Turings Bombes

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Turings Bombes
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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

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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

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Example
UNIV ERSIT YHALL
URUXI CHDII FOEQA DIIYD RYHMN NQOVW
UNIV ERSIT YHALL
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Need to check for all possible rotor positions at
setting 1
ROTORS setting 1setting 2setting 3
OEQADIIYD RYHMN
UNIVERSITYHALL
P L U G B O A R D
P L U G B O A R D
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Checking one rotor setting
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
OEQADIIYD RYHMN
UNIVERSITYHALL
and continue
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Menu is a summary of relationships
U
O
N
E
T
D
L
M
I
R
Q
10
7
8
S
Y
H
A
V
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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

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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

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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
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What it looked like
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Schematic
Red 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

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Simplified example with 8 lettersa,b,c,d,e,f,g,h

• 123456789
• BEACHHEAD
• EDBGEAHDB

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Simplified example with 8 letters
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Simplified example with 8 letters
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Simplified example with 8 letters
Turings Version
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Simplified example with 8 letters
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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

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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

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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