Pseudo-random sequences are essential ingredients of every modern digital communication system including cellular telephones, GPS, secure internet transactions and satellite imagery. Each application requires pseudo-random sequences with specific statistical properties. This book describes the design, mathematical analysis and implementation of pseudo-random sequences, particularly those generated by shift registers and related architectures such as feedback-with-carry shift registers. The earlier chapters may be used as a textbook in an advanced undergraduate mathematics course or a graduate electrical engineering course; the more advanced chapters provide a reference work for researchers in the field. Background material from algebra, beginning with elementary group theory, is provided in an appendix.
Algebra and number theory have always been counted among the most beautiful and fundamental mathematical areas with deep proofs and elegant results. However, for a long time they were not considered of any substantial importance for real-life applications. This has dramatically changed with the appearance of new topics such as modern cryptography, coding theory, and wireless communication. Nowadays we find applications of algebra and number theory frequently in our daily life. We mention security and error detection for internet banking, check digit systems and the bar code, GPS and radar systems, pricing options at a stock market, and noise suppression on mobile phones as most common examples. This book collects the results of the workshops "Applications of algebraic curves" and "Applications of finite fields" of the RICAM Special Semester 2013. These workshops brought together the most prominent researchers in the area of finite fields and their applications around the world. They address old and new problems on curves and other aspects of finite fields, with emphasis on their diverse applications to many areas of pure and applied mathematics.
Two domains that describe the behavior of a feedback shift register were developed. These are the sequence and polynomial domains, which are analogous to the frequency and time domains in the description of continuous systems. The domains are related by an expansion of orthogonal functions. The synthesis procedure developed in the polynomial domain consists of four steps: (1) constructing a finite field with the necessary properties; (2) finding the polynomials that correspond to the desired output sequences; (3) obtaining the polynomial that describes the shift register as a product of the polynomials that represent the desired output sequence; and (4) obtaining the feedback network from the polynomial that describes the shift register. In the procedure, the output sequences are mapped to the roots of irreducible polynomials, thereby providing an algebraic description of the register's behavior. To synthesize the shift register in the sequence domain, several properties of the output sequences are needed. The class of sequences and state graphs corresponding to shift-register behavior is established. The cycles and output sequences of a simple, circulating shift register are used to synthesize an arbitrary feedback shift register. (Author).
This book constitutes the refereed proceedings of the 5th International Conference on Sequences and Their Applications, SETA 2008, held in Lexington, KY, USA in September 2008. The 32 revised full papers presented were carefully reviewed and selected. The papers are organized in topical sections on probabilistic methods and randomness properties of sequences; correlation; combinatorial and algebraic foundations; security aspects of sequences; algorithms; correlation of sequences over rings; nonlinear functions over finite fields.
This book constitutes the thoroughly refereed post-proceedings of the Third International Conference on Sequences and Their Applications, SETA 2004, held in Seoul, Korea in October 2004. The 30 revised full papers presented together with 4 invited survey articles were carefully selected during two rounds of reviewing and improvement from initially 59 submissions. The papers are organized in topical sections on complexity of sequences, perfect sequences, sequence construction, sequences modulo z, sequence generator properties and applications, multi-dimensional sequences, optics and OFDM applications, and polynomials and functions.
This book provides a comprehensive treatment of methodologies and applications including CDMA telephony, coded radar, and stream cipher generation.
This volume is concerned with the individual steps in the pathway of retrovirus morphogenesis and maturation starting at the point where the components of the virion have been synthesized within the infected cell and ending once the infectious virion has been released from this cell. An introductory chapter provides a comparative description of the structure and morphology of infectious viruses. A novel feature is the organization according to individual steps in the pathway of virus particle formation rather than according to individual viruses or virus groups as has been done in most previous reviews. This novel concept should allow a comparative discussion of the similarities and differences within this complex virus family regarding the specific aspects of formation of an infectious virion.
Scramblers and shift register generators (SRG) have been used for decades in the shaping of digital transmission signals and in generating pseudo-random binary sequences for transmission applications. In recent years more attention has been paid to this area than ever before due to the change of today's telecommunication environment. This publication presents the theory and applications of three scrambling techniques - Frame Synchronous Scrambling (FSS), Distributed Sample Scrambling (DSS) and Self Synchronous Scrambling (SSS) with an emphasis on their application in digital transmission. Based on the authors' research over the past ten years, this is the first book of its kind.
Now that CDMA has been accepted as a key component of worldwide 3G systems, service providers, capacity planners, engineers and technicians need to understand the best methods and tools for maximizing throughput, capacity, and quality. This book provides that expertise.
From the reviews: "This is a textbook in cryptography with emphasis on algebraic methods. It is supported by many exercises (with answers) making it appropriate for a course in mathematics or computer science. [...] Overall, this is an excellent expository text, and will be very useful to both the student and researcher." Mathematical Reviews
This book constitutes the thoroughly refereed post-proceedings of the International Workshop of Sequences, Subsequences and Consequences, SSC 2007, held in Los Angeles, CA, USA, in May/June 2007. The 16 revised invited full papers and 1 revised contributed paper presented together with 3 keynote lectures were carefully reviewed and selected for presentation in the book. The theory of sequences from discrete symbol alphabets has found practical applications in many areas of coded communications and in cryptography, including: signal patterns for use in radar and sonar; spectral spreading sequences for CDMA wireless telephony; key streams for direct sequence stream-cipher cryptography; and a variety of forward-error-correcting codes. The workshop permits leading researchers on sequences from around the world to present their latest results and recent developments in this important field.
In 1988, for the first time, the two international conferences AAECC-6 and ISSAC'88 (International Symposium on Symbolic and Algebraic Computation, see Lecture Notes in Computer Science 358) have taken place as a Joint Conference in Rome, July 4-8, 1988. The topics of the two conferences are in fact widely related to each other and the Joint Conference presented a good occasion for the two research communities to meet and share scientific experiences and results. The proceedings of the AAECC-6 are included in this volume. The main topics are: Applied Algebra, Theory and Application of Error-Correcting Codes, Cryptography, Complexity, Algebra Based Methods and Applications in Symbolic Computing and Computer Algebra, and Algebraic Methods and Applications for Advanced Information Processing. Twelve invited papers on subjects of common interest for the two conferences are divided between this volume and the succeeding Lecture Notes volume devoted to ISSACC'88. The proceedings of the 5th conference are published as Vol. 356 of the Lecture Notes in Computer Science.
Originally adopted in military networks as a means of ensuring secure communication when confronted with the threats of jamming and interception, spread-spectrum systems are now the core of commercial applications such as mobile cellular and satellite communication. This book provides a concise but lucid explanation and derivation of the fundamentals of spread-spectrum communication systems. The level of presentation is suitable for graduate students with a prior graduate-level course in digital communication and for practicing engineers with a solid background in the theory of digital communication. As the title indicates, the author focuses on principles rather than specific current or planned systems. Although the exposition emphasizes theoretical principles, the choice of specific topics is tempered by their practical significance and interest to both researchers and system designers. Throughout the book, learning is facilitated by many new or streamlined derivations of the classical theory. Problems at the end of each chapter are intended to assist readers in consolidating their knowledge and to provide practice in analytical techniques. Principles of Spread-Spectrum Communication Systems is largely self-contained mathematically because of the four appendices, which give detailed derivations of mathematical results used in the main text.
This volume contains the proceedings of the 11th International Conference on Finite Fields and their Applications (Fq11), held July 22-26, 2013, in Magdeburg, Germany. Finite Fields are fundamental structures in mathematics. They lead to interesting deep problems in number theory, play a major role in combinatorics and finite geometry, and have a vast amount of applications in computer science. Papers in this volume cover these aspects of finite fields as well as applications in coding theory and cryptography.