Class in Introduction to Cryptography-

Amos Fiat (fiat@math.tau.ac.il)
1st Semester, 2003/2004 - Wednesday 13:00-16:00.
School of Mathematical Sciences,
Tel-Aviv University

Powerpoint Slides

(Based upon slides originally produced by Benny Chor and added to/revised by myself).

1. Lecture 1. - 29/10/2003 - Administration, Outline, Bio, Basic Definitions for Encryption, One time pads.
2. Lecture 2 - Symmetric Encryption, Stream ciphers, Block ciphers, modes of operation, Repeated encryption, meet in the middle, time space tradeoffs.
3. Lecture 3 - Algebra Background: Groups, Rings, Fields, GF(p^k), and the AES.
4. Lecture 4 - Data Integrity and Authentication: CBC MAC, hash function based authentication, HMAC; Number theory: quadratic residues, Chinese Remainder Theorem, factoring via square roots, Pollards rho method, quadratic sieve.
5. Lecture 5 - More on number theory, quadratic residues, Legendre and Jacobi symbols, Soloway-Strassen Primality Testing, discrete logs, Diffie Hellman key exchange.
6. Lecture 6 - Testing Primitive Elements in Zp, Fermat test, Carmichel numbers,Miller-Rabin primality testing, Manindra Agrawal, Neeraj Kayal, Nitin Saxena.
7. Lecture 7 - RSA.
8. Lecture 8 - Factoring and Discrete log algorithms, Digital Signatures, El Gamal, DSA
9. Lecture 9 - Interactive proofs, Zero Knowledge Proofs, Fiat-Shamir.
10. Lecture 10 -Performance Improvements: Fast Arithmetic, Montegomery representation, Batch RSA, Elliptic Curves.
11. Lecture 11 - to be revised.
12. Lecture 12 - to be revised.
13. Lecture 13 - to be revised.
14. Lecture 14 - to be revised.

Homework Assignments:

1. Answers to Crypto Excercise #1 by Michal and Yael.
2. Copy of pages from book for problem set 2: page 1. page 2. page 3.