Chaoping Xing - Böcker

Coding theory is concerned with successfully transmitting data through a noisy channel and correcting errors in corrupted messages. It is of central importance for many applications in computer science or engineering. This book gives a comprehensive introduction to coding theory whilst only assuming basic linear algebra. It contains a detailed and rigorous introduction to the theory of block codes and moves on to more advanced topics like BCH codes, Goppa codes and Sudan's algorithm for list decoding. The issues of bounds and decoding, essential to the design of good codes, features prominently. The authors of this book have, for several years, successfully taught a course on coding theory to students at the National University of Singapore. This book is based on their experiences and provides a thoroughly modern introduction to the subject. There are numerous examples and exercises, some of which introduce students to novel or more advanced material.

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.

Coding theory is concerned with successfully transmitting data through a noisy channel and correcting errors in corrupted messages. It is of central importance for many applications in computer science or engineering. This book gives a comprehensive introduction to coding theory whilst only assuming basic linear algebra. It contains a detailed and rigorous introduction to the theory of block codes and moves on to more advanced topics like BCH codes, Goppa codes and Sudan's algorithm for list decoding. The issues of bounds and decoding, essential to the design of good codes, features prominently. The authors of this book have, for several years, successfully taught a course on coding theory to students at the National University of Singapore. This book is based on their experiences and provides a thoroughly modern introduction to the subject. There are numerous examples and exercises, some of which introduce students to novel or more advanced material.

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

Harald Niederreiter's pioneering research in the field of applied algebra and number theory has led to important and substantial breakthroughs in many areas. This collection of survey articles has been authored by close colleagues and leading experts to mark the occasion of his 70th birthday. The book provides a modern overview of different research areas, covering uniform distribution and quasi-Monte Carlo methods as well as finite fields and their applications, in particular, cryptography and pseudorandom number generation. Many results are published here for the first time. The book serves as a useful starting point for graduate students new to these areas or as a refresher for researchers wanting to follow recent trends.

The reach of algebraic curves in cryptography goes far beyond elliptic curve or public key cryptography yet these other application areas have not been systematically covered in the literature. Addressing this gap, Algebraic Curves in Cryptography explores the rich uses of algebraic curves in a range of cryptographic applications, such as secret sharing, frameproof codes, and broadcast encryption. Suitable for researchers and graduate students in mathematics and computer science, this self-contained book is one of the first to focus on many topics in cryptography involving algebraic curves. After supplying the necessary background on algebraic curves, the authors discuss error-correcting codes, including algebraic geometry codes, and provide an introduction to elliptic curves. Each chapter in the remainder of the book deals with a selected topic in cryptography (other than elliptic curve cryptography). The topics covered include secret sharing schemes, authentication codes, frameproof codes, key distribution schemes, broadcast encryption, and sequences. Chapters begin with introductory material before featuring the application of algebraic curves.

The reach of algebraic curves in cryptography goes far beyond elliptic curve or public key cryptography yet these other application areas have not been systematically covered in the literature. Addressing this gap, Algebraic Curves in Cryptography explores the rich uses of algebraic curves in a range of cryptographic applications, such as secret sharing, frameproof codes, and broadcast encryption. Suitable for researchers and graduate students in mathematics and computer science, this self-contained book is one of the first to focus on many topics in cryptography involving algebraic curves. After supplying the necessary background on algebraic curves, the authors discuss error-correcting codes, including algebraic geometry codes, and provide an introduction to elliptic curves. Each chapter in the remainder of the book deals with a selected topic in cryptography (other than elliptic curve cryptography). The topics covered include secret sharing schemes, authentication codes, frameproof codes, key distribution schemes, broadcast encryption, and sequences. Chapters begin with introductory material before featuring the application of algebraic curves.

This volume contains the refereed proceedings of the Workshop on Cryptography and Computational Number Theory, CCNT'99, which has been held in Singapore during the week of November 22-26, 1999. The workshop was organized by the Centre for Systems Security of the Na­ tional University of Singapore. We gratefully acknowledge the financial support from the Singapore National Science and Technology Board under the grant num­ ber RP960668/M. The idea for this workshop grew out of the recognition of the recent, rapid development in various areas of cryptography and computational number the­ ory. The event followed the concept of the research programs at such well-known research institutions as the Newton Institute (UK), Oberwolfach and Dagstuhl (Germany), and Luminy (France). Accordingly, there were only invited lectures at the workshop with plenty of time for informal discussions. It was hoped and successfully achieved that the meeting would encourage and stimulate further research in information and computer security as well as in the design and implementation of number theoretic cryptosystems and other related areas. Another goal of the meeting was to stimulate collaboration and more active interaction between mathematicians, computer scientists, practical cryptographers and engineers in academia, industry and government.

It has long been recognized that there are fascinating connections between cod­ ing theory, cryptology, and combinatorics. Therefore it seemed desirable to us to organize a conference that brings together experts from these three areas for a fruitful exchange of ideas. We decided on a venue in the Huang Shan (Yellow Mountain) region, one of the most scenic areas of China, so as to provide the additional inducement of an attractive location. The conference was planned for June 2003 with the official title Workshop on Coding, Cryptography and Combi­ natorics (CCC 2003). Those who are familiar with events in East Asia in the first half of 2003 can guess what happened in the end, namely the conference had to be cancelled in the interest of the health of the participants. The SARS epidemic posed too serious a threat. At the time of the cancellation, the organization of the conference was at an advanced stage: all invited speakers had been selected and all abstracts of contributed talks had been screened by the program committee. Thus, it was de­ cided to call on all invited speakers and presenters of accepted contributed talks to submit their manuscripts for publication in the present volume. Altogether, 39 submissions were received and subjected to another round of refereeing. After care­ ful scrutiny, 28 papers were accepted for publication.

This book constitutes the refereed proceedings of the 5th International Conference on the Theory and Application of Cryptology and Information Security, ASIACRYPT'99, held in Singapore in November 1999. The 31 revised full papers presented together with one invited paper were carefully reviewed and selected from a total of 96 submissions. The book is divided in topical sections on assymetric key cryptosystems, cryptanalysis, elliptic curve cryptosystems, public key cryptosystems, integers and computation, network security, random numbers, key management, and authentication.

This book constitutes the refereed proceedings of the 6th International Conference on Cryptology and Network Security, CANS 2007, held in Singapore, in December 2007. The 17 revised full papers presented were carefully reviewed and selected. The papers are organized in topical sections on signatures, network security, secure keyword search and private information retrieval, public key encryption, intrusion detection, email security, denial of service attacks, and authentication.

This book constitutes the refereed proceedings of the Second International Workshop on Coding and Cryptology, IWCC 2009, held in Zhangjiajie, China, in June 2009. The 21 revised full technical papers, except one, are contributed by the invited speakers of the workshop. The papers were carefully selected during two rounds of reviewing and improvement for inclusion in the volume and address all aspects of coding theory, cryptology and related areas - such as combinatorics - theoretical or applied. Topics addressed are coding theory, secure codes, hash functions, combinatorics, boolean functions, authentication, cryptography, protocols, sequences, and secure communications.

This book constitutes the refereed proceedings of the Third International Workshop on Coding and Cryptology, IWCC 2011, held in Qingdao, China, May 30-June 3, 2011. The 19 revised full technical papers are contributed by the invited speakers of the workshop. The papers were carefully reviewed and cover a broad range of foundational and methodological as well as applicative issues in coding and cryptology, as well as related areas such as combinatorics.

This book contains a selection of papers submitted to the Workshop on Coding, Cryptography and Combinatorics (CCC 2003). An important feature of the book are invited surveys on key topics such as Boolean functions in cryptology, correlation attacks on LFSR sequences, decoding algorithms for linear codes, LDPC codes, and towers of function fields. There are also carefully selected contributed papers on many aspects of coding theory, cryptology and combinatorics, for instance, new constructions of codes, decoding algorithms, coding bounds, digital nets, cryptanalysis of cryptosystems and other cryptographic schemes, linear complexity of sequences, cross-correlation of sequences, authentication codes, fast arithmetic for cryptosystems, capacity regions, and combinatorial tableaux. The reader will be informed about current reesearch in these very active areas. The book is of interest for postgraduate students and researchers in mathematics, computer science, information theory and electrical engineering.

The fields of cryptography and computational number theory have recently witnessed a rapid development, which was the subject of the CCNT workshop in Singapore in November 1999. Its aim was to stimulate further research in information and computer security as well as the design and implementation of number theoretic cryptosystems and other related areas. Another achievement of the meeting was the collaboration of mathematicians, computer scientists, practical cryptographers and engineers in academia, industry and government. The present volume comprises a selection of refereed papers originating from this event, presenting either a survey of some area or original and new results. They concern many different aspects of the field such as theory, techniques, applications and practical experience. It provides a state-of-the-art report on some number theoretical issues of significance to cryptography.