>>> From the UK National Archives, two of Alan Turing's crypto-related papers for the GC&CS, the predecessor of the GCHQ (Government Communications Headquarters, Britain's version of the NSA).

Also included here is Turing's 1940 report "describing the methods he and his colleagues at Bletchley Park had used to break into the German Enigma cipher systems." The NSA released a copy in 1996. Below is the copy from the UK National Archives.

**"Mathematical Theory of ENIGMA Machine" (a/k/a "Prof's book") **[PDF - 156 pages]

From the UK National Archives:

Mathematical theory of ENIGMA machine by Alan Mathison Turing. (1) Also known as 'Prof's book'. (2) Pages 8, 124-128 and 131 are missing. (3) A comment dated 8 Feb 1978 is attached to Page 143.

**"Paper on Statistics of Repetitions" **[PDF - 11 pages]

**"The Applications of Probability to Cryptography" **[PDF - 47 pages]

From the UK National Archives:

As the country marks the centenary of Alan Turing's birth, two of his mathematical research papers, believed to have been written whilst he was at Bletchley Park during World War II, have been released by GCHQ to The National Archives.

Because of continuing sensitivity the papers had been retained at GCHQ, but they have now been reassessed as suitable for release.

The papers, called 'Paper on Statistics of Repetitions' and 'The Applications of Probability to Crypt', were written in an era when typographical errors would be corrected by hand and mathematical notation handwritten.

The first, '**Paper on Statistics of Repetitions**', is an informal report in which Turing works out the best statistical means of testing whether two cipher messages use the same key in parts of the message. This was very important in the exploitation of such messages at Bletchley Park.

The second, longer, paper titled '**The Applications of Probability to Cryptography**', demonstrates that Turing was determined to apply rigorous probability analysis to a wide range of cryptanalytic problems of the day. A particular highlight is where Turing uses life expectancy to examine conditional probability. The associated example, 'Hitler is now of age 52', adds piquancy and suggests that the paper was written between April 1941 and April 1942. Bletchley Park's output of decrypts was almost certainly enabled by the techniques in this paper.

Date: 1945 Jan 01 - 1946 Dec 31

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Contains public sector information licensed under the Open Government Licence v3.0.