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At the end of the course, the students are able to - to name and explain means to achieve security in modern communication and storage systems, - to understand and analyze basic cryptographic schemes, - to understand the challenges of post-quantum cryptography and to name which schemes are post-quantum secure, - for code-based cryptography: to choose a suitable error-correcting code, adapt its parameters, evaluate it, and implement it in software, - to understand and implement known attacks on code-based cryptographic schemes, - to give an overview of symmetric cryptography and authentication, - identify hard problems in lattice and explain how to build cryptosystems based on lattices, - identify various design challenges and interplay between design parameters, - identify security issues in DSSs, - to understand the basic principle and different forms of private information retrieval (PIR), - give an overview of known results related to complexity, capacity, and coding methods used for PIR

- Motivation and practical need for secure systems - Short overview of classical cryptography: symmetric and public-key cryptography - Short introduction to linear error-correcting codes: generator and parity-check matrix, dual code, minimum distance, MDS codes - Post-quantum cryptography: threat of a quantum computer - Code-based cryptography (McEliece & Niederreiter schemes, attacks, other code-based systems) - Lattice-based cryptography (Shortest Vector Problem, Closest Vector Problem, Subset-Sum cryptosystems, NTRU cryptosystem, Ring Learning with Errors) - Private information retrieval: basic idea (security vs anonymity vs privacy as concepts), toy schemes for 1-3 servers; computational vs. information-theoretic PIR; review of communication complexity results - Private information retrieval over coded databases: PIR rate and capacity results

- Mathematical basics (in particular linear algebra) - Recommended: some knowledge in channel coding (can be taken in parallel to this lecture)

In an accompanying tutorial, the content of the lecture is applied by calculating problems and programming small tasks.

In a final written exam about the content of the lecture, the students should demonstrate their understanding of the considered security schemes and the respective applications. They have to show (while using only one handwritten sheet of notes) that they can evaluate and design the respective security and coding schemes for the considered applications (post-quantum cryptography, authentication, distributed data storage, private information retrieval).

The slides will be provided. If necessary, current research papers to each of the topics are uploaded.