John W. Herivel (born 1918/1919) is a British science historian and former World War II codebreaker at Bletchley Park. 1918 (MCMXVIII) was a common year starting on Tuesday of the Gregorian calendar (see link for calendar) or a common year starting on Wednesday of the Julian calendar. ... 1919 (MCMXIX) was a common year starting on Wednesday (see link for calendar). ... Combatants Allies: • Soviet Union, • UK & Commonwealth, • USA, • France/Free France, • China, • Poland, • ...and others Axis: • Germany, • Japan, • Italy, • ...and others Commanders Strength Casualties Full list Full list World War II, also known as the Second World War, was a large scale military conflict that took place between 1939 and 1945. ... Cryptanalysis (from the Greek kryptós, hidden, and analýein, to loosen or to untie) is the study of methods for obtaining the meaning of encrypted information without access to the secret information which is normally required to do so. ... During World War II, British and American cryptographers at Bletchley Park broke a large number of Axis codes and ciphers, including the German Enigma machine. ...

As a codebreaker, Herivel is remembered chiefly for the discovery of what was soon dubbed the Herivel tip or Herivelismus. The "tip" was an insight into the habits of German operators of the Enigma cipher machine that allowed Bletchley Park to easily deduce part of the daily key. For a brief but critical few months from May 1940, the Herivel tip in conjunction with "cillies" (another class of operator error) was the main technique used to solve Enigma. A three-rotor German military Enigma machine showing, from bottom to top, the plugboard, the keyboard, the lamps and the finger-wheels of the rotors emerging from the inner lid (version with labels). ... A key is a piece of information that controls the operation of a cryptography algorithm. ...

Herivel has published books and articles on Isaac Newton, Joseph Fourier, and Christiaan Huygens. Sir Isaac Newton, PRS, (4 January [O.S. 25 December 1642] 1643 – 31 March [O.S. 20 March] 1727) was an English physicist, mathematician, astronomer, alchemist, inventor and natural philosopher who is generally regarded as one of the most influential scientists in history. ... Jean Baptiste Joseph Fourier (March 21, 1768 - May 16, 1830) was a French mathematician and physicist who is best known for initiating the investigation of Fourier series and their application to problems of heat flow. ... Christiaan Huygens Christiaan Huygens (pronounced in English (IPA): ; in Dutch: ) (April 14, 1629–July 8, 1695), was a Dutch mathematician and physicist; born in The Hague as the son of Constantijn Huygens. ...

Education and recruitment to Bletchley Park

John Herivel was born in Belfast, and attended Methodist College Belfast from 1924 to 1936. In 1939 he was awarded a scholarship to study mathematics at Cambridge University^[1]. Shortly thereafter, Herivel was recruited to Bletchley Park by his former supervisor Gordon Welchman, head of the newly formed Hut 6 section created to solve Army and Air Force Enigma^[2]. Herivel, then aged 21, arrived at Bletchley on 29 January 1940^[3], and was brought up to speed on Enigma by Alan Turing and Tony Kendrick^[4]. Belfast (Béal Feirste in Irish) is a city in the United Kingdom. ... It has been suggested that Methodist College Chess Club be merged into this article or section. ... The University of Cambridge is the second-oldest university in the English-speaking world, with one of the most selective sets of entry requirements in the United Kingdom. ... William Gordon Welchman (15 June 1906–8 October 1985) was a British mathematician and World War II codebreaker at Bletchley Park. ... Hut 6 at Bletchley Park in 2004 Hut 6 was a wartime section of Bletchley Park tasked with the solution of German Army and Air Force Enigma machine ciphers. ... January 29 is the 29th day of the year in the Gregorian calendar. ... Alan Turing is often considered the father of modern computer science. ...

At the time, Hut 6 were having only limited success with the Enigma network known as "Red"^[2][4][5]. Herivel was working alongside David Rees, another Cambridge mathematician recruited by Welchman, in nearby Elmers School, testing candidate solutions and working out plugboard settings^[2]. The process was slow, however, and Herivel was determined to find a method to improve their attack, and would spend his evenings trying to think up ways to do so^[4]. One evening in the middle of February 1940 he was considering the procedures followed by a German operator when using Enigma, and identified a potential mistake that could greatly aid the codebreakers^[4].

Operator error

Three rotors inside an Enigma machine. In the middle rotor, the ring setting pin can be seen with a red indicating arrow adjacent to the 01 position. To adjust the ring setting, the pin could be lifted and the ring turned until at the desired position.

At the start of each day, the operator would set the "ring settings" (German: Ringstellung) on the Enigma rotors; that is, the position of the ring of letters (or numbers) around the rotor. The ring settings were taken from a codebook, but changed daily, and had to be altered at the start of each day before any messages could be sent. The ring settings could be adjusted before or after inserting the rotors into the machine. Herivel assumed that at least some of the operators would adjust them after^[6]. In the normal course of things, adjusting the rotors inside the machine would likely leave the correct ring setting at the top, or near the top, of the rotors^[7]. Categories: Cryptography stubs | Cryptography ...

Furthermore, for each message, the sending operator would follow a standard procedure. He would first select a starting position for the rotors, the ground setting (German: Grundstellung): GKX, for example. He would then use Enigma with the rotors set to GKX to encrypt a second starting position, the message setting, which he might choose to be RTQ; RTQ might encrypt to LLP (before May 1940 the message setting would be repeated then encrypted, but this makes no difference to Herivel's observation). The operator would then turn his rotors to RTQ and encrypt the actual message. Included in the preamble to the message, unencrypted, would be the ground setting (GKX) as well as the encrypted message setting (LLP). A receiving Enigma operator could use this information to recover the message setting and then decrypt the message.

The ground setting (GKX in the above example) should have been chosen at random, but Herivel reasoned that if an operator were lazy, or in a hurry, or otherwise under pressure, he might simply use whatever rotor setting was currently showing on the machine^[6]. If this was the first message of the day, and the operator had set the ring settings with the rotors already inside the machine, then the rotor position currently showing on the machine could well be the ring setting itself, or else very close to it. (If this situation occurred in the above example, then GKX would be the ring setting, or very close to it). Moreover, the ground setting was sent unencrypted in the preamble to the message, which could then be easily spotted by the codebreakers at Bletchley Park.

Exploiting the tip

The next day, Herivel's colleagues agreed that his idea was a possible way into Enigma^[3]. Hut 6 began looking for the effect predicted by the Herivel tip, and arranged to have the first messages of the day from each transmitting station to be sent to them early^[6]. They plotted the indicators in a grid termed a "Herivel square"^[8], an example of which is shown below. The rows and columns of the grid are labelled with the alphabet. Each ground setting received would be entered into the grid by finding the column corresponding to the first letter, the row corresponding to the second letter, and entering the third letter into the cell where the row and column intersected. For example, GKX would be recorded by entering a X in the cell in column G and row K.

 A B C D E F G H I J K L M N O P Q R S T U V W X Y Z ---------------------------------------------------------- Z| |Z Y| S |Y X| |X W| L |W V| |V U| E |U T| |T S| |S R| K |R Q| S |Q P| |P O| |O N| N |N M| X |M L| W T |L K| X Y |K J| W X |J I| |I H| Q |H G| |G F| |F E| A |E D| |D C| V |C B| J |B A| P |A ---------------------------------------------------------- A B C D E F G H I J K L M N O P Q R S T U V W X Y Z 

The Herivel tip suggested that there would be a cluster of entries close together, such as the cluster around GKX in the above example. This would narrow the options for the ring settings down from 17,576 (26³) to a small set of possibilities, perhaps 6–30, which could be tested individually.

The effect predicted by Herivel was not immediately apparent in the Enigma traffic^[7], however, and Bletchley Park relied chiefly on a different technique to get into Enigma: the method of "perforated sheets", which had been passed on by Polish cryptologists. The situation changed on 1 May 1940, when the Germans changed their indicating procedure, rendering the perforated sheets obsolete. Hut 6 was suddenly unable to decipher Enigma. The method of perforated sheets was a codebreaking technique used against the Enigma machine (see Cryptanalysis of the Enigma). ... May 1 is the 121st day of the year in the Gregorian calendar (122nd in leap years). ... 1940 (MCMXL) was a leap year starting on Monday (the link is to a full 1940 calendar). ...

Fortunately for the codebreakers, the pattern predicted by the Herivel tip began to manifest itself. David Rees spotted a cluster in the indicators^[6], and on 22 May an Air Force message sent on 20 May was decoded, the first since the change in procedure^[9]. The Herivel tip was used in combination with another class of operator mistake, known as "cillies", in order to solve the settings and decipher the messages^[7][10]. This method was used for several months until codebreaking machines, the bombes, arrived^[11]. May 22 is the 142nd day of the year in the Gregorian calendar (143rd in leap years). ... 20 May is the 140th day of the year in the Gregorian Calendar (141st in leap years). ... The Bombe replicated the action of several Enigma machines wired together. ...

Gordon Welchman speculates that the Herivel tip was a vital part of breaking Enigma at Bletchley Park, writing, "If Herivel had not been recruited in January 1940, who would have thought of the Herivel tip, without which we whould have been defeated in May 1940 — unable to maintain continuity until the bombes began to arrive many months later? Let there be no misconceptions about this last point. Loss of continuity would, at all stages, have been very serious, if not disastrous"^[12].

Because of the importance of his contribution, Herivel was singled out and introduced to Winston Churchill during a visit to Bletchley Park^[13]. He also taught Enigma cryptanalysis to a party of Americans assigned to Hut 6 in an intensive two- week course^[14]. Herivel later worked in administration in the "Newmanry", the section responsible for solving German teleprinter ciphers using machine methods such as the Colossus computers^[15]. Sir Winston Leonard Spencer-Churchill, KG, OM, CH, TD, FRS (30 November 1874 – 24 January 1965) was a British politician, best known as Prime Minister of the United Kingdom during the Second World War. ... Cryptanalysis (from the Greek kryptós, hidden, and analýein, to loosen or to untie) is the study of methods for obtaining the meaning of encrypted information, without access to the secret information which is normally required to do so. ... Hut 6 at Bletchley Park in 2004 Hut 6 was a wartime section of Bletchley Park tasked with the solution of German Army and Air Force Enigma machine ciphers. ... A Colossus Mark II computer. ...

In 2005, researchers studying a set of Enigma-encrypted messages from World War II noted the occurrence of the Herivel tip in messages from August 1941^[16].

After World War II

After the end of the war, Herivel taught mathematics in a school for a year^[1]. He then lectured at Queen's University Belfast, where he was a reader in the History and Philosophy of Science^[17], and later moved to All Souls College, Oxford^[1]. He has published books and articles on Isaac Newton, Joseph Fourier and Christiaan Huygens. His books include: The Queens University of Belfast Queens University, Belfast (QUB) - or officially The Queens University of Belfast - is a university in Belfast, Northern Ireland. ... All Souls College (in full: The College of All Souls of the Faithful Departed, of Oxford) is one of the constituent colleges of the University of Oxford in the United Kingdom. ... Sir Isaac Newton, PRS, (4 January [O.S. 25 December 1642] 1643 – 31 March [O.S. 20 March] 1727) was an English physicist, mathematician, astronomer, alchemist, inventor and natural philosopher who is generally regarded as one of the most influential scientists in history. ... Jean Baptiste Joseph Fourier (March 21, 1768 - May 16, 1830) was a French mathematician and physicist who is best known for initiating the investigation of Fourier series and their application to problems of heat flow. ... Christiaan Huygens Christiaan Huygens (pronounced in English (IPA): ; in Dutch: ) (April 14, 1629–July 8, 1695), was a Dutch mathematician and physicist; born in The Hague as the son of Constantijn Huygens. ...

• The Background to Newton's "Principia": a study of Newton's dynamical researches in the years 1664-84 (Oxford, 1965)
• Joseph Fourier: The Man and the Physicist (Clarendon, 1984)

See also

• Cryptanalysis of the Enigma

This article or section contains information that has not been verified and thus might not be reliable. ...

References

• Hugh Sebag-Montefiore, Enigma: The Battle for the Code, 2000, ISBN 0753811308.
• Gordon Welchman, The Hut Six Story, first published 1982, new edition 1997, published by M & M Baldwin, ISBN 0947712348.
• Michael Smith, Station X: The Codebreakers of Bletchley Park, 1998, ISBN 0752221892.

Footnotes

1. ^ ^{a b c} Methody Matters, the Newsletter of Methodist College Belfast, issue 04, July 2001
2. ^ ^{a b c} Sebag-Montefiore, 2000, p. 90
3. ^ ^{a b} Welchman, 1997, p. 200
4. ^ ^{a b c d} Smith, 1998, p. 42
5. ^ Welchman, 1997, p. 230
6. ^ ^{a b c d} Smith, 1998, p. 43
7. ^ ^{a b c} Sebag-Montefiore, 2000, p. 91
8. ^ Welchman, 1997, p. 100
9. ^ Sebag-Montefiore, 2000, p. 92
10. ^ Welchman, 1997, pp. 104–110
11. ^ Welchman, 1997, p. 231
12. ^ Welchman, 1997, p. 223
13. ^ Smith, 1998, p. 78
14. ^ American 6813 Division History, October 1945 (online)
15. ^ Jack Good, "Enigma and Fish", pp. 160–161 in F. H. Hinsley and Alan Stripp, eds. Codebreakers: The Inside Story of Bletchley Park, Oxford University Press, 1993
16. ^ Geoff Sullivan and Frode Weierud, "Breaking German Army Ciphers" in Cryptologia 24(3), July 2005, pp. 210–212
17. ^ Encyclopedia Britannica, author information (online)

External links

• Enigma 1940 and the Herivel Tip — notification of a lecture by Herivel; includes a brief biography and photograph.
• "Mind of a Codebreaker", companion web site to "Decoding Nazi Secrets", originally broadcast on November 9, 1999. Part one and part two. (Contains similar material on the Herivel Tip to Smith, 1998).