Bletchley Park’s work on JN

Abstract This article describes the work done by codebreakers in the Naval Section at Bletchley Park on the primary World War II Japanese naval cipher JN-25. It also describes the relationship between the US Navy’s OP-20-G and Bletchley Park’s JN-25 codebreakers. To put the work at Bletchley Park into context, the initial breaks into JN-25, the changes to JN-25, the formal agreements between OP-20-G and the Government Code and Cypher School, and various techniques that used differencing of additive-enciphered code are described in detail. In many cases, the story is told using the words of the World War II codebreakers. Acknowledgements Three people have been strong influences on the author, and each, in some way, encouraged that the author explore Bletchley Park’s work on JN-25. David Kahn (1930–2024) pre-eminent historian of cryptology. In 2009, the author made his first presentation at a Center for Cryptology History Symposium. David Kahn attended that presentation and after it sought out the author to encourage various explorations and to express his hope that more mathematicians would become active in cryptologic history. Over the years, Kahn commented on the author’s writing and reviews. One of Kahn’s suggestions was: “Use active verbs.” Thomas Ralph Erskine CB (1933–2021) esteemed lawyer, historian of cryptology, and author. In 2008, after an article about the Polish codebreakers that was written by the author appeared in a mathematics journal, Ralph contacted him to say that he “could have made it better.” For the next thirteen years, Ralph nudged the author into several explorations, provided references, commented on the author’s writing, and sent titles of books that should be reviewed – and he made an important introduction. Edward Hugh Simpson CB (1922–2019) statistician, Bletchley Park codebreaker, and civil servant. In 2011, Ralph Erskine (electronically) introduced the author to Edward Simpson. For the next eight years, Edward patiently explained the work of Bletchley Park’s JN-25 Cryptographic Party while the author described what he had learned about the work done by OP-20-G on JN-25. In statistics, the Simpson Paradox and Simpson’s Index of Diversity are named after Edward. Disclosure statement No potential conflict of interest was reported by the author(s). Notes 1 Colombo is located in Sri Lanka (formerly Ceylon) in the Indian Ocean. FECB returned to Colombo in September 1943. 2 Kilindini Harbour is located inland from Mombasa, Kenya on the east coast of Africa. 3 Erskine (Citation2006, 5) claims that Joseph Wenger, OP-20-G deputy director and head of the cryptanalytic section, viewed Naval Section as primarily existing to keep Bletchley Park informed of Japanese naval codebreaking developments. 4 When Kahn was preparing to give the first Henry F. Schorreck Memorial Lecture (24 May 2007) and was searching for problems to present in his talk “The Future of the Past” (Kahn Citation2008), Ralph Erskine suggested that one of the problems should be the origins of differencing, but Kahn did not include it in his presentation. 5 Code A was organized by categories and was a one-part code within each category. 6 The garble check was a method of error detection. Error detection requires the creation of a pattern that, when absent, indicates that an error has occurred. Codebreakers search for patterns in what appears to be randomness; therefore, the error detection pattern was something that could be exploited by the codebreakers. 7 It should be noted that commonly used words and phrases had more than one clear code group assigned to them. 8 In mathematical terminology, false addition means addition of digits modulo 10. 9 There were 100 additive strips in total. 10 This situation is analogous to attacking a machine cipher after the details of the machine and the indicators have been recovered: the machine can be set according to the indicators, and the plaintext can be read. 11 A US Navy study described results from their exploring ciphers 42 through 60. See (Office of the Chief of Naval Operations Citation1946, V-D-1 – V-D-6. 12 Kilindini codebreakers discovered these three limitations: No digit could occur more than twice in the same five-digit additive (“The Three-figure Rule”). Consecutive additives in a line never had the same first digit. The ten additives in a column had different last digits. 13 The National Cryptologic Museum Online Collection contains the image of a small basket (Object ID 2007.1203.1547) that “contained a set of four-digit numbers, which were drawn by hand” and was “used by the Japanese in preparing books of random additive numbers.”. 14 Subtraction, like addition, was done digit-by-digit. Because addition was done without carries, subtraction was done by borrowing as needed. In mathematical terms, subtraction, like addition, was done modulo 10. For example, subtracting 8 from 7 is thought of as subtraction 8 from 17, and the result is 9. Similarly, subtracting 6 from 2 is thought of as subtracting 6 from 12, and the result is 6. 15 Often, the British terminology for additive-enciphered code was “long subtractor.” “Long” refers to the long list of additives contained in the additive table. “Subtractor” refers to a preference to encipher and decipher using subtraction for both rather than what is described above: add to encipher and subtract to decipher. Bletchley Park codebreaker Tony Phelps (See Footnote 51.), using four-digit code groups and additives, described the process. “As you have seen, when a person is enciphering a message with an additive, he adds the code group (say 4713) to the key (say 1624) to get the group he transmits (5337). But the recipient then has to subtract the key from what he receives to get back the original group. [Adding to encipher and subtracting to decipher often caused confusion.] If, however, the key is used as a subtractor, then the problem cannot arise. The sender subtracts his code group 4713 from the key [1624] to get 7911 [which is what is transmitted]. The recipient similarly subtracts 7911 from the key [1624] to get back 4713.” (Phelps Citationn.d.(b), 10) 16 To subtract the additive 04486 from the enciphered code group 53948 using the conversion square shown in , the cipher clerk would search down column 0 (additive digit) to locate the digit 5 (enciphered code group) and then determine the digit of the row 2 (clear code group). Similarly, down column 4 to digit 3 would determine row 4, down column 4 to digit 9 would determine row 3, down column 8 to digit 4 would determine row 9, and down column 6 to digit 8 would determine row 6. Therefore, the clear code group would be 24396. 17 The additive indicator group is partially determined by the last five digits of the date/time indicator in reverse order (which is why those five digits are repeated at the end of the message). 18 David Kahn did not use the term depth in The Codebreakers. Kahn used the term superimposition, which is the term used by Kerckhoffs in 1883 in La Cryptographie Militaire. Kahn (Citation1996, 236) repeats a portion of an example of superimposition given by Kerckhoffs (1883, 176). The example in La Cryptographie Militaire consists of 13 short messages (between 14 and 29 characters each) that have all been enciphered using the same running key. 19 Edward Hugh Simpson Citation1996 (1922–2019) was a statistician and British civil servant. He came to Bletchley Park in October 1942 as a member of the Italian Naval Section. After Italy left the war in September 1943, he was asked to lead the JN-25 Cryptographic Party. In 1949 he published a paper that described what would be called Simpson’s Index of Diversity, which was based on work done at Bletchley Park. In 1951 he published a statistical result now called Simpson’s Paradox. Simpson was a civil servant in the Department of Education and Science rising to deputy secretary. He retired in 1982 (Christensen Citation2019). 20 It is appropriate to note that differencing depends on addition having the mathematical property of being commutative. False addition is commutative, but the conversion squares that were implemented in February 1945 were not commutative. Therefore, differencing could not be used on versions of JN-25 that used conversion squares (which began on 20 February 1945). 21 See (Kahn Citation1996, 1065, endnote for page 440). See also comments about Hardie’s example that appear in Section 4.9 of this article. 22 Kahn in his “Preface” to The Codebreakers (Kahn Citation1996, xiii) mentions Hardie “foremost” among those who helped him in the preparation of the book. Hardie (1920–1999) was an El Paso ophthalmologist. He graduated from Texas A & M in December 1941 with a degree in electrical engineering and enlisted in the Army the following month. Hardie was an officer and served in a Washington, DC code room, landed in France about one month after D Day, and returned to Arlington Hall at the end of the war. He left the Army and began medical school at Johns Hopkins. Hardie describes his cryptologic experiences in “Cryptographer’s Way,” which is available online (Hardie Citation1967). 23 See (Kahn 1967, 1065, endnote for page 440). 24 Kahn (1967, 238) nicely and briefly describes this. 25 JN-11 was introduced on 1 March 1943 as an auxiliary fleet cipher and merchant shipping cipher. JN-11 was similar in structure to JN-25; it was additive-enciphered code with four-digit code groups. Valid code groups were four-digit numbers that had a remainder of one when divided by three. 26 Ralph Erskine suggested 1941 as the date of the appendix. 27 The reference to Captain Morgan is (Office of the Chief of Naval Operations Citationn.d.(c), V-1). 28 Initially Morgan was a civilian in the Foreign Office, but later he served in the Army Intelligence Corps. Until April 1941 Morgan served in Hut 5, and, from 1941, he served in the Research Section and became its Head. Morgan rose to the rank of Major. 29 Bletchley Park Research Officer Thomas Cheetham pointed out three other possible authors: Edward Morgan, John O’Connor Morgan, and Donald Cecil Morgan. Edward Morgan served in the Royal Navy Volunteer Reserve (RNVR) and was a member of Naval Section at Bletchley Park working on Japanese ciphers from 1943 until 1945. John O’Connor Morgan also served in the RNVR and worked from August 1944 until 1945 at Bletchley Park as a Japanese translator. Donald Cecil Morgan was an Army officer working in Naval Section on JN-11 from October 1943 until October 1945. The appendix reads as if it were written by a mathematician, and if that were true that would suggest Gerry Morgan. Ralph Erskine attributed the appendix to Gerry Morgan. Additional evidence in favor of Gerry Morgan is that when the Bletchley Park JN-25 codebreakers were stuck trying to attack JN-25N-62 Gerry Morgan and John Tiltman became involved in the attack (which was unsuccessful for both Bletchley Park and OP-20-G). 30 Hollerith machines were electromechanical tabulating machines that were invented by Herman Hollerith for the 1890 US Census. The now common terminology is “IBM machines.” 31 Whelan comments that the initial installation of Hollerith equipment was made in May 1940. 32 Because the difference a – b is known, it only necessary to know or assume one of a and b; the other can then be determined. 33 Donovan and Mack (Citation2014, 195 – 196) use relation 2 to determine b and c in terms of a. 34 As an example, for JN-25 Code L, which will be discussed later, the 100 most frequent clear code groups were 17.2% of the groups that appeared in messages; the 200 most frequent were 25.6%; and the 400 most frequent were 35.9% (Simpson Citation1945a HW 8/149, inserted between pages 12 and 13). 35 Rather than recovering additives that would have to be subtracted from the enciphered groups to recover the clear code groups, British and American codebreakers recovered “subtractors” – the numbers that when added to the enciphered groups recovered the clear code groups. For example, in column 1 of , the subtractor that has been recovered is 22435. 22435 + 06009 = 28434, 22435 + 92851 = 14286, 22435 + 45085 = 67410, 22435 + 70518 = 92943, 22435 + 82206 = 04631 (which is marked with an “x” because it does not scan), and 22435 + 28808 = 40233. The corresponding additive is 88675; subtracting 88675 from each of the enciphered groups would yield the same results. Notice that 22435 + 88675 = 00000; 22435 is the “negative” of 88675. See Footnote 15. 36 A comment on page V-A-9 states that in actual practice a difference table is not usually used when adjacent columns have been recovered. In the example of , based on the adjacent columns, clear code groups that are likely to appear in column 2 can be guessed. 37 Simpson (Citation2011(b)) is a brief description of the use of a difference table at Bletchley Park. 38 “A/T” refers to “Auxiliary table” or “Alternate table.” The meaning of “A/T following two groups” is that the next two clear code groups should be interpreted by their alternate meanings in the auxiliary table. 39 The corresponding subtractor would be 15421. 40 94275 + 95689 = 89854 and 89172 + 95689 = 74751. 41 Also included in Office of the Chief of Naval Operations (Citationn.d.(c), R.I.P. 214), is an interesting section titled “Weakness of Differencing in a Four-digit Code.” (Office of the Chief of Naval Operations Citationn.d.(c), V-6–V-11) It is an explanation of why four-digit additives that “look good” can be incorrect. The basic problem is that when working with four-digit groups, considering the differences of a 100-group difference table, the number of high frequency clear code groups is a much larger percentage of the total number of groups than if the code were five-digit. Also, the number of possible differences of clear code groups is smaller. Therefore, it would be more likely that a difference that occurred in two columns resulted from different pairs of clear code groups. The conclusion is that using differencing to recover additives from five-digit code is more likely to be correct than using differencing to recover additives from four-digit code. It appears that this section was written by OP-20-G. This weakness is likely the reason that OP-20-G searched for the stronger relations of Morgan’s Method when attacking JN-11. 42 The theorem is named after the English statistician and Presbyterian minister Thomas Bayes (1701–1761). The theorem was published in 1763 based on Bayes’ notes. Statistical thought can be divided into Bayesian and frequentist, the latter being the more familiar – it is what is taught in “general education statistics.” Frequentists base their results on frequencies of events after conducting many trials. Bayesians begin with some “prior knowledge” and then modify that knowledge as evidence for or against an event is accumulated. Because cryptanalysts cannot typically conduct experiments but must rely on the intercepts that they have been given, using Bayesian statistics is common in cryptanalysis. 43 John William Scott “Ian” Cassels (1922–2015) began serving at Bletchley Park in 1943 after receiving an MA in mathematics from Edinburgh University. He was assigned to the JN-25 Cryptographic Party. He received his PhD in mathematics from Trinity College, Cambridge in 1949 and was immediately elected a Fellow. In 1967 he became the Sadlerian Professor of Pure Mathematics. He explored various areas of number theory and received numerous honors and awards for his mathematical accomplishments. 44 Marshall Hall, Jr. (1910–1990) received a BA in mathematics from Yale University in 1932 and was awarded a fellowship that allowed him to spend one year at Trinity College, Cambridge working with the famous mathematician G. H. Hardy. Upon returning to the United States, Hall accepted a position with an insurance company, but in 1934 he was offered and accepted a position as a graduate student at Yale. He received his PhD in 1936 under the direction of Øystein Ore, but he was also guided by Howard Engstrom, who directed OP-20-G’s machine research section during World War II. In 1946, Hall accepted a position at The Ohio State University, and in 1959 he moved to the California Institute of Technology. During the Korean War, Hall returned to service as a codebreaker. Hall was a well-known group theorist and combinatorist who received numerous awards for his mathematical achievements. 45 This reference is to “Cryptographic History of the Work on German Naval Enigma.” 46 Prior to breaking the indicator system, codebreakers might try to align messages by searching for “double repeats” in two messages. “Double repeats” means that two enciphered groups appear exactly the same distance apart in two different messages. Then a possibility is that these double repeats occurred because the same pair of clear code groups were enciphered by the same pair of additives in each message. The US Navy developed a scanner Copperhead I that searched for double repeats (See Christensen, Antrobus, and Simpson Citation2019, 97–98.). 47 It would not be obvious, for example, that column 64 was 5 columns to the left of column 19 or that row 95 was 5 rows above row 16 as they are arranged in . 48 Hall was a liaison on Japanese matters to Bletchley Park from January to July 1944. 49 Simpson and his colleague Ian Cassels wrote an internal history “GC&CS Naval Cryptanalytic Studies Volume IX: The Japanese Fleet General Purpose System II,” which describes Bletchley Park’s implementation of Hall’s Weights, but it is still withheld by Government Communications Headquarters (GCHQ). Former GCHQ Historian Tony Comer commented in the “Forward” to Joel Greenberg’s The Bletchley Park Codebreakers in their own Words that: “I was regularly challenged, for example, to release material about the cryptanalysis of Japanese systems but consistently refused: the sensitivity is not in what systems were solved, but in how cryptanalysts approached the tasks of breaking them.” (Greenberg Citation2022, 8). 50 OP-20-G did, however, experiment with Hall’s Weights and developed two other simpler systems of weights that could be implemented by machines. (See Christensen, Antrobus, and Simpson Citation2019, 114–126). 51 Anthony John (Tony) Phelps was a Foreign Office civilian at Bletchley Park beginning in December 1942. He was initially assigned to Naval Section as a cryptanalyst on Italian Navy ciphers. After Italy left the war, he moved to Japanese Navy ciphers, including JN-25 and JN-11. From August 1944 until the end of the war, he served with the FECB in Colombo. 52 Holtwick (Citation1971, SRH 355, 433) notes that a 6 October 1941 letter from Lietwiler acknowledges the arrival of a Jeep IV at Station CAST. 53 “Jeep” likely comes – phonetically – from the designation GYP that appears in OP-20-GYP. OP-20-G designated US Naval Communications. Y designated cryptanalysis. P designated Pacific. IV possibly refers to “equipment.” The term “jeeping” seems to be used in OP-20-G documents to describe the use of a difference table. 54 The Depth Analyzer that is pictured appeared in a temporary exhibit at the International Spy Museum during spring and summer 2021. During that exhibit, the date given for the analyzer was 1942. 55 In this article, what is identified in as an M-4 machine can now also be identified as a “Parke Machine” or “RIP-71” based on a comment by US Navy codebreaker Jack Holtwick (Citation1971, SRH 355, Appendix 90G). Parke refers to US Navy codebreaker Lee W. Parke. 56 The machines apparently resulted from a promise by Howard Engstrom, head of the research section of OP-20-G during an October 1943 visit to Bletchley Park. (McIntyre n.Citationd. HW 8/55, 59) See Section 5.3. 57 “Fruit” is an informal British term for a slot machine. The NCR machine was called “Fruit” because of the similarity of its appearance to a slot machine. 58 A column of enciphered groups that were in depth could be entered on the machine, and a potential additive could be subtracted from all of them in one operation. The patterns of the colors of the digits in each row signaled scanning or not. 59 The drawing was made by German mathematician/codebreaker Eric Hüttenhain. (See (Weierud and Zabell Citation2020, 102–104) for information about Hüttenhain). 60 Dahkle’s article uses material from a 1955 unpublished University of Munich thesis Hilfgeräte der Kryptographie by Willi Jenson, who served as an electrical engineer in OKW/Chi (see Dahkle Citation2020, 62–63). 61 OP-20-G also had a device called “Mathew” (or “Matthew”) that falsely subtracted (or added) groups from two Letterwriter tapes (Christensen and Antrobus Citation2015, footnote 36, 225). 62 Weierud and Zabell (Citation2020, 106) mention the Witzkiste and refer to TICOM I-31 (See TICOM I-31, 21–22). 63 For information about Rohrbach see Weierud and Zabell (Citation2020, 130–131). 64 A nearly identical description of differencing appears in notes by David Kahn of a 5 May 1962 interview with Rohrbach. (Kahn Citation1962). 65 On the other hand, Fabian in his 4 May 1983 oral history interview, which was also conducted by Robert D. Farley who interviewed Whitlock, commented that he did not remember the incident nor did he remember Anderson (Fabian Citation1983, 30). 66 This document was provided to the author by Ralph Erskine. 67 Captain Jack Holtwick noted in SRH 355 that “Immediately after 7 December 1941, the [Fourteenth Naval District which was headquartered at Pearl Harbor] was assigned joint responsibility for JN-25. In reply to a request a list of the one hundred highest frequency groups was supplied by dispatch and used by HOLTWICK as the basis for a difference table produced by machine which was invaluable in additive recovery. Within a matter of a very few days the cryptanalytic section of the unit was fully engaged in work on JN-25.” (Holtwick Citation1971, SRH 355, 399). 68 Foss noted that subtracting ciphertext messages and looking for repeated differences in different columns was being used to attack JNA 10 in spring 1941 (Foss Citationn.d., HW 8/51, 24). 69 On the other hand, Edward Simpson in his Bletchley Park Oral History commented that the codebreakers in the Italian Section who worked on the Libia subtractor cipher (and who were later added to the JN-25 Cryptographic Party) were not an important customer of the Hollerith Section and that he did not recall ever getting analysis done by the Hollerith Section (Simpson Citation2012, 12). 70 Frank Rowlett, when describing the training that he and the other “SIS first-codebreakers” received, does not indicate any emphasis on enciphered codes. Their codebreaking skills were primarily developed by attacking hand ciphers and machine ciphers. They did have experience constructing codes. (Rowlett Citation1998). 71 Brigadier John Hessell Tiltman (1894–1982) was one of the most significant Bletchley Park codebreakers. He joined the military in September 1914 and served in France from October 1915 until May 1917 where he was wounded. In 1918 Tiltman served with the British military mission in Siberia, and in 1920 he was assigned temporary duty with GC&CS. This assignment led to his working as a codebreaker of Russian diplomatic ciphers in India. In 1925 Tiltman retired from the army but continued to work as a civilian codebreaker. He was recalled to military service as a codebreaker for World War II. During the 1930s Tiltman broke a series of Japanese military ciphers. One in particular would have an impact on World War II. On 1 December 1937, the Japanese military introduced an additive-enciphered code that Tiltman broke in September 1938 while at Bletchley Park during the Munich Crisis. The breaking of that cipher led to his solution of JN-25. He was primarily known for his work on non-machine ciphers, but he recovered the nearly 4000 characters of Tunny key that led to William Tutte’s solution of Tunny. He was a prime mover behind the special relationship that developed between British and US codebreakers. Tiltman retired from GCHQ in 1964 but served as a special consultant at NSA until 1960. For information about Tiltman see (Clabby Citation2007), (Erskine and Freeman Citation2003), and (Liberty Citation2022). 72 Hugh Foss, who directed Bletchley Park’s Naval Section I J, spreads the credit for breaking JN-25 to include others: “In the Autumn of 1939 Captain (later Lt. Colonel) [Richard] Pritchard, [Charles] Barham and [Malcolm] Burnett, with help from Tiltman, had broken the Naval five-figure cypher (JN 25) on material sent home from Singapore and Burnett had taken it out with him to F.E.C.B.” (Foss n.Citationd., HW 8/51, 6). 73 Agnes Meyer Driscoll (1889–1971) was a legend in US Navy codebreaking. She joined the Navy as a chief yeoman in 1918 working in the Code and Signal Section of Naval Communications. For a brief time beginning in 1923 she took a position with Edward Hebern’s cipher machine company. In 1924 Driscoll returned to the Navy becoming part of the Research Desk. She first broke the transposition of the Japanese Red Book Code. This success was followed by her breaking of the Red Book’s successor the Blue Book – also code enciphered by transposition. Both of these ciphers were ancestors of JN-25. In 1940, Driscoll made the first US break into JN-25. Then the Navy assigned her to Enigma. Driscoll ignored advice from the British and refused to use machine methods; her attack on Enigma involved construction of a catalog – a method that British Enigma codebreakers declared unlikely to work. In fact, Driscoll had little impact on codebreaking after her work on JN-25. Driscoll retired from the NSA in 1959. For information about Driscoll see (Johnson Citation2015). 74 British codebreakers viewed the fifth digit as being appended to the four-digit page number-line number and then enciphered by a five-digit additive. American codebreakers viewed the four-digit page number-line number as being enciphered by a four-digit additive and then a fifth digit was appended. 75 Recall that each three-digit page number was a multiple of 3 minus 1. If the page numbers were 3m − 1 and 3n − 1 and the additive was additive, then the enciphered starting points would have been (3m – 1 + additive) and (3n – 1 + additive). The difference of these enciphered groups is (3m – 1 + additive) − (3n – 1 + additive) = 3m – 3n = 3(m – n), which is a multiple of 3. 76 Donovan and Mack (Citation2014, sections 9.5–9.7) speculate slightly differently how Tiltman determined that the additive pages numbers differed by multiples of 3 and how he determined that the clear code groups were divisible by 3. 77 This undated document was provided by Ralph Erskine. It describes the breaking of the encipherment of the starting points that was in use from the introduction of JN-25 on 1 June 1939 until 1 October 1940. 78 US Naval Intelligence had received copies of the Red Book Code from entries into the Japanese council in New York. The Research Desk in Naval Communications was established to exploit that codebook. The Red Book Code was enciphered by transposition. The transposition cipher was broken by Agnes Driscoll. She and her Navy codebreaking team later recovered both the transposition and the codebook for the Blue Book Code. 79 The NCR additive recovery machine to which Turing’s report refers is described in (Christensen Citation2014) and in (Donovan and Mack Citation2014, 169–171). See also . 80 See (Christensen Citation2014, 176). 81 Turing’s visit to Washington occurred just prior to but on the same US visit as his visit to Dayton. 82 The participants were: M. P. Charlesworth, P. E. Charvet, D. W. Lucas, L. P. Wilkinson, A. M. Turing, H. M. Last, G. R. Driver, T. F. Higham, and C. H. Roberts. 83 The 3 January sessions were “Short historical sketch,” morning, Denniston and “Transposition,” afternoon, Oliver Strachey. The 5 January sessions were “Operational intelligence,” morning, W. F. Clarke and “Double transposition,” afternoon, Oliver Strachey. (Short Course Citation1939, HW 62/21). 84 Bletchley Park historian David Kenyon suggests that the initials refer to Helen Clara Lunn, who was a veteran of Room 40 and worked in the Diplomatic Section on Russian intercepts. 85 Several documents in the William Friedman Collection of Official Papers might provide a bit more evidence that Tiltman discussed his 1938 codebreaking during the January 1939 short course. In April 1942, when visiting the United States, Tiltman presented to Friedman copies of materials from a Signal Intelligence Course. Volume I has a sticker labeling the document as “Col. Tiltman’s S. I. Course.” Included in that course is an exercise that involves a code having clear code groups that are divisible by 3. (Tiltman’s S. I. Course, Citation1942 a,Citationb,Citationc,Citationd,Citatione) These courses were conducted in Bedford. Codebreaker Tony Phelps describes what he was taught in (Phelps n.Citationd,(a), 17–22) and (Phelps Citationn.d.(b), 3 – 10). Phelps commented that the course was designed to “demonstrate cryptographic skills and develop cryptographic techniques.” (Phelps Citationn.d.(a), 22) Tiltman, on the other hand, commented that the course “was supposed to assess what the best use of a particular man was. … [It] was entirely unpractical.” (Tiltman Citation1978b, 34) Foss stated that: “The ISSIS course – Inter Service Special Intelligence School – had been started by Tiltman to select, train and give confidence to potential cryptanalysts.” (Foss n.Citationd. HW 8/51, 20). 86 Researcher and writer Joel Greenberg, who has written about Alastair Denniston and Gordon Welchman, states that: “[Alan Turing] was not involved in breaking Japanese code and cipher systems.” (Greenberg Citation2022, 303). 87 GC&CS also broke both codes. Rijneveld (Citation2013) describes how the Dutch SIGINT unit Kamer 14 in the Dutch East Indies broke the Blue Book Code. 88 Changes were made in AD which then became the Flag Officers’ cipher. 89 Pfenningwerth’s quotes from Nave come from Nave’s unpublished autobiography. 90 Several codebreakers from Sydney University became part of SIB. See Donovan and Mack (Citation2014, 71–73). 91 After March 1942, JN-25 was regularly read until the end of the war with the exception of 38 days ending in May 1943 (when JN-25E-19 was implemented with a new cipher and a change from Use 1 to Use 2) and from 25 July until 15 October 1944 (when JN-25N with grilles was implemented). (The History of GYP-1 n.Citationd., 117) Not mentioned in this US Navy comment is the introduction of the ordinate ciphers in December 1943. 92 There is some speculation that the division of JN-25 into channels occurred because the Japanese had read war correspondent Stanley Johnston’s report on the Battle of Midway that first appeared in the Chicago Tribune on 6 June 1942. Johnston’s story revealed information that should have suggested to the Japanese that the US Navy had obtained information about the Japanese plans to attack Midway from JN-25 intercepts. On the other hand, the number of Japanese messages in JN-25 had increased dramatically since the opening of the war in the Pacific, and splitting JN-25 into channels was a reasonable step. For more information about the incident involving Johnston, see (Carlson Citation2017). 93 Hugh Foss, William Keith, Gordon Flintham, Daphne Crouch, Dora Mackenzie, June Campbell, Jean Clarkson, Captain R. Divers, Pat Ranken, George Mayne, Hayden John, Leslie Brown, Basil Russell, and an “unnamed lady” inherited from Arab Diplomatic who did not stay in the section (Foss Citationn.d., HW 8/51, 34). 94 The text of the agreement appears in Erskine (Citation1999). 95 The BRUSA circuit was activated during the summer of 1944. 96 Thomas Ralph Erskine CB (1933–2021) was a British civil servant. Although he was a barrister, he never practiced; he served in the Northern Ireland Office, rising to the position of First Legislative Counsel. Erskine crafted the legislation for the 1985 Anglo-Irish Agreement. He served until 1993. Erskine was a highly-respected historian and researcher on codebreaking associated with Bletchley Park (Weierud Citation2021). 97 “R” for “registry.” After N.S. II J was formed, it worked on Japanese naval long subtractor ciphers while N.S. I J worked on other Japanese naval ciphers. When N.S. III J was formed, it consisted of the bookbuilders/translators. 98 Foss noted that Mrs. Parsons had a home nearby Bletchley Park and that she had transferred to his section from the Turkish section when that section moved to London (Foss Citationn.d., HW 8/51, 60). 99 Erskine (Citation2006) describes the evolution of communications among the various agencies working on Japanese naval ciphers. 100 Parsons (Citationn.d., HW 8/152, 12) noted that SUSAN traffic arrived by mail from Washington 14 days to one month after intercept. 101 By the end of the war the Processing Party handled all major Japanese naval subtractor systems: JN-11, JN-87, JN-23C, JN-74, JN-29, and JN-19 (Parsons Citationn.d., HW 8/152, 1–3). 102 At that time, the JN-25 Processing Party consisted of about 60 people (Parsons Citationn.d., HW 8/152, 27). 103 Erskine (Citation2006, 5) gives totals for N.S. J II as: 80 working on JN-25, 50 working on JN-11, and 36 working on minor codes. More cryptanalysts and linguists were assigned to JN-11 than JN-25 because JN-11 was more manageable for Bletchley Park. 104 Simpson noted that when he arrived at Bletchley Park and was assigned to the Italian Naval Section he received no formal training – just on-the-job experience (Simpson Citation2017, 3). Tony Phelps, another codebreaker in the Italian Naval Section, described a rather general introductory course that covered hand ciphers, a bit about Enigma, and the basics of additive-enciphered codes, but the course did not seem to provide instructions in more detailed cryptanalytic methods that were in use at Bletchley Park. (See Footnote 85.) 105 In August 1943, a subsection of Naval Section was established to conduct research on Japanese naval attaché systems, Japanese machine ciphers, and miscellaneous ciphers – mostly other than subtractors. The section also did research into some new or unsolved Japanese systems. Geoffrey C. Wall and Violet Rosina Cane were given responsibility for this subsection, which was designated N.S. I J(W); the “W” being for “Wall.” Wall mentions a problem that he and Cane worked on while waiting to take Japanese language training. “Before the language part of the course began Miss Cane and I were able to help Mr. [Gordon Edward] Flintham get J.N.A. 10 started. J.N.A. 10 was the name of the Japanese Naval Attaché subtractor cypher. When we saw it Flintham had reduced J.N.A. 10 to a “classical” subtractor problem. We had not had a subtractor problem of this kind to deal with for three years and the technique of 1939 and 1940 was obviously not going to be adequate. However, discussion both within the section and with Major Morgan, the head of Research Section, had in the interval suggested that more powerful methods existed. These were tried and were completely successful; within a few hours a start had been made on additive recovery on relative base.” (Wall Citationn.d., HW 8/142, 6) This might be further evidence that Major Morgan was the developer of Morgan’s Method and might be referring to an example of its use. Wall’s subsection participated in two later attacks on JN-25. The first was an attack on JN-25K-45, which was in use from 1 February until 31 March 1944. F. G. Foster and Basil Edwin Russell participated in the attack. Wall recorded that work as occurring during May to September 1944. Both codebook K and additive table 45 were out of use when the attack began. The codebook had been captured, about 1800 intercepts were available, 16 pages of additives (1600 of 100,000) were available, and the indicator system was known. Using the usual process, “which involved a Hollerith catalogue and a hard slog,” (Wall Citationn.d., HW 8/142, 10) 35 messages were wholly or partially read. The other attack was on L-49 and will be mentioned later. Cane (1916 – 2008) studied mathematics at Newnham College, Cambridge and received a BA in 1938. She then worked at the Board of Trade. In 1941 she began studying for a PhD at the University of Aberdeen. However, she did not complete her study and returned to England where she served at Bletchley Park from 1942 until the end of the war. After the war, Cane became a well-known applied statistician. See Gandy, Lorenzo-Arribas, and Startup (Citation2022). 106 See Erskine (Citation2006, 5) for a brief, but more general discussion of the work of N.S. II J. 107 The codebreakers from the Italian Naval Section did not, in fact, move. They stayed in the same rooms. (Simpson Citation2017, 3). 108 Cifrario Libia was the main Italian naval subtractor. It was four-digit additive-enciphered code and was never read currently by Bletchley Park codebreakers. 109 For information about the various Japanese language courses see (Kornicki Citation2021). 110 Horizontal stripping is the recovery of text additives by reading the partial texts produced in the messages by the additives already recovered, and by deducing from them what words should go in the gaps. Vertical stripping is the recovery of text additives from enciphered code groups that are in depth by arithmetical methods – such as differencing or the use of difference tables – without reference to context (Simpson Citation1945, HW 8/149, 9). 111 Mrs. Parson noted, however, that “During October, November and December 1943, we had a lot of sick leave in the [processing] party due to influenza and nervous disability.” (Parsons Citationn.d., HW 8/152, 33). 112 The third and fourth transmitted groups contained information about the starting point of the additive string. The third transmitted group was the encipherment of the five digits: three-digit page number followed by two-digit row number of the starting point. The fourth transmitted group was the encipherment of the five digits: two-digit column number followed by three-digit page number of the starting point. The last two transmitted groups were similarly constructed but contained information about the row number and the column number of the ending point of the additive string. 113 “Report for … Boone” (1947, 10–11) states that: “[On 9 December 1943] Honolulu reported receipt of certain documents captured during the successful attack on Tarawa. The Japanese had attempted to destroy these at the last moment, but were not completely successful. At first, it was reported that these fragments included nothing that belonged to cipher 36, but did include a part of the additive table for 38, the minor cipher, in which the usage might be expected to be the same (J-38 was ultimately recovered by reading these sheets[)]. Although the enemy may have suspected that these J ciphers had been compromised since mid-December he applied emergency use to them, nonetheless J-36 and 38 continued in use for another month, through January 9, 1944. The fragments seized at Tarawa, therefore, contributed heavily to current decryption at this time.”. 114 Also included in the capture were copies of additive tables 36 and 38 and codebooks J and H. (Boone Citation1947, 13–14). 115 The messenger encountered many delays in his travel – one fortunate. A plane on which he was scheduled to travel crashed in “the Mississippi.” (Boone Citation1947, 13). 116 More information about Hall’s Weights and other systems of weights that were developed by OP-20-G can be found in (Simpson Citation2011(c)) (Christensen, Antrobus, and Simpson Citation2019). 117 The work of the Freebornery and Mr. Freeborn’s relationships to his clients deserves exploration. Simpson briefly comments about his relationship with Freeborn in (Simpson Citation2011(a), 138–139). 118 Wall’s subsection N.S. I J(W) attacked L-49. Wall described this effort as “Our most serious failure.” Their attack began with no codebook and no additive table and a special use. Washington was able to provide some information about the special use, but Wall concluded that their attempt should have waited until more was known of the L codebook. Basil Edwin Russell and F. J. Foster participated in the effort. The subsection “worked for several months but the production was negligible and in the end [they] had to give up.” (Wall Citationn.d., HW 8/142, 10–11). 119 See Sims (Citation1997) for a copy of the agreement. 120 The US Army version was SIGABA. 121 An ECM (SIGABA) equipped with an adaptor or a British Typex equipped with an adapter could function as a CCM. 122 Colonel Hugh O’Donel Alexander (1909–1974) was twice British chess champion. He graduated from King’s College, Cambridge in 1931 with a first in mathematics and spent one year as a post-graduate student with the famous number theorist G. H. Hardy. Hardy said of Alexander that he was the only genuine mathematician he knew who did not become a professional mathematician. From 1932 until 1938, Alexander taught mathematics at Winchester College and then left to become head of research for the John Lewis Partnership. He became a Bletchley Park codebreaker in 1940 working in Hut 6 but in March 1941 transferred to Hut 8 where he became deputy director under Alan Turing. Alexander became director of Hut 8 in November 1942 when, as Hugh Denham, one of Alexander’s Bletchley Park colleagues, commented: “the Prof [Turing] moved on to research work, which suited him better.” Alexander was apparently an excellent manager. In October 1944, Alexander transferred to N.S. II J.; Denham commented about the change that: “This was a less satisfying job than the earlier one, since the primary centres were elsewhere – Washington and Pearl Harbor, and to a lesser extent Melbourne and Colombo.” After the war, Alexander briefly returned to John Lewis but in 1949 became head of cryptanalysis at GCHQ, a position he kept until 1971. Alexander is also known as one of the “Wicked Uncles” – the four codebreakers whose letter to Churchill prompted the “Action this Day Memo.” (Denham Citation1974) (O’Connor and Robertson Citation2005). 123 These notes were provided to the author by Ralph Erskine. 124 Wilfred Bodsworth GC&CS liaison to OP-20-G beginning in July 1944. 125 Commander Charles A. Ford was the head of OP-20-GYP, Cryptanalysis and Decryption (Pacific). As noted before, Engstrom was head of research. 126 See (Christensen et al. Citation2025) and Office of the Chief of Naval Operations Citation1946, R.I.P. 171, III-F-1 – III-F-14. 127 The page from TNA HW 8/142 was provided by Ralph Erskine. 128 Blind jeeping was a method of additive recovery developed by OP-20-G. They had some success with it as a method of breaking into JN-25, but Bletchley Park did not have much success with it. The method requires having about 20 messages that begin and end on the same page of additives. An initial assumption is made that all the messages are in depth, and the columns are then worked by differencing in an attempt to recover additives. Blind jeeping assumes that two or more messages are actually in depth and from differences of the messages that are in depth additives can be recovered. The method typically produces lots of false additives that must be checked and, therefore, requires many people to check potential additives. 129 It should be noted that Washington referred to the successful methods as being “methods developed in Washington,” and Cassels referred to Washington using British results. 130 See (Christensen et al. Citation2025) and (Office of the Chief of Naval Operations Citation1946, R.I.P. 171, III-F-1 – III-F-14). 131 Codebook K was recovered in February 1944 in the Marshall Islands, and 16 pages of additive table 45 arrived in Washington on 7 March 1944 (Boone Citation1947, 18). 132 See Footnote 118. 133 In late April 1944, Number 3 Shinko Maru, which was enroute from Marcus Island, to Wake Island, was sunk by the submarine USS Tambor. The ship sank before it could be boarded, but the Japanese had no reliable evidence that boarding had not occurred. Panic set in because the ship was carrying G codebooks and copies of the two future cipher books noted in the quote along with publications about other cipher systems (General History of OP-20-3-GYP-1 Citationn.d., 14). 134 Actually, only code G was compromised (Boone Citation1947, 17). 135 Cipher clerks who were not holding RU were instructed to implement a special Use on channels A and B until the possibly-compromised material had been replaced. 136 Erskine (Citation2006, 10–11) describes another synthetic method. 137 JN-40 had been introduced on 1 September 1942 as an auxiliary fleet cipher and merchant shipping cipher. It was a substitution-transposition cipher. JN-40 was replaced on 1 March 1943 by JN-11. JN-147 was a minor operations code. 138 The black set consists of all multiples of 3. The blue set consists of all multiples of 3 minus 2. The red set consists of all multiples of 3 minus 1. Additional information Notes on contributors Chris Christensen Chris Christensen teaches cryptology and mathematics at Northern Kentucky University. His interest in cryptology began, after reading Enigma by Robert Harris, with an exploration of the mathematical methods used by the Polish codebreakers to attack Enigma. This interest evolved into various explorations of the contributions of mathematicians to cryptology – especially the contributions of mathematicians to Allied attacks on World War II Japanese naval ciphers.