Outlines and analyzes combinatorial algorithms for generation, enumeration and search applications. This work introduces the important combinatorial algorithmic techniques. It covers group algorithms, graph isomorphisms, hill-climbing and heuristic search algorithms.

The practice of modeling is best learned by those armed with fundament al methodologies and exposed to a wide variety of modeling experience. Ideally, this experience could be obtained by working on actual model ing problems. But time constraints often make this difficult. Applied Mathematical Modeling provides a collection of models illustrating the power and richness of the mathematical sciences in supplying insight into the operation of important real-world systems. It fills a gap wit hin modeling texts, focusing on applications across a broad range of d isciplines.

An effective blend of carefully explained theory and practical applications, this text imparts the fundamentals of both information theory and data compression. Although the two topics are related, this unique text allows either topic to be presented independently, and it was specifically designed so that the data compression section requires no prior knowledge of information theory.The treatment of information theory, while theoretical and abstract, is quite elementary, making this text less daunting than many others. After presenting the fundamental definitions and results of the theory,...

Although a vast literature exists on the subject of RSA and public-key cryptography, there is no single source that reveals recent developments in the area. This book provides a rigorous and detailed treatment of public-key cryptography (PKC), from RSA, the first public key system devised in 1978, to the latest applications of PKC, including electronic cash, secret broadcasting, secret balloting systems, various banking and payment protocols, high security logins, smart cards, and biometrics. Accessible to anyone from the senior undergraduate to the research scientist, RSA and Public-Key...

Sums of Squares of Integers is the first book to combine elementary methods with analytic methods of modular functions to study the representation of integers as sums of squares. It is the first book to tell how to compute the number of representations of an integer n as the sum of s squares for any s and n. This book is also the first to give a proof of Szemeredi's theorem, an important result in modern number theory. It discusses how the modern theory of modular forms complements and clarifies the classical, fundamental results about sums of squares. This text includes applications to such...

This book explores the depth and breadth of the field of cryptology. It begins by tracing the development of cryptology from inception to modern-day practice. The remainder of the book explores the modern aspects and applications of cryptography, covering symmetric- and public-key cryptography, cryptographic protocols, key management, message authentication, e-mail and Internet security, and advanced applications. Nearly 200 diagrams, examples, figures, and tables along with abundant references and exercises complement the discussion. It is designed such that the non-professional reader may...

Researchers and practitioners of cryptography and information security are constantly challenged to respond to new attacks and threats to information systems. Authentication Codes and Combinatorial Designs presents new findings and original work on perfect authentication codes characterized in terms of combinatorial designs, namely strong partially balanced designs (SPBD).
Beginning with examples illustrating the concepts of authentication schemes and combinatorial designs, the book considers the probability of successful deceptions followed by schemes involving three and four...

Diophantine analysis is an extremely active field in number theory because of its many open problems and conjectures. Requiring only a basic understanding of number theory, Diophantine Analysis is built around the detailed theory of continued fractions and features many applications and examples. The author includes many new topics related to discrete mathematics, such as factoring large integers, error-free computing, and factoring polynomials. He also provides problem sections at the end of each chapter, where open problems are discussed along with other new topics, such as Apry's proof of...

Combinatorial theory is one of the fastest growing areas of modern mathematics. Focusing on a major part of this subject, Introduction to Combinatorial Designs, Second Edition provides a solid foundation in the classical areas of design theory as well as in more contemporary designs based on applications in a variety of fields.

After an overview of basic concepts, the text introduces balanced designs and finite geometries. The author then delves into balanced incomplete block designs, covering difference methods, residual and derived designs, and resolvability. Following a chapter...