Article

The Flaw in the JN-25 Series of Ciphers, II

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Abstract

From 1939 to 1945 the Imperial Japanese Navy made heavy use of a series of additive cipher systems generically named JN-25 by the cryptanalytic unit of the United States Navy. Most of these consisted of a code-book assigning a five-digit ‘group’, always a multiple of three, to each word or phrase in a very long list and encrypting these by ‘false’ (non-carrying) addition of a five-digit group (‘the additive’) taken from a long table of essentially random such groups. These ‘false sums’ were transmitted, usually by radio, to the intended recipient. The American jargon for these was GATs, or groups as transmitted. (Note 1 given after the main text discusses changes in the source of additives introduced in the later stages of the Pacific War. This is not relevant to the mathematical consequences of such use of only multiples of three, which is the main theme of this paper.) The author's earlier paper explains how this use of multiples of three provided a route for relatively rapid recovery of the additive and, thus, the decryption of intercepts. Another quite different and rather surprising source of insecurity inherent in this use of multiples of three was noted only in 1943 and became the basis of a process code-named ‘Mamba’ needed in 1944. This paper explains one consequence of the statistics underlying Mamba: the use of multiples of three in JN-25 codebooks betrays itself very quickly. Note 2 mentions other aspects of Mamba.

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... My paper [4] describes how, between August 1939 and February 1940, Turing and a few colleagues assisted in developing a method to discover potential decryptions of columns of smaller depth that contain common decrypted 5-groups x i − b. In fact, there is another method which (usually) was more productive. ...
... The paper gives a contrived example of one use of such a device. The following text in a report (December 1942) was written by Turing and quoted in [4]: SUBTRACTOR MACHINE. At Dayton we also saw a machine for aiding one in the recovery of subtractor [5-]groups when messages have been set in depth. ...
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