Enigma

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Enigma
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Zimmerman Telegram

• Proposal by Arthur Zimmerman, Germanys Foreign
  Minister
• To offer Mexico New Mexico, Texas and Arizona in
  return for declaring war on the US
• To invite Japan to attack the US from the west
• With US tied down, Germany would begin
  unrestricted submarine warfare in the Atlantic
• Encrypted telegram sent to German Ambassador in
  Washington
• Captured and decrypted by the British
• Resulted in US entry into WWI

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New Issues by 1918

• Marconi had invented the radio
• Military Upside generals are in direct contact
  with soldiers in the field without laying land
  lines
• Military Downside
• communication was public to anyone with a radio
  receive
• Many more ciphertexts could be captured by enemy
• Georges Painvin broke ADFGX in 1918 and foiled a
  German artillery attack on Paris

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Georges Painvin

• Broke ADFGX in March, 1918

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Rotor Machines

• Response to the cat and mouse game of
  encrypt/decrypt played out by cryptographers and
  cryptoanalysts
• Several were invented in the 20s
• Enigma, invented by Arthur Scherbius
• Broken by three Polish cryptoanalysts in the
  30s.
• Passed their technique on to the British in 1939,
  two months before the invasion of Poland
• Extended by the British who were able to decode
  German messages throughout the war

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Alan Turing

• Led the team that built a device called a bombe
  that decrypted enigma-encrypted messages
• Work done in secret at Bletchley Park

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Bletchley Park

• Home of the Government Code and Cypher School
• Sign read Golf Club and Chess Society

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Enigma

• Three rotors, L, M, N, each with 26 settings
• Reversing drum, R
• Plugboard, S, that has pairs of plugs that can be
  used to interchange seven pairs of letters

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Mechanism

• Key is pressed
• N turns 1/26 of a turn
• L, M also rotate, but much less often
• When electricity reaches R, it is sent back
  through L, M, N but along a different path
• Electricity lights a bulb that is the encrypted
  character
• Security resides in the initial settings of the
  rotors, the settings of the plugs on the
  plugboard and the internal wiring of the rotors
• Settings of the rotors and plugboard constitute
  the key and are changed frequently

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The Key

• How Many Different Settings for the Rotors and
  PlugBoard?
• The Cryptographic Mathematics of Enigma
• 3,283,883,513,796,974,198,700,882,069,882,752,878,
  379,955,261,095,623,685,444,055,315,226,006,433,61
  5,627,409,666,933,182,371,154,802,769,920,000,000,
  000 different settings
• Approximately 3 10114.
• About 1080 atoms in the observable universe

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Breaking the Code

• Each operator had a codebook with different
  settings to be used for the next month
• If settings were used unmodified, all messages
  during a given day would have same
  substitutionsvulnerable to frequency analysis
• Instead, for each message
• Choose a key
• Encrypt the key using the daily settings
• Since each message uses a different key,
  frequency analysis is not possible.
• Flaw Protocol required that enigma operators
  transmit the encrypted key twice at the beginning
  of each message.