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

Primality Testing and Integer Factorization in Public-Key Cryptography: Advances in Information Security, cartea 11

Autor Song Y. Yan
en Limba Engleză Hardback – 2 dec 2008
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.
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Specificații

ISBN-13: 9780387772677
ISBN-10: 0387772677
Pagini: 371
Ilustrații: XVIII, 371 p. 40 illus.
Dimensiuni: 155 x 235 x 23 mm
Greutate: 0.68 kg
Ediția:2nd ed. 2009
Editura: Springer Us
Colecția Springer
Seria Advances in Information Security

Locul publicării:New York, NY, United States

Public țintă

Research

Cuprins

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

Recenzii

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)

Textul de pe ultima copertă

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.

Caracteristici

New section on quantum factoring and post-quantum cryptography Exercises and research problems grouped into new section after each chapter; thus more suitable as advanced graduate text