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Details of HW 25/38
Reference: HW 25/38

'Paper on Statistics of Repetitions'

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
Held by: The National Archives, Kew
Former reference in its original department: CCR 151
Legal status: Public Record(s)
Closure status: Open Document, Open Description
Access conditions: Retained Until 2012
Record opening date: 17 April 2012

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