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Class text

Lectures

• Classical ciphers and their analysis
  • Shift and Affine ciphers
  • Vigenere, Playfair, and ADFGX.
  • Simple subsitution cipher
  • Linear Feedback Shift Register Sequences
  • The Enigma
• Basic number theory
  • Notes on Modular Arithmetic and GCD's
    Note: These notes are in Postscript. You need a Postscript viewer to read them. Windows users, download and install both AFPL Ghostscript and GSView
    • GSview 4.1
    • AFPL Ghostscript 7.03
  • Example of finite field GF(9).
• DES
• RC4
• More number theory
  • Fermat's little theorem; Euler's Phi Function; Chinese Remainder Theorem; cyclicity of finite fields
  • Applications: RSA Public Key cryptosystem and Diffie-Hellman key establishment.
  • Square roots, Finite Fields ( GF(p^k) = Z_p[x]/f(x) )
  • Application: Rijndael
  • RSA
    • Primality testing: Miller-Rabin
    • Primality testing: Sollovay-Strassen (optional reading)
  • Zero Knowledge
    • Knowledge Complexity of Interactive Proof Systems" by Goldwasser, Micali and Rackoff. SIAM J Comp, Vol 18, No 1, Feb 1989.

  Project Assignments

  • Project 1: Automated cryptanalysis of Vigenere ciphers
    Due: 14 February.
    • Sample Vigenere, Chap. 2, problem 7.
    • Sample Vigenere, Chap. 2, problem 8.
    • Sample Vigenere, Chap. 2, problem 9.
  • Project 2: Automated cryptanalysis of Substitution ciphers
    Due: 28 February.
    • Sample plaintext, for digram collection.
    • Sample ciphertext, find the key for this text.
  • Project 3: Implement Rijndael and try the square attack. Verify the facts about balanced and Lambda-sets as presented in the AES Proposal for Rijndael, pages 36 and 37. This proposal also gives numerous hints for implementation.