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Primality Testing and Integer Factorization in Public-Key Cryptography

  • Book
  • © 2004

Overview

Authors:
  1. Song Y. Yan

    1. Coventry University, UK

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Part of the book series: Advances in Information Security (ADIS, volume 11)

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Table of contents (4 chapters)

  1. Front Matter

    Pages i-xvi
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  2. Number-Theoretic Preliminaries

    • Song Y. Yan
    Pages 1-97

  3. Primality Testing and Prime Generation

    • Song Y. Yan
    Pages 99-137

  4. Integer Factorization and Discrete Logarithms

    • Song Y. Yan
    Pages 139-191

  5. Number-Theoretic Cryptography

    • Song Y. Yan
    Pages 193-222

  6. Back Matter

    Pages 223-237
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Keywords

About this book

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.

Reviews

From the reviews of the second edition:

"The well-written and self-contained second edition ‘is designed for a professional audience composed of researchers practitioners in industry.’ In addition, ‘this book is also suitable as a secondary text for graduate-level students in computer science, mathematics, and engineering,’ as it contains about 300 problems. … Overall … ‘this monograph provides a survey of recent progress in Primality Testing and Integer Factorization, with implications in factoring-based Public Key Cryptography.’" (Hao Wang, ACM Computing Reviews, April, 2009)

Authors and Affiliations

  • Coventry University, UK

    Song Y. Yan

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