Lectures
Lectures are on Mondays from 10:15 to 12:00 in Delta (Narva mnt 18) - room 2034 and through Panopto (or Zoom), and on Mondays from 13:15 to 14:00 through Panopto (or Zoom). Office hours are Tuesday from 09:30 to 11:00 in Delta R3072 (Narva mnt 18).
To join virtually through Panopto/Zoom, the link is given at Moodle. The lecture notes will be shared.
Outline
1. First meeting, course organization, basic primitives, definitions in public key cryptography (encryption, key encapsulation mechanism, identification schemes, digital signature)
2. Discrete logarithm problem (DLP), Diffie-Hellman key exchange, ElGamal public key encryption
3. Integer factorization problem, RSA cryptosystem, primality testing
4. Modular exponentiation algorithms, RSA and Chinese Remainder Theorem
5. Algorithms for integer factorization problem
6. Algorithms for DLP
7. Elliptic curve cryptography, Elliptic curve Diffie-Hellman key exchange
8. Elliptic curve digital signature algorithm (ECDSA) over prime fields, algorithms for ECDLP, Edwards curves, Montgomery curves
9. Real-world examples of traditional public key cryptosystems
10. Basic primitives and definitions in post-quantum cryptography, post-quantum families, computationally hard problems
11. Introduction to lattices, LLL algorithm and properties of LLL reduced basis, Regev cryptosystem
12. Lattice-based key encapsulation mechanisms (KEM) and their primitives
13. Lattice-based signature schemes and their primitives
14. Arithmetic operations (polynomial multiplication, matrix-vector product) for lattice-based cryptography
15. Project presentations
16. Project presentations