This book summarizes knowledge built up within Hewlett-Packard over a number of years, and explains the mathematics behind practical implementations of elliptic curve systems. Due to the advanced nature of the mathematics there is a high barrier to entry for individuals and companies to this technology. Hence this book will be invaluable not only to mathematicians wanting to see how pure mathematics can be applied but also to engineers and computer scientists wishing (or needing) to actually implement such systems.

Since the appearance of the authors' first volume on elliptic curve cryptography in 1999 there has been tremendous progress in the field. In some topics, particularly point counting, the progress has been spectacular. Other topics such as the Weil and Tate pairings have been applied in new and important ways to cryptographic protocols that hold great promise. Notions such as provable security, side channel analysis and the Weil descent technique have also grown in importance. This second volume addresses these advances and brings the reader up to date. Prominent contributors to the research literature in these areas have provided articles that reflect the current state of these important topics. They are divided into the areas of protocols, implementation techniques, mathematical foundations and pairing based cryptography. Each of the topics is presented in an accessible, coherent and consistent manner for a wide audience that will include mathematicians, computer scientists and engineers.

This volume is the second part of a four-volume set (CCIS 190, CCIS 191, CCIS 192, CCIS 193), which constitutes the refereed proceedings of the First International Conference on Computing and Communications, ACC 2011, held in Kochi, India, in July 2011. The 72 revised full papers presented in this volume were carefully reviewed and selected from a large number of submissions. The papers are organized in topical sections on database and information systems; distributed software development; human computer interaction and interface; ICT; internet and Web computing; mobile computing; multi agent systems; multimedia and video systems; parallel and distributed algorithms; security, trust and privacy.

Like its bestselling predecessor, Elliptic Curves: Number Theory and Cryptography, Second Edition develops the theory of elliptic curves to provide a basis for both number theoretic and cryptographic applications. With additional exercises, this edition offers more comprehensive coverage of the fundamental theory, techniques, and application

Crypto 2001, the 21st Annual Crypto conference, was sponsored by the Int- national Association for Cryptologic Research (IACR) in cooperation with the IEEE Computer Society Technical Committee on Security and Privacy and the Computer Science Department of the University of California at Santa Barbara. The conference received 156 submissions, of which the program committee selected 34 for presentation; one was later withdrawn. These proceedings contain the revised versions of the 33 submissions that were presented at the conference. These revisions have not been checked for correctness, and the authors bear full responsibility for the contents of their papers. The conference program included two invited lectures. Mark Sherwin spoke on, \Quantum information processing in semiconductors: an experimentalist’s view." Daniel Weitzner spoke on, \Privacy, Authentication & Identity: A recent history of cryptographic struggles for freedom." The conference program also included its perennial \rump session," chaired by Stuart Haber, featuring short, informal talks on late{breaking research news. As I try to account for the hours of my life that ?ew o to oblivion, I realize that most of my time was spent cajoling talented innocents into spending even more time on my behalf. I have accumulated more debts than I can ever hope to repay. As mere statements of thanks are certainly insu cient, consider the rest of this preface my version of Chapter 11.

Eurocrypt is a series of open workshops on the theory and application of cryptographic techniques. These meetings have taken place in Europe every year since 1982 and are sponsored by the International Association for Cryptologic Research. Eurocrypt '93 was held in the village of Lofthus in Norway in May 1993. The call for papers resulted in 117 submissions with authors representing 27 different countries. The 36 accepted papers were selected by the program committee after a blind refereeing process. The papers are grouped into parts on authentication, public key, block ciphers, secret sharing, stream ciphers, digital signatures, protocols, hash functions, payment systems, and cryptanalysis. The volume includes 6 further rump session papers.

The discrete logarithm problem based on elliptic and hyperelliptic curves has gained a lot of popularity as a cryptographic primitive. The main reason is that no subexponential algorithm for computing discrete logarithms on small genus curves is currently available, except in very special cases. Therefore curve-based cryptosystems require much smaller key sizes than RSA to attain the same security level. This makes them particularly attractive for implementations on memory-restricted devices like smart cards and in high-security applications. The Handbook of Elliptic and Hyperelliptic Curve Cryptography introduces the theory and algorithms involved in curve-based cryptography. After a very detailed exposition of the mathematical background, it provides ready-to-implement algorithms for the group operations and computation of pairings. It explores methods for point counting and constructing curves with the complex multiplication method and provides the algorithms in an explicit manner. It also surveys generic methods to compute discrete logarithms and details index calculus methods for hyperelliptic curves. For some special curves the discrete logarithm problem can be transferred to an easier one; the consequences are explained and suggestions for good choices are given. The authors present applications to protocols for discrete-logarithm-based systems (including bilinear structures) and explain the use of elliptic and hyperelliptic curves in factorization and primality proving. Two chapters explore their design and efficient implementations in smart cards. Practical and theoretical aspects of side-channel attacks and countermeasures and a chapter devoted to (pseudo-)random number generation round off the exposition. The broad coverage of all- important areas makes this book a complete handbook of elliptic and hyperelliptic curve cryptography and an invaluable reference to anyone interested in this exciting field.