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ABSTRACT: The bombe was an electromechanical machine devised by Alan Turing and Gordon Welchman for breaking the. German Enigma cipher in World War II. The way in which it used a reductio ad absurdum logic to reduce 263 possibilities to a few is a unique example of ingenious circuit design, which is described in detail. Its relationship to the Polish version of the 'bombe' is explored. The importance of the diagonal board is shown as is the threat that this device faced from the German's use of the `Enigma-Uhr'.
KEYWORDS: Enigma machine, Bletchley Park, Alan Turing, Gordon Welchman, Bombe, diagonal board, Ehigma Uhr, cryptanalysis.
INTRODUCTION
Today we perform cryptographic algorithms using state-of-the-art semiconductor devices, so that long keys and heavy computation can be used. We are accustomed to the idea that cryptanalysis needs stronger computing resources than those employed by the crypto user. But this is a recent phenomenon. For nearly all the long history of cryptology, paper and pencil was the only technology for both cryptography and cryptanalysis. In this period, ingenuity was the main tool of the cryptanalyst. Success depended on the relative simplicity of pencil and paper algorithms.
The change from pencil and paper to electronics went in three stages. First there was the introduction of simple mechanical devices during the 19th Century, but cryptanalysis did not gain much from this change. Then the period from about 1930 to 1950 saw a transition from simple mechanisms to electronics, by way of electro-mechanical techniques, pioneered in telephone switching.
There were not many widely used electro-mechanical designs, but they form a fascinating subject of study because of their short life and their combination of mechanical and electrical ingenuity. Our subject in this paper is a remarkable electromechanical machine for cryptanalysis, the "bombe".
Because the cryptographic machine of World War II have mostly been kept secret by Governments, there are few for study and those of the German forces stand out. There were two on-line cipher machines in wide use, the Siemens and Halske T52, [1-4], and the Lorenz SZ40/42, [5], both appearing in a number of variants as the war progressed. The largest quantity of cipher material was produced by an off-line machine called Enigma.
British cryptanalysts took an interest in all...