Encryption

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Encryption

• Discrete Math
• March 7, 2006
• Harding University
• Jonathan White

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Outline

• Terms
• Types of Attacks
• Classical Techniques
• Substitution
• Caesar
• Monoalphabetic
• Playfair
• Shifting
• Rail Fence Cipher
• Rotor Machines (Enigma)

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Outline (2)

• Data Encryption Standard (DES)
• Triple DES
• Blowfish
• MD5, SHA-1
• RSA
• Quantum Computers

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Terms

• Plaintext
• Ciphertext
• Cipher
• Key
• Cryptography
• Symmetric Encryption
• Asymmetric Encryption

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Terms

• Security by Obscurity
• Brute Force Search Attack
• Dictionary Attack
• Man in the Middle Attack
• Cipher Attacks
• Plaintext Attacks
• Steganography
• Unconditional security
• Computational security

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Brute Force Attacks

• Brute Force Searches
• Simply try every possible key
• Effort required is proportionate to the key size
• You must recognize the plaintext once you see it!
• Typically uses no knowledge about the cipher, the
  cipher text, or the plaintext, so it is very easy
  to do.

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Dictionary Attacks

• For this attack, you have already encrypted a
  large amount of plaintext.
• You simply search what youve already encrypted
  for a match.
• This is how most password crackers work.
• Is your password something common like
• An English word?
• A variation of your username?
• Numbers or letters at the beginning or end
  appended to the above?
• Blank?
• Guessing, along with dictionary attacks, have
  proven to break 50 of all passwords.
• Older Unix systems only allow 8 character
  passwords

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Plaintext Attacks

• Plaintext Attacks
• Attack the language the plaintext was written in
• Human languages are very redundant
• Ever seen Wheel of Fortune?
• ASCII characters are also very predictable
• C/Java/Lisp code is very redundant
• Military communications are very redundant
• Most ciphers overcome this by appending a bit of
  random characters to the end of the message
• Called padding.

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Cipher Attacks

• Attack something that is known about the cipher
• For example, if you encrypt 0 and 1 in RSA, the
  ciphertext is the exact same
• Ciphers typically have periodic behavior, which
  can be attacked.
• However, most modern ciphers have been
  extensively studied and have very few potential
  attacks.
• No Security by Obscurity
• In fact, you want people to try and crack your
  cipher it just makes you look better when they
  cant crack it.

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Unconditional Security

• Very difficult to provide.
• One of the only known unconditional secure
  algorithms is a random, one time pad, key that is
  as long as the message.
• Since the key is completely random, you can just
  add the letters in the key and the message
  together and send them. The cipher text bears no
  statistical relationship between the plaintext.
• You can only use the key once though.
• However, how do you distribute the key?
• Russian nuclear crisis.

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Classical Substitution Ciphers

• Where letters of the plaintext are replaced by
  other letters or symbols.
• Or, if viewed as bit patterns, a sequence of bits
  in the plaintext is replaced with a sequence of
  bits in the plaintext.
• Very easy to use.
• Theyve been around the longest.
• The key is the mapping that you used from the
  plaintext to the cipher text.

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Caesar Cipher

• Earliest known substitution cipher.
• Used in military affairs.
• Replaces each letter in the plaintext by the nth
  letter down in the alphabet, wrapping back
  around.
• In this case, the key is just the shift number
  that you chose.
• To unencrypt, you just subtract the n from the
  ciphertext to get the original.

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Caesar Example

• Encrypt this message with a shift of 5
• The brown fox ate the sheep

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Cryptanalysis of Caesar

• Only have 26 possible orders.
• Very easy to defeat using brute force.
• You do need to recognize when you have the
  plaintext, however.

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Monoalphabetic Cipher

• Rather than just shifting the alphabet, you could
  just jumble the letters arbitrarily.
• Each plaintext letter then maps to a different
  ciphertext letter.
• The key is then 26 characters long.
• So, we have 26! possible keys.
• But, this does not conceal the language
  characteristics.
• Also, tables exist for double and triple letter
  frequencies such as ing, th, ou, etc
• These ciphers dont change the relative letter
  frequencies.

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Monoalphabetic Example

• Let the key and plaintext be
• QWERTYUIOPASDFGHJKLZXCVBNM
• If we wish to replace these letters
• GO TO THE MALL
• The ciphertext is

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Playfair Cipher

• A 5 x 5 matrix of letters based on a keyword.
• Fill in letters of keyword without duplicates
• Then, just fill in the rest of the matrix with
  the rest of the alphabet going in order.
• J and I are the same letter in the playfair
  cipher so, there are only 25 letters in the
  alphabet.

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Playfair Encrypting/Decrypting

• Plaintext is encrypted 2 letters at a time
• If a pair is a repeated letter, insert a filler
  letter like x
• Exp balloon becomes ba lx lo on
• If both letters fall in the same row, replace ach
  with the letter to the right (wrapping back to
  start from the end)
• Exp ar encrypts as rm
• If both letters fall in the same column, replace
  each with the letter below it, wrapping bottom to
  top.
• Exp mu encrypts as cm
• Otherwise, each letter is replaced by the one in
  its row in the column of the other letter of the
  pair.
• Exp hs encrypts to bp, ea encrypts to
  im

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Playfair Security

• We have 25 x 25 potential combinations 625!
  potential ways to encrypt.
• Widely used for many years, including WW1.
• But, it can be broken, given a few hundred
  letters.
• With a computer, this is quite simple, because
  some of the plaintext structure still remains.

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Transposition Ciphers

• These hide the message by rearranging the letter
  order.
• The actual letters arent altered.
• However, the ciphertext will still have the same
  relative frequency as the original text.
• These are typically incredibly quick.

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Rail Fence Cipher

• Write your message horizontally across a narrow
  sheet of paper.
• Wrap the paper around a circular post that both
  you and the person you wish to send the message
  to both posses one of.
• Then, just write down the letters you see
  starting at the top of the post.
• Very insecure.

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The Enigma Machine

• Used by the Germans in WW2 to encrypt and decrypt
  messages.
• Used a series of rotors connected to a complex
  electrical circuit and some initial letter swaps
  to encrypt messages.
• Produced incredibly strong encryption for its
  time.
• Decryption was exactly the same as encryption
  provided you knew the starting position.
• http//www.enigmaco.de/enigma.swf

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Enigma Machine 2

• The interesting thing about the Enigma is that
  the substitution pattern changes after every
  keystroke.
• No longer just a simple substitution cipher.
• There are 263 possible start positions for the
  rotors.
• This would be relatively easy to solve.
• But, this does remove a lot of the letter
  frequencies apparent in the German language.
• There are still 26! ways to substitute the
  original letters.
• Altogether, (if a few mishaps hadnt occurred),
  this cipher cant be beat by humans.

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Enigma Machine 3

• Mishaps
• Letters couldnt encrypt to themselves.
• Sometimes test messages were sent by lazy
  operators that only used one letter.
• Repeating the same greeting in every message.
• Please Respond, Dear, weather reports
• Always using X for the space key.
• Letting operators always choose their passphrase.
• Mother/Father/Girlfriends name, city, favorite
  soccer team
• Stolen codebooks
• Helps for a little while
• Stolen machines
• What really allowed the Polish and British
  intelligence agencies to crack the Enigma.
• Only around 15 machines were ever captured.

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Enigma Machine 4

• In order to test potential codes, the Americans
  designed one of the first computers. This was
  aided by Alan Turing, a British citizen.
• By the end of the war, all Enigma communications
  could be broken in under 3 days. However, the
  Allies didnt always use this information.
• Battle of the Bulge.
• Many officials have estimated that by cracking
  the Enigma, WW2 ended 1 year earlier than it
  would have.