Commentary on Alan M. Turing: The Applications of Probability to Cryptography

Sandy Zabell*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)191-214
Number of pages24
Issue number3
StatePublished - Jul 2012


  • Alan Turing
  • Bayes's theorem
  • I. J. Good
  • Jerzy Neyman
  • Markov chain
  • R. A. Fisher
  • Vigenère cipher
  • crib
  • cryptanalysis
  • deciban
  • depths
  • factor theorem
  • half-deciban
  • index of coincidence
  • letter subtractor cipher
  • odds
  • prior probabilities
  • probability
  • simple columnar transposition
  • theory of repeats

ASJC Scopus subject areas

  • Computer Science Applications
  • Applied Mathematics


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