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

Introduction

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.

Keywords

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 https://doi.org/10.1007/978-0-387-77268-4
  • 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
  • About this book