Bøger af Chaoping Xing

Asiacrypt'99 was held in Singapore on 14-18 November 1999. Asiacrypt is one of the major events in the cryptology research community. Asiacrypt'99, the ?fth annual Asiacrypt conference, was sponsored by the Asiacrypt Steering Comm- tee and the Centre for Systems Security of the National University of Singapore, and in cooperation with the International Association for Cryptology Research. As the Program Co-Chairs of Asiacrypt'99, we are extremely honored to or- nize this event, which showcases the state-of-the-art development of cryptology research at the conclusion of this millennium. This year, a total of 96 research papers were submitted to Asiacrypt'99. The portfolio of country of origin of submissions serves as a good indicator of the - ternational reputation of the conference. Countries from which submissions or- inated include: Australia, Belgium, China, Estonia, France, Germany, Greece, India, Iran, Japan, Korea, Norway, Russia, Saudi Arabia, Switzerland, Sin- pore, Spain, Taiwan, Thailand, The Netherlands, Turkey, Ukraine, UK, USA and Yugoslavia. Through a stringent refereeing process by the Program C- mittee, 31 papers of outstanding quality were accepted and are included in the conference proceedings. Accepted papers were authored by researchers from the following countries: Australia, Belgium, France, Germany, India, Japan, China, Singapore, Switzerland, Taiwan, The Netherlands, UK, and USA.

Ever since the seminal work of Goppa on algebraic-geometry codes, rational points on algebraic curves over finite fields have been an important research topic for algebraic geometers and coding theorists. The focus in this application of algebraic geometry to coding theory is on algebraic curves over finite fields with many rational points (relative to the genus). Recently, the authors discovered another important application of such curves, namely to the construction of low-discrepancy sequences. These sequences are needed for numerical methods in areas as diverse as computational physics and mathematical finance. This has given additional impetus to the theory of, and the search for, algebraic curves over finite fields with many rational points. This book aims to sum up the theoretical work on algebraic curves over finite fields with many rational points and to discuss the applications of such curves to algebraic coding theory and the construction of low-discrepancy sequences.

This textbook equips graduate students and advanced undergraduates with the necessary theoretical tools for applying algebraic geometry to information theory, and it covers primary applications in coding theory and cryptography. Harald Niederreiter and Chaoping Xing provide the first detailed discussion of the interplay between nonsingular projective curves and algebraic function fields over finite fields. This interplay is fundamental to research in the field today, yet until now no other textbook has featured complete proofs of it. Niederreiter and Xing cover classical applications like algebraic-geometry codes and elliptic-curve cryptosystems as well as material not treated by other books, including function-field codes, digital nets, code-based public-key cryptosystems, and frameproof codes. Combining a systematic development of theory with a broad selection of real-world applications, this is the most comprehensive yet accessible introduction to the field available. Introduces graduate students and advanced undergraduates to the foundations of algebraic geometry for applications to information theory Provides the first detailed discussion of the interplay between projective curves and algebraic function fields over finite fields Includes applications to coding theory and cryptography Covers the latest advances in algebraic-geometry codes Features applications to cryptography not treated in other books