Elementary Cryptography

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Elementary Cryptography

• Concepts of encryption
• Symmetric (secret key) Encryption
• (DES AES)
• Asymmetric (public key) Encryption
• (RSA)
• Key exchange protocols and certificates
• Digital Signatures
• Cryptographic hash functions

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Elementary CryptographyTerminology Background

• Sender (A), Recipient (B), Transmission media (T)
• Interceptor / intruder (C) (availability)
• C might block message from reaching R
• C might intercept message (confidentiality)
• C might modify message (integrity)
• C might fabricate an authentic-looking message
  (integrity)

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Terminology Background

• Encryption process of encoding a message
• Decryption transforming encoded message back to
  normal
• Encrypt encode , encipher
• Decrypt decode, decipher
• Cryptosystem system for encryption and
  decryption
• Plaintext original form of message
• Ciphertext encoded form of message

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Terminology Background

• Algorithms rules for encryption and decryption
• Key value used to encrypt message
• C E(K, P) where Pplaintext, K key, E
  encryption algorithms, and C ciphertext
• Symmetric encryption P D(K, E(K,P))
• Asymmetric encryption P D(KD, E(KE,P))
• Keyless cipher
• Cryptography (hidden writing) uses encryption
  to hide message
• Cryptanalysis attempts to find meanings in
  encrypted messages
• Cryptology study of encryption and decryption

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Types of Encryption

• Substitution one or more characters are
  replaced with another
• Transpositions (permutations) order of
  characters is rearranged
• Hybrid combinations of the two types

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Substitution Ciphers

• Caesar Cipher
• Each letter is translated a fixed number of
  positions in the alphabet
• Ci E(pi) pi 3
• Plaintext A B C D E F G H I J K L
• Ciphertext d e f g h i j k l m n o
• Easy to perform easy to break
• Look for double letters and then use common words
  with double letters

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Other Substitution Ciphers

• Use a key to scramble the letters
• A B C D E F G H I J K L M N O
• c i p h e r s a b d f g j k l
• Rearrange using a fixed distance between letters
  (e.g. every 3rd)
• A B C D E F G H I J K L M N O
• a d g j m p s v y b e h k n r

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Complexity of Substitution Encryption and
Decryption

• Substitution encryption algorithms can be
  performed by direct lookup in tables and are O(n)
  algorithms

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One-Time Pads

• The pad consists of a large number of pages where
  each page contains a non-repeating key
• The sender would write the keys above the message
  (e.g. a 300 character message would require 30
  pages of 10 character keys)
• The message is scrambled using a Vigenere tableau
  built from the message and key
• Problem is synchronizing the receivers pad with
  the senders pad

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Vernum Cipher

• One-time pad consists of an arbitrary long
  non-repeating sequence of numbers that are
  combined with the plaintext
• Each plaintext character is represented by its
  numeric equivalent and is added to one of the
  random numbers. The ciphertext character is
  computed from the sum mod 26
• Repeated characters are typically represented by
  different ciphertext characters

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Book Ciphers

• Uses a passage from a book to form the letters at
  the top of a Vigenere Tableau
• Computes ciphertext character by taking the
  intersection of the plaintext character and
  corresponding character at that position from the
  book passage
• Relatively easy to break using frequency
  distributions

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Transpositions (Permutations)

• Columnar Transposition rearranging plaintext
  message into columns and then reading it row by
  row
• YES COMPUTER SECURITY IS FUN would be written
• Y M R R S
• E P S I F
• S U E T U
• C T C Y N
• O E U I X
• is encrypted as ymrrs epsif suetu ctcyn
  oeuix where the X is just filler.
• Transposition algorithms require a constant
  amount of time per character and are O(n)
  algorithms, but space required to store results
  and delay in waiting for all characters to be
  read are dependent on the size of the plaintext

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Cryptanalysis

• Attempt to break a single message
• Attempt to recognize patterns in encrypted
  messages
• Attempt to infer some meaning without breaking
  the encryption
• Attempt to deduce the key
• Attempt to find weaknesses in the implementation
  or environment of use of encryption
• Attempt to find general weaknesses in an
  encryption algorithm

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Breakable Encryption

• An encryption algorithm is called breakable when,
  given enough time and data, an analyst can
  determine the algorithm
• May be impractical
• A 25-character message of just uppercase letters
  has 2625 (1035) possible decipherments. A
  computer performing 1010 operations/sec would
  take 1011 years

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Cryptoanalysis of Substitution Ciphers

• Brute force would require trying checking 26!
  permutations which at one permutation per
  microsecond would take over a thousand years
• Look for short words, words with repeated
  patterns, common first and last letters
• Look at frequency distributions
• Could reduce time to hours

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Cryptoanalysis of Transposition Algorithms

• Compute letter frequencies of ciphertext if
  appear with normal frequency, then assume a
  transposition algorithm was used
• By shifting text, look for common digrams (e.g
  EN)and trigrams (e.g. ENT)