A couple of papers by Alan Turing have appeared on the arXiv.

No, that’s right – *The Applications of Probability to Cryptography* and *The Statistics of Repetitions* are two papers Turing wrote during the Second World War, and they’re now available on the arXiv, transcribed into modern LaTeX by Ian Taylor.

The papers were declassified in 2012, and are currently held by the National Archives in Kew. Somewhat inconveniently, although the Crown Copyright has expired, the National Archives is charging £3.30 to download scans of each paper, which might be the motivation for this re-setting.

When the papers were first declassified in 2012, the National Archives had this to say:

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.

### More information

The Applications of Probability to Cryptography typeset on the arXiv by Ian Taylor (and the original at the National Archives)

The Statistics of Repetitions typeset on the arXiv by Ian Taylor (and the original at the National Archives)

Alan Turing papers on code breaking released by GCHQ, previously.