Lecture 2 Overview

							Lecture 2 Overview
                   Cryptography
• Secret writing
      – Disguised data cannot be read, modified, or fabricated
        easily
      – Feasibility of complexity for communicating parties
• Encryption : encoding (encipher)
           plaintext              cipher text
           C = E(c) (E = encryption rule)
• Decryption : decoding (decipher)
           Cipher text            plaintext
           P = D(c) (D = decryption rule)

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                     Encryption
Keyless                                                                Original
             plaintext                       ciphertext                plaintext
                                Encryption                Decryption

Symmetric key

                                                                       Original
             plaintext                       ciphertext                plaintext
                                Encryption                Decryption


Asymmetric key
                                                                       Original
             plaintext                       ciphertext                plaintext
                                Encryption                Decryption

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                   Symmetric Encryption System
• Secret Key
• Both sender and receiver share one key
• Encryption and decryptions algorithms are
  closely related
• N * (N-1) /2 keys are needed for N users to
  communicate in pairs
• Key must be kept secret


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                   Asymmetric Encryption System
• Public Key

• One key must be kept secret, the other can be
  freely exposed – private key and public key

• Only the corresponding private key can
  decrypt what has been encrypted using the
  private key

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                   Cryptanalysis
• How to break an encryption!

• Cryptanalyst
      – Deduce the original meaning of the ciphertext
      – Determine the decryption algorithm that matches
        the encryption one used


     Breakable Encryption!

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                   Substitution Ciphers
• Substitute a character or a symbol for each
  character of the original message
• Caesar Cipher
      – Ci = pi + 3
• Permutation
      – Alphabet is scrambled, each plaintext letter maps
        to a unique ciphertext letter
      – Key can be used to control the permutation to be
        used

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                   Cryptanalysis of substitution ciphers

• Clues
      – Short words,
      – Words with repeated patterns,
      – Common initial and final letters, …


• Knowledge of language may simplify it
      – English E, T, O, A occur far more than J, Q, X, Z
      – Digrams, Trigrams, and other patterns
      – Context
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                   One-Time Pads
• One-Time Pad
      – Set of sheets of paper with keys, glued into a pad
      – Pre-arranged charts (Vignere Tableau)

• Vernam Cipher
      – random numbers

• Book Ciphers
      – access to identical objects

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                   Transposition Ciphers
• The order of letters is rearranged

• Columnar transposition

• cryptanalysis using digrams




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             Lecture 3
           Entropy


                             CS 450/650

                       Fundamentals of
                 Integrated Computer Security


Slides are modified from David Madison
                   Exercise
Decrypt the following encrypted quotation:



       fqjcb rwjwj vnjax bnkhj whxcq
        nawjv nfxdu mbvnu ujbbf nnc




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                   Ciphers
• The intent of cryptography is to provide
  secrecy to messages and data

• Substitutions
      – ‘hide’ letters of plaintext


• Transposition
      – scramble adjacent characters


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                   Entropy
• Shannon demonstrated mathematical
  methods of treating communication channels,
  bandwidth, and the effects of random noise
  on signals


      – pi is the probability of a given message (or piece of
        information)
      – n is the number of possible messages (or pieces of
        information)
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                   Example 1
• Suppose there is only one possible signal
      – i.e., n = 1, and p1 = 1


                                  H = -1 x log 1 = 0

• There is only one possible message that has a
  probability of 1
      – Since there is no uncertainty, the entropy in this
        case is zero
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                   Example 2
• There are only two possible, equally probable,
  messages.
           H = -(0.5 log (0.5) + 0.5 log(0.5))
             = - ( 0.5(-1)+0.5 (-1)) = 1

• There are two possible equally probable
  messages, and the uncertainty (entropy) is 1
      – one bit can specify two possible conditions,
             • i.e., 0 or 1

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                   Example 3
• There are 1024 (= 210) possible signals, all of
  equal probability (pi = 2-10).

                          H = -(210 x 2-10 log(2-10)) = 10

• There are 1024 equally probably possible
  messages, and the uncertainty (entropy) is 10
  bits.

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                   Entropy
• Entropy gives an indication of the complexity,
  or randomness, of a message or a data set.

• Generally, signals or data sets with high
  entropy,
      – Have a greater chance of a data transmission error
      – Require greater bandwidth to transmit
      – Have smaller capacity for compression
      – Appear to have a greater degree of "disorder”

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                   Entropy
• English language (and most other human
  languages) have a relatively low entropy due
  to the frequency of certain characters
      – the letters 'e' and 't‘
• Information can be compressed using
  algorithms that "squeeze out" the
  redundancies in a message
      – making the compressed version much smaller, and
        much more random
             • Compressing a file twice doesn't reduce the size !
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                   Entropy and Cryptography
• Through cryptography, we increase the
  uncertainty in the message for those who do
  not know the key
• Plaintext has an entropy of zero as there is no
  uncertainty about it.
      – This class is CS 450
• Encryption using one of x equally probable
  keys increases the entropy to x
      – KBXT LWER ACMF OSJU

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                   Entropy and Cryptography
• With a perfect cipher “all keys are essentially
  equivalent”
      – having an encrypted sample won't help the
        cryptanalyst do his or her job
      – an encrypted message is similar to a signal that is
        buried in noise;
             • the higher the noise level, the more difficult it is to
               extract the message
• A good cipher will make a message look like
  noise
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                   Entropy and Cryptography
• Encryption should "scramble" the original
  message to the maximum possible extent

• Algorithms should take a message through a
  sequence of substitutions and transpositions

• Shannon:
      – “Encrypting a message will intentionally increase
        the message's entropy”

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                   Shannon Characteristics of ‘Good’ Ciphers

1. “The amount of secrecy needed should determine
   the amount of labor appropriate for the encryption
   and decryption”
      –      Hold off the interceptor for required time duration
2. “The set of keys and enciphering algorithm should
   be free from complexity”
      –      There should not be restriction on choice of keys or types
             of plaintext
3. “The implementation of the process should be as
   simple as possible”
      –      Hand implementation, software bugs
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                   Shannon Characteristics of ‘Good’ Ciphers

4. “Errors in ciphering should not propagate and cause
   corruption of further information in the message”
      –      An error early in the process should not throw off the
             entire remaining cipher text


5. “The size of the enciphered text should be no larger
   than the text of original message”
      –      A ciphertext that expands in size cannot possibly carry
             more information than the plaintext



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                   Trustworthy Encryption Systems
• Commercial grade encryption
      1. Based on sound mathematics
      2. Analyzed by competent experts
      3. Test of time


DES: Data Encryption Standard
RSA: River-Shamir-Adelman
AES: Advanced Encryption Standard

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                   Stream and Block Ciphers
• Stream
   – Converts one symbol of plaintext into a
     symbol of ciphertex



• Block
   – Encrypts a group of plaintext symbols as
     one block

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                   Confusion and Diffusion
• Confusion
   – Has complex relation between plaintext,
     key, and ciphertext
   – The interceptor should not be able to
     predict what will happen to ciphertext by
     changing one chatracter in plaintext
   – Example
             • Caesar Cipher
             • One time pad
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                   Confusion and Diffusion
• Diffusion
  – Cipher should spread information from
    plaintext over entire ciphertext
  – The interceptor should require access to
    much of ciphertext to infer algorithm
  – Example
             • Caesar Cipher
             • One time pad


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