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Primality Testing and Integer Factorization in Public-Key Cryptography Song Y. Yan

Primality Testing and Integer Factorization in Public-Key Cryptography By Song Y. Yan

Primality Testing and Integer Factorization in Public-Key Cryptography by Song Y. Yan

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Summary

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).

Primality Testing and Integer Factorization in Public-Key Cryptography Summary

Primality Testing and Integer Factorization in Public-Key Cryptography by Song Y. Yan

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.

Primality Testing and Integer Factorization in Public-Key Cryptography 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

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

Additional information

NPB9780387772677
9780387772677
0387772677
Primality Testing and Integer Factorization in Public-Key Cryptography by Song Y. Yan
Song Y. Yan
Advances in Information Security
New
Hardback
Springer-Verlag New York Inc.
2008-12-02
371
N/A
Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
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Customer Reviews - Primality Testing and Integer Factorization in Public-Key Cryptography