Review of The Mathematics of Secrets: Cryptography from Caesar Cyphers to Digital Encryption

The Mathematics of Secrets: Cryptography from Caesar Cyphers to Digital Encryption
by Joshua Holden

Princeton University Press, Princeton, NJ, 2017
392 pp., illus. 99 b&w. Trade, $29.95
ISBN: 978-0-691-14175-6

Reviewed by
Phil Dyke
October 2017

This is a 300-odd page book about cryptography, written by a professor of mathematics whose primary interest is in the detailed mathematics of cryptography.  It should be a very difficult read, but it really isn’t.  What the author has managed to do is to write a book that is full of detail but remains interesting for the non-expert reader. How has he managed this? Through his writing style and by using historical anecdotes throughout as a break from relentless mathematics, I mean arithmetic. It helps that the mathematics is about numbers and not much else. All you need in the way of mathematical knowledge is what a 16-year-old might know.

Cryptography started with simple substitution codes, replacing one letter with another (Caesar cipher) thousands of years ago and has gotten gradually more intricate. The book, chapter by chapter, carefully takes the reader through the developments of cryptography and highlights the major developments. These include using more than one alphabet, using computers, stream cyphers, the distinction between private and public key encryption and finally quantum computing. The non-serial nature of quantum computing speeds up the ability to crack ciphers and presents challenges to experts as they design procedures that enable us to continue to use online purchases and banking securely. This reviewer was very pleased to see an acknowledgement of the UK work of James Ellis and Clifford Cocks who came up with the RSA algorithm years before Ron Rivest, Adi Shamir and Leonard Adleman published it in 1978. This algorithm is still heavily used worldwide for internet security, yet Cocks was prevented to tell anyone yet alone publish anything because all his work came under the UK Official Secrets Act (he worked for GCHQ).  By the time some kind of acknowledgement was eventually allowed in 1998, his collaborator James Ellis had already died.

The book cannot really be called an easy read, nor can it be easily digested by readers new to the subject. The expertise of the author lends an authoritative air to the writing, though at times the details can be hard going if not technically difficult.  There is simply a lot there. It is by some way the best book I have seen on this subject and should be useful to students as well as enjoyable to casual readers.