Cryptography

Lecturer: Prof. Dr. Arne Meier

Frequency: Every two years (even years) in the winter semester

Course type: Lecture and exercise (2V + 1Ü + 2S, 7 ECTS)

Examination: Oral exam

The module provides in-depth knowledge of the most important cryptographic methods and protocols. Upon successful completion of the course, students will be able to evaluate common methods in terms of correctness and security. They will develop new cryptographic primitives.

Outline:

• Classical methods (Caesar, Vigenère cipher) and their weaknesses
• Perfect security (Shannon)
• Modern symmetric encryption methods (AES) and modes of operation (CBC, CTR) and their security
• Modern security concepts (indistinguishability, pseudorandom functions, semantic security)
• One-way functions (weak and strong, complexity-theoretic relations)
• Asymmetric methods (RSA, Elgamal, Diffie-Hellman) and their security
• Generation of prime numbers and generators (Miller-Rabin-Selfridge)
• Hash functions (Merkle-Damgård, sponge functions, SHA-2, SHA-3)
• Digital signatures (RSA, Elgamal, DSA, LD-OTS)
• Pseudorandom numbers and generators (hardcore predicates, Blum-Micali, pseudorandom OTP, Blum-Blum-Shub)
• Zero-Knowledge Proofs (interactive proof systems, CZK, PZK, Fiat-Shamir)
• Outlook: Electronic currency and post-quantum cryptography