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.