Abstract

Combinatorial design theory is a very active area of mathematical research, with many applications in communications and information theory, computer science, statistics, engineering, and life sciences. As one of the fundamental discrete structures, combinatorial designs are used in fields as diverse as error-correcting codes, statistical design of experiments, cryptography and information security, mobile and wireless communications, group testing algorithms in DNA screening, software and hardware testing, and interconnection networks. This monograph provides a tutorial on combinatorial designs, which gives an overview of the theory. Furthermore, the application of combinatorial designs to authentication and secrecy codes is described in depth. This close relationship of designs with cryptography and information security was first revealed in Shannon's seminal paper on secrecy systems. We bring together in one source foundational and current contributions concerning design-theoretic constructions and characterizations of authentication and secrecy codes.

Combinatorial Designs for Authentication and Secrecy Codes

Authenticity and secrecy are two crucial concepts in cryptography and information security. Although independent in their nature, certain applications require that both aspects hold simultaneously. In the case if unconditional, or information-theoretic, security authentication and secrecy codes can be used to maximise the likelihood of detecting deception. The construction of such codes is of great importance and has been considered by many researchers over the last few decades.

Combinatorial Designs for Authentication and Secrecy Codes describes in depth classical and current interconnections between combinatorial designs and authentication and secrecy codes. Moreover, it provides a tutorial overview on the theory of combinatorial designs. These fundamental discrete structures find applications in fields as diverse as error-correcting codes, statistical design of experiments, cryptography and information security, mobile and wireless communications, group testing algorithms in DNA screening, software and hardware testing, and interconnection networks. In particular, the last few years have witnessed an increasing body of work in the communications and information theory literature that makes substantial use of results in combinatorial design theory.

Combinatorial Designs for Authentication and Secrecy Codes is a succinct in-depth review and tutorial of a subject that promises to lead to major advances in computer and communication security.