15-503/15-859P Introduction to Theoretical Cryptography

Spring 2006, MW 3:00-4:20, Wean 4623


Lecture Notes

(in PDF format)
  1. (Introduction to Zero-Knowledge), by Ryan
    Optional reading: Proving a Theorem in Zero-Knowledge. Pages 1-7 are most relevant, but beware of typos.

  2. (Visual Cryptography), by Michelle

  3. (More on Zero-Knowledge: Subset Sum), by Yinmeng

  4. (Formal Definitions of IP and Zero-Knowledge), by Ryan

  5. (Vertex Cover; Definition of Bit Commitment), by Yinmeng

  6. (ZK: Graph Isomorphism and Non-Isomorphism), by George

  7. (Extended GCD; Continued Fractions) by Brandon

  8. (More on CF; Chinese Remainder Representation), by Don

  9. (More on CRR; Prime Number Theorem), by Ryan

  10. (Generating Random Factored Integers), by Ryan

  11. (Multiplication, Exponentiation, Fermat's Little Theorem, and the Beginnings of Primality Testing), by Yinmeng

  12. (Pseudo-primality tests, Randomized Primality Tests), by Ryan

  13. (Discrete Logarithm, Quad. Residues), by Ryan

  14. (Principal Square Roots and Coin Flipping Over the Telephone), by Ryan

  15. (More on Principal Square Roots, Coin Flipping Into a Well), by Yinmeng

  16. Midterm Review (no scribe notes)

  17. Midterm Exam

  18. (Back to ZK: Proving That You Know a Factorization), by Ryan and Yinmeng

  19. (Back to ZK: Proving That You Know a Factorization 2, in above pdf)
  20. (Back to ZK: Proving That You Know a Factorization 3, in above pdf)

  21. (Public Key Encryption with f(x)=x^2) by Yinmeng

  22. (Oblivious Transfer), by Ryan, (Alternate Version), by Yinmeng

  23. (All-or-Nothing Certified Mail), by Ryan
    For more information on oblivious transfer, see Rafail Ostrovsky's lecture notes.

  24. (All-or-Nothing Certified Mail 2, see above pdf)

    (The below are still in progress... note that the final will not depend on them.)

  25. (ZK Proof That g is a Generator), by Ryan

  26. (The Science of Modern Cryptography), by Ryan

  27. (Give Me a Bit and I Will Take a Mile), by Ryan

  28. (Final Lecture), by Ryan

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