Codes and cryptography. (English) Zbl 0678.94003

Welsh, Dominic

Oxford Science Publications. Oxford (UK): Clarendon Press. ix, 257 p. £35.00/hbk; £13.95/pbk (1988).

This book is written on the base of a course given to undergraduates at Oxford on the mathematics of Communication Theory. The author sets himself the task of introducing “the subject in as short a space as possible to students with no previous knowledge of the area”. Although the emphasis is on the secrecy systems the consideration in Chapter 4 and Chapter 9 are a completely sufficient introduction into coding theory and computational complexity respectively. The treatment and the problems at the end of these chapters provoke the inquisitive reader to examine more carefully these huge and rich research problems areas.
The first three chapters introduce (in reasonable extent) the reader to the basic notions and results of information theory: entropy, information, the noisy and noiseless coding theorems, Huffman coding algorithm etc. Also, the general source theory (including Markov source) and the approximation of English by the discussed mathematical models of source are considered (chapters 5 and 6).
The rest of the chapters contains a survey of the cryptosystems used from antiquity up to now. At present, in the time of large computer networks and electronic mailing systems, the necessity of keeping the messages confidental and authentificating their sources stimulate the creation of many modern security systems. The main ones are described in the book under review and some of them are: the randomized encryption, the idea of one-way functions, DES and the main public-key cryptosystems. The authentication and digital signature systems are also considered.
The necessary mathematical background is kept to a minimum - only a knowledge of elementary modern algebra and very basic probability are required. In conclusion, I would mention that the book with its extensive bibliography (217 titles) is an excellent introduction to the subject and ensure a good base for the reader to make a choice of future options for his scientific research.

Reviewer: N.Manev

MSC:

94A60	Cryptography
94-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to information and communication theory
68-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to computer science
94B05	Linear codes (general theory)

Keywords:

error-correcting codes; secrecy systems; coding theory; computational complexity; information theory; entropy; coding theorems; Huffman coding algorithm; source theory; cryptosystems; security systems; randomized encryption; one-way functions; DES; public-key cryptosystems; authentication; digital signature systems