Discover the first unified treatment of today's most essential information technologies— Compressing, Encrypting, and Encoding With identity theft, cybercrime, and digital file sharing proliferating in today's wired world, providing safe and accurate information transfers has become a paramount concern. The issues and problems raised in this endeavor are encompassed within three disciplines: cryptography, information theory, and error-correction. As technology continues to develop, these fields have converged at a practical level, increasing the need for a unified treatment of these three cornerstones of the information age. Stressing the interconnections of the disciplines, Cryptography, Information Theory, and Error-Correction offers a complete, yet accessible account of the technologies shaping the 21st century. This book contains the most up-to-date, detailed, and balanced treatment available on these subjects. The authors draw on their experience both in the classroom and in industry, giving the book's material and presentation a unique real-world orientation. With its reader-friendly style and interdisciplinary emphasis, Cryptography, Information Theory, and Error-Correction serves as both an admirable teaching text and a tool for self-learning. The chapter structure allows for anyone with a high school mathematics education to gain a strong conceptual understanding, and provides higher-level students with more mathematically advanced topics. The authors clearly map out paths through the book for readers of all levels to maximize their learning. This book: Is suitable for courses in cryptography, information theory, or error-correction as well as courses discussing all three areas Provides over 300 example problems with solutions Presents new and exciting algorithms adopted by industry Discusses potential applications in cell biology Details a new characterization of perfect secrecy Features in-depth coverage of linear feedback shift registers (LFSR), a staple of modern computing Follows a layered approach to facilitate discussion, with summaries followed by more detailed explanations Provides a new perspective on the RSA algorithm Cryptography, Information Theory, and Error-Correction is an excellent in-depth text for both graduate and undergraduate students of mathematics, computer science, and engineering. It is also an authoritative overview for IT professionals, statisticians, mathematicians, computer scientists, electrical engineers, entrepreneurs, and the generally curious.

CRYPTOGRAPHY, INFORMATION THEORY, AND ERROR-CORRECTION A rich examination of the technologies supporting secure digital information transfers from respected leaders in the field As technology continues to evolve Cryptography, Information Theory, and Error-Correction: A Handbook for the 21ST Century is an indispensable resource for anyone interested in the secure exchange of financial information. Identity theft, cybercrime, and other security issues have taken center stage as information becomes easier to access. Three disciplines offer solutions to these digital challenges: cryptography, information theory, and error-correction, all of which are addressed in this book. This book is geared toward a broad audience. It is an excellent reference for both graduate and undergraduate students of mathematics, computer science, cybersecurity, and engineering. It is also an authoritative overview for professionals working at financial institutions, law firms, and governments who need up-to-date information to make critical decisions. The book’s discussions will be of interest to those involved in blockchains as well as those working in companies developing and applying security for new products, like self-driving cars. With its reader-friendly style and interdisciplinary emphasis this book serves as both an ideal teaching text and a tool for self-learning for IT professionals, statisticians, mathematicians, computer scientists, electrical engineers, and entrepreneurs. Six new chapters cover current topics like Internet of Things security, new identities in information theory, blockchains, cryptocurrency, compression, cloud computing and storage. Increased security and applicable research in elliptic curve cryptography are also featured. The book also: Shares vital, new research in the field of information theory Provides quantum cryptography updates Includes over 350 worked examples and problems for greater understanding of ideas. Cryptography, Information Theory, and Error-Correction guides readers in their understanding of reliable tools that can be used to store or transmit digital information safely.

Information Theory, Coding & Cryptography has been designed as a comprehensive book for the students of engineering discussing Source Encoding, Error Control Codes & Cryptography. The book contains the recent developments of coded modulation, trellises for codes, turbo coding for reliable data and interleaving. The text balances the mathematical rigor with exhaustive amount of solved, unsolved questions along with a database of MCQs.

Although devoted to constructions of good codes for error control, secrecy or data compression, the emphasis is on the first direction. Introduces a number of important classes of error-detecting and error-correcting codes as well as their decoding methods. Background material on modern algebra is presented where required. The role of error-correcting codes in modern cryptography is treated as are data compression and other topics related to information theory. The definition-theorem proof style used in mathematics texts is employed through the book but formalism is avoided wherever possible.

The NATO Advanced Research Workshop on Enhancing Cryptographic Primitives with Techniques from Error Correcting Codes has been organized in Veliko Tarnovo, Bulgaria, on October 6-9, 2008 by the Institute of Mathematics and Informatics of the Bulgarian Academy of Sciences in cooperation with COSIC, KU Leuven and in the framework of the NATO Science for Peace and Security program. Goal of the organizers was to gather international experts from both fields - coding theory and cryptography - in order to exchange ideas, define new challenges and open problems for future research. These proceedings present the state-of-the-art in the current research on cryptography applying techniques and results from coding theory. Enhancing Cryptographic Primitives with Techniques from Error Correcting Codes is divided into two parts. In the first part the papers based on the lectures of the invited speakers, and in the second part the papers based on the talks of the participants in the workshop are included.

Offers a comprehensive introduction to the fundamentalstructures and applications of a wide range of contemporary codingoperations This book offers a comprehensive introduction to the fundamentalstructures and applications of a wide range of contemporary codingoperations. This text focuses on the ways to structure informationso that its transmission will be in the safest, quickest, and mostefficient and error-free manner possible. All coding operations arecovered in a single framework, with initial chapters addressingearly mathematical models and algorithmic developments which led tothe structure of code. After discussing the general foundations ofcode, chapters proceed to cover individual topics such as notionsof compression, cryptography, detection, and correction codes. Bothclassical coding theories and the most cutting-edge models areaddressed, along with helpful exercises of varying complexities toenhance comprehension. Explains how to structure coding information so that itstransmission is safe, error-free, efficient, and fast Includes a pseudo-code that readers may implement in theirpreferential programming language Features descriptive diagrams and illustrations, and almost 150exercises, with corrections, of varying complexity to enhancecomprehension Foundations of Coding: Compression, Encryption,Error-Correction is an invaluable resource for understandingthe various ways information is structured for its secure andreliable transmission in the 21st-century world.

This text presents a careful introduction to methods of cryptology and error correction in wide use throughout the world and the concepts of abstract algebra and number theory that are essential for understanding these methods. The objective is to provide a thorough understanding of RSA, Diffie–Hellman, and Blum–Goldwasser cryptosystems and Hamming and Reed–Solomon error correction: how they are constructed, how they are made to work efficiently, and also how they can be attacked. To reach that level of understanding requires and motivates many ideas found in a first course in abstract algebra—rings, fields, finite abelian groups, basic theory of numbers, computational number theory, homomorphisms, ideals, and cosets. Those who complete this book will have gained a solid mathematical foundation for more specialized applied courses on cryptology or error correction, and should also be well prepared, both in concepts and in motivation, to pursue more advanced study in algebra and number theory. This text is suitable for classroom or online use or for independent study. Aimed at students in mathematics, computer science, and engineering, the prerequisite includes one or two years of a standard calculus sequence. Ideally the reader will also take a concurrent course in linear algebra or elementary matrix theory. A solutions manual for the 400 exercises in the book is available to instructors who adopt the text for their course.

For many everyday transmissions, it is essential to protect digital information from noise or eavesdropping. This undergraduate introduction to error correction and cryptography is unique in devoting several chapters to quantum cryptography and quantum computing, thus providing a context in which ideas from mathematics and physics meet. By covering such topics as Shor's quantum factoring algorithm, this text informs the reader about current thinking in quantum information theory and encourages an appreciation of the connections between mathematics and science.Of particular interest are the potential impacts of quantum physics:(i) a quantum computer, if built, could crack our currently used public-key cryptosystems; and (ii) quantum cryptography promises to provide an alternative to these cryptosystems, basing its security on the laws of nature rather than on computational complexity. No prior knowledge of quantum mechanics is assumed, but students should have a basic knowledge of complex numbers, vectors, and matrices.

This textbook forms an introduction to codes, cryptography and information theory as it has developed since Shannon's original papers.

This book discusses both the theory and practical applications of self-correcting data, commonly known as error-correcting codes. The applications included demonstrate the importance of these codes in a wide range of everyday technologies, from smartphones to secure communications and transactions. Written in a readily understandable style, the book presents the authors’ twenty-five years of research organized into five parts: Part I is concerned with the theoretical performance attainable by using error correcting codes to achieve communications efficiency in digital communications systems. Part II explores the construction of error-correcting codes and explains the different families of codes and how they are designed. Techniques are described for producing the very best codes. Part III addresses the analysis of low-density parity-check (LDPC) codes, primarily to calculate their stopping sets and low-weight codeword spectrum which determines the performance of th ese codes. Part IV deals with decoders designed to realize optimum performance. Part V describes applications which include combined error correction and detection, public key cryptography using Goppa codes, correcting errors in passwords and watermarking. This book is a valuable resource for anyone interested in error-correcting codes and their applications, ranging from non-experts to professionals at the forefront of research in their field. This book is open access under a CC BY 4.0 license.