Primality Testing and Integer Factorization in Public-Key Cryptography
Primality Testing and Integer Factorization in Public-Key Cryptography by Song Y. Yan is a comprehensive examination of key concepts in cryptography, published by Springer US on November 29, 2010. This softcover reprint of the hardcover second edition from 2009 spans 371 pages and is presented in English. The book addresses the Primality Testing Problem (PTP) and the Integer Factorization Problem (IFP), detailing the advancements in primality testing and the ongoing challenges associated with integer factorization, which is crucial for the security of public-key cryptosystems like RSA.
Readers will find a thorough survey of recent developments in these areas, including a comparison of various testing algorithms such as the Rabin-Miller probabilistic test, the Atkin-Morain elliptic curve test, and the AKS deterministic test. This volume is tailored for advanced students in computer science and mathematics, serving as both a secondary text and a reference for practitioners and researchers in the fields of cryptography, security, and number theory. The book aims to provide insights into the computational complexities that underpin public-key cryptography and its reliance on the intractability of integer factorization.
Official synopsis Publisher
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.
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.
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.
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