ICOM6045 Topic 1 Cryptography

ICOM6045 Fundamentals of E-Commerce Security

Topic 1 Cryptography

Definition

• Process of transforming information to make it unreadable to anyone except those possessing the key

Purpose

• Data confidentiality

Transpositions/Permutations

• An encryption in which the letters of the message are rearranged
• Function
  • Try to break established patterns
• Example
  • Columnar transposition
    • Rearrangement of the characters of the plaintext into columns
    • Based on characteristic patterns of pairs of adjacent letters, called digrams
    • Analysis
      • Compute the letter frequencies
        • Break the text into columns by compare a block of ciphertext characters against characters successively farther away in the ciphertext.
        1. Do common digrams appear.
        1. Do most of the digram look reasonable
• Complexity
  • No additional work
  • Require storage for all characters of the message
  • Not good for long message
• Alternative
  • Permute the characters of the plaintext with a fixed period d

Confusion

• Cipher that makes relationship between the plaintext/key pair and the ciphertext as complex as possible
• Good confusion
  • poly-alphabetic substitution with a long key
• Bad confusion
  • Caesar cipher

Diffusion

• Cipher that spreads the information from the plaintext over the entire ciphertext
• Change in the plaintext should affect many parts of the ciphertext
• Good diffusion
  • DES
  • Transposition cipher
• Bad diffusion
  • Substitutin cipher

Cryptanalysis

• Index of coincidence (A tool to rate how wella particular distribution matches the distribution of letter in English)
• Procedure
  • Measure of roughness(variance)
  • If the distribution is perfectly flat
• Examine
  • Is it encrypted
  • How is it encrypted
  • What is the key

Types

Symmetric Key Encryption

• Procedure (Single key)
  • Original message
  • Key -> Encryption algorithm
  • Encrypted message
  • Encrypted message sent over Internet
  • Encrypted message arrives destination
  • Key -> Decryption algorithm
  • Original message
• Algorithms
  • DES(Data Encryption Standard)
    • Most commonly used block cipher
    • Purpose
      • Facilitate hardware implementation
    • Form
      • A block cipher with 56-bit key (64-bit including parity bits)
      • “Feistel” network structure
  • AES(Advanced Encryption Standard)
  • RC4
• Stream cipher
  • Definition
    • Convert one symbol of plaintext immediately into a symbol of ciphertext
  • Advantage
    • Speed of transformation
    • Low error propagation
  • Disadvantage
    • Low diffusion
    • Possible for malicious insertions and modifications
• Block cipher
  • Definition
    • Encrypt a group of plaintext symbol as one block
  • Advantage
    • Diffusion
    • Immunity to insertion
  • Disadvantage
    • Slowness of encryption
    • Error propagation
• Kasiski method
  • Search for repeated sequence of characters
  • Example
    • 3 occurrences of the 11-character sequence
    • Distance between first 2 sequence = 141- 90 = 51
    • Distance between second 2 sequences = 213 - 141 = 72
    • The common divisor between 51 and 72 is 3
    • Estimated key length is 3
• “Perfect” substitution cipher
  • Definition
    • Many alphabets for an unrecognizable distribution
    • No apparent pattern for the choice of an alphabet at a particular point
  • Function
    • Confuse the Kasiski method
    • Index of coincidence would be close to 0.038
• Application
  • Caesar cipher
    • Definition
      • The message is enciphered with a 27-symbol alphabet (A->Z) and the blank, the blank is translated to itself
    • Permutation
      • Each letter is translated to a fixed number of letters after it in the alphabet
    • The “real” Caessar cipher by Julius Caesar used a shift of 3
  • Mono-alphabetic substitutions
    • Definition
      • The alphabet is scrambled, and each plaintext letter maps to a unique ciphertext letter
    • Permutation
      • A permutation is a recording of the elements of a series
      • A permutation can be a function
      • Some permutations can’t be represented as simple equation
    • Weakness
      • Frequency distribution
  • Polyalphabetic substitutions
    • Definition
      • Combine distributions that are high with ones that are low
    • Analysis
      • Use Kasiski method to predict likely numbers of enciphering alphabets
      • If no numbers emerge fairly regularly, may not a poly-alphabetic substitution
      • Compute the index of coincidence to validate the predictions from step 1
      • When step 1 and 3 indicate a promising value, separate the ciphertext into appropriate subsets and independently compute index of coincidence of each subset
    • Example
      • Rotor Machines
  • Vigenere cipher
    • Definition
      • Vigenere tableau
        • A collection of 26 permutations
        • Written in a 26*26 matrix
    • Permutation
      • Use a key (keyword) -> select particular permutaion
  • One-time pad
    • Definition
      • Based on a large nonrepeating set of keys (written on paper and glued together into a pad)
    • Procedure
      • Sender writes key one time above the letters of the plaintext
      • Encipher the plaintext with a chart like Vigenere tableau
      • Sender destroys the key
      • Receiver takes the appropriate number of keys
      • Decipher the message
    • Example
      • Vernam cipher
        • Involves an arbitrarily long nonrepeating sequence of numbers that are combined with the plaintext
        • Possible attack
        • Random number generator

Public Key Encryption

• Procedure (Everyone has 2 keys)
  • Original message
  • Encryption key -> Encryption algorithm
    • Plaintext <- Encryption
      • The original form of a message
    • Ciphertext <- Decryption
      • The encrypted form a message
    • Original plaintext
  • Encrypted message
  • Encrypted message sent over Internet
  • Encrypted message arrives destination
  • Decryption key -> Decryption algorithm
  • Original message
• Algorithms
  • RSA