Computational Number Theory and Modern Cryptography

Computational Number Theory and Modern Cryptography (Information Security (Wiley))
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.

Table of Contents

Part I Preliminaries
1 Introduction 3
2 Fundamentals 35

Part II Computational Number Theory
3 Primality Testing 159
4 Integer Factorization 191
5 Discrete Logarithms 235

Part III Modern Cryptography
6 Secret-Key Cryptography 265
7 Integer Factorization Based Cryptography 293
8 Discrete Logarithm Based Cryptography 337
9 Elliptic Curve Discrete Logarithm Based Cryptography 353

Part IV Quantum Resistant Cryptography
10 Quantum Computational Number Theory 379
11 Quantum Resistant Cryptography 401