Primality Testing and Integer Factorization in Public-Key Cryptography

  • Song Y. Yan

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

Table of contents

  1. Front Matter
    Pages i-xviii
  2. Song Y. Yan
    Pages 1-125
  3. Song Y. Yan
    Pages 127-207
  4. Song Y. Yan
    Pages 287-351
  5. Back Matter
    Pages 353-372

About this book


Although the Primality Testing Problem (PTP) has been proved to be solvable in deterministic polynomial-time (P) in 2002 by Agrawal, Kayal and Saxena, the Integer Factorization Problem (IFP) still remains unsolvable in P. The security of many practical Public-Key Cryptosystems and Protocols such as RSA (invented by Rivest, Shamir and Adleman) relies on the computational intractability of IFP. This monograph provides a survey of recent progress in Primality Testing and Integer Factorization, with implications to factoring-based Public Key Cryptography.

Notable features of this second edition are the several new sections and more than 100 new pages that are added. These include a new section in Chapter 2 on the comparison of Rabin-Miller probabilistic test in RP, Atkin-Morain elliptic curve test in ZPP and AKS deterministic test in P; a new section in Chapter 3 on recent work in quantum factoring; and a new section in Chapter 4 on post-quantum cryptography.

To make the book suitable as an advanced undergraduate and/or postgraduate text/reference, about ten problems at various levels of difficulty are added at the end of each section, making about 300 problems in total contained in the book; most of the problems are research-oriented with prizes ordered by individuals or organizations to a total amount over five million US dollars.

Primality Testing and Integer Factorization in Public Key Cryptography is designed for practitioners and researchers in industry and graduate-level students in computer science and mathematics.


DES Discrete Logarithms Elliptic Curve Cryptography Factorization Integer Number theory Primality Prime Prime Generation Prime number Public Key cryptography currentsmp

Authors and affiliations

  • Song Y. Yan
    • 1
  1. 1.Dept. Math.Harvard Univ. Dept. Math.CambridgeU.S.A.

Bibliographic information

  • DOI
  • Copyright Information Springer Science+Business Media, LLC 2009
  • Publisher Name Springer, Boston, MA
  • eBook Packages Computer Science
  • Print ISBN 978-0-387-77267-7
  • Online ISBN 978-0-387-77268-4
  • Series Print ISSN 1568-2633
  • Buy this book on publisher's site