Sergey Nikolenko

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nikolenko (in Russian)

Teaching activities

Cryptography

This course is presented in the «Academic University of Physics and Technology» as part of the recently established Chair of Mathematics and Computer Science.

The course itself (all lecture notes are in Russian):

1. Introduction. The subject of cryptography. Secret-key cryptography.

2. Block cipher modes of operation. Public-key cryptography. Cryptographic primitives. Factoring and discrete logarithm. RSA, Diffie-Hellman, ElGamal. RSA and ElGamal signature schemes.

Lecture notes by Catherine Tuzova (.pdf, 276kb)

3. Elliptic curves: definitions, irreducible components, singular and nonsingular points. Estimating the number of points over a finite field. Hasse theorem.

4. Resultants. Basic properties. Intersection numbers. Existence and uniqueness of intersection numbers.

5. Bezout theorem. Addition on an elliptic curve. The group law: associativity.

6. Weierstrass equation, canonical equations for different characteristics, coordinate formulas for the group law. Jacobi coordinates and their advantages. The discrete log problem on an elliptic curve.

7. Factoring. Fermat's method, Kraitchik's method. Quadratic sieve. Polynomial sieve.

8. The discrete log problem. The Pohlig-Hellman attack. The Pollard's rho attack. Idea of the index calculus method.

9. The index calculus method in details. Complexity of the index calculus attack.

10. Secret sharing. Blackley and Shamir. Verifiable secret sharing. Proactive secret sharing.

11. Interactive proof systems. Completeness and correctness. Sample IPS for Graph-ISO and Graph-NISO.

12. The zero knowledge property. Simulating the view. ZK definitions. A ZK protocol for Graph-ISO. A not quite ZK protocol for Graph-NISO.

13. Zero knowledge definitions: black box vs. code access. ZK with advice. A correct ZK protocol for Graph-NISO.

14. Oblivious transfer: Rabin's OT, 1-2-OT scheme. Secure multi-party computation. Bit commitment. Coin flip in the well. Probabilistic secure multi-party computation (poker over the phone).