Abstract
Several of the cipher machines developed and used as encryption systems before and during WW2 are briefly described, as is a typical additive (cipher) system. Their respective cryptanalyses have both common and distinctive features, resulting in a fundamental difference emerging in relation to the way messages sent in each cipher system could be fully transformed back to the original plain text.
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- 1.
References here are Frank Rowlett: The Story of Magic: Memoirs of an American Cryptologic Pioneer, Aegean Park Press, 1988, and Ronald Clark: The Man who Broke Purple, London 1977. The book Machine Cryptology and Modern Cryptanalysis by C. Deavours and L. Kruh (Artech, 1985) gives some technical information. But the key document is Friedman’s report of 14 October 1940, entitled Preliminary Historical Report on the Solution of the ‘B’ Machine, which is NARA RG457 document SRH-159 and is in the cryptocellar section of Frode Weierud’s website.
- 2.
It is only fair to point out that a female junior member of the staff of GCCS had advocated testing to see whether alphabetical order worked. Some more on this incident is to be found in Mavis Batey’s book Dilly: The Man Who Broke Enigmas.
NARA item RG457, Box 580, NR 1417 Tentative Use of Enigma and other Machine Uses may be found on the Tony Sale web site. It gives information on Jade and Coral.
- 3.
The method of using this redundant encryption is too complicated to explain here. Undoubtedly it was a great achievement. The analogous blunder with the IJA cipher 2468 was exploited in a quite different way. See Chap. 14, particularly its Appendix 2.
Cryptologist Abraham Sinkov of the US Army was shown the Enigma and work on deciphering it at Bletchley Park in January and February 1941. It is probable but not certain that this assisted him in assessing the importance of the early stages of finding patterns in the indicators of cipher 2468 at Central Bureau in Brisbane early in 1943.
- 4.
The Melbourne file is MP1074/7 1/4/1941 to 30/4/1941, barcode 4169362. This gem is buried among thousands of other high-level secret messages of the WW2 era. The British response may well be in MP1074/7 too, but is better left to the imagination. On page 79 of The Man who Broke Purple, Ronald Clark states that Friedman was told before 1930 by the Dutch Army that it was making some use of (civilian) Enigma.
- 5.
Steven Bellovin found an old code book in the Library of Congress which describes the invention of the one-time pad by Frank Miller of California some 25 years earlier. See his paper in Cryptologia 35(3), July 2011, 203–222. It is not clear whether Miller’s idea was ever implemented. It is possible that the idea made its way to Vernam. The principal text in this chapter has been left without incorporating Miller’s contribution to additive cipher systems and the one-time pad.
- 6.
See pages 52–53 of Ronald Clark’s The Man Who Broke Purple.
- 7.
Tiltman’s letter is mentioned by Paul Gannon on page 146 of his Colossus: Bletchley Park’s Greatest Secret. The notes refer to TNA files HW 14/24 of 12 December 1941 and HW 14/46 of 29 May 1942.
- 8.
The person most responsible for this achievement, Bill Tutte, gave an account of his role on 19 June 1998 in the talk FISH and I, now widely available. An original SZ42 is in the library of the Mathematics Department of the University of Uppsala in Sweden. A photograph, by David Kahn, is in Cryptologia, 3(4), October 1979, page 210.
- 9.
The key GYP-1 Bible or Cryptanalysis of JN-25 (NARA RG38, CNSG Library, Boxes 16 and 18, 3222/65) comments on another incident on page 9: ‘This is an illustration of the fact that errors committed by the enemy afford most valuable information as to the nature of his system of secret communication’.
- 10.
On page 270 of his 1984 book Enigma, W. Kozaczuk quotes Peter Calvocoressi, a senior figure at GCCS in WW2, as saying: ‘In order to break a machine cipher, two things are needed: mathematical theory and mechanical aids.’ This applies to some of the non-machine ciphers of the era, and in particular to JN-25. The ‘Hall weights’ of Sect. 15.3 are an example of a mathematical theory.
Stephen Budiansky has written more on this subject. See, for example, Codebreaking with IBM machines in WW2 in Cryptologia 25(4), October 2001, 241–255.
- 11.
Much useful information about the defences of Normandy was picked up by decrypting reports sent back to Tokyo by Japanese diplomats using Purple. See Carl Boyd, Hitler’s Japanese Confidant: General Oshima and Magic Intelligence 1941–1945, University of Kansas Press 1993. Further, the ISK group at Bletchley Park, originally headed by Dilly Knox, was able to read the Enigma traffic of the German intelligence service and so check that all German spies in the UK had been identified and were under the control of the British. Thus the deception campaign was known to be working well.
- 12.
In 1940 the German Army seized a British Typex machine—broadly similar to the Enigma—without the rotors. A decision was made that allocating serious resources into investigating it would not be justified.
In fact some details of the wiring and other aspects of the Enigma and its rotors were initially obtained by bribery from H.-T. Schmidt and later by physical capture. The Typex instructions issued in Australia—no doubt at the instigation of the British—included having a hammer around to facilitate the destruction of the rotors just prior to being captured. More on this matter is in Sect. 13.7.
- 13.
The Lectures at Conference of Chief Cipher Officers of April 1945 survive in the NAA Canberra as item A705 201/23/453. The master plan for RAAF cipher security was orally explained but is not in the written version. Item A705 201/24/510 makes it clear that additive cipher systems were being used less by the RAAF by July 1944 and even less by April 1945. Item A705 201/28/323 (1945) Cyphers—procedure re type X indicators includes on page 46A the quoted comment on insecure encipherment of indicators. The final quote is from A705 201/28/325—Typex indicators.
- 14.
There is great irony here. The JN-25 operators were given written instructions to ‘tail’ and enough actually did so. This practice greatly weakened the security of various JN-25 systems in 1940–1943. Much more on this is given in Sect. 9.22.
- 15.
See Note 5 of Chap. 1.
- 16.
The Australian military used additive systems, particularly in the early stages of the Pacific War. Thus NAA Brisbane file BNO407/4 deals with signals between the armed forces in Queensland in 1942. It was agreed to use ‘Inter-service Cipher G33/2 with comtab tables’ for all transmissions. The NAA Recordsearch index has several entries under recyphering, one of the then current words used to describe the use of additives.
The NAA Canberra file A1196 37/501/407 contains the report of a cipher unit set up on Los Negros, an island east of Manus Island, in March 1944 immediately after its recapture. It is noted that ‘book cipher was found to be inadequate and the use of machines quickly enabled us to overtake the volume of work’. This confirms what one may well have suspected: additive systems were rather clumsy.
Two relevant files are in the A1196 section of NAA. 12/501/90 reveals that the RAAF was producing additive tables in August 1941. 12/501/133 shows that 12 months later the RAN revealed to the RAAF how tabulators could assist in such work.
The book Betrayal at Pearl Harbor by James Rusbridger and Eric Nave (Summit Books, New York, 1991) contains on pages 83–84 sample pages of a JN-25 code book. The sample of additive table that follows has a 12 × 15 display of additives rather than the 10 × 10 mentioned elsewhere in this chapter. Minor variations like this may be disregarded.
- 17.
This appears not to be mentioned in the archives, but may well be important. After the capture the USN had a large sample of IJN telegraphic jargon. It also gained some knowledge of the frequency of the more common words and phrases.
- 18.
In fact the groups in the sample table were selected by letting the computer calculate \(\sqrt{\pi }-\sqrt{e}\) to 400 decimal places. Such methods of generating large numbers of groups without following an evident pattern were not available in WW2. Indirect evidence as to how the Japanese manufactured tables of random digits survives. See Note 10 of Chap. 13.
The matter is not far removed from the problem of choosing book groups for code books. Likewise the randomness of the selection of a starting point in the additive table is important. These matters are also discussed in Sect. 13.6.
- 19.
George Aspden, formerly of CBB, recalled seeing some captured encrypting forms in 1945. They had four lines with the functions shown in the example.
The decryption process needs ‘false subtraction’:
$$\displaystyle{\begin{array}{l@{\qquad }l@{\qquad }l@{\qquad }l@{\qquad }l@{\qquad }l@{\qquad }l@{\qquad }l@{\qquad }l@{\qquad }l@{\qquad }l@{\qquad }l@{\qquad }l} \text{GAT} \qquad &\qquad &\qquad &3049 \qquad &\qquad &\qquad &1442 \qquad &\qquad &\qquad &6243 \qquad &\qquad &\qquad &3526\\ \text{additive} \qquad &\qquad &\qquad &\mathit{8363 } \qquad &\qquad &\qquad &\mathit{0221 } \qquad &\qquad &\qquad &\mathit{1907 } \qquad &\qquad &\qquad &\mathit{5100} \\ \text{book group}\qquad &\qquad &\qquad &5786 \qquad &\qquad &\qquad &1221 \qquad &\qquad &\qquad &5346 \qquad &\qquad &\qquad &8426\\ \qquad \end{array} }$$An extra complication called ‘Op-20-G Usage’ is needed in Chap. 15. In decrypting IJN ciphers the ‘false negatives’ of the original additive table were stored, but not the table itself. The decryption process then took the form:
$$\displaystyle{\begin{array}{l@{\qquad }l@{\qquad }l@{\qquad }l@{\qquad }l@{\qquad }l@{\qquad }l@{\qquad }l@{\qquad }l@{\qquad }l@{\qquad }l@{\qquad }l@{\qquad }l} \text{GAT} \qquad &\qquad &\qquad &3049 \qquad &\qquad &\qquad &1442 \qquad &\qquad &\qquad &6243 \qquad &\qquad &\qquad &3526\\ \text{neg. add.} \qquad &\qquad &\qquad &\mathit{2747 } \qquad &\qquad &\qquad &\mathit{0889 } \qquad &\qquad &\qquad &\mathit{9103 } \qquad &\qquad &\qquad &\mathit{5900} \\ \text{book group}\qquad &\qquad &\qquad &5786 \qquad &\qquad &\qquad &1221 \qquad &\qquad &\qquad &5346 \qquad &\qquad &\qquad &8426\\ \qquad \end{array} }$$The motivation was to replace false subtraction by false addition, less prone to error.
- 20.
The reference is page 3 of part G of the CBTR. ‘To indicate the method of encipherment and materials in use, a four-figure group, the discriminant, preceded the message. This was originally unenciphered, but from August (19)44 was enciphered with materials set aside for that purpose. … Encipherment of discriminants was part of a general scheme to give all traffic the same external features.’ The early naval JN-25 systems were readily distinguished by the practice of transmitting its messages in groups of five digits. However from late 1942 onwards there were JN-25 code books being used with up to five different additive tables concurrently and so discriminants were needed. The word ‘channel’ was the jargon for any one of the combination of code book and additive table.
It was possible to transmit a 4-digit system with four groups of five representing five groups of four. This would have been prone to error.
- 21.
The CBTR, part G, page 9, makes it clear that the group used after the last group on a page of additives was usually the first group on that same page. In effect each page in a book of additives was yet another separate cipher. For the naval additive systems of the JN-25 series the group used after the last group on a page was the first group on the next page. This turned out to be quite important: see the discussion of tailing in Sect. 9.22. In view of the vast number of enciphering systems used for various purposes in different parts of the Pacific Theatre of operations in 1941–1945, it is difficult to determine which practice was more common.
Some later JN-25 codebooks were used with up to five different tables of additives at once. These were called ‘channels’.
- 22.
This particular blunder did happen in WW1. See page 14 of Patrick Beesly’s Room 40. This is confirmed by A. G. Denniston’s comment ‘The Germans, whose folly was greater than our stupidity, reciphered the numbers of the messages thus offering the simplest and surest entrée into their reciphering tables.’ See document DENN1/2 at Churchill College, Cambridge, or Robin Denniston’s Thirty Secret Years (2007).
The CBTR (Part G, page 2) notes that this happened in WW2 IJA codes. It comments ‘Since the serials (serial numbers) ran consecutively they were predictable and therefore of great use in extracting keys’.
The RN had adopted the practice of referring to a message sent at, say, 08.48 (Greenwich mean time) on the tenth day of a month as 0848Z/10. The month would be mentioned only if there was ambiguity.
- 23.
- 24.
The point here is that by adding one suitable fixed group to all the non-primary book groups in a JN-25 code book all the book groups obtained would be multiples of three. The ‘one suitable fixed group’ that achieved this result would be unique. (Highly contrived exceptions to this last remark are to be found in Appendix 4 of Chap. 10.)
Suppose that the following are 20 book groups in a 5-digit additive cipher. They are in fact all scanning, that is the sums of their digits are all multiples of three.
$$\displaystyle{\begin{array}{l@{\quad }l@{\quad }l@{\quad }l@{\quad }l@{\quad }l@{\quad }l@{\quad }l@{\quad }l@{\quad }l} 80169\quad &83997\quad &92208\quad &32949\quad &17580\quad &64995\quad &00933\quad &35604\quad &23985\quad &96423\\ 93294\quad &19515\quad &58113\quad &07320\quad &09774\quad &78765\quad &35655\quad &50502\quad &11367\quad &78492\\ \quad \end{array} }$$The enemy cryptanalyst cannot read the code book, but may be able to calculate the (false) difference between any pair of these primary groups. It is convenient to store this information by selecting one such book group and assigning a specific (but arbitrary) group to it. For example, it may be convenient to take the first to be \(40697 = 80169 - 40572\). Then, to preserve the known differences, the 20 non-primary book groups are each obtainable from the corresponding primary book group by subtraction of 40572. So they are:
$$\displaystyle{\begin{array}{l@{\quad }l@{\quad }l@{\quad }l@{\quad }l@{\quad }l@{\quad }l@{\quad }l@{\quad }l@{\quad }l} 40697\quad &43425\quad &52736\quad &92477\quad &77018\quad &24423\quad &60461\quad &95132\quad &83413\quad &56951\\ 53722\quad &79043\quad &18641\quad &67858\quad &69202\quad &38293\quad &95183\quad &10030\quad &71895\quad &38920\\ \quad \end{array} }$$The recovery of the first batch of 20 groups from the second needs either extra information (see Chap. 12) or special inspiration.
- 25.
The reference is AWM124 4/71. Patrick Beesly’s book Very Special Intelligence gives more information on the use of these codes by the RN. The manual in the AWM makes it clear that by July 1942 the RN was urging the use of one-time pads whenever possible to protect the security both of the message to hand and other messages.
The NAA item A1606 I8/1 Part 2 contains a message dated 22 June 1949 from Britain offering to supply one-time pads for communications between all British Commonwealth countries. By then the quantity of confidential traffic would have been much less than in WW2.
- 26.
Protocols would be needed to prevent re-use of OTP pages.
- 27.
The Sinkov oral history interview is in the National Cryptologic Museum oral history series. See page 31 of the document. Note that the account of the Sio capture given there is somewhat inaccurate. The CBTR has a section on these 3-digit systems.
- 28.
The quote is from Part D of the CBTR. The text was probably written by Professor Room or at least with his active involvement. The word ‘3-digit’ has been dropped from the quoted text as the comments apply with equal force to 4-digit and 5-digit systems. The CBTR may be overstating the difficulty in breaking into a properly used additive cipher.
Possibility (3) in the CBTR extract: ‘The code book must be heavily patterned and these patterns are clear from the differences of groups in the same column when the messages have been set in depth’ is examined in detail in Appendix 1 of Chap. 12.
Stephen Budiansky’s meritorious Battle of Wits gives another account of additive cipher systems. However its main emphasis is on the European Theatre of Operations.
Those attacking the Enigma tended to use ‘cribs’, that is common words or phrases that could be anticipated in a message, in attempts to recover the original setting. This could have been thwarted by the simple device of spelling such crib words badly, such as by randomly inserting the letters ‘Q’ and ‘Y’.
- 29.
Auguste Kerckhoffs in his 1883 paper Cryptologie Militaire (already mentioned in Chap. 1) sets out in Part II six desiderata for military cryptography. By 1937 greater cryptographic sophistication had rather changed the requirements, but four of the six will be given here: (1) the system should be practically, if not theoretically, indecipherable; (4) it should be compatible with telegraphic transmission; (5) it should be portable; and (6) it should be easily used. Chapter 13 applies the maxims of this chapter to the additive ciphers prevalent in Japanese communications in WW2.
- 30.
Bengt Beckman’s book Codebreakers gives on page 54 a Swedish report on exploiting Russian errors with an additive cipher system in 1940: the Russian failure to change a superenciphering (additive) table when a code book was replaced saved the Swedish team several months. Other errors noted in that report resemble those listed in this book.
Chapter 9 discusses the partial change in the JN-25B system made in December 1941.
- 31.
This point is to be found in Tiltman’s Reminiscences, which have survived in NARA College Park RG457 as in Box 1417, NR 4632. It is fully compatible with the views of Wing-Commander Lees. The need to have appropriate personnel designing cipher systems was noted by Kerckhoffs at the end of Part II of his Cryptographie Militaire paper and is repeated from Chap. 1 for emphasis: Do not use new cryptographic systems invented by people without the necessary experience.
And indeed it is repeated by William Friedman on page 157 of the NSA booklet The Friedman Legacy. ‘Cryptographic invention must be guided by technically qualified cryptanalytic people.’
Of course if the specialists are not experienced and sophisticated and instruct operators to ‘tail’ (Chap. 9) then security may be non-existent.
On page 116 of her Dilly: The Man Who Broke Enigmas Mavis Batey notes that ‘the biggest gift the Italians gave us was that they insisted on their operators spelling out full stops as XALTX’. Experienced security people would have stopped that error.
- 32.
If operators in the field need to select letters randomly from the 26-letter alphabet, they can use a common pack of 52 playing cards with each letter written on the face of two cards. The pack can then be shuffled and a card selected. The Herivel tip used at one stage to work out Enigma indicators depended on no such randomising device being used regularly.
- 33.
This maxim is the central theme of Chap. 14. Stereotyping is included here: it is an insecure cipher practice.
- 34.
In particular it was not appropriate for the Japanese Embassy in Washington to use Purple to report on discussions with the US State Department and particularly not on documents emanating from the Department.
- 35.
Breaches in the security of Allied Comint are discussed in Chap. 19. These were not identified by the Axis. Chapter 16 mentions how the German Navy gave away the secret that it was reading the cipher system used by the Atlantic convoys by putting current information from that source in an Enigma message.
It has been argued that the Japanese Army and Navy leadership in WW2 put little faith in any aspect of intelligence and so would not have insisted on this precaution.
- 36.
For example the RAAF 14 W/T Unit on Los Negros, east of Manus Island, in 1944 had Typex machines with special rotors. See NAA Canberra item A1196 37/501/407. The US Army and Navy were very careful with Sigaba/ECM machines for another very valid reason: they did not want to present the Germans with technology that could be used to upgrade Enigma.
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Donovan, P., Mack, J. (2014). Major Encryption Systems. In: Code Breaking in the Pacific. Springer, Cham. https://doi.org/10.1007/978-3-319-08278-3_8
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