Computational number theory and modern cryptography
by Yan, Song Y.
"The only book to provide a unified view of the interplay between computationalnumber theory and cryptographyComputational number theory and modern cryptography are two of the most important and fundamental research fields in information security. There are many textbooks on computational number theory or cryptography. However, textbooks integrating both topics are rare. This book not only introduces the basic concepts and results in the two fields, but also introduces many advanced topics. Mat…
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- Full title :Computational number theory and modern cryptography / Song Y. Yan.
Summary
"The only book to provide a unified view of the interplay between computationalnumber theory and cryptographyComputational number theory and modern cryptography are two of the most important and fundamental research fields in information security. There are many textbooks on computational number theory or cryptography. However, textbooks integrating both topics are rare. This book not only introduces the basic concepts and results in the two fields, but also introduces many advanced topics. Mathematical ideas are presented first, thereupon treating cryptography as an immediate application of the mathematical ideas. The author covers topics from number theory which are relevant for applications in public-key cryptography. The most popular public-key cryptosystems are based on difficult computational problems, such as factorization of large positive integers and the discrete logarithm problem in finite fields or on elliptic curves over finite fields. The book also covers modern topics, such as coding and lattice based cryptography, which are relevant for so-called post-quantum cryptography. The author goes over the basics in the first six chapters, followed by application to the most common cryptographic algorithms in the following three chapters. Finally areas of current research are touched in the last three chapters. Serious mathematical problems behind these applications will be explained at the level accessible to computer scientists and engineers. Makes deep mathematical problems accessible to computer scientists and engineers Based on classroom tested materials used in the US, UK and China Exercises included in every chapter Instructor resources available on the book's Companion Website "--
"This book not only introduces the basic concepts and results in the two fields, but also introduces many advanced topics"--
Edition Statements
- Publication Date:2013.
Publication Statements
- Publisher(s):Higher Education Press, Wiley
- Place of Publication:Singapore
- Language:eng
- Publication Date:2013.
The Physical Object
- Description:xii, 418 pages : : illustrations ; : 26 cm.
Edition Identifiers
- ISBN:9781118188583, 1118188586
- oclc:ocn809560712
- LC Classification:QA76.9.A25
- Dewey Decimal:005.8/2
Table of Contents
Part I Preliminaries -- 1 Introduction -- 2 Fundamentals -- Part II Computational Number Theory -- 3 Primality Testing -- 4 Integer Factorization -- 5 Discrete Logarithms -- Part III Modern Cryptography -- 6 Secret-Key Cryptography -- 7 Integer Factorization Based Cryptography -- 8 Discrete Logarithm Based Cryptography -- 9 Elliptic Curve Discrete Logarithm Based Cryptography -- Part IV Quantum Resistant Cryptography -- 10 Quantum Computational Number Theory -- 11 Quantum Resistant Cryptography.
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