CSIS 5857: Encoding and Encryption

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CSIS 5857 Encoding and Encryption

• Lecture 4
• History and Background Part 2 -- Polyalphabetic
  Substitution Ciphers

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Polyalphabetic Substitution

• Single plaintext character may map to multiple
  possible ciphertext characters
• Frequency analysis attacks much harder
• Example Vigenére cipher
• Key some word or phrase of length n
• Ci (Pi Ki mod n) mod 26

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Vigenére cipher
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Vigenére cipher

• Example
• Key python
• Plaintext rabbitwithbigpointyteeth
• Ciphertext

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Polyalphabetic Substitution

• Vigenére cipher still vulnerable to
  frequency-based cryptanalysis
• Guess key size n
• Treat like n different monoalphabetic
  substitutions
• General principleLarger n ? more secure

(that is, number of characters before repetition)
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Enigma

• Developed by Germany in WW2
• Arguably most complex pre-computer substitution
  cipher

Flash simulation at http//enigmaco.de/enigma/eni
gma.html
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Enigma
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Enigma

• Consists of 3 to 5 rotors
• Each rotor is a monoalphabetic mapping of a
  plaintext character to a ciphertext character
• Output of one rotor fed into input of next rotor
  so final output the result of 3 to 5
  monoalphabetic substitutions
• Rotors turn after each character!
• Fast rotor every character
• Middle rotor every 26 characters
• Slow rotor every 26 x 26 676 characters

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Enigma
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Enigma

• C typed as first character
• C connected to 26 on fast rotor ?
• 26 connected to 7 on middle rotor ?
• 7 connected to 20 on slow rotor ?
• 20 connected to E (then reflected back through)
• C typed as second character (after fast rotator
  turns one character)
• C connected to 25 on fast rotor ?
• 25 connected to 23 on middle rotor ?
• 23 connected to 9 on slow rotor ?
• 9 connected to O (then reflected back through)

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Enigma

• 26 x 26 x 26 17,576 characters entered before
  repetition
• Essentially invulnerable to frequency-based
  cryptanalysis (particularly if rotors changed at
  regular intervals)
• Required Alan Turings Bletchley Group to crack
• Captured machines to understand patterns
• Large numbers of known plaintexts
• Exhaustive searches using primitive computers

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One-Time Pad

• Idea Make key as long as the message
  itself!(Joseph Mauborgne)
• Unconditionally securesince inherently ambiguous
  for attacker

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One-Time Pad

• Example
• Ciphertext NZAKBMK
• Possible Vigenére keys wtnkxmm and nlvwker
  Ciphertext NZAKBMK NZAKBMK Possible keys
  nlvwker wtnkxmmPlaintext goforit runaway
• Which key is correct?We have no way of
  knowingsince both are plausible plaintext!

???
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One-Time Pad

• Only get to use a key for one message
• Unlikely that different possible keys would still
  both result in plausible plaintext for more than
  one message
• Adversary could find correct key by process of
  elimination
• Ciphertext WMGKZX WMGKZX Possible
  keys nlvwke wtnkxm Plaintext jblopt
  attack
• Would need to securely distribute a new key for
  each message!

This is the one!