Cryptography: theory and applications

We will discuss several advanced results on the theory of cryptograpy and their applications. Here is a overview on the topics:

• Elliptic and hyper-elliptic curves: mathematical basics; for which groups do we only know generic algorithms for solving the DLP; which groups should not be used; Dual_EC_DRBG
• Non-commutative groups in cryptography: mathematical basics; protocols and cryptographic schemes and their security.
• Lattice-based cryptography: mathematical basics; public-key cryptosystems from the worst-case shortest vector problem;
• Secure multiparty computation: Yao's result.
• Homomorphic encryption: overview on homomorphic encryption systems, their security; fully homomorphic encryption using ideal lattices.
• Indifferentiability vs random oracle model vs ideal cipher model and their implicatiosn for the "real world".
• Factoring and solving the DLP on quantum computers: Shor's algorithms.
• RSA vs factoring using only generic algorithms.
• SSL/TLS attacks: Lucky 13, BEAST; overview on the attacks, design flaws in the protocols.
• RSA vs acustic cryptanalysis and overview on side-channel attacks in general.