Details
Primality Testing and Integer Factorization in Public-Key Cryptography
Advances in Information Security, Band 11 2nd ed. 2009
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149,79 € |
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| Verlag: | Springer |
| Format: | |
| Veröffentl.: | 03.04.2009 |
| ISBN/EAN: | 9780387772684 |
| Sprache: | englisch |
| Anzahl Seiten: | 371 |
Dieses eBook enthält ein Wasserzeichen.
Beschreibungen
<P>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.</P>
<P>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.</P>
<P>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.</P>
<P>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.</P>
<P>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.</P>
Number-Theoretic Preliminaries.- Primality Testing and Prime Generation.- Integer Factorization and Discrete Logarithms.- Number-Theoretic Cryptography.
<P>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. </P>
<P></P>
<P>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. </P>
<P></P>
<P>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. </P>
<P></P>
<P><EM>Primality Testing and Integer Factorization in Public Key Cryptography</EM> is designed for practitioners and researchers in industry and graduate-level students in computer science and mathematics. </P>
<P></P>
<P>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. </P>
<P></P>
<P>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. </P>
<P></P>
<P><EM>Primality Testing and Integer Factorization in Public Key Cryptography</EM> is designed for practitioners and researchers in industry and graduate-level students in computer science and mathematics. </P>
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
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