From: To: Date: Sunday, March 27, 2005 2:43 PM 

     
    Feb 1-----------------------------------------------------------------
    (1)
        discussion of the class
           projects, homework, points, etc.

        fundamentals of cryptography
           cryptographic framework
             plaintext, ciphertext, key, transformations, spaces
           computational framework
             simple substitution
             permutation
             non-standard alphabets

           cryptanalysis
             terms 
                ciphertext only, known plaintext, chosen plaintext, 
                chosen ciphertext, chosen text

                unconditionally secure, computationally secure

             attack example -brute force attack
                example (table)
           
             substitution techniques
                Caesar Cipher
                  key space
                  Z/26
                  the problem of the recognition of text
             monoalphabetic substitution-----
                frequency attack
                  distribution of English characters, digrams, trigrams, etc.
                      example
                      histogram

    Stinson -- pp 1-11
    Singh      pp 1-12


   Feb 3 ------------------------------------------------------------------
   (2)
            substitution ciphers
                efficient representation of key
                special case
                    affine cipher
                    Z/26   some facts about Z/n the integers mod n
                      ring with zero divisors
                      interpretation of negative numbers
                      computational properties
                         not ordered, the existence of multiplicative 
                           identities

             

             some improvements to monoalphabetic substitution
                 

                Playfair cipher
                   digrammatic substitution
                   binary version

                Hill Cipher -- linear algebra over Z/n
                   general method
                   example

                Homophonic ciphers
                   Beale cipher
                     practical method of construction
                     examples
    
   Stinson --pp. 12 - 18
   Singh   --pp  13 - 20 

   Feb. 8 -----------------------------------------------------------------  
    (3)      
             polyalphabetic substitution----         
                definition
                examples
                  Alberti Wheel  stream
                  also -- Thomas Jefferson's cipher machine

                Vigenere ciphers
                  a little history

                  tools
                    the index of coincidence  (IC)
                    measure of roughness (MR)
                    IC table
             
                  cryptanalysis of Vig. ciphers
                    with the method of Kasiski and Babbage
                    together with IC and IMC (index of mutual
                    coincidence)
 
                      example
                        automated attacks (Oscar et al)

             cryptanalysis of Hill's cipher
                setting up a matrix equation with chosen
                plaintext and solving for K the key matrix
 
   Stinson -- pp. 19 - 30
   Singh   -- pp  21 - 44

  Feb.10 -----------------------------------------------------------------
   (4)
            
             Transposition ciphers

                simple example
                columnar transposition
                   variations
                     double columnar transpositions
                hexagonal placement with transformations
                     (relation to groups!)
                some info on (finite) groups
                  order of a group
                  order of an element
                  LaGrange's theorem
                  subgroups
                    examples


                Rubik's cube transposition

       Stinson   31-44 
       Singh     45-98


  Feb 15  ----------------------------------------------------------------
   (5)

               cryptanalysis of Vig. ciphers  **continued**
                    with the method of Kasiski and Babbage
                    together with IC and IMC (index of mutual
                    coincidence)
 
                      example
                        automated attacks (Oscar et al)

              cryptanalysis of Hill's Cipher


              LFSR ciphers
                 linear feedback shift register
                 the basic setup
                    the seed, taps, keystream


                 cryptanalysis of LFSR ciphers

             Famous unsolved ciphers
                 Kryptos  - cipher at the CIA Yahoo group
                 Beale cipher - gold in Virginia
                 Zodiac - second cipher 
                 Elgar's cipher
                 Poe's cipher  (and its solution)
                 Voynich manuscript                 


         Stinson 45-54
         Singh  45-98


  Feb. 17-----------------------------------------------------------------
   (6)
             
                   

                   read carefully material in Singh on Rotor machines
                   simpler example =two rotor machine
                     idempotent property
                     discussion of key space


                   more on the integers mod n   ( Z/n)  (handout)
                   reduced residues, groups, rings

                      some info on (finite) groups
                      order of a group
                      order of an element
                      LaGrange's theorem
                            subgroups
                             examples





      Stinson 155-164  
      Singh  99-115
      



  Feb. 22-------------------------------------------------------------
            
            the 'kryptos' cipher
               yahoo group
            gcd algorithm
            mult. inverse algorithm 
            Finite Fields
               Galois fields
                  example
            Chinese remainder theorem
            




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  Feb. 24

           Exam 1  ***************************************

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    March 1

          exams returned
          review of CRT
          self inverses in Galois fields
          Conditional probability
             Entropy
         
                properties of entropy
                example
                key equivocation
  
          Stinson   read up to 62
          Singh     read up to 150
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    March 3

            character entropy
            unicity distance 

            intractable problems
               Satisfiability
               Traveling Salesman
               solving nonlinear Boolean equations

             Feistel Structure

            Stinson  62-72
            Singh 150-   
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    March 8

             Lucifer 
                overall design
                small example  (handout)
   
             discussion of the terms
                perfect secrecy            
                unconditional security     (Stinson p. 45)
                computational security
                provable security 

             discussion of stream ciphers and random number generators(handout)
                FIPS tests for PRNG
                RC4
                A5
                generation of pseudo random numbers using cellular automata

             Stinson  73-83
             Singh 150-170
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    March 10
 
             DES 
               history     (handout)
               detailed look
               different modes of operation CBC, etc.

               MACs   

             Stinson 83-101
                   students not responsible for differential or linear
                                               cryptanalysis
             Singh  170-190

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     March 15  no class

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     March 17   
              
              Stenography
                example - steganography in graphic images 

              AES                   (hand out)
                  overall structure
                  different phases

              Knapsack cipher  


              Stinson 102-113
              Singh 170-243
 
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     March 21-25   Spring Break

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     March 29

              review of Knapsack method  (handout)

***-----------you are responsible up to here for exam ----------------

              Public key Cryptographic
                   basic ideas
                     paper of Diffie, Hellman
                     public and private keys
                RSA
                  fundamentals
                  definition of e,d 
                  verification of the method
                  primes and their propterties
                     The Prime Number Theorem

              discussion of up coming exam

              Stinson 155-170
              Singh 244-268 
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     March 31

               Exam

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     April 5

               probabilistic primes
                   method of construction
                   Legendre symbol
                   Jacobi symbol
               quadratic residues
                   examples
               Solovay Strassen test
               Miller Rabin test

               Stinson 170-182
               singh
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      April 7  
    
               Factoring
                 factoring methods
                   complexity discussion
                   Pollard's p-1 method

                 timing attack
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      April 12
               method of ElGamal
                  discrete log problem  DLP
                    space-time tradeoff  attack on DLP
               
               Diffie- Hellman key exchange
                   man-in-the-middle attck
                   simplified station to station protocol

            
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      April 14
                                                               
  
              a probabilistic (Las Vegas)  algorithm for finding
              the square roots of quadratic residues in Z/p, p=prime
               
                          
              digital signatures, hashes
              signing and verifying functions
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      April 19
               examples of signatures
                    RSA, Elgamal

                      
                    handouts:
 
                       threshold scheme  (2)
                       the discrete log problem
                       attack strategies and classic protocol flaws
                       computing square roots of quadratic residues
                                  (Las Vegas algorithms)
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     April 21               
             
               Exam 3



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     April  26

            Diffie-Hellman key exchange
                 man-in-the-middle
                 using certificates
            brief discussion of GPG, OpenSSL 
            Secret Sharing
                the method of Shamir
            protocols
               mental poker
                 cheating ?
            
               
                      
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     04/28   


              oblivious bit transfe
              zero-knowledge proofs ..
                  using quadratic residues
                  log in process
                zero-knowledge proofs
                  the graph isomorphism problem
                  a dialogue for graph non-isomorphism
                     graph isomorphism
              




             discussion of the group isomorphism problem
              example
               an isomorphism between (Z/5^*,*) and (Z/4,+)
            
              elliptic curve cryptography
                examples
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     5/3     Ellliptic curve cryptography
             Elliptic curve factoring
   

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5/5
             Quantum Cryptography
                 order of measurement
                 the commutator
                 polarized photons
               computing the commutator
               detecting an eavesdropper
               key exchange
                                                                             
                                                                               
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  5/10
               review of Quantum cryto
               class awards
               guest speaker - Dr. Larry Wagoner

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    May  12

              continuation of Quantum cryptography

              student evaluations                                                                  
                                                                               
    May  17

              no class