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Advances in Information Security

Primality Testing and Integer Factorization in Public-Key Cryptography

Authors: Yan, Song Y.

  • Includes a new section on quantum factoring and post-quantum cryptography
  • New edition more suitable as an advanced graduate text as exercises and research problems grouped into new section after each chapter
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Buy this book

eBook $149.00
price for USA in USD (gross)
  • ISBN 978-0-387-77268-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $199.99
price for USA in USD
  • ISBN 978-0-387-77267-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $199.00
price for USA in USD
  • ISBN 978-1-4419-4586-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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.

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)

“This is the second edition of a book originally published in 2004. … I used it as a reference in preparing lectures for an advanced cryptography course for undergraduates, and it proved to be a wonderful source for a general description of the algorithms. … the book will be a valuable addition to any good reference library on cryptography and number theory … . It contains descriptions of all the main algorithms, together with explanations of the key ideas behind them.” (S. C. Coutinho, SIGACT News, April, 2012)


Table of contents (4 chapters)

  • Number-Theoretic Preliminaries

    Yan, Dr. Song Y.

    Pages 1-125

  • Primality Testing and Prime Generation

    Yan, Dr. Song Y.

    Pages 127-207

  • Integer Factorization and Discrete Logarithms

    Yan, Dr. Song Y.

    Pages 209-285

  • Number-Theoretic Cryptography

    Yan, Dr. Song Y.

    Pages 287-351

Buy this book

eBook $149.00
price for USA in USD (gross)
  • ISBN 978-0-387-77268-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $199.99
price for USA in USD
  • ISBN 978-0-387-77267-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $199.00
price for USA in USD
  • ISBN 978-1-4419-4586-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Primality Testing and Integer Factorization in Public-Key Cryptography
Authors
Series Title
Advances in Information Security
Series Volume
11
Copyright
2009
Publisher
Springer US
Copyright Holder
Springer-Verlag US
eBook ISBN
978-0-387-77268-4
DOI
10.1007/978-0-387-77268-4
Hardcover ISBN
978-0-387-77267-7
Softcover ISBN
978-1-4419-4586-0
Series ISSN
1568-2633
Edition Number
2
Number of Pages
XVIII, 371
Number of Illustrations
40 b/w illustrations
Topics