Ebook: Primality Testing and Integer Factorization in Public-Key Cryptography
Author: Song Y. Yan (auth.)
- Tags: Data Encryption, Data Structures Cryptology and Information Theory, Systems and Data Security, Coding and Information Theory, Data Structures, Computer Communication Networks
- Series: Advances in Information Security 11
- Year: 2009
- Publisher: Springer US
- Edition: 2
- Language: English
- pdf
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.
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.
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.
Content:
Front Matter....Pages 1-17
Number-Theoretic Preliminaries....Pages 1-125
Primality Testing and Prime Generation....Pages 1-81
Integer Factorization and Discrete Logarithms....Pages 1-77
Number-Theoretic Cryptography....Pages 1-65
Back Matter....Pages 1-20
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.
Content:
Front Matter....Pages 1-17
Number-Theoretic Preliminaries....Pages 1-125
Primality Testing and Prime Generation....Pages 1-81
Integer Factorization and Discrete Logarithms....Pages 1-77
Number-Theoretic Cryptography....Pages 1-65
Back Matter....Pages 1-20
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