Commentary on Alan M. Turing: The Applications of Probability to Cryptography
- 11 July 2012
- journal article
- editorial
- Published by Taylor & Francis Ltd in Cryptologia
- Vol. 36 (3), 191-214
- https://doi.org/10.1080/01611194.2012.697811
Abstract
In April 2012, two papers written by Alan Turing during the Second World War on the use of probability in cryptanalysis were released by GCHQ. The longer of these presented an overall framework for the use of Bayes's theorem and prior probabilities, including four examples worked out in detail: the Vigenère cipher, a letter subtractor cipher, the use of repeats to find depths, and simple columnar transposition. (The other paper was an alternative version of the section on repeats.) Turing stressed the importance in practical cryptanalysis of sometimes using only part of the evidence or making simplifying assumptions and presents in each case computational shortcuts to make burdensome calculations manageable. The four examples increase roughly in their difficulty and cryptanalytic demands. After the war, Turing's approach to statistical inference was championed by his assistant in Hut 8, Jack Good, which played a role in the later resurgence of Bayesian statistics.Keywords
This publication has 10 references indexed in Scilit:
- Fisher, Neyman, and the Creation of Classical StatisticsPublished by Springer Science and Business Media LLC ,2011
- A conversation with I. J. GoodStatistical Science, 1996
- Alan Turing and the Central Limit TheoremThe American Mathematical Monthly, 1995
- R. A. Fisher and Fiducial ArgumentStatistical Science, 1992
- R. A. Fisher on the History of Inverse ProbabilityStatistical Science, 1989
- The Interface Between Statistics and Philosophy of ScienceStatistical Science, 1988
- Studies in the History of Probability and Statistics. XXXVII A. M. Turing's statistical work in World War IIBiometrika, 1979
- Frequentist probability and frequentist statisticsSynthese, 1977
- The concepts of irreducibility and full indecomposability of a matrix in the works of Frobenius, König and MarkovLinear Algebra and its Applications, 1977
- The Joint Probability Generating Function for Run-Lengths in Regenerative Binary Markov Chains, with ApplicationsThe Annals of Statistics, 1973