Recent books edited

B. Beckman: Codebreakers: Arne Beurling and the Swedish Crypto Program during World War II, American Mathematical Society, Providence, 2002, 259 pp., $39, ISBN 0-8218-2889-4 All stories about cryptanalytical work prior and during the World War II read like a thriller. The book under review is no exception. The author, the former head of the cryptanalytical section of FRA (The Radio Agency of the Swedish Defence Forces), presents a well of information. Its highlight is the detailed description of Arne Beurling’s solution of the German Siemens machine, one of the most magnificent achievements of cryptanalysis of that time. During the previous century, in the thirties and the first half of the forties, the cryptanalytical work of cryptographic “superpowers” (Poland, England, and USA) became dominated by mathematicians. The transition of secret services to the search of cryptanalytical talents among graduates of mathematics departments probably started in Poland and people like Marian Rejewski became the founders of modern mathematically based cryptology. Well known are the contributions of Alan Turing to the war efforts in Bletchley Park. Arne Beurling is another, though less known, example of a top class mathematician serving his country as a cryptanalytician during the war times. The book starts with an explanation of what a code and a cipher is. Then the author overviews the Swedish cryptanalytical history to the end of the World War II. Most of the book is based on declassified Swedish documents and it traces the work of Arne Beurling in solving various ciphers used by different countries during the war, including the top secret German ciphers. For the reviewer it is particularly interesting to read about the Beurling solution of the cipher used by a Czech resident in Sweden named Vanìk to communicate with the Czechoslovak Government exiled in London. The second part of the book is dedicated to the life and mathematical work of Arne Beurling, a close friend and collaborator of Lars Ahlfors. The book can be highly recommended to anyone interested in the role of mathematics in classical cryptology and in the history of the 20th century. (jtu)