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Primality Testing and Integer Factorization in Public-Key Cryptography [electronic resource] /by Song Y. Yan.

by Yan, Song Y [author.]; SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Advances in Information Security: 11Publisher: Boston, MA : Springer US : 2009.Description: XVIII, 371 p. 40 illus. online resource.ISBN: 9780387772684.Subject(s): Computer science | Computer Communication Networks | Data protection | Data structures (Computer science) | Data encryption (Computer science) | Coding theory | Computer Science | Data Encryption | Data Structures, Cryptology and Information Theory | Systems and Data Security | Coding and Information Theory | Data Structures | Computer Communication NetworksOnline resources: Click here to access online
Contents:
Number-Theoretic Preliminaries -- Primality Testing and Prime Generation -- Integer Factorization and Discrete Logarithms -- Number-Theoretic Cryptography.
In: Springer eBooksSummary: 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.
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Number-Theoretic Preliminaries -- Primality Testing and Prime Generation -- Integer Factorization and Discrete Logarithms -- Number-Theoretic Cryptography.

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.

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