inf462 - Cryptography (Vollständige Modulbeschreibung)

Fundamental knowledge on algorithms, discrete structures, and linear algebra as for instance covered in the following bachelor courses at the UOL:

• Inf030 Programmierung, Datenstrukturen und Algorithmen
• Mat950 Diskrete Strukturen
• Mat955 Linear Algebra für Informatik

Students understand the foundations of modern cryptography. The students can explain the formal security definitions of the most essential cryptographic primitives and can apply proof techniques to show that a given cryptographic construction meets a given security definition. They can identify underlying cryptographic assumptions, analyze them and discuss them in context. In addition, the students are able to build cryptographic primitives that provably meet specific security goals.

Professional competences
The students

• understand definitions of security for different cryptographic primitives,
• discuss the importance of cryptography,
• formalize cryptographic assumptions, and
• carry out security proofs of cryptographic primitives

Methological competence

The students

• use cryptographic concepts and techniques to increase security, in particular regarding which protection goals can be achieved with which cryptographic techniques,
• apply cryptographic mechanisms in simple scenarios, and
• question the properties and limits of cryptographic concepts and combine different concepts in a meaningful way

Social competences

The students

• solve problems partially in small groups and thus improve their willingness to cooperate and their communication skills
• present solutions to cryptographic problems in front of the exercise group,
• discuss their different solutions within the exercise group, and
• improve their English language skills.

Self-competencies

The students

• motivate themselves to work on questions and problems in the domain of cryptography,
• justify their own actions with theoretical and methodical knowledge, and
• critically reflect on proposed solutions in relation to social expectations and consequences, taking into account the methods taught.

The course provides a rigorous treatment of the basic paradigms and principles of modern cryptography. It puts an emphasis on formal definitions of security, precise assumptions, and rigorous proofs of security in well-defined models.

Concretely, the course deals with the formal and rigorous treatment of the following concepts and primitives:

• Private-Key Encryption:
  • Definition of secure encryption and the concept of provable security
  • Pseudorandom number generators
  • Constructing secure encryption schemes based on pseudorandomness
  • Security under Chosen-Plaintext Attacks (CPA)
  • Pseudorandom functions and the construction of CPA-secure encryption
  • Pseudorandom permutations and block ciphers
  • Security against Chosen-Ciphertext Attacks (CCA)
• Message Authentication Codes (MACs) and hash functions
• Cryptographic assumptions
• Key management        
• Public-key cryptography
  • Recap on RSA
  • Attacks on RSA and mitigation
  • The KEM/DEM paradigm
  • Homomorphic Encryption (particularly Paillier)
  • Secret Sharing and Threshold Encryption
• Advanced topics (varying per semester), e.g.:
  • Secure Multiparty Computation
  • Post-Quantum Cryptography
  • Zero-Knowledge Proofs

 While some of the above topics are typically covered on a very high level in an introductory course on IT security, it should be stressed that this course on cryptography differs substantially by a much more in-depth treatment of the topics with a focus on formal definitions, precise assumptions, and rigorous proofs.
 

• J. Katz and Y. Lindell. Introduction to Modern Cryptography. 3rd edition. Chapman & Hall, ISBN 978-0-815-35436-9, 2020
• D. Boneh and V. Shoup. A Graduate Course in Applied Cryptography. Version 0.6, 2023. Available at: http://toc.cryptobook.us/

Written or oral exam

The concretely chosen form of examination will be announced in the first week of the course.