عنوان

Primality Testing and Integer Factorization in Public-Key Cryptography

1475738161

1475738188

9781475738162

9781475738186

b542355

Primality Testing and Integer Factorization in Public-Key Cryptography

[Book]

by Song Y. Yan.

Boston, MA

Springer US : Imprint : Springer

2004

Advances in information security, 11.

1. Number-Theoretic Preliminaries --;2. Primality Testing and Prime Generation --;3. Integer Factorization and Discrete Logarithms --;4. Number-Theoretic Cryptography.

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

Computer science.

Data structures (Computer science)

Information theory.

by Song Y. Yan.

Song Y Yan

[Book]

Y