Primality Testing and Integer Factorization in Public-Key Cryptography

by Song Y. Yan

Overview

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 prools 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.

Product Details

ISBN-13:	9780387772677
Publisher:	Springer US
Publication date:	12/02/2008
Series:	Advances in Information Security , #11
Edition description:	2nd ed. 2009
Pages:	371
Product dimensions:	6.30(w) x 9.30(h) x 0.90(d)

Table of Contents

Number-Theoretic Preliminaries.- Primality Testing and Prime Generation.- Integer Factorization and Discrete Logarithms.- Number-Theoretic Cryptography.

Editorial 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)

From the Publisher