# Learning outcomes/objectives

## Knowledge

After successful completion of the module students know:

- the basic mathematics of quantum computing
- how quantum computers threaten cryptography
- the techniques underlying modern quantum-safe cryptography
- how security proofs work
- important proof techniques for post-quantum cryptography
- the current state of post-quantum security standardization
- at least one standardization-candidate cryptosystem in more detail

## Skills

After successful completion of the module, students will be able to:

- analyze simple quantum programs
- write simple post-quantum security proofs
- follow complex security proofs
- connect complex (real-life) post-quantum secure cryptosystems with their basic versions
- understand security-relevant design decisions
- implement post-quantum cryptosystems

## Competencies

Based on the knowledge and skills acquired in the module, students will be able to:

- orient themselves in the post-quantum security landscape based on solid foundations
- enter research into post-quantum security
- follow both industry and academic research, development and standardization of post-quantum crypto
- make educated decisions related to cryptographic systems
- join teams working on cryptographic systems (research / implementation)

# Content

- Foundations
- Mathematical foundations of quantum mechanics
- Quantum computing (programming quantum computers)
- Cryptographic security proofs
- Quantum random-oracle model

- Insecurity of existing cryptography
- RSA / discrete logarithm based cryptosystems
- Shorâ€™s algorithm

- Elementary post-quantum schemes
- Learning with errors (LWE) problem
- Decoding problems
- Regev cryptosystems and variants
- McEliece and variants

- Hardening encryption schemes with hash functions
- Quantum random-oracle model (QROM)
- Fujisaki-Okamoto transform
- Security proofs in the QROM

- Real-world post-quantum secure systems
- Overview over NIST-standardization process
- One cryptosystem in detail (e.g., Kyber)