synopsis Number Theoretic Methods in Cryptography by : Igor Shparlinski
The book introduces new techniques which imply rigorous lower bounds on the complexity of some number theoretic and cryptographic problems. These methods and techniques are based on bounds of character sums and numbers of solutions of some polynomial equations over finite fields and residue rings. It also contains a number of open problems and proposals for further research. We obtain several lower bounds, exponential in terms of logp, on the de grees and orders of • polynomials; • algebraic functions; • Boolean functions; • linear recurring sequences; coinciding with values of the discrete logarithm modulo a prime p at suf ficiently many points (the number of points can be as small as pI/He). These functions are considered over the residue ring modulo p and over the residue ring modulo an arbitrary divisor d of p - 1. The case of d = 2 is of special interest since it corresponds to the representation of the right most bit of the discrete logarithm and defines whether the argument is a quadratic residue. We also obtain non-trivial upper bounds on the de gree, sensitivity and Fourier coefficients of Boolean functions on bits of x deciding whether x is a quadratic residue. These results are used to obtain lower bounds on the parallel arithmetic and Boolean complexity of computing the discrete logarithm. For example, we prove that any unbounded fan-in Boolean circuit. of sublogarithmic depth computing the discrete logarithm modulo p must be of superpolynomial size.
Author |
: Samuel S. Wagstaff, Jr. |
Publisher |
: CRC Press |
Total Pages |
: 336 |
Release |
: 2019-08-22 |
ISBN-10 |
: 9781420057690 |
ISBN-13 |
: 1420057693 |
Rating |
: 4/5 (90 Downloads) |
Synopsis Cryptanalysis of Number Theoretic Ciphers by : Samuel S. Wagstaff, Jr.
At the heart of modern cryptographic algorithms lies computational number theory. Whether you're encrypting or decrypting ciphers, a solid background in number theory is essential for success. Written by a number theorist and practicing cryptographer, Cryptanalysis of Number Theoretic Ciphers takes you from basic number theory to the inner workings of ciphers and protocols. First, the book provides the mathematical background needed in cryptography as well as definitions and simple examples from cryptography. It includes summaries of elementary number theory and group theory, as well as common methods of finding or constructing large random primes, factoring large integers, and computing discrete logarithms. Next, it describes a selection of cryptographic algorithms, most of which use number theory. Finally, the book presents methods of attack on the cryptographic algorithms and assesses their effectiveness. For each attack method the author lists the systems it applies to and tells how they may be broken with it. Computational number theorists are some of the most successful cryptanalysts against public key systems. Cryptanalysis of Number Theoretic Ciphers builds a solid foundation in number theory and shows you how to apply it not only when breaking ciphers, but also when designing ones that are difficult to break.
Author |
: Igor Shparlinski |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 434 |
Release |
: 2003-02-12 |
ISBN-10 |
: 3764366540 |
ISBN-13 |
: 9783764366544 |
Rating |
: 4/5 (40 Downloads) |
Synopsis Cryptographic Applications of Analytic Number Theory by : Igor Shparlinski
The book introduces new ways of using analytic number theory in cryptography and related areas, such as complexity theory and pseudorandom number generation. Cryptographers and number theorists will find this book useful. The former can learn about new number theoretic techniques which have proved to be invaluable cryptographic tools, the latter about new challenging areas of applications of their skills.
Author |
: J. H. Loxton |
Publisher |
: Cambridge University Press |
Total Pages |
: 249 |
Release |
: 1990-04-19 |
ISBN-10 |
: 9780521398770 |
ISBN-13 |
: 0521398770 |
Rating |
: 4/5 (70 Downloads) |
Synopsis Number Theory and Cryptography by : J. H. Loxton
Papers presented by prominent contributors at a workshop on Number Theory and Cryptography, and the annual meeting of the Australian Mathematical Society.
Author |
: Neal Koblitz |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 245 |
Release |
: 2012-09-05 |
ISBN-10 |
: 9781441985927 |
ISBN-13 |
: 1441985921 |
Rating |
: 4/5 (27 Downloads) |
Synopsis A Course in Number Theory and Cryptography by : Neal Koblitz
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.
Author |
: Song Y. Yan |
Publisher |
: John Wiley & Sons |
Total Pages |
: 432 |
Release |
: 2013-01-29 |
ISBN-10 |
: 9781118188583 |
ISBN-13 |
: 1118188586 |
Rating |
: 4/5 (83 Downloads) |
Synopsis Computational Number Theory and Modern Cryptography by : Song Y. Yan
The only book to provide a unified view of the interplay between computational number theory and cryptography Computational number theory and modern cryptography are two of the most important and fundamental research fields in information security. In this book, Song Y. Yang combines knowledge of these two critical fields, providing a unified view of the relationships between computational number theory and cryptography. The author takes an innovative approach, presenting mathematical ideas first, thereupon treating cryptography as an immediate application of the mathematical concepts. The book also presents topics from number theory, which are relevant for applications in public-key cryptography, as well as modern topics, such as coding and lattice based cryptography for post-quantum cryptography. The author further covers the current research and applications for common cryptographic algorithms, describing the mathematical problems behind these applications in a manner accessible to computer scientists and engineers. Makes mathematical problems accessible to computer scientists and engineers by showing their immediate application Presents topics from number theory relevant for public-key cryptography applications Covers modern topics such as coding and lattice based cryptography for post-quantum cryptography Starts with the basics, then goes into applications and areas of active research Geared at a global audience; classroom tested in North America, Europe, and Asia Incudes exercises in every chapter Instructor resources available on the book’s Companion Website Computational Number Theory and Modern Cryptography is ideal for graduate and advanced undergraduate students in computer science, communications engineering, cryptography and mathematics. Computer scientists, practicing cryptographers, and other professionals involved in various security schemes will also find this book to be a helpful reference.
Author |
: Lawrence C. Washington |
Publisher |
: CRC Press |
Total Pages |
: 533 |
Release |
: 2008-04-03 |
ISBN-10 |
: 9781420071474 |
ISBN-13 |
: 1420071475 |
Rating |
: 4/5 (74 Downloads) |
Synopsis Elliptic Curves by : Lawrence C. Washington
Like its bestselling predecessor, Elliptic Curves: Number Theory and Cryptography, Second Edition develops the theory of elliptic curves to provide a basis for both number theoretic and cryptographic applications. With additional exercises, this edition offers more comprehensive coverage of the fundamental theory, techniques, and application
Author |
: Harald Niederreiter |
Publisher |
: World Scientific |
Total Pages |
: 460 |
Release |
: 2002-12-03 |
ISBN-10 |
: 9789814487665 |
ISBN-13 |
: 981448766X |
Rating |
: 4/5 (65 Downloads) |
Synopsis Coding Theory And Cryptology by : Harald Niederreiter
The inaugural research program of the Institute for Mathematical Sciences at the National University of Singapore took place from July to December 2001 and was devoted to coding theory and cryptology. As part of the program, tutorials for graduate students and junior researchers were given by world-renowned scholars. These tutorials covered fundamental aspects of coding theory and cryptology and were designed to prepare for original research in these areas. The present volume collects the expanded lecture notes of these tutorials. The topics range from mathematical areas such as computational number theory, exponential sums and algebraic function fields through coding-theory subjects such as extremal problems, quantum error-correcting codes and algebraic-geometry codes to cryptologic subjects such as stream ciphers, public-key infrastructures, key management, authentication schemes and distributed system security.
Author |
: Alfred J. Menezes |
Publisher |
: CRC Press |
Total Pages |
: 810 |
Release |
: 2018-12-07 |
ISBN-10 |
: 9780429881329 |
ISBN-13 |
: 0429881320 |
Rating |
: 4/5 (29 Downloads) |
Synopsis Handbook of Applied Cryptography by : Alfred J. Menezes
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.