Page 166: There is a more complete technical description of the Enigma available on-line from the late Tony Sale's Codes and Ciphers in the Second World War. This includes the exact specification of the rotor wirings.
Another very useful on-line explanation is given by Graham Ellsbury on his website The Enigma and the Bombe.
Page 181: In fact the logic of the Bombe had become clear before the beginning of 1940. The material available to me in 1983 did not allow me to document the extraordinary speed of progress in 1939. We now have a document dated 1 November 1939, referring to the 'superbombe. . . now being made at Letchworth. See this Sources page.
It is a significant fact that GC&CS acted, without any delay, on a highly ambitious, very expensive, completely novel engineering project, purely on the recommendation of Turing and Welchman who were new young recruits. They could not even be sure that the Bombe would be of any use, because by the time it was built, the German system might have been upgraded. As it turned out, the risk-taking was amply rewarded. One side-effect was, perhaps, that it gave AT a rather rosy view of how an organisation could jump at his ideas and act with alacrity and efficiency. In 1946 he found the NPL very different. It's also worth noting that all this happened while the much derided Neville Chamberlain was still Prime Minister; the first Bombe was already installed and working when Churchill took over.
Page 183: 'But Alan had seen. . .' This what he called the principle of 'simultaneous scanning'. His explanation of this idea is on page 104 of his typewritten report on the Enigma methods, released in 1996. See the page in the Sources section of this site.
Page 185 and note 4.10: Turing was indeed 'the emissary' to the Polish cryptanalysts near Paris in January 1940. The main reason why I cast doubt on the statement in The Secret War was that Harry Hinsley, when I interviewed him, had thought it unlikely. In fact, the evidence was already available in 1979 but only in a Polish-language source. This book, Enigma by W. Kozaczuk, appeared in an English translation by C. Kasparek in 1984.
It was a pity that I missed this source, but I was able to include it in the 1992 Vintage edition and in all 2012 editions. Kasparek drew on Rejewski's 1975 recollections and gave a very striking passage describing Turing's table talk.
"Why, that's a powerful poison!" said Turing in a raised voice.This passage is quoted on this Sources page, together with further comment on the codebreaking methods used at this period before Turing's first Bombe was ready.
Page 195: A vivid picture of the late 1940 period, when Turing's work on naval Enigma was stymied, is documented by the Operation Ruthless plan of September 1940, conceived by none other than Commander Ian Fleming, later famous as the creator of James Bond. This plan for a 'pinch' was abandoned in October 1940, and Birch reported Turing and Twinn as 'all in a stew' about the cancellation, explaining the desperate need for papers as soon as possible. See the transcription on this site here.
Page 196: AT wrote two papers on the application of Bayesian statistics to Banburismus: The applications of probability to cryptography, document in National Archives HW 25/37,
Paper on statistics of repetitions, document in National Archives HW 25/38.
Page 197: In 1983 I could only guess at the uses of Turing's weights of evidence and what the 'important method called Banburismus' was. My guesses were not bad: in fact Banburismus was a method of first (1) identifying where parts of different messages had probably been enciphered on the same rotor positions (2) using these 'depths' to deduce the identity of the outermost rotor and if possible the middle rotor too. The effect of this would be to reduce the Bombe search time by a considerable factor. This was revealed by Jack Good in his article in Codebreakers, F. H. Hinsley and Alan Stripp (eds.), Oxford University Press (1993), paperback edition with corrections (1994).A very clear account of Banburismus is included in the Cryptographic History of Work on the German Naval Enigma by C. H. O'D. Alexander, who joined Hut 8 in March 1941. The document is in the National Archives at HW25/1. A transcription is available on Graham Ellsbury's website. This account gives many extra details regarding the methods, the people, the dates, and events in the naval war.
Page 205 (page 258 in new edition): It is now very commonly asserted that Winston Churchill issued some statement to the effect that Turing made the greatest single contribution to Allied victory in the Second World war. See for example this BBC article of 2009, which has been much quoted by others. I do not know of any documentary source for this statement, and I have never seen any date or context claimed for when Churchill is supposed to have said or written it. See further comment from an article on the Churchill Centre website by Jonathan Schilling, which considers the claim unlikely to be true. The BBC article has now (2015) been amended to include a disclaimer.
Page 224: With the addition of the fourth rotor, I said, the cryptanalytic problem had become 'only 26 times worse'. But this 26-fold expansion of the space of rotor start positions had the effect that there would be not be enough 'depths' — parts of messages enciphered on the same rotor positions — thus making the Banburismus method impossible. So the situation was in fact much worse than that factor of 26 might indicate.
Page 230: The transmission error that gave away the Fish cipher system was in fact made on 30 August 1941. The error was not quite as simple as that of advancing the key by one place, and the work of teasing out the key was not trivial. It is attributed to J. H. Tiltman (see page 204).
Page 233 (page 294 in new edition): The text lacks an indicator for note 4.48. It should have been placed after the words 'Peter Hilton' at the top of the page. In fact, all three quotations on that page come from Hilton's reminiscences.
There is further material in the Alan Turing Internet Scrapbook: Critical Cryptanalysis