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The flaw in the jn25 series of ciphers

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Abstract

The principal series of operational ciphers of the Imperial Japanese Navy [IJN] from 1939 to 1945, collectively called JN25, used five-digit code groups which were all multiples of three. This is shown to have been a quite unnecessary major flaw with very considerable consequences.

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... MI Involvement: U.S. Naval Intelligence had broken the JN-25 [19] Code of the Japanese prior to World War II and had been intercepting enemy naval traffic. In analyzing the traffic, CDR John Rochefort (in command of the code-breaking effort) was able to determine the target of the attack by using a false (spoofed) message. ...
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During World War II, The National Cash Register Company built an additive recovery machine for the U.S. Navy. The machine was designed to attack the Imperial Japanese Navy cipher JN-25, which was a superenciphered code. This article describes how that machine, called “Fruit” by the British, implemented three methods of additive recovery: the known-word method, the difference method, and Knepperizing.
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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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