ICOM6045 Topic 1 Cryptography

作者: Arthur | 760 字, 4 分钟 | 2020-10-21 | 分类: Notes

hku, icmo6045, internet, security

翻译: EN

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

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Arthur

作者

Arthur

区块链(Golang)开发工程师,香港大学计算机系硕士在读。喜欢探索学习新科技,空闲时也折腾Notion等效率工具。 在GitHub关注我