This textbook provides an introduction to the mathematics on which modern cryptology is based. It covers not only public key cryptography, the glamorous component of modern cryptology, but also pays considerable attention to secret key cryptography, its workhorse in practice. Modern cryptology has been described as the science of the integrity of information, covering all aspects like confidentiality, authenticity and non-repudiation and also including the protocols required for achieving these aims. In both theory and practice it requires notions and constructions from three major disciplines: computer science, electronic engineering and mathematics. Within mathematics, group theory, the theory of finite fields, and elementary number theory as well as some topics not normally covered in courses in algebra, such as the theory of Boolean functions and Shannon theory, are involved.

Although essentially self-contained, a degree of mathematical maturity on the part of the reader is assumed, corresponding to his or her background in computer science or engineering. Algebra for Cryptologists is a textbook for an introductory course in cryptography or an upper undergraduate course in algebra, or for self-study in preparation for postgraduate study in cryptology.

Autorentext

Alko R. Meijer spent some 30 years in academia, including 18 years as professor in the Department of Mathematics and Applied Mathematics at the University of Natal, gradually moving from pure Algebra into its applications, before eventually entering the field of cryptology as a full-time occupation. He is currently a director of Ciphertec c.c. which provides consultation services on communication and data storage security, including in-house courses in cryptology for industry. He has served a term of office as president of the South African Mathematical Society and has represented South Africa at international standards committee meetings dealing with cryptology.

Inhalt

Prerequisites and Notation.- Basic Properties of the Integers.- Groups, Rings and Ideals.- Applications to Public Key Cryptography.- Fields.- Properties of Finite Fields.- Applications to Stream Ciphers.- Boolean Functions.- Applications to Block Ciphers.- Number Theory in Public Key Cryptography.- Where do we go from here?.- Probability.