Charles Babbage (1791-1871) was renowned in his lifetime as a cryptographer, as well as for his calculating engines. His brief publications on cyphers indicated that he had very effective methods for decypherment, but he did not publish details of any of his methods. Franksen has made a thorough study of Babbage’s manuscripts in the British Library, which contain much material on cryptography. For many years, up to 1857, Babbage worked on a book about “The philosophy of decyphering.” His manuscripts include working notes on decyphering various cryptograms, many of which had been published in the Agony Column of The Times of London.

The tabular cypher, published by Blaise de Vigenere in 1586, was regarded as the most secure type of cypher. It was based on tables of cyclically shifted alphabets, using keywords cyclically. In 1846, Babbage was challenged by his nephew to decypher a message. He found that the message consisted of three parts, each a Vigenere cypher with its own keyword. In his endeavours to solve those cyphers, he reduced the Vigenere method to the compact algebraic formulation: Translation=cypher−key + 1 (modulo the length of the alphabet). That algebraic formulation converted the art of crypotography into a science. It was reinvented and published by de Viaris, in 1888. In 1854, John H. B. Thwaites claimed a prize for his cypher, and he published a cyphered message as a challenge. That cryptogram was examined by Charles Babbage, together with his son Henry Prevost Babbage, who succeeded in finding the key. Charles Babbage published the solution, and remarked that “It may be laid down as a principle that it is never worth the trouble of trying any inscrutable cypher, unless the author has himself decyphered some very difficult cypher.”

Babbage’s work on cryptography provides a well-documented instance of a first-class scientific mind tackling difficult problems, trying a wide variety of approaches, and attempting to formulate clear symbolism and sets of rules. Franksen found that, in order to analyse Babbage’s work, he needed to consider fundamental concepts of the nature of mathematics, the formulation of scientific laws, principles of invariance, group theory, Klein’s Erlanger Program, number theory, the meanings of various forms of measurement, and many other matters. He exhibits some runic inscriptions by Vikings, which include cyphers of types similar to those which Babbage gathered from the Agony Column of The Times of London, a thousand years later. Magic squares are often regarded as one of the most pure and useless forms of mathematics; whereas they have been found useful in cryptography.

In 1871, MacMillan’s Magazine published a very perceptive article on “Cyphers and cypher-writing.” David Kahn has suggested [1] that the article might have been written by Charles Babbage, although it was signed C. P. B. But Franksen points out (p. 317) that the article was actually signed G. P. B. In fact, that article was written by George Parker Bidder, Jr. (1836-1896) who was a renowned mental calculator, like his father of the same name (cf. Minutes and Proceedings of the Institute of Civil Engineers, 1896.) On p. 81, the date of the destruction of Lindisfarne monastery by Vikings should be 793, not 733.

Franksen provides listings of terminal sessions with APL, illustrating various types of cyphers. This book was published for the APL84 Conference at Helsinki in June 1984. It includes a lengthy preface by Herman H. Goldstine, telling of Franksen’s distinguished achievements in systems engineering. This remarkable book should be of interest to many people who are concerned with scientific thinking. It is to be hoped that the book will become widely available.