Spring 2003
 01/27
         discussion of class
              point system
              grading, ciphers, projects, exams, etc.

         fundamentals of cryptography
              mathematical framework
                 encryption and decryption as mappings on spaces
                    plaintext, ciphertext and keys as spaces

 01/29

         computational frameworks
             modulo systems
               rings, groups, fields
 
             cancellation law, multiplicative inverses
             Euler totient function
             the case of the integers mod a prime
                Wilson's theorem
                its inverse
                Fermat's Little Theorem

         simple substitution as a cipher system
             shift ciphers
             affine ciphers
               size of the key space
             cryptanalysis of monoalphabetic substitution
               single letter frequencies
               digram, trigram frequencies
               other characteristics ..letters which begin words
                 letters which end words, a letters 'socialibilty'
               an example

 02/3
         Reduced residues
         computation of the Euler totient function
            properties of the Euler totient function
         Euler's generalization of FLT            
            discussion of group theory
              LaGrange's theorem on finite groups
                 subgroups           
        
 02/5    revisit to reduced residues, Euler's generalization
         discussion of Vigenere, homophonic, Hill ciphers (and
         others) 
         discussion of transposition ciphers and stream ciphers
         cryptanalysis

 02/10   cryptanalysis of Vigenere cipher
             method of Kasiski and Babbage
             statistical method of Friedman
                index of coincidence (IC)

 02/12   cryptanalysis of Vigenere cipher...an example
             computing the key length
                       decomposition of the ciphertext
                       relative key shifts
                          mutual index of coincidence 
         cryptanalysis of Hill Cipher
                       of columnar transposition
         cryptanalysis of LFSR

 02/17  too much snow


 02/19  too much snow
  

 02/24  famous unsolved Ciphers
         Galois fields

 02/26   more on Galois fields
             addition
             division
                 by shift and exclusive or
         finding inverses in groups by powers
             the integers mod n -- reduced residues
             using Fermat's little theorem
        
             in Galois fields, using phi(p_m) = 2^n-1
                 an example

      
 
 03/03   Exam
__________________________________________________________________________

 03/05   discussion of information theory
            probability
            entropy
              examples
            equivocation
            perfect secrecy
              sufficient conditions


 03/10   continued discussion of perfect secrecy
             computational security
         review - product ciphers         
         Lucifer
             an example on the handout
                system of nonlinear equations
 
         DES
            a short history
            the overall structure
               permutation
               expansion
               S boxes 


  03/12  more on DES
         triple DES
             DES as a set of permutations
         four different variants, ECB, CBC, etc.
         MAC
          MACs and MACs with secrecy
          discussion of public key cryptography
            the overall idea
            RSA  -how it works
   

  

  03/17  RSA
          an algorithm for fast exponentiation
          quadratic residues
             in the case Z/p
         

  03/19   04/02  probabilistic primes
            Legendre symbol
            Jacobi symbol
            Solovay Strassen test
            Pollard's rho - method of factorization

  03/24 - 27  Spring Break


  03/31     factoring methods
            discussion of complexity
            Pollard's Rho
            Pollard's p-1 
            El Gamal's crytosystem



_____________________________________________________________________________


  04/02   Exam 2
             ciphers 3 and 4 due
             projects 1-4 due
             Homework #2 due
 
  04/07   El-Gamal, Merkle-Hellman Knapsack Cipher, space-time trade-off
          attack on DLP
                           handouts:
                             p-1 factoring method
                             diffie hellman
                             threshold scheme

  04/9   Diffie-Hellman key exchange, man-in-the middle attack
         simplied station to station protocol
         Threshold schemes (secret sharing)
         a probabilistic (Las Vegas)  algorithm for finding
         the square roots of quadratic residues in Z/p, p=prime
                          handouts:
                            
                            threshold scheme  (2)
                            the discrete log problem
                            attack strategies and classic protocol flaws
                            computing square roots of quadratic residues
                                  (Las Vegas algorithms)
              

  04/14   zero-knowledge proofs ..
                using quadratic residues
                log in process
         

  04/16    zero-knowledge proofs
              the graph isomorphism problem
                a dialogue for graph non-isomorphism
                               graph isomorphism
           digital signatures
              signing and verifying functions
              examples
                RSA, Elgamal

          

  
  04/21   protocols
            computing square roots of quadratic residues (mod p)
            the easy case, a probabilistic algorithm for the hard case
            oblivious bit transfer
            mental poker
                cheating
             

  04/23   exam 3


  04/28   discussion of the group isomorphism problem
              example
               an isomorphism between (Z/5^*,*) and (Z/4,+)
          more on elliptic curve cryptography
             examples

  04/30    Elliptic curve factoring
           Quantum Cryptography 


  05/05   quantum cryptography
            order of measurement
               the commutator
            polarized photons
               computing the commutator
            detecting an eavesdropper
            key exchange
         
        
  

  05/07    review , discussion of final
          

          

                  

  05/13  last day of classes                    
  05/21  final (Wed)                      

              same room 1-3pm