Yan, Song Y. <br/><br/>
Primality Testing and Integer Factorization in Public-Key Cryptography  [electronic resource] / 
by Song Y. Yan. 
 - XVIII, 371 p. 40 illus.  online resource. 
 - Advances in Information Security,  11  1568-2633 ; .
 - Advances in Information Security,  11 .
<br/><br/>Number-Theoretic Preliminaries -- Primality Testing and Prime Generation -- Integer Factorization and Discrete Logarithms -- Number-Theoretic Cryptography. 
<br/><br/> 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. 
<br/><br/><label>ISBN: </label>9780387772684 99780387772684 
<br/><br/><label>Standard No.: </label>10.1007/978-0-387-77268-4  doi 
<br/><br/><label>Subjects--Topical Terms: </label><br/>COMPUTER SCIENCE.<br/>COMPUTER COMMUNICATION NETWORKS.<br/>DATA PROTECTION.<br/>DATA STRUCTURES (COMPUTER SCIENCE).<br/>DATA ENCRYPTION (COMPUTER SCIENCE).<br/>CODING THEORY.<br/>COMPUTER SCIENCE.<br/>DATA ENCRYPTION.<br/>DATA STRUCTURES, CRYPTOLOGY AND INFORMATION THEORY.<br/>SYSTEMS AND DATA SECURITY.<br/>CODING AND INFORMATION THEORY.<br/>DATA STRUCTURES.<br/>COMPUTER COMMUNICATION NETWORKS.