Primality Testing and Integer Factorization in Public-Key Cryptography

By Song Y. Yan

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  • ISBN13: 978-0-3877-7267-7
  • 392 Pages
  • User Level: Science
  • Publication Date: April 3, 2009
  • Available eBook Formats: PDF

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Full Description
The Primality Testing Problem (PTP) has now proved to be solvable in deterministic polynomial-time (P) by the AKS (Agrawal-Kayal-Saxena) algorithm, whereas the Integer Factorization Problem (IFP) still remains unsolvable in (P). There is still no polynomial-time algorithm for IFP. Many practical public-key cryptosystems and protocols such as RSA (Rivest-Shamir-Adleman) rely their security on computational intractability of IFP. Primality Testing and Integer Factorization in Public Key Cryptography, Second Edition, provides a survey of recent progress in primality testing and integer factorization, with implications to factoring based public key cryptography. Notable new features are the comparison of Rabin-Miller probabilistic test in RP, Atkin-Morain elliptic curve test in ZPP and AKS deterministic test. This volume is designed for advanced level students in computer science and mathematics, and as a secondary text or reference book; suitable for practitioners and researchers in industry.
Table of Contents

Table of Contents

  1. Preface to the Second Edition.
  2. Preface to the First Edition.
  3. Number
  4. Theoretic Preliminaries.
  5. Primality Testing and Prime Generation.
  6. Integer Factorization and Discrete Logarithms.
  7. Number
  8. Theoretic Cryptography.
  9. Bibliography.
  10. Index.
  11. About the Author.

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