INVITATION TO CRYPTOLOGY

Mathematics and Computer Education, Fall 2004 by Rauff, James V

INVITATION TO CRYPTOLOGY by Thomas H. Barr Prentice Hall, 2002, 396 pp.

When a textbook calls itself an "invitation" to a field, we expect it to be welcoming, informative, and self-contained. We also expect it to tell us something about the history of the field, to reveal its major ideas and current trends, and to provide a foundation for further study. Thomas Barr's Invitation to Cryptology meets all of these expectations.

Invitation to Cryptology begins with a short history of cryptology. Included are the Spartan scytale, Bacon's bilateral cipher, the Wheatstone-Playfair cipher, and the World War I German military cipher known as ADFGVX. Also included in this chapter are brief introductions to Data Encryption Standard (DES) and public-key cryptography, both of which are examined in detail later in the book. Barr also takes a quick view of future trends in cryptography, including zero-knowledge proof protocols and quantum cryptography. This chapter also includes some mathematical preparation through discussion of general functions and permutations. The chapter concludes with some definitions of basic cryptological terms.

The second chapter of Invitation to Cryptology takes a detailed look at transposition and substitution ciphers. Included here are shift ciphers, affine ciphers, monoalphabetic and poly alphabetic substitution ciphers, keyword columnar transposition ciphers, the Vignere cipher, and the Hill matrix cipher. Deciphering techniques based upon letter frequencies are also discussed here, including the Friedman & Kasiski tests. A detailed cryptanalysis of the Vignere cipher is given as an example. All the mathematics needed to understand these techniques is patiently presented as needed (modular arithmetic, matrices, probability).

Chapter three is devoted to stream and block ciphers. The mathematics needed here (Boolean functions, computational complexity, number theory, hash functions) is up a notch in difficulty from the previous chapter, but Barr's careful presentation keeps the reader right on track and in full grasp of what is happening and why. Ciphering schemes and underlying themes discussed in this chapter include binary Vignere and one-time pads, feedback shift registers, Feistel networks, and message authentication codes.

The fourth chapter is a detailed examination of public-key cryptography. Barr maintains his careful development of topics and attention to mathematical prerequisites. He explains prime factorization, the Euclidean algorithm, the Prime Number Theorem, the subset-sum problem, Fermat's Little Theorem, and the Primitive Root Theorem. These mathematical notions are then applied as Barr takes the reader through a lucid explanation of the Merkle-Hellman knapsack, the RSA cryptosystem, and the Diffie-Hellman key agreement protocol. This chapter also includes a discussion of digital signatures and the fiat-Shamir zero-knowledge protocol.

A common strength of these five chapters of Invitation to Cryptology is the high quality and variety of the exercises. Barr's exercises test the student's basic understanding of the mathematics and the algorithms as well as extending the concepts. Several programming exercises also appear at appropriate places in the text.

The final chapter of Invitation to Cryptology begins with two crypotological case studies: DES and PGP (Pretty Good Privacy), a freeware encryption-decryption program. The reader is treated to clear explanations of both systems and is invited to write his or her own implementation of a simplified DES. The chapter (and book) concludes with a discussion of public-key infrastructure (announcing public keys, key distribution, certificate authority, etc.) and the law and legal/ethical issues regarding cryptography.

Invitation to Cryptology is a well-written introduction to the history, basic concepts, and current applications and trends of writing, breaking, and securing ciphered information. Barr is careful to include all the mathematical information necessary to understand the techniques, strengths, and weaknesses of a variety of ciphers. I recommend this book for a general introductory course in Cryptology as well as for self-study.

Reviewed by James V. Rauff

Millikin University