This is the unique book on cross-fertilisations between stream ciphers and number theory. It systematically and comprehensively covers known connections between the two areas that are available only in research papers. Some parts of this book consist of new research results that are not available elsewhere. In addition to exercises, over thirty research problems are presented in this book. In this revised edition almost every chapter was updated, and some chapters were completely rewritten. It is useful as a textbook for a graduate course on the subject, as well as a reference book for researchers in related fields. · Unique book on interactions of stream ciphers and number theory. · Research monograph with many results not available elsewhere. · A revised edition with the most recent advances in this subject. · Over thirty research problems for stimulating interactions between the two areas. · Written by leading researchers in stream ciphers and number theory.

This book is almost entirely concerned with stream ciphers, concentrating on a particular mathematical model for such ciphers which are called additive natural stream ciphers. These ciphers use a natural sequence generator to produce a periodic keystream. Full definitions of these concepts are given in Chapter 2.This book focuses on keystream sequences which can be analysed using number theory. It turns out that a great deal of information can be deducted about the cryptographic properties of many classes of sequences by applying the terminology and theorems of number theory. These connections can be explicitly made by describing three kinds of bridges between stream ciphering problems and number theory problems. A detailed summary of these ideas is given in the introductory Chapter 1.Many results in the book are new, and over seventy percent of these results described in this book are based on recent research results.

In cryptography, ciphers is the technical term for encryption and decryption algorithms. They are an important sub-family that features high speed and easy implementation and are an essential part of wireless internet and mobile phones. Unlike block ciphers, stream ciphers work on single bits or single words and need to maintain an internal state to change the cipher at each step. Typically stream ciphers can reach higher speeds than block ciphers but they can be more vulnerable to attack. Here, mathematics comes into play. Number theory, algebra and statistics are the key to a better understanding of stream ciphers and essential for an informed decision on their safety. Since the theory is less developed, stream ciphers are often skipped in books on cryptography. This book fills this gap. It covers the mathematics of stream ciphers and its history, and also discusses many modern examples and their robustness against attacks. Part I covers linear feedback shift registers, non-linear combinations of LFSRs, algebraic attacks and irregular clocked shift registers. Part II studies some special ciphers including the security of mobile phones, RC4 and related ciphers, the eStream project and the blum-blum-shub generator and related ciphers. Stream Ciphers requires basic knowledge of algebra and linear algebra, combinatorics and probability theory and programming. Appendices in Part III help the reader with the more complicated subjects and provides the mathematical background needed. It covers, for example, complexity, number theory, finite fields, statistics, combinatorics. Stream Ciphers concludes with exercises and solutions and is directed towards advanced undergraduate and graduate students in mathematics and computer science.

Papers presented by prominent contributors at a workshop on Number Theory and Cryptography, and the annual meeting of the Australian Mathematical Society.

Building on the success of the first edition, An Introduction to Number Theory with Cryptography, Second Edition, increases coverage of the popular and important topic of cryptography, integrating it with traditional topics in number theory. The authors have written the text in an engaging style to reflect number theory's increasing popularity. The book is designed to be used by sophomore, junior, and senior undergraduates, but it is also accessible to advanced high school students and is appropriate for independent study. It includes a few more advanced topics for students who wish to explore beyond the traditional curriculum. Features of the second edition include Over 800 exercises, projects, and computer explorations Increased coverage of cryptography, including Vigenere, Stream, Transposition,and Block ciphers, along with RSA and discrete log-based systems "Check Your Understanding" questions for instant feedback to students New Appendices on "What is a proof?" and on Matrices Select basic (pre-RSA) cryptography now placed in an earlier chapter so that the topic can be covered right after the basic material on congruences Answers and hints for odd-numbered problems About the Authors: Jim Kraft received his Ph.D. from the University of Maryland in 1987 and has published several research papers in algebraic number theory. His previous teaching positions include the University of Rochester, St. Mary's College of California, and Ithaca College, and he has also worked in communications security. Dr. Kraft currently teaches mathematics at the Gilman School. Larry Washington received his Ph.D. from Princeton University in 1974 and has published extensively in number theory, including books on cryptography (with Wade Trappe), cyclotomic fields, and elliptic curves. Dr. Washington is currently Professor of Mathematics and Distinguished Scholar-Teacher at the University of Maryland.

It is now a decade since the appearance of W. Diffie and M. E. Hellmann's startling paper, "New Directions in Cryptography". This paper not only established the new field of public-key cryptography but also awakened scientific interest in secret-key cryptography, a field that had been the almost exclusive domain of secret agencies and mathematical hobbyist. A number of ex cellent books on the science of cryptography have appeared since 1976. In the main, these books thoroughly treat both public-key systems and block ciphers (i. e. secret-key ciphers with no memo ry in the enciphering transformation) but give short shrift to stream ciphers (i. e. , secret-key ciphers wi th memory in the enciphering transformation). Yet, stream ciphers, such as those . implemented by rotor machines, have played a dominant role in past cryptographic practice, and, as far as I can determine, re main still the workhorses of commercial, military and diplomatic secrecy systems. My own research interest in stream ciphers found a natural re sonance in one of my doctoral students at the Swiss Federal Institute of Technology in Zurich, Rainer A. Rueppe1. As Rainer was completing his dissertation in late 1984, the question arose as to where he should publish the many new results on stream ciphers that had sprung from his research.

From the world's most renowned security technologist, Bruce Schneier, this 20th Anniversary Edition is the most definitive reference on cryptography ever published and is the seminal work on cryptography. Cryptographic techniques have applications far beyond the obvious uses of encoding and decoding information. For developers who need to know about capabilities, such as digital signatures, that depend on cryptographic techniques, there's no better overview than Applied Cryptography, the definitive book on the subject. Bruce Schneier covers general classes of cryptographic protocols and then specific techniques, detailing the inner workings of real-world cryptographic algorithms including the Data Encryption Standard and RSA public-key cryptosystems. The book includes source-code listings and extensive advice on the practical aspects of cryptography implementation, such as the importance of generating truly random numbers and of keeping keys secure. ". . .the best introduction to cryptography I've ever seen. . . .The book the National Security Agency wanted never to be published. . . ." -Wired Magazine ". . .monumental . . . fascinating . . . comprehensive . . . the definitive work on cryptography for computer programmers . . ." -Dr. Dobb's Journal ". . .easily ranks as one of the most authoritative in its field." -PC Magazine The book details how programmers and electronic communications professionals can use cryptography-the technique of enciphering and deciphering messages-to maintain the privacy of computer data. It describes dozens of cryptography algorithms, gives practical advice on how to implement them into cryptographic software, and shows how they can be used to solve security problems. The book shows programmers who design computer applications, networks, and storage systems how they can build security into their software and systems. With a new Introduction by the author, this premium edition will be a keepsake for all those committed to computer and cyber security.

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.

Once the privilege of a secret few, cryptography is now taught at universities around the world. Introduction to Cryptography with Open-Source Software illustrates algorithms and cryptosystems using examples and the open-source computer algebra system of Sage. The author, a noted educator in the field, provides a highly practical learning experienc

Developed from the author's popular graduate-level course, Computational Number Theory presents a complete treatment of number-theoretic algorithms. Avoiding advanced algebra, this self-contained text is designed for advanced undergraduate and beginning graduate students in engineering. It is also suitable for researchers new to the field and pract