The Story of Mamba: Aligning Messages Against Recovered Additives

Abstract

A postwar report shows that during World War II, OP-20-GM, the research section of Naval Communications, planned and the Naval Computing Machine Laboratory engineered and produced at least 27 different codebreaking machines or attachments, and did developmental work on others. This is the story of one of those machines: Mamba. The documentation relating to Mamba is thorough enough that it is possible to track the development of Mamba from an idea based upon the garble-check properties built into the Japanese naval ciphers JN-25 and JN-11 through planning and engineering to a finished machine.

Keywords:

• additive systems
• Copperhead
• cryptanalytic machines
• JN-11
• JN-25
• Mamba
• NCML
• OP-20-GM
• superenciphered code

Acknowledgments

The authors thank Ralph Erskine for being so willing to share his documents and knowledge of JN-25 and other cryptologic topics; Edward Simpson for communications about the British attack on JN-25; René Stein for her help in conducting this research; Debbie Anderson, whose exploration of the work of her father Joe Desch and the work at the NCML led to this exploration; Don MacDonald for communications about the cryptologists with whom he worked; and the Department of Mathematics of the University of Louisville, the Mathematics Department of the U.S. Naval Academy, and the Mathematical Association of America for opportunities to present portions of this research.

Notes

¹A picture of the U.S. Navy cryptologic mathematicians taken in October 1945 and brief biographies of most of the mathematicians are in [9].

²John Redman's brother, Captain Joseph Redman, became the Director of Naval Communications (DNC) shortly after the departure from that position of Rear Admiral Leigh Noyes on 24 February 1942. The organization of OP-20-G that is described is the organization at the end of February 1942.

³Howard Engstrom (1902–1962) was a member of the U.S. Navy Reserve, and he was an associate professor of mathematics at Yale until he was called to active duty.

⁴The course and recruitment are described in [11]. Course materials can be found at http://www.nku.edu/~christensen/US Navy Elementary Course in Cryptanalysis.htm.

⁵In a postwar report [26], among the reasons mentioned by Capt. R. I. Meader for locating the NCML at NCR were that NCR had a competent engineering staff that was flexible enough to permit great expansion, NCR had a relatively large manufacturing facility, Dayton had “hundreds of small shops experienced in precision work and available for subcontracting,” NCR had an isolated building that could be secured and placed under a 24-hour Marine guard, and Dayton was only “12 hours by rail and 3 hours by plane from Washington D.C.,” which made liaison with OP-20-GM extremely easy.

⁶Dayton was the home of inventors, a kind of Silicon Valley of that time. The Wright Brothers’ shop was in Dayton, the inventor Charles Kettering had founded Dayton Engineering Laboratories Company (DELCO), and Joseph Desch was conducting research at NCR to use tubes to count electronically.

⁷Joseph Desch (1907–1987) was inducted into the NSA Hall of Honor in 2011. http://www.nsa.gov/about/cryptologic_heritage/hall_of_honor/2011/desch.shtml.

⁸There were several reasons for OP-20-G to focus its initial efforts against German ciphers. Prior to the beginning of World War II, the U.S. Navy's primary cryptologic target was the Japanese Navy. Based upon these earlier efforts, after the attack on Pearl Harbor, OP-20-G was able to make progress against Japanese naval ciphers. However, earlier, when war broke out in Europe, the U.S. Navy found itself unprepared to attack German ciphers. The British Government Code and Cypher School (GC&CS) had successes against the German Enigma cipher machine, but on 1 February 1942, the German Navy introduced a four-rotor Enigma using a new cipher (called Shark by the British), and GC&CS was blacked out from reading communications with the U-boats that were attacking the Atlantic convoys. The blackout lasted until the end of 1943, and Shark was not currently read until September 1944. During the blackout, OP-20-G was concerned whether GC&CS would be able to break Shark on its own; they were also concerned during the Battle of Britain (10 July–31 October 1940) that Germany might invade Britain and therefore, GC&CS might not continue to operate.

⁹The story of the development of the U.S. Navy cryptologic bombe is told in The Secret in Building 26 by Jim DeBrosse and Colin Burke [14] and in It Wasn't All Magic by Colin Burke [8].

¹⁰References used for the history of JN-25 were Edward Simpson's description of his work attacking JN-25 at Bletchley Park [16, pp. 127–146]; “JN-25 Cryptographic System” [22]; “R.I.P. 171 Techniques and Procedure used in the Cryptanalysis of JN-25 by Station Negat Reg. No. 1” [32]; “GCCS—Cryptographic Memorandum No. 82, The Function, Organization and Distribution of Japanese Naval Codes and Ciphers 1 August–31 December 1944” [17]; “Historical Notes Book Ciphers” [1]; “Historical Notes Strip Ciphers” [2]; and “The History of GYP-1” [20].

¹¹In November 1944, JN-25 began using strips (Ransuuban) to generate the additive tables. Code N (Nan) was used both as a strip cipher and as a book cipher. Codes P and R were used only as strip ciphers.

¹²The label JN-25 A-1 did not appear until 1942. The first version of JN-25 was originally called AN, and the first cipher was called Cipher 1. JN-25 B-6 was originally called AN-1, cipher number 1. AN apparently stood for “Administrative Naval.”

¹³Book 1 of additives had 300 pages of 100 additives, which were arranged in ten rows and ten columns. The rows and columns were numbered by single digits in the usual order.

¹⁴There is much controversy about how much of JN-25 could be read prior to the attack on Pearl Harbor and, therefore, how aware the British and Americans were of the impending attack. After the attack, of course, JN-25 traffic increased dramatically.

¹⁵Many reasons are suggested by various authors for the splitting: The split might have resulted from the Japanese analysis of their defeat at Midway, it might have resulted from the Chicago Tribune story of the Battle of Midway that stated that the U.S. Navy was able to set the trap for the Japanese fleet because of intelligence obtained from Japanese messages, or it might have resulted from a belief on the part of the Japanese that the volume of JN-25 was too high for a single channel.

¹⁶Previous to Use #1, instructions for enciphering the starting position had been issued, but they were not called “uses.”

¹⁷The references for the history of JN-11 were “R.I.P. 214, History of JN-11, Japanese Fleet Auxiliary System, Reg. 1 and 4” [21] and “GCCS—Cryptographic Memorandum No. 119, The JN 11 Cyphers Naval General Purpose System” [18].

¹⁸Because of this garble-check, JN-11 could have no more than 3,333 clear code groups. The garble-check was dropped from JN-11 on 1 April 1944, and that change will play a part in Mamba's story. After the garble-check was dropped, JN-11 had 6,600 clear code groups.

¹⁹Like JN-25, in November 1944, JN-11 became a strip cipher.

²⁰Lawrence Steinhardt had been a student and a research assistant for Vannevar Bush at MIT. Steinhardt would, after the war, work for Engineering Research Associates (ERA), a company that sprang from the Navy's need for codebreaking computers (see [9, pp. 273–274]). Bush and his colleagues had been working on designing a rapid comparator for the Navy codebreakers. The story of Bush's effort to build the comparator, how the comparator project blended with other Navy codebreaking machine projects, and the beginnings of ERA is told in [7] and [8].

²¹Names of snakes were given to machines that were designed to attack Japanese ciphers.

²²There are no documents describing Copperhead III and Copperhead IV; however, in Capt. R. I. Meader's postwar report of the work accomplished at the NCML in Dayton, he stated that “development work on Copperhead IV & V … was accomplished” [26, p. 16].

²³This section and the next are based upon “A Tentative Method for the Alignment of JN-25 Traffic without the Use of Code or Keys” [29].

²⁴No distinction will be made between service in the USN and the USNR. Except in text quotations, abbreviations for ranks will be the modern abbreviations.

²⁵Dr. Lawrance E. Shinn held a doctorate in bacteriology from the University of Pittsburgh. He served with the Armed Forces Security Agency (AFSA) and the National Security Agency (NSA) after World War II. In 1961, Shinn headed NSA's collection operations in the Far East. He had been chief of NSA's Office of Asiatic Communist Countries (ACOM) since 1959 (see [3, pp. 57–58]). Shinn died on 11 December 1968 at age 58 [NSA Newsletter, January 1969, p. 7].

²⁶Edward Simpson is a retired British senior civil servant. He was introduced to statistical thinking during his service as a cryptanalyst at Bletchley Park from 1942 to 1945. He first served in the Italian Naval Section and moved to JN-25 in August 1943 after Italy surrendered. He introduced “Simpson's Paradox” and “Simpson's Index of Diversity.”

²⁷This section is based on the 30 March 1944 document, “A proposed method for placement of partially keyed messages in additive systems when some additives are available” [23].

²⁸E. W. Knepper was an officer in the USN and served with OP-20-GY during World War II. Donald McDonald, who served in OP-20-GY-1, -2 during World War II and later with the AFSA and the NSA, recalled, “I did know Ed Knepper slightly while in GY. He was clearly regarded by the old-timers around as an expert cryptanalyst on the JN-25 system. At the time I think he was a Navy Cdr. … I saw him in Japan around 1955” [25]. [19, p. 15] includes a reference to a 7 March 1958 memorandum for “Captain E. W. Knepper, USN, Chief of Staff, Production, NSA.”

²⁹The keying system is the key additive system.

³⁰A similar distribution exists for the false digital sums of the four-digit JN-11 code groups. Initially, the JN-11 garble-check was that the clear code groups were divisible by 3 with remainder 1 (i.e., congruent to 1 modulo 3). The theoretical distribution for the false sums of JN-11 clear code groups is

Table

.

³¹The number of maximals was always four, but considerable testing was done to choose between using four minimal predictions 2, 3, 6, and 9 or only two minimal predictions 6 and 9. The decision was to use four maximals and four minimals.

³²This example is a modification of an example in [31, between pages 222 and 223].

³³The sum of the relative frequencies for the maximal predictions is 0.145 + 0.145 +0.176 + 0.176 = 0.642, and the sum of the relative frequencies for the minimal predictions is 0.028 + 0.028 +0.053 + 0.053 = 0.162. In this example, the second alignment is correct.

³⁴A problem with using the ratio of the number of maximals to the number of minimals is that the number of minimals could be quite small or even 0, and therefore, the ratio could be quite large.

³⁵This section is based upon a 30 March 1944 document, “Digital Alignment of JN Traffic by Machine” [23].

³⁶OP-20-G had another machine called Mathew (which in some documents is spelled “Matthew”) that falsely subtracted or added groups from two Letterwriter tapes (see [4, pp. 6–8] or [12, pp. 6–8]).

³⁷The report estimates that each alignment would take “about 2 seconds” to check. Based upon 2,000 high-frequency clear code groups on the scanning loop and an average day's traffic (450 messages of average length 100), the report estimates that it would take half a day to attempt to align the messages and additives.

³⁸A manual version of this process—called “dragging”—is described by Bletchley Park JN-25 codebreaker Edward Simpson in [16, p. 140].

³⁹John Howard, like Lawrence Steinhardt, had been an MIT student prior to the war. He was the project manager for Vannevar Bush's 1930s Memex project and became director of development for ERA after the war (see [7] and [9]).

⁴⁰The Comparator was engineered by NCR and produced by Gray Manufacturing. It had been in use since September 1943 to align messages in depth using Friedman's index of coincidence. See [7, p. 238], [12, pp. 20–23], [4, pp. 20–23], or [8, pp. 37–49].

⁴¹The I.C. Machine was produced by Eastman Kodak. Like the Comparator, it was designed to align messages in depth. See [7, pp. 235–236], [12, pp. 27–29], or [4, pp. 27–29].

⁴²Hypo was another comparator. It was built by Eastman Kodak for Agnes Driscoll's Enigma group. See [7, pp. 237–238] and [8, pp. 69–70].

⁴³Steinhardt's proposed Copperhead V was never built. Like Copperhead I, it would have aligned messages in depth, but unlike Copperhead I, which worked with the five-digit groups, Copperhead V would have replaced the five-digit groups by their false digital sums.

⁴⁴This section is based upon the 2 May 1944 document, “Minutes of Conference on 5 April 1944 Regarding Mamba” [23].

⁴⁵Howard H. Campaigne was recruited by the Navy from the mathematics faculty at the University of Minnesota. Campaigne had submitted a design for an encryption device to the Navy. Although the Navy turned down the device, they offered Campaigne the correspondence course in elementary cryptanalysis. He received his commission on 5 December 1941. Two days later, the United States was at war. After the war, Campaigne continued to serve with successor agencies to OP-20-G. He eventually became director of research for the NSA [9, pp. 269–270].

⁴⁶The requirements are listed in a 6 April 1944 document, “Stripping Machine Requirements” [23].

⁴⁷This section is based on “Proposal for Mamba” [23].

⁴⁸Recall that on 1 December 1943, JN-25 became an ordinate cipher. Even if the indicator system were broken, messages could only be placed on a page of 180 additives.

⁴⁹Recall that JN-11 messages could be placed in one part of the additive book.

⁵⁰Colin Burke [8, p. 150] claimed that “it was expected that Mamba would vastly reduce the amount of hand work needed for the JN11 system. But the Mambas arrived after the specific system they were designed for ‘died.’ To salvage some of the investment, at least one was modified to perform what was called a ‘maximal-minimal’ attack on JN25.” Documents examined for this article suggest that alignment of JN-25 messages against recovered additives was part of the original problem for which Mamba was designed.

⁵¹It appears that Howard is commenting about the keying (indicator) system, which typically changed every ten days. (Note the last sentence of the quote.) Text additive books did not change that frequently.

⁵²Pete Deffert is mentioned in [8, pp. 51–52]. The reference suggests that Deffert was a Navy engineer.

⁵³“P” refers to Pacific.

⁵⁴On additive cards, any column that corresponded to a recovered additive and therefore was punched with maximals or minimals had a punch in row 12. On message cards, any column that corresponded to a message group and therefore has a false digital sum punched in the column had row 12 punched. For each alignment, the total overlap was the number of columns for which there was a punch in row 12 of both the additive cards and the message card.

⁵⁵This section is based on 2 May 1944, “Mamba I”; 2 May 1944, “Comment on the Suggested Design of Mamba”; 5 May 1944, “Minutes of Conference of 3 May 1944 Regarding Mamba”; 6 May 1944, “Sample MAMBA Cards–Description of”; and 6 May 1944, “Minutes of Conference of 6 May 1944 Regarding Mamba” [23].

⁵⁶This section is based on 10 May 1944, “Special Cipher Machines—Construction of”; 6 June 1944, “Mamba—N-2000”; and 17 June 1944, “MAMBA I Project—Transfer of responsibility and records of” [23].

⁵⁷Acme Pattern & Tool Company was founded in 1930 by Karl A. Stein and located at 232 North Findlay Street in Dayton. An ad for the company says, “Wood and metal patterns. Brass and aluminum heat treated aircraft castings. Tools, dies, jigs, fixtures and special machinery and engineering.”

⁵⁸Desch noted that no classified information was given to Acme. He stated that Howard supplied them with faked sample maximal, minimal, and message cards.

⁵⁹The Battle of Biak spanned 27 May 1944 until 17 August 1944.

⁶⁰There were six grilles. On average, 52 additives were blacked out on a 180-additive page (books 58, 59, 60, and 61) and 71 blacked out on a 200-additive page (books 62, 66, 67, 70, and perhaps others).

⁶¹A “bust” is a message that contains an error in encipherment that jeopardizes the security of the message [17, p. 15].

⁶²Or by capture of cryptographic materials as occurred, for example, on Saipan on 17 July 1944.

⁶³The P ciphers that followed the Nan ciphers also did not scan, but all other (earlier versions) of JN-25 did scan. JN-11 had dropped its garble-check on 1 April 1944.

⁶⁴Although the restriction of RO probably accounted for much of the change, the loss of territory controlled by the Japanese was likely also a factor.

⁶⁵A copy of “Liaison Report No. 6” was provided by Ralph Erskine and is in possession of the authors.

⁶⁶9 August 1944, “Memorandum for Mamba Files” [23].

⁶⁷Howard said, “Perhaps this number is too small in view of the fact that MAMBAS might be sent to Station ‘H’ [Station Hypo in Honolulu], and also because GY-P is attempting the MAMBA process on several long jobs in which there is no pagination [presumably JN-11 ‘jobs’].”

⁶⁸A copy of this page was provided to the authors by Ralph Erskine. The document can be found in the British National Archives. The file is NACP, HCC, box 1429, nr 4724, “CCM, 1943–1945.”

⁶⁹Desch and the people of the NCML were also the target of Meader's pressure to “get things done.” See [14, p. 105].

⁷⁰25 September 1944, “Communication from Washington to Dayton, serial number 450.” A copy of this document was provided by Debbie Desch Anderson and is in possession of the authors.

⁷¹10 October 1944, “Possible jobs for HYPO on MAMBA problems” [23].

⁷²25 October 1944, “MAMBA—Installation and Testing of” [23].

⁷³Probably because with the introduction of the Nan ciphers JN-25 on 25 July 1944, JN-25 clear code groups no longer scanned.

⁷⁴17 November 1944, “Mamba—Construction of” [23].

⁷⁵14 November 1944, “Memorandum for Mamba File”.

⁷⁶Howard also stated that “MAMBA is expected to be ready for initial testing within two weeks and the engineers feel that they now have adequate material for so doing.”

⁷⁷This section is based on March 1945, “Communications Intelligence Technical Paper 4, Operational and Maintenance Procedure for Mamba” [27].

⁷⁸“MAMBA” [23].

⁷⁹Recall that JN-25 dropped the scanning property on 25 July 1944 with the introduction of N-62. The new garble-check was that no 0's would appear in the clear code groups. JN-11 had dropped its garble-check on 1 April 1944.

⁸⁰Meader's postwar report [26] stated that only one Mamba was constructed.

⁸¹See “MAMBA” [23].

Additional information

Notes on contributors

Chris Christensen

Jared Antrobus is an undergraduate mathematics and statistics major at Northern Kentucky University. He is interested in cryptology and computer algorithms, and he loves a good story. When this article appears, he expects to be a graduate student.

Jared Antrobus

Chris Christensen teaches mathematics and cryptology at Northern Kentucky University. He survived childhood because of a reasoned fear of snakes. When this article appears, he expects to be exploring the Japanese Coral cipher machine.