Banburismus
Encyclopedia
Banburismus was a cryptanalytic
process developed by Alan Turing
at Bletchley Park
in England
during the Second World War. It was used by Bletchley Park's Hut 8
to help break German Kriegsmarine
(Naval) messages enciphered on Enigma machine
s. The process used sequential
conditional probability
to infer information about the likely settings of the Enigma machine. It gave rise to Turing's invention of the ban
as a measure of the weight of evidence in favour of a hypothesis. This concept was later applied in Turingery
and all the other methods used for breaking the Lorenz cipher
.
The aim of Banburismus was to reduce the time required of the electromechanical Bombe
machines by identifying the most likely right-hand and middle wheels of the Enigma. Hut 8 performed the procedure continuously for two years, stopping only in 1943 when sufficient bombe time became readily available. Banburismus was a development of the "clock method
" invented by the Polish cryptanalyst Jerzy Różycki
.
Hugh Alexander
was regarded as the best of the Banburists. He and I. J. Good
considered the process more an intellectual game than a job. It was "not easy enough to be trivial, but not difficult enough to cause a nervous breakdown".
and a trigram lookup table. These trigram tables were in a book called the Kenngruppenbuch (K book). However, without the bigram tables, Hut 8 were unable to start attacking the traffic. A breakthrough was achieved after the Narvik pinch in which the disguised armed trawler
Polares, which was on its way to Narvik
in Norway
, was seized by HMS Griffin
in the North Sea
on 26 April 1940. The Germans did not have time to destroy all their cryptographic documents, and the captured material revealed the precise form of the indicating system, supplied the plugboard connections and Grundstellung for April 23 and 24 and the operators' log, which gave a long stretch of paired plaintext and enciphered message for the 25th and 26th.
The bigram tables themselves were not part of the capture, but Hut 8 were able to use the settings-lists to read retrospectively, all the Kriegsmarine traffic that had been intercepted from 22 to 27 April. This allowed them do a partial reconstruction of the bigram tables and start the first attempt to use Banburismus to attack Kriegsmarine traffic, from 30 April onwards. Eligible days were those where at least 200 messages were received and for which the partial bigram-tables deciphered the indicators. The first day to be broken was 8 May 1940, thereafter celebrated as "Foss's Day" in honour of Hugh Foss
, the cryptanalyst who achieved the feat.
This task took until November that year, by which time the intelligence
was very out of date, but it did show that Banburismus could work. It also allowed much more of the bigram tables to be reconstructed, which in turn allowed April 14 and June 26 to be broken. However, the Kriegsmarine had changed the bigram tables on 1 July. By the end of 1940, much of the theory of the Banburismus scoring system had been worked out.
The First Lofoten pinch from the trawler Krebs on 3 March 1941 provided the complete keys for February - but no bigram tables or K book. The consequent decrypts allowed the statistical scoring system to be refined so that Banburismus could become the standard procedure against Kriegsmarine Enigma until mid 1943.
The principle behind Banburismus is relatively simple (and seems to be rather similar to the Index of Coincidence
). If two sentences in English or German are written down one above the other, and a count is made of how often a letter in one message is the same as the corresponding letter in the other message; there will be more matches than would occur if the sentences were random strings of letters. For a random sequence, the repeat rate for single letters is expected to be 1 in 26, and for the German Navy messages it was shown to be 1 in 17. If the two messages were in depth, then the matches occur just as they did in the plaintexts. However, if the messages were not in depth, then the two ciphertexts will compare as if they were random, giving a repeat rate of about 1 in 26. This allows an attacker to take two messages whose indicators differ only in the third character, and slide them against each other looking for the giveaway repeat pattern that shows where they align in depth.
The comparison of two messages to look for repeats was made easier by punching the messages onto thin cards about 250 mm high (10") by several metres wide (they had different cards for different lengths of message). A hole at the top of a column on the card represented an 'A' at that position, a hole at the bottom represented a 'Z'. The two message-cards were laid on top of each other on a light-box and where the light shone through, there was a repeat. This made it much simpler to detect and count the repeats. The cards were printed in Banbury
, England. They became known as 'banburies' at Bletchley Park, and hence the procedure using them was Banburismus.
The application of the scritchmus procedure (see below) gives a clue as to the possible right hand rotor.
Message with indicator "VFX":
YNSCFCCPVIPEMSGIZWFLHESCIYSPVRXMCFQAXVXDVUQILBJUABNLKMKDJMENUNQ
Hut 8 would punch these onto banburies and count the repeats for all valid offsets -25 letters to +25 letters. There are two promising positions:
This offset of eight letters shows nine repeats, including two bigrams, in an overlap of 56 letters.
The other promising position looks like this:
This offset of seven shows just a single trigram in an overlap of 57 letters.
Turing's method of accumulating a score of a number of decibans allows the calculation of which of these situations is most likely to represent messages in depth. As might be expected, the former is the winner with odds of 5:1 on, the latter is only 2:1 on.
Turing calculated the scores for the number of single repeats in overlaps of so many letters, and the number of bigrams and trigrams. Tetragrams often represented German word in the plaintext and their scores were calculated according to the type of message (from traffic analysis), and even their position within the message. These were tabulated and the relevant values summed by Banburists in assessing pairs of messages to see which were likely to be in depth.
Bletchley Park used the convention that the indicator plaintext of "VFX", being eight characters ahead of "VFG", or (in terms of just the third, differing, letter) that "X = G+8".
If this is then compared at progressive offsets with the known letter-sequence of an Enigma rotor, quite a few possibilities are discounted due to violating either the "reciprocal" property or the "no-self-ciphering" property of the Enigma machine:
The so called "end-wheel alphabet" is already limited to just nine possibilities, merely by establishing a letter-chain of five letters derived from a mere four message-pairs. Hut 8 would now try fitting other letter-chains — ones with no letters in common with the first chain — into these nine candidate end-wheel alphabets.
Eventually they will hope to be left with just one candidate, maybe looking like this:
Not only this, but such an end-wheel alphabet forces the conclusion that the end wheel is in fact "Rotor I". This is because "Rotor II" would have caused a mid-wheel turnover as it stepped from "E" to "F", yet that's in the middle of the span of the letter-chain "F----A--D---O". Likewise, all the other possible mid-wheel turnovers are precluded. Rotor I does its turnover between "Q" and "R", and that's the only part of the alphabet not spanned by a chain.
That the different Enigma wheels were given different turnover points was, presumably, a measure by the designers of the machine to improve its security. However, this very complication allowed Bletchley Park to deduce the identity of the end wheel.
The workload of doing this is beyond manual labour, so BP punched the messages onto 80-column cards and used Hollerith machines to scan for tetragram repeats or better. That told them which banburies to set up on the light boxes (and with what overlap) to evaluate the whole repeat pattern.
Armed with a set of probable mid-wheel overlaps, Hut 8 could compose letter-chains for the middle wheel much in the same way as was illustrated above for the end wheel. That in turn (after Scritchmus) would give at least a partial middle wheel alphabet, and hopefully at least some of the possible choices of rotor for the middle wheel could be eliminated from turnover knowledge (as was done in identifying the end wheel).
Taken together, the probable right hand and middle wheels would give a set of bombe runs for the day, that would be significantly reduced from the 336 possible.
.
Cryptanalysis
Cryptanalysis is the study of methods for obtaining the meaning of encrypted information, without access to the secret information that is normally required to do so. Typically, this involves knowing how the system works and finding a secret key...
process developed by Alan Turing
Alan Turing
Alan Mathison Turing, OBE, FRS , was an English mathematician, logician, cryptanalyst, and computer scientist. He was highly influential in the development of computer science, providing a formalisation of the concepts of "algorithm" and "computation" with the Turing machine, which played a...
at Bletchley Park
Bletchley Park
Bletchley Park is an estate located in the town of Bletchley, in Buckinghamshire, England, which currently houses the National Museum of Computing...
in England
England
England is a country that is part of the United Kingdom. It shares land borders with Scotland to the north and Wales to the west; the Irish Sea is to the north west, the Celtic Sea to the south west, with the North Sea to the east and the English Channel to the south separating it from continental...
during the Second World War. It was used by Bletchley Park's Hut 8
Hut 8
Hut 8 was a section at Bletchley Park tasked with solving German naval Enigma messages. The section was led initially by Alan Turing...
to help break German Kriegsmarine
Kriegsmarine
The Kriegsmarine was the name of the German Navy during the Nazi regime . It superseded the Kaiserliche Marine of World War I and the post-war Reichsmarine. The Kriegsmarine was one of three official branches of the Wehrmacht, the unified armed forces of Nazi Germany.The Kriegsmarine grew rapidly...
(Naval) messages enciphered on Enigma machine
Enigma machine
An Enigma machine is any of a family of related electro-mechanical rotor cipher machines used for the encryption and decryption of secret messages. Enigma was invented by German engineer Arthur Scherbius at the end of World War I...
s. The process used sequential
Sequential analysis
In statistics, sequential analysis or sequential hypothesis testing is statistical analysis where the sample size is not fixed in advance. Instead data are evaluated as they are collected, and further sampling is stopped in accordance with a pre-defined stopping rule as soon as significant results...
conditional probability
Conditional probability
In probability theory, the "conditional probability of A given B" is the probability of A if B is known to occur. It is commonly notated P, and sometimes P_B. P can be visualised as the probability of event A when the sample space is restricted to event B...
to infer information about the likely settings of the Enigma machine. It gave rise to Turing's invention of the ban
Ban (information)
A ban, sometimes called a hartley or a dit , is a logarithmic unit which measures information or entropy, based on base 10 logarithms and powers of 10, rather than the powers of 2 and base 2 logarithms which define the bit. As a bit corresponds to a binary digit, so a ban is a decimal digit...
as a measure of the weight of evidence in favour of a hypothesis. This concept was later applied in Turingery
Turingery
Turingery or Turing's Method was a hand codebreaking method devised by the mathematician and cryptanalyst Alan Turing at the British Government Code and Cypher School at Bletchley Park during World War II...
and all the other methods used for breaking the Lorenz cipher
Lorenz cipher
The Lorenz SZ40, SZ42A and SZ42B were German rotor cipher machines used by the German Army during World War II. They were developed by C. Lorenz AG in Berlin. They implemented a Vernam stream cipher...
.
The aim of Banburismus was to reduce the time required of the electromechanical Bombe
Bombe
The bombe was an electromechanical device used by British cryptologists to help decipher German Enigma-machine-encrypted signals during World War II...
machines by identifying the most likely right-hand and middle wheels of the Enigma. Hut 8 performed the procedure continuously for two years, stopping only in 1943 when sufficient bombe time became readily available. Banburismus was a development of the "clock method
Clock (cryptography)
In cryptography, the clock was a method devised by Polish mathematician-cryptologist Jerzy Różycki, at the Polish General Staff's Cipher Bureau, to facilitate decrypting German Enigma ciphers.-Method:...
" invented by the Polish cryptanalyst Jerzy Różycki
Jerzy Rózycki
Jerzy Witold Różycki was a Polish mathematician and cryptologist who worked at breaking German Enigma-machine ciphers.-Life:Różycki was born in what is now Ukraine, the fourth and youngest child of Zygmunt Różycki, a pharmacist and graduate of Saint Petersburg University, and Wanda, née Benita. ...
.
Hugh Alexander
Conel Hugh O'Donel Alexander
Conel Hugh O'Donel Alexander, CMG, CBE was an Irish-born British cryptanalyst, chess player, and chess writer. He worked on the German Enigma machine at Bletchley Park during World War II, and was later the head of the cryptanalysis division at GCHQ for over 20 years...
was regarded as the best of the Banburists. He and I. J. Good
I. J. Good
Irving John Good was a British mathematician who worked as a cryptologist at Bletchley Park with Alan Turing. After World War II, Good continued to work with Turing on the design of computers and Bayesian statistics at the University of Manchester...
considered the process more an intellectual game than a job. It was "not easy enough to be trivial, but not difficult enough to cause a nervous breakdown".
History
In the first few months after arriving at Bletchley Park in September 1939, Alan Turing correctly deduced that the message-settings of Kriegsmarine Enigma signals were enciphered on a common Grundstellung (starting position of the rotors), and were then super-enciphered with a bigramBigram
Bigrams or digrams are groups of two written letters, two syllables, or two words, and are very commonly used as the basis for simple statistical analysis of text. They are used in one of the most successful language models for speech recognition...
and a trigram lookup table. These trigram tables were in a book called the Kenngruppenbuch (K book). However, without the bigram tables, Hut 8 were unable to start attacking the traffic. A breakthrough was achieved after the Narvik pinch in which the disguised armed trawler
Naval trawler
A naval trawler is a vessel built along the lines of a fishing trawler but fitted out for naval purposes. Naval trawlers were widely used during the First and Second world wars. Fishing trawlers were particularly suited for many naval requirements because they were robust boats designed to work...
Polares, which was on its way to Narvik
Narvik
is the third largest city and municipality in Nordland county, Norway by population. Narvik is located on the shores of the Narvik Fjord . The municipality is part of the Ofoten traditional region of North Norway, inside the arctic circle...
in Norway
Norway
Norway , officially the Kingdom of Norway, is a Nordic unitary constitutional monarchy whose territory comprises the western portion of the Scandinavian Peninsula, Jan Mayen, and the Arctic archipelago of Svalbard and Bouvet Island. Norway has a total area of and a population of about 4.9 million...
, was seized by HMS Griffin
HMS Griffin (H31)
HMS Griffin was a G-class destroyer, built for the Royal Navy in the mid-1930s. During World War II, the ship participated in the Norwegian Campaign of April–May 1940 and the Battle of Dakar in September before being transferred to the Mediterranean Fleet in November...
in the North Sea
North Sea
In the southwest, beyond the Straits of Dover, the North Sea becomes the English Channel connecting to the Atlantic Ocean. In the east, it connects to the Baltic Sea via the Skagerrak and Kattegat, narrow straits that separate Denmark from Norway and Sweden respectively...
on 26 April 1940. The Germans did not have time to destroy all their cryptographic documents, and the captured material revealed the precise form of the indicating system, supplied the plugboard connections and Grundstellung for April 23 and 24 and the operators' log, which gave a long stretch of paired plaintext and enciphered message for the 25th and 26th.
The bigram tables themselves were not part of the capture, but Hut 8 were able to use the settings-lists to read retrospectively, all the Kriegsmarine traffic that had been intercepted from 22 to 27 April. This allowed them do a partial reconstruction of the bigram tables and start the first attempt to use Banburismus to attack Kriegsmarine traffic, from 30 April onwards. Eligible days were those where at least 200 messages were received and for which the partial bigram-tables deciphered the indicators. The first day to be broken was 8 May 1940, thereafter celebrated as "Foss's Day" in honour of Hugh Foss
Hugh Foss
Hugh Rose Foss was a British cryptographer.-Life:Foss was born in Kobe, Japan, where his father the Rt Revd Hugh Foss was a missionary bishop, and he learned Japanese....
, the cryptanalyst who achieved the feat.
This task took until November that year, by which time the intelligence
Military intelligence
Military intelligence is a military discipline that exploits a number of information collection and analysis approaches to provide guidance and direction to commanders in support of their decisions....
was very out of date, but it did show that Banburismus could work. It also allowed much more of the bigram tables to be reconstructed, which in turn allowed April 14 and June 26 to be broken. However, the Kriegsmarine had changed the bigram tables on 1 July. By the end of 1940, much of the theory of the Banburismus scoring system had been worked out.
The First Lofoten pinch from the trawler Krebs on 3 March 1941 provided the complete keys for February - but no bigram tables or K book. The consequent decrypts allowed the statistical scoring system to be refined so that Banburismus could become the standard procedure against Kriegsmarine Enigma until mid 1943.
Principles
Banburismus utilised a weakness in the indicator procedure (the encrypted message settings) of Kriegsmarine Enigma traffic. Unlike the German Army and Airforce Enigma procedures, the Grundstellung was provided by key lists, and so was the same for all messages on a particular day (or pair of days). This meant that the three-letter indicators were all enciphered with the same rotor settings so that they were all in depth with each other. Normally, the indicators for two messages were never the same, but it could happen that, part-way through a message, the rotor positions became the same as the starting position of the rotors for another message, the parts of the two messages that overlapped in this way were in depth.The principle behind Banburismus is relatively simple (and seems to be rather similar to the Index of Coincidence
Index of coincidence
In cryptography, coincidence counting is the technique of putting two texts side-by-side and counting the number of times that identical letters appear in the same position in both texts...
). If two sentences in English or German are written down one above the other, and a count is made of how often a letter in one message is the same as the corresponding letter in the other message; there will be more matches than would occur if the sentences were random strings of letters. For a random sequence, the repeat rate for single letters is expected to be 1 in 26, and for the German Navy messages it was shown to be 1 in 17. If the two messages were in depth, then the matches occur just as they did in the plaintexts. However, if the messages were not in depth, then the two ciphertexts will compare as if they were random, giving a repeat rate of about 1 in 26. This allows an attacker to take two messages whose indicators differ only in the third character, and slide them against each other looking for the giveaway repeat pattern that shows where they align in depth.
The comparison of two messages to look for repeats was made easier by punching the messages onto thin cards about 250 mm high (10") by several metres wide (they had different cards for different lengths of message). A hole at the top of a column on the card represented an 'A' at that position, a hole at the bottom represented a 'Z'. The two message-cards were laid on top of each other on a light-box and where the light shone through, there was a repeat. This made it much simpler to detect and count the repeats. The cards were printed in Banbury
Banbury
Banbury is a market town and civil parish on the River Cherwell in the Cherwell District of Oxfordshire. It is northwest of London, southeast of Birmingham, south of Coventry and north northwest of the county town of Oxford...
, England. They became known as 'banburies' at Bletchley Park, and hence the procedure using them was Banburismus.
The application of the scritchmus procedure (see below) gives a clue as to the possible right hand rotor.
Example
Message with indicator "VFG": XCYBGDSLVWBDJLKWIPEHVYGQZWDTHRQXIKEESQSSPZXARIXEABQIRUCKHGWUEBPFMessage with indicator "VFX":
YNSCFCCPVIPEMSGIZWFLHESCIYSPVRXMCFQAXVXDVUQILBJUABNLKMKDJMENUNQ
Hut 8 would punch these onto banburies and count the repeats for all valid offsets -25 letters to +25 letters. There are two promising positions:
XCYBGDSLVWBDJLKWIPEHVYGQZWDTHRQXIKEESQSSPZXARIXEABQIRUCKHGWUEBPF
YNSCFCCPVIPEMSGIZWFLHESCIYSPVRXMCFQAXVXDVUQILBJUABNLKMKDJMENUNQ
- -- - - - - --
This offset of eight letters shows nine repeats, including two bigrams, in an overlap of 56 letters.
The other promising position looks like this:
XCYBGDSLVWBDJLKWIPEHVYGQZWDTHRQXIKEESQSSPZXARIXEABQIRUCKHGWUEBPF
YNSCFCCPVIPEMSGIZWFLHESCIYSPVRXMCFQAXVXDVUQILBJUABNLKMKDJMENUNQ
---
This offset of seven shows just a single trigram in an overlap of 57 letters.
Turing's method of accumulating a score of a number of decibans allows the calculation of which of these situations is most likely to represent messages in depth. As might be expected, the former is the winner with odds of 5:1 on, the latter is only 2:1 on.
Turing calculated the scores for the number of single repeats in overlaps of so many letters, and the number of bigrams and trigrams. Tetragrams often represented German word in the plaintext and their scores were calculated according to the type of message (from traffic analysis), and even their position within the message. These were tabulated and the relevant values summed by Banburists in assessing pairs of messages to see which were likely to be in depth.
Bletchley Park used the convention that the indicator plaintext of "VFX", being eight characters ahead of "VFG", or (in terms of just the third, differing, letter) that "X = G+8".
Scritchmus
Scritchmus was the part of the Banburismus procedure that could lead to the identification of the right-hand (fast) wheel. The Banburist might have evidence from various message-pairs (with only the third indicator letter differing) showing that "X = Q-2", "H = X-4" and "B = G+3". He or she would search the deciban sheets for all distances with odds of better than 1:1 (i.e. with scores ≥ +34). An attempt was then made to construct the 'end wheel alphabet' by forming 'chains' of end-wheel letters out of these repeats. They could then construct a "chain" as follows:
G--B-H---X-Q
If this is then compared at progressive offsets with the known letter-sequence of an Enigma rotor, quite a few possibilities are discounted due to violating either the "reciprocal" property or the "no-self-ciphering" property of the Enigma machine:
G--B-H---X-Q
ABCDEFGHIJKLMNOPQRSTUVWXYZ ......... is possible
G--B-H---X-Q
ABCDEFGHIJKLMNOPQRSTUVWXYZ ......... is impossible (G enciphers to B, yet B enciphers to E)
G--B-H---X-Q
ABCDEFGHIJKLMNOPQRSTUVWXYZ ......... is impossible (H apparently enciphers to H)
G--B-H---X-Q
ABCDEFGHIJKLMNOPQRSTUVWXYZ ......... is impossible (G enciphers to D, yet B enciphers to G)
G--B-H---X-Q
ABCDEFGHIJKLMNOPQRSTUVWXYZ ......... is impossible (B enciphers to H, yet H enciphers to J)
G--B-H---X-Q
ABCDEFGHIJKLMNOPQRSTUVWXYZ ......... is impossible (Q apparently enciphers to Q)
G--B-H---X-Q
ABCDEFGHIJKLMNOPQRSTUVWXYZ ......... is impossible (G apparently enciphers to G)
G--B-H---X-Q
ABCDEFGHIJKLMNOPQRSTUVWXYZ ......... is impossible (G enciphers to H, yet H enciphers to M)
G--B-H---X-Q
ABCDEFGHIJKLMNOPQRSTUVWXYZ ......... is possible
G--B-H---X-Q
ABCDEFGHIJKLMNOPQRSTUVWXYZ ......... is possible
G--B-H---X-Q
ABCDEFGHIJKLMNOPQRSTUVWXYZ ......... is possible
G--B-H---X-Q
ABCDEFGHIJKLMNOPQRSTUVWXYZ ......... is impossible (H enciphers to Q, yet Q enciphers to W)
G--B-H---X-Q
ABCDEFGHIJKLMNOPQRSTUVWXYZ ......... is impossible (X enciphers to V, yet Q enciphers to X)
G--B-H---X-Q
ABCDEFGHIJKLMNOPQRSTUVWXYZ ......... is impossible (B enciphers to Q, yet Q enciphers to Y)
G--B-H---X-Q
ABCDEFGHIJKLMNOPQRSTUVWXYZ ......... is impossible (X enciphers to X)
Q G--B-H---X->
ABCDEFGHIJKLMNOPQRSTUVWXYZ ......... is possible
-Q G--B-H---X->
ABCDEFGHIJKLMNOPQRSTUVWXYZ ......... is impossible (Q enciphers to B, yet B enciphers to T)
X-Q G--B-H--->
ABCDEFGHIJKLMNOPQRSTUVWXYZ ......... is possible
-X-Q G--B-H-->
ABCDEFGHIJKLMNOPQRSTUVWXYZ ......... is impossible (X enciphers to B, yet B enciphers to V)
--X-Q G--B-H->
ABCDEFGHIJKLMNOPQRSTUVWXYZ ......... is possible
---X-Q G--B-H->
ABCDEFGHIJKLMNOPQRSTUVWXYZ ......... is impossible (X enciphers to D, yet B enciphers to X)
H---X-Q G--B->
ABCDEFGHIJKLMNOPQRSTUVWXYZ ......... is impossible (Q enciphers to G, yet G enciphers to V)
-H---X-Q G--B->
ABCDEFGHIJKLMNOPQRSTUVWXYZ ......... is impossible (H enciphers to B, yet Q enciphers to H)
B-H---X-Q G-->
ABCDEFGHIJKLMNOPQRSTUVWXYZ ......... is possible (note the G enciphers to X, X enciphers to G property)
-B-H---X-Q G->
ABCDEFGHIJKLMNOPQRSTUVWXYZ ......... is impossible (B enciphers to B)
--B-H---X-Q G->
ABCDEFGHIJKLMNOPQRSTUVWXYZ ......... is possible
The so called "end-wheel alphabet" is already limited to just nine possibilities, merely by establishing a letter-chain of five letters derived from a mere four message-pairs. Hut 8 would now try fitting other letter-chains — ones with no letters in common with the first chain — into these nine candidate end-wheel alphabets.
Eventually they will hope to be left with just one candidate, maybe looking like this:
NUP
F----A--D---O
--X-Q G--B-H->
ABCDEFGHIJKLMNOPQRSTUVWXYZ
Not only this, but such an end-wheel alphabet forces the conclusion that the end wheel is in fact "Rotor I". This is because "Rotor II" would have caused a mid-wheel turnover as it stepped from "E" to "F", yet that's in the middle of the span of the letter-chain "F----A--D---O". Likewise, all the other possible mid-wheel turnovers are precluded. Rotor I does its turnover between "Q" and "R", and that's the only part of the alphabet not spanned by a chain.
That the different Enigma wheels were given different turnover points was, presumably, a measure by the designers of the machine to improve its security. However, this very complication allowed Bletchley Park to deduce the identity of the end wheel.
Middle wheel
Once the end wheel is identified, these same principles can be extended to handle the middle rotor, though with the added complexity that you are now looking for overlaps in message-pairs sharing just the first indicator letter, and that the overlaps could therefore occur at up to 650 characters apart.The workload of doing this is beyond manual labour, so BP punched the messages onto 80-column cards and used Hollerith machines to scan for tetragram repeats or better. That told them which banburies to set up on the light boxes (and with what overlap) to evaluate the whole repeat pattern.
Armed with a set of probable mid-wheel overlaps, Hut 8 could compose letter-chains for the middle wheel much in the same way as was illustrated above for the end wheel. That in turn (after Scritchmus) would give at least a partial middle wheel alphabet, and hopefully at least some of the possible choices of rotor for the middle wheel could be eliminated from turnover knowledge (as was done in identifying the end wheel).
Taken together, the probable right hand and middle wheels would give a set of bombe runs for the day, that would be significantly reduced from the 336 possible.
Further reading
- Sebag-Montefiore, HughHugh Sebag-MontefioreHugh Sebag-Montefiore is a British writer. He trained as a barrister before becoming a journalist and then a non-fiction writer. His second book "Dunkirk: Fight to the Last Man" was published in 2006...
. Enigma — the battle for the code. Cassell Military Paperbacks, London, 2004. ISBN 978-1-407-22129-8
.
External links
- The 1944 Bletchley Park Cryptographic Dictionary
- "All You Ever Wanted to Know About Banburismus but were Afraid to Ask" — the whole procedure researched in detail, with a worked example.