The cracking of Enigma in World War II

1
The cracking of Enigmain World War II
CS 4235 Project 1 Security Events - Threats
and Vulnerabilities

• John Bibb
• Harry Caplan
• Abhishek Chhikara
• Vladimir Grantcharov
• Aditi Kulkarni
• Nigel Lawrence
• Andrew Muldowney
• Hou Nguyen
• Sofia Tania

2
What is Enigma?

• rotor machine used for the encryption and
  decryption of secret messages
• Developed in early 1920s
• Combination of mechanical and electrical
  subsystems
• Keyboard
• Rotating disks (rotors)
• display lamps

3
What happened?
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Cracking the Enigma

• Enigma has so many possibilities, that an
  important aspect of breaking them, is deducing
  their logical structure.
• Enigma generated a polyalphabetic substitution
  cipher with a long period. Given three
  single-notched rotors, the period was 16,900 (
  26 25 26).7
• A letter could never be encrypted to itself. This
  property was of great help in using cribs and
  could be used to eliminate a crib in a particular
  position. It was this feature that the British
  mathematician and logician Alan Turing would
  exploit in designing the British bombe.
• A second Enigma weakness was that the plugboard
  connections were reciprocal, so that if A was
  plugged to N, then N likewise became A.
• A number of the officially-specified procedures
  for using Enigma also provided avenues for
  attack. Thus, for machines where there was a
  choice of more rotors than there were slots for
  them, a rule stipulated that no rotor should be
  in the same slot in the scrambler as it had been
  for the immediately preceding configuration.
  Also, no wheel order could be repeated on the
  monthly setting sheet.
• It has been suggested by some who worked at
  breaking Enigma at Bletchley Park that the Enigma
  should have been unbreakable in practice, had its
  operating procedures been better thought out and
  had its operators been less ill-disciplined.
• http//upload.wikimedia.org/wikipedia/commons/6/6c
  /Enigma-action.svg
• http//enigmaco.de/enigma/enigma.swf Working Model

5
Bomba

• Designed about October 1938 by Polish Cipher
  Bureau Bomba
• Each bomb essentially constituted an
  electrically-powered aggregate of six Enigmas and
  took the place of some one hundred workers
• Using the knowledge that the first three letters
  of a message were the same as the second three,
  Polish mathematiciancryptologist Marian Rejewski
  was able to determine the internal wirings of the
  Enigma machine and thus to reconstruct the
  logical structure of the device.
• In mid-November 1938 the bombs were
• ready, and the reconstructing of daily keys now
  took
• about two hours.
• Up to July 25, 1939, the Poles had been breaking
• Enigma messages for over six and a half years
• without telling their French and British allies.

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Bombe

• On December 15, 1938, two new rotors were
  introduced.
• Creator of Bomba "we quickly found the wirings
  within the new rotors, but their
  introduction...raised the number of possible
  sequences of drums from 6 to 60...and hence also
  raised tenfold the work of finding the keys. Thus
  the change was not qualitative but quantitative.
• A bombe would consist of a number of these sets
  of rotors wired up according to a menu prepared
  by codebreakers. At each position of the rotors,
  an electrical test would be applied. For a large
  number of the settings, the test would lead to a
  logical contradiction, ruling out that setting.
  If the test did not lead to a logical
  contradiction, the machine would stop and ring a
  bell, and the candidate solution would be
  examined further, typically on a replica of the
  German Enigma machine, to see if that decryption
  produced German.
• Typically, there were many false matches
• before the correct match was found.
• Designed by Alan Turing
• Eventually over 200 Built by both
• US and British Forces
• Also built to contend with late model
• 4 rotor Enigmas

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What was the impact?
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Impact

• Germans thought Enigma unbreakable
• Used for all top secret communication
• Dutch Idea -gt German Spy -gt French Spymasters -gt
  British French Polish Efforts -gt Breakthrough
  by Poland -gt Later Britain
• From 1933 1940
• Marginal Impact

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The Breakthrough

• Year 1941 beyond
• Allies detected German round-up near Greece
• Allies Mediterranean fleet defeated the Italians
  at the Battle of Matapan
• Allies gained important advantage in North Africa
• German U-Boat program brought to standstill
• 90 European Intelligence summaries provided to
  US based on Enigma
• Larger context Information is Power

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Repercussions

• Undermined Axis offensive
• May have ended the war early
• Contributed to the eventual Allied victory

11
Why did this attack succeed?
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Elements of Enigma

• Plaintext
• Algorithm
• Key
• It takes all three elements to
• perform the decryption.

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Getting The Plaintext

• Infrastructure Y stations

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Getting The Algorithm

• The role of mathematicians

Marian Rejewski Photo from Wikipedia
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Getting The Key

• The role of mathematicians

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Getting The Key

• Clues based on patterns in messages
• Opening
• Spruchnummer (Message Number)
• An die Gruppe (To the group) Air Force
  messages
• Content
• Weather reports
• Keinebesondere Ereignisse (Nothing to report)
• Duplicate messages

17
What happened inthe aftermath?
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Perspective of Nazis

• After the code was broken, the Nazis were
  unwilling to see the evidence of it as a breaking
  of the code rather, they assumed that the British
  simply had exceptional spies who were leaking
  information. Thus they concentrated their efforts
  on finding these spies, instead of adapting their
  code further.

http//cultureandcommunication.org/deadmedia/index
.php/Enigma_machineAftermath
19
Consequences

• Hitler postponed invasion of Britain until spring
  1941, after a failed invasion in Oct 1940.

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Significance of Codebreak

• It is estimated that the success of the efforts
  to code break the German Enigma machine helped
  The Allies defeat Nazi Germany two years earlier
  than they would without it. This saved countless
  lives, and making it one of the most successful
  intelligence operations in history.

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Popularity of the Event

• The Enigma intercepts came to be known by the
  codename ULTRA and while they were perhaps not
  directly responsible for winning the war as
  sometimes credited, the information provided by
  the Bletchley Park cryptanalysts certainly
  shortened the war and saved many lives.

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What was done tomake systems less vulnerable to
thiskind of threat?
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Modification Before WWII

• Added two rotors
• Operators stopped sending individual message
  settings twice at the start of each message
• Eliminated the original method of attack

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Modifications During WWII

• Occasionally added new rotors, but never on a
  widespread scale
• Triton
• New version of Enigma
• Had 4 wheels instead of 3

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What chapter in thebook will be helpfulin
understandingthis event?

• Chapter 2 - Elementary Cryptography

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Sources

• Marian Rejewskis photo http//en.wikipedia.org/w
  iki/FileMR_1932_small.jpg
• http//www.enigmahistory.org/main.html
• http//www.ams.org/featurecolumn/archive/enigma.ht
  ml
• http//www.iwm.org.uk/upload/package/10/enigma/eni
  gma9.htm
• http//math.usask.ca/encryption/lessons/lesson00/p
  age8.html
• http//library.thinkquest.org/28005/flashed/timema
  chine/courseofhistory/bombe.shtml
• http//plus.maths.org/issue34/features/ellis/