CSE565: S' Upadhyaya

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CSE565 Computer SecurityLecture 2 Basic
Encryption Decryption
Shambhu Upadhyaya Computer Science Eng.
University at Buffalo Buffalo, New York, 14260
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Overview

• Lecture 2 Overview
• Terminology (5 minutes)
• Encryption by Substitutions Transpositions (45
  minutes)

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Announcements

• Recitation for next week
• Properties of Arithmetic
• Inverses
• Divisors
• Prime Numbers
• Greatest Common Divisor
• Recitation for the following week
• Modular arithmetic
• Basic properties
• Operations

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Terminology

• Encryption
• A process of encoding a message
• Decryption
• It is the reverse process
• Encryption Algorithms
• A key K is generally used
• Symmetric encryption
• Asymmetric encryption

Original Plaintext
Plaintext
Ciphertext
Encryption
Decryption
PD(C) D(E(P))
P(p1,p2, pn)
C(c1,c2, cm) CE(P)
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Cryptography Cryptanalysis

• Cryptography
• Hidden writing -- encryption to conceal text
• Cryptanalysis
• Break an encryption
• Attempt to break a single message
• Attempt to recognize patterns in encrypted
  messages
• Attempt to find general weaknesses
• Breakable Encryption
• Given enough time and data, encryption can be
  broken
• Practicality is an issue
• Risky to proclaim an algorithm secure!

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Substitutions Transpositions

• Substitutions
• Monoalphabetic Ciphers
• Polyalphabetic Ciphers
• These are called Stream Ciphers
• Transpositions
• Permutation
• These are Block Ciphers

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Monoalphabetic Ciphers

• Caesar Cipher
• Formula
• Treaty Impossible --gt wuhdwb lpsrvvleoh
• Advantages Disadvantages
• Easy to perform
• Simple, so easy to predict the pattern
• Repeat characters give clue to break
• Permutation Cipher
• Use a key
• ABCDE
• K eyab.
• Since key is short, most plaintext letters are
  only one or two positions off
• Time complexity of these algorithms -- linear in
  n where n is the no. of characters in plaintext

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Polyalphabetic Substitution Ciphers

• Main problem with mono-alphabetic ciphers is the
  non-flat frequency distribution
• A flat distribution gives no information to
  cryptanalyst
• Flattening by combining distributions
• Two or more separate encryption alphabets for the
  same character of the plaintext
• E.g., one encryption for characters in odd
  positions and another for at even positions
• Reduces the repeat symbols in the ciphertext
• Makes it hard to break
• (Discussion of an example)

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Vigenere Tableau

• Need to smooth out peaks and valleys of frequency
  distribution
• Can be done by extending no. of permutations
• Extreme case -- extend to 26 permutations
• A 26 X 26 table is used (discussion of example)
• Key word of length 3 is sufficient to smooth out
  the distribution
• Cryptanalysis of Polyalphabetic Substitution
• Reading exercise
• Focus on Kasiski method and Index of Coincidence
  method (Look up Ref. Texts)
• (http//www.trincoll.edu/depts/cpsc/cryptography/v
  igenere.html)

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Perfect Substitution Cipher

• Requires an infinite non-repeating sequence of
  alphabets
• This will confound the cryptanalyst
• One-Time pads
• Vernam Cipher
• Uses an arbitrarily long sequence of numbers
• Formula
• Random Numbers
• Middle digits of phone numbers in a residential
  directory
• Pseudo random numbers -- linear congruential
  random number generator
• Formula

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Transpositions

• It is a method where letters of the message are
  rearranged
• Goal here is diffusion rather than confusion
• Information is spread widely across the
  ciphertext
• Columnar transposition is an easy one
• Characters are rearranged into columns
• (Study of an example)
• Encipherment/Decipherment Complexity
• Algorithm is constant in the amount of work per
  character
• Time is proportional to length of message
• Space required is directly proportional to
  message length
• Output characters cannot be produced until all
  characters are read in
• Delay depends on the length of the message
• Not appropriate for long messages

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Cryptanalysis

• Digrams, trigrams other patterns used to break
  encryption
• Digram -- letter pairs such as -re- -th- -en-
  -ed- etc.
• Trigram -- groups such as ent, and, ing, thi etc.
• Cryptanalysis by trial error using a moving
  window for comparison
• This is a reading exercise! (http//en.wikipedia.o
  rg/wiki/Transposition_cipher)
• Double transposition algorithm makes breaking
  more difficult
• It uses transposition of a transposed text
• Discussion of example

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Summary

• Stream Ciphers
• Mono and poly-alphabetic encryptions
• Since they convert one symbol of plaintext
  immediately into a symbol of ciphertext
• Features include a) speed of transformation, b)
  low error propagation
• Disadvantages are a) low diffusion, b)
  susceptible to malicious insertions
• Block Ciphers
• Columnar transposition algorithm and fractionated
  Morse
• Group of plaintext symbols are encrypted as one
  block
• Features include a) diffusion, b) immunity to
  insertions
• Disadvantages are a) slowness of encryption, b)
  error propagation