Cryptography Lecture 4

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CryptographyLecture 4

• Substitution
• Transposition

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Reading Assignment

• Reading assignments for Lecture 4
• Required
• Pfleeger Ch. 2.2, 2.3, 2.4
• Reading assignments for next class
• Required
• Pfleeger Ch 2.5

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Encryption and Decryption
Plaintext
Ciphertext
Plaintext
Encryption
Decryption
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Cryptanalysis

• Cryptanalysts goal
• Break message
• Break key
• Break algorithm

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Taxonomy of Attacks

• Ciphertext-only attack attacker has ciphertext
  for messages encrypted with E. Deduce keys
  and/or plaintext messages.
• Known plaintext attack attacker additionally
  knows the plaintext of the messages. Deduce keys
  or a decryption algorithm.
• Chosen plaintext attack attacker can obtain the
  ciphertext for selected plaintext messages.
  Deduce as above.
• Chosen ciphertext attack attacker can obtain
  decrypted (plaintext) versions of selected
  ciphertext. Deduce as above.

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Breakable versus Practically breakable

• Unconditionally secure impossible to
  decrypt. No amount of ciphertext will enable a
  cryptanalyst to obtain the plaintext
• Computationally secure an algorithm that is not
  breakable in practice based on worst case
  scenario
• Breakable all algorithms (except one-time pad)
  are theoretically breakable

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What makes a good cryptosystem?

• A good cryptosystem is one whose security does
  not depend upon the secrecy of the algorithm.
• From Bruce Schneier
• Good cryptographers rely on peer review to
  separate the good algorithms from the bad.''

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Secret Key Cryptosystem
Plaintext
Ciphertext
Plaintext
Encryption
Decryption
Sender
Recipient
K
CE(K,M) MD(K,C)
K needs secure channel
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Secret Key Cryptosystem Vulnerabilities (1)

• Passive Attacker (Eavesdropper)
• Obtain and/or guess key and cryptosystem use
  these to decrypt messages
• Capture text in transit and try a ciphertext-only
  attack to obtain plaintext.

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Secret Key Cryptosystem Vulnerabilities (2)

• Active Attacker
• Break communication channel (denial of service)
• Obtain and/or guess key and cryptosystem and use
  these to send fake messages
• No third party authentication

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Inherent Weaknesses of Symmetric Cryptography

• Key distribution must be done secretly (difficult
  when parties are geographically distant, or don't
  know each other)
• Need a key for each pair of users
• n users need n(n-1)/2 keys
• If the secret key (and cryptosystem) is
  compromised, the adversary will be able to
  decrypt all traffic and produce fake messages

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Basic Encryption Techniques

• Substitution (confusion)
• Permutation (diffusion)
• Combinations and iterations of these

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Simple Alphabetic Substitution

• Assign a new symbol to each plain text symbol
  randomly or by key, e.g.,
• C ?K, A ?H, B ? L

• MCAB
• C KHL
• Advantages large key space 26!
• Disadvantages trivially broken for known
  plaintext attack, repeated pattern, letter
  frequency distributions unchanged

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Polyalphabetic Substitution

• Frequency distribution reflects the distribution
  of the underlying alphabet ? cryptanalysts find
  substitutions
• E.g., English e 14 , t 9.85, a 7.49, o-
  7.37,
• Need flatten the distribution
• E.g., combine high and low distributions
• t ? a (odd position), b (even position)
• x ? a (even position) , b (odd position)

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Cryptanalysis of Polyalphabetic Substitution

• Determine the number of alphabets used
• Solve each piece as monoalphabetic subst.
• Kasiski Method
• Uses regularity of English letters, letter
  groupings, full words
• e.g., endings -th, -ing, -ed, -ion, -ation,
  -tion,
• beginnings im-, in-, re-, un-, ...
• patterns -eek-, -oot-, -our-,
• words of, end, to, with, are, is,

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One-Time Pad

• Perfect Secrecy!
• Large, non-repeating set of keys
• Key is larger than the message
• Advantages immune to most attacks
• Disadvantages
• Need total synchronization
• Need very long, non-repeating key
• Key cannot be reused
• Key management printing, storing, accounting for

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Transposition

• Letters of the message are rearranged
• Break patterns, e.g., columnar transposition
• Plaintext this is a test
• t h i s
• i s a t tiehssiatst!
• e s t !
• Advantages easy to implement
• Disadvantages
• Trivially broken for known plaintext attack
• Easily broken for cipher only attack

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Cryptanalysis

• Rearrange the letters
• Digrams, Trigrams, Patterns
• Frequent digrams -re-, -th-, -en-, -ed-,
• Cryptanalysis
• Compute letter frequencies ? subst. or perm.
• Compare strings of ciphertext to find reasonable
  patterns (e.g., digrams)
• Find digram frequencies

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Double Transposition

• Two columnar transposition with different number
  of columns
• First transposition breaks up adjacent letters
• Second transposition. breaks up short patterns

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Product Ciphers

• One encryption applied to the result of the other
  En(En-1((E1(M)))), e.g.,
• Double transposition
• Substitution followed by permutation, followed by
  substitution, followed by permutation
• Broken for
• Chosen plaintext

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Steam Ciphers

• Convert one symbol of plain text into a symbol of
  ciphertext based on the symbol (plain), key, and
  algorithm
• Advantages
• Speed of transformation
• Low error propagation
• Disadvantages
• Low diffusion
• Vulnerable to malicious insertion and
  modification

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Block Ciphers

• Encrypt a group of plaintext as one block and
  produces a block of ciphertext
• Advantages
• Diffusion
• Immunity to insertions
• Disadvantages
• Slowness of encryption
• Error propagation

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Next Class
Data Encryption Standard