Turing’s Bombes. Solve Enigma using known plaintext Depending on German patterns, e.g. weather...
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Transcript of Turing’s Bombes. Solve Enigma using known plaintext Depending on German patterns, e.g. weather...
![Page 1: Turing’s Bombes. Solve Enigma using known plaintext Depending on German patterns, e.g. weather reports Sometimes setup by seeding/farming Depended on.](https://reader035.fdocuments.net/reader035/viewer/2022062906/5a4d1b517f8b9ab0599a7d6c/html5/thumbnails/1.jpg)
Turing’s Bombes
![Page 2: Turing’s Bombes. Solve Enigma using known plaintext Depending on German patterns, e.g. weather reports Sometimes setup by seeding/farming Depended on.](https://reader035.fdocuments.net/reader035/viewer/2022062906/5a4d1b517f8b9ab0599a7d6c/html5/thumbnails/2.jpg)
Solve Enigma using known plaintext
• Depending on German patterns, e.g. weather reports
• Sometimes setup by seeding/farming
• Depended on Engima characteristics:– No letter enciphered to itself– Self-inverse of cipher
![Page 3: Turing’s Bombes. Solve Enigma using known plaintext Depending on German patterns, e.g. weather reports Sometimes setup by seeding/farming Depended on.](https://reader035.fdocuments.net/reader035/viewer/2022062906/5a4d1b517f8b9ab0599a7d6c/html5/thumbnails/3.jpg)
Procedure (by hand)• Find a crib – piece of known plaintext• Find its alignment
– No letter matches reduces possibilities– All possible alignments may need to be tested
• Test an alignment by working through possible plugboard settings for every rotor setting– Inconsistency eliminates this rotor setting– Consistent plugboard setting makes this rotor
setting a likely candidate – test it on the rest of the message
![Page 4: Turing’s Bombes. Solve Enigma using known plaintext Depending on German patterns, e.g. weather reports Sometimes setup by seeding/farming Depended on.](https://reader035.fdocuments.net/reader035/viewer/2022062906/5a4d1b517f8b9ab0599a7d6c/html5/thumbnails/4.jpg)
Example
URUXI CHDII FOEQA DIIYD RYHMN NQOVWUNIV ERSIT YHALL
UNIV ERSIT YHALL
OEQADIIYD RYHMN
UNIVERSITYHALL
ENIGMA
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OEQADIIYD RYHMN
UNIVERSITYHALL
PLUGBOARD
ROTORSsetting 1setting 2setting 3
… PLUGBOARD
Need to check for all possible rotor positions at setting 1
![Page 6: Turing’s Bombes. Solve Enigma using known plaintext Depending on German patterns, e.g. weather reports Sometimes setup by seeding/farming Depended on.](https://reader035.fdocuments.net/reader035/viewer/2022062906/5a4d1b517f8b9ab0599a7d6c/html5/thumbnails/6.jpg)
Checking one rotor settingOEQADIIYD RYHMN
UNIVERSITYHALL
ABCDEFGHIJKLM NOPQRSTUVWXYZJNPXFEZVRAQUS 1 BWCKIMYLHODTG
BAONURQJZHPTS 2 DCKGFMLEYXWVI
VGIMPYBWCZURD 3 TXESLQNKAHOFJ
FSWUGAEQPVTRO 4 YMIHLBKDJCZNX
UILXONWVBRQCT 5 FESKJPMAHGDZYTZWXPGFONQRVS 6 IHEJKMAYLCDUB
HNUXKSYARQEML 7 BPOJIFVCTZDGW
MENVBZLQSYWGA 8 CRXHOIUTDKPJF
OVRUGHEFYMNZJ 9 KAXSCQWDBTPIL
QEGYBKCVMOFTI 10 ZJXASRLWHUPDN
OWPFGDEVTNSXQ 11 JACMYKIZHBLRU
IFRYJBNZAEWOP 12 GLMVCUXSQKTDH
YSEMCWXPZRNQD 13 KUHLJBVOTFGAI
LMVJUNWZRDPAB 14 FTKYIXOECGSQH
Assume I-A
and continue
1 V-Q, M-Y, R-T, S-H,
3 8 6 7
2 I-R, L-Y, K-Y
10 10 11
3 N-I, G-I, W-I
6 8 8
![Page 7: Turing’s Bombes. Solve Enigma using known plaintext Depending on German patterns, e.g. weather reports Sometimes setup by seeding/farming Depended on.](https://reader035.fdocuments.net/reader035/viewer/2022062906/5a4d1b517f8b9ab0599a7d6c/html5/thumbnails/7.jpg)
Menu is a summary of relationships
U
N E
I
TDLM
O
R Q
YHAV S
1
13 14 2 5 9
36
4 12 11
10 78
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Checking a rotor setting
• All possible plugboard connections for a letter are generated – means this setting cannot work
• All plugboard connections generated are consistent – means this is a likely rotor setting
• All but one plugboard setting are generated – means the other is likely correct
![Page 9: Turing’s Bombes. Solve Enigma using known plaintext Depending on German patterns, e.g. weather reports Sometimes setup by seeding/farming Depended on.](https://reader035.fdocuments.net/reader035/viewer/2022062906/5a4d1b517f8b9ab0599a7d6c/html5/thumbnails/9.jpg)
How to mechanize this?• Need an enigma for each link indicated• Enigmas should be set the given number of
steps apart – if the link is X, then it should be X-1 steps ahead of link 1.
• Double-ended, so they can be chained together.
• Need to arrange feedback into the system
![Page 10: Turing’s Bombes. Solve Enigma using known plaintext Depending on German patterns, e.g. weather reports Sometimes setup by seeding/farming Depended on.](https://reader035.fdocuments.net/reader035/viewer/2022062906/5a4d1b517f8b9ab0599a7d6c/html5/thumbnails/10.jpg)
How to mechanize this?• Each letter has 26 wires, one for each possible
plugboard setting• One wire is selected for one letter (say I-A as in
our example)• Current goes through that wire into the enigma
set at position 8 (and the one at position 3)• All the outputs of 8 are linked to Y, but only one
(M-Y) is activated.• This is attached to the M-Y wire feeding into
enigma set at position 10. All its 26 outputs go to R. Output I-R is selected.
• The I inputs now go into R at positions 3 and 8 and the process continues
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How to mechanize this?
• Turing had the idea of this mechanism• Welchman added the observation that the
links are all two-way– If M-Y is selected, then Y-M should also be
selected.– He devised a wiring that made connections so
the circuits reflected this – the “diagonal board”
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What it looked like
![Page 13: Turing’s Bombes. Solve Enigma using known plaintext Depending on German patterns, e.g. weather reports Sometimes setup by seeding/farming Depended on.](https://reader035.fdocuments.net/reader035/viewer/2022062906/5a4d1b517f8b9ab0599a7d6c/html5/thumbnails/13.jpg)
What it looked like
![Page 14: Turing’s Bombes. Solve Enigma using known plaintext Depending on German patterns, e.g. weather reports Sometimes setup by seeding/farming Depended on.](https://reader035.fdocuments.net/reader035/viewer/2022062906/5a4d1b517f8b9ab0599a7d6c/html5/thumbnails/14.jpg)
SchematicRed = top drum, Green = middle drum, Blue = bottom drum
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One set of drums = One Enigma
• Set of three rotors and reflector• Left wires are 26 letters in• Right wire are 26 letters out• These wires are used to connect
according to the menu
![Page 16: Turing’s Bombes. Solve Enigma using known plaintext Depending on German patterns, e.g. weather reports Sometimes setup by seeding/farming Depended on.](https://reader035.fdocuments.net/reader035/viewer/2022062906/5a4d1b517f8b9ab0599a7d6c/html5/thumbnails/16.jpg)
Simplified example with 8 lettersa,b,c,d,e,f,g,h
123456789BEACHHEADEDBGEAHDB
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Simplified example with 8 letters
![Page 18: Turing’s Bombes. Solve Enigma using known plaintext Depending on German patterns, e.g. weather reports Sometimes setup by seeding/farming Depended on.](https://reader035.fdocuments.net/reader035/viewer/2022062906/5a4d1b517f8b9ab0599a7d6c/html5/thumbnails/18.jpg)
Simplified example with 8 letters
![Page 19: Turing’s Bombes. Solve Enigma using known plaintext Depending on German patterns, e.g. weather reports Sometimes setup by seeding/farming Depended on.](https://reader035.fdocuments.net/reader035/viewer/2022062906/5a4d1b517f8b9ab0599a7d6c/html5/thumbnails/19.jpg)
Simplified example with 8 letters
Turing’s Version
![Page 20: Turing’s Bombes. Solve Enigma using known plaintext Depending on German patterns, e.g. weather reports Sometimes setup by seeding/farming Depended on.](https://reader035.fdocuments.net/reader035/viewer/2022062906/5a4d1b517f8b9ab0599a7d6c/html5/thumbnails/20.jpg)
Simplified example with 8 letters
![Page 21: Turing’s Bombes. Solve Enigma using known plaintext Depending on German patterns, e.g. weather reports Sometimes setup by seeding/farming Depended on.](https://reader035.fdocuments.net/reader035/viewer/2022062906/5a4d1b517f8b9ab0599a7d6c/html5/thumbnails/21.jpg)
Circuits carry out trace electricallyProcess
• Set voltage to one wire for selected letter– For example E-A
• Register includes all wires for a selected letter– For example all E wires
• For a given position of the rotors, let circuit build
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Circuits carry out trace electricallyThree outcomes
• Circuits cascade until all E wires are connected to voltage – indicates rotor setting does not work
• Circuits cascade until all but one E wire are connected – indicates the rotor setting works for the unselected wire
• Circuits are consistent, only one E wire (and only one for any other letter) is live – indicates rotor setting is likely solution
![Page 23: Turing’s Bombes. Solve Enigma using known plaintext Depending on German patterns, e.g. weather reports Sometimes setup by seeding/farming Depended on.](https://reader035.fdocuments.net/reader035/viewer/2022062906/5a4d1b517f8b9ab0599a7d6c/html5/thumbnails/23.jpg)
Bombe rotates through rotor settings
• When all wires in E register are on, continue to next setting
• When one or more wires are not on, stop– Could be one of the situations that indicates a
possible rotor setting– The setting must be checked for consistency– If consistent, then check to see if decode
results
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Bombe capacity• One row of Bombe has 12 pseudo-enigmas
connected (means max of 12 links)• Each of three rows is set to a different rotor
order• Top rotors move at 120 rpm
– This means 26 * 120 rotor positions per minute!– 5 2/3 minutes to check all 17,576 positions for
the given rotor order• Motion stops as described
– rotor position needs to be recorded and checked, then bombe is restarted
![Page 25: Turing’s Bombes. Solve Enigma using known plaintext Depending on German patterns, e.g. weather reports Sometimes setup by seeding/farming Depended on.](https://reader035.fdocuments.net/reader035/viewer/2022062906/5a4d1b517f8b9ab0599a7d6c/html5/thumbnails/25.jpg)
Bombe• Once one message is broken for an
enigma group (army, naval, etc), then all messages can be decoded for that day
• At midnight, a new day-key would take effect and the process would start again