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I was reading How frequently did the KMT use telegrams to communicate; from where (roughly) and to whom?, which contains a quote:

Following is a telegram code "dictionary" used by Japan military that already decoded the Chiang Kai-shek KMT army telegram code during World war 2. Even USA military know about such "open code", but USA never notify Chiang Kai-shek about the issue of leaking military secret, because USA itself want to know KMT army movement.

(Original source of quote)

However, no citation is provided, so I'm not sure if the quote's assertions are correct. I remember having read something vaguely similar, possibly in connection with the "China hands". So my question is: is it known if the US managed to eavesdrop on KMT communications during World War 2?

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Evidently, yes. The recently declassified 1946 History of the Signal Security Agency Volume II The General Cryptanalytic Problems has information on this subject. The section covering solution of Chinese secret communications is pp.180-189. (This is the internal end-of-war report of the US Army's codebreaking organization.)

Messages of both the KMT and the Japanese puppet Wang Jingwei regime were read; the report calls them the Chungking and Nanking governments, respectively. A number of different KMT codes (that the SSA nicknamed CNA, CNB, etc, through CNY) were attacked. On page 185 it says "Two of the largest (CNG and CNH), used mainly by Dr. T. V. Soong in his correspondence with the Chinese Mission in Washington (SINODEFENS), had been isolated..."

On pp. 187-188 the extent of results is described:

Progress during the past year has continued in the Far Eastern field. Complete or partial solutions of four major Chungking systems were effected, and translations have been submitted in all of them. Of these four, CNL is one of the principal Chinese Foreign Office systems; it is a code enciphered by substitution and is the first two-part Chinese code to be solved in the Signal Security Agency. Of the other three, CNM (an Air Force code), CNP (a General Staff code), and CNT (a military and naval attache system) are codes enciphered by digraphic substitution or by keyed columnar transposition. CNT, used by attaches throughout the world, employs a total of about 400 transposition sequences and at least 18 paginations of the basic code; most of the traffic is now fully readable as a result of the year's work. One minor system, CNX, was completely solved during the past year, and a special system, introduced for the United Nations Conference on International Organization and made up of transposition encipherments of several known codes, was partially read.

This work was done with the help of the British "Government Code and Cypher School".

The report does not discuss how many messages were read, nor what use was made of their work.

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