Bücher von Song Y. Yan

Mathematicians do not study objects, but relations among objectsj they are indifferent to the replacement of objects by others as long as relations do not change. Matter is not important, only form interests them. HENRI POINCARE (1854-1912) Computer scientists working on algorithms for factorization would be well advised to brush up on their number theory. IAN STEWART [219] The theory of numbers, in mathematics, is primarily the theory of the prop- erties of integers (i.e., the whole numbers), particularly the positive integers. For example, Euclid proved 2000 years aga in his Elements that there exist infinitely many prime numbers. The subject has long been considered as the purest branch of mathematics, with very few applications to other areas. How- ever, recent years have seen considerable increase in interest in several central topics of number theory, precisely because of their importance and applica- tions in other areas, particularly in computing and information technology.

RSA is the first workable and practicable public-key cryptographic system, based on the use of large prime numbers. It is also the most popular and widely-used cryptographic system in today's digital world, for which its three inventors Rivest, Shamir and Adleman received the year 2002 Turing Award, the equivalent Nobel Prize in Computer Science.Cryptanalytic Attacks on RSA covers almost all major known cryptanalytic attacks and defenses of the RSA cryptographic system and its variants. Since RSA depends heavily on computational complexity theory and number theory, background information on complexity theory and number theory is presented first. This is followed by an account of the RSA cryptographic system and its variants.Cryptanalytic Attacks on RSA is designed for a professional audience of practitioners and researchers in industry and academia and as a reference or secondary text for advanced level students in computer science, applied mathematics, electrical & communication engineering.

This book provides the basic theory, techniques, and algorithms of modern cryptography that are applicable to network and cyberspace security. It consists of the following nine main chapters: Chapter 1 provides the basic concepts and ideas of cyberspace and cyberspace security, Chapters 2 and 3 provide an introduction to mathematical and computational preliminaries, respectively. Chapters 4 discusses the basic ideas and system of secret-key cryptography, whereas Chapters 5, 6, and 7 discuss the basic ideas and systems of public-key cryptography based on integer factorization, discrete logarithms, and elliptic curves, respectively. Quantum-safe cryptography is presented in Chapter 8 and offensive cryptography, particularly cryptovirology, is covered in Chapter 9. This book can be used as a secondary text for final-year undergraduate students and first-year postgraduate students for courses in Computer, Network, and Cyberspace Security. Researchers and practitioners working in cyberspace security and network security will also find this book useful as a reference.

The author discusses quantum algorithms for solving the Integer Factorization Problem (IFP), the Discrete Logarithm Problem (DLP), and the Elliptic Curve Discrete Logarithm Problem (ECDLP) and for attacking IFP, DLP and ECDLP based cryptographic systems.

This book introduces basic concepts and ideas of quantum computing and quantum computational complexity. It discusses almost all known quantum attacks on IFP, DLP and ECDLP based public-key cryptosystems and covers many alternative post-quantum cryptosystems.

Intended for advanced level students in computer science and mathematics, this key text, now in a brand new edition, provides a survey of recent progress in primality testing and integer factorization, with implications for factoring based public key cryptography.

This professional book covers almost all known cryptanalytic attacks and defenses of the RSA cryptographic system and its variants. It presents useful guidelines for proper use of RSA in information security and is the first book to cover its subject exclusively.

This book provides a good introduction to the classical elementary number theory and the modern algorithmic number theory, and their applications in computing and information technology, including computer systems design, cryptography and network security.