Rings and Finite Fields in Modern Cryptography
|Year||Feb 19-23, 2024|
|Modern cryptography studies techniques to protect communication and computation against different forms of adversarial behavior. Implementing cryptographic schemes presents a challenging task, and requires a deep understanding of cryptographic schemes as well as the underlying mathematical structures. This course is focused on teaching a basic understanding on selected cryptographic applications and the underlying mathematics, with a focus on rings and finite fields. The course will explain selected topics from symmetric and public-key cryptography, as well as advanced cryptographic primitives, together with efficient implementation techniques for modern (distributed) systems combining CPUs, GPUs, and FPGAs. We will further illustrate the need for ASICs in cryptography, and discuss the benefits and challenges of using such architectures.|
|The students will understand the cryptographic notions and the underlying mathematical structures, and will be able to observe and recognize how mathematical parameter choices and targeted implementation technology affect the performance of the system, thus developing an intuition for good trade-offs between sufficient cryptographic strength and implementation efficiency.|
|Preliminary course schedule 2024:|
|Morning sessions: 09:00-11:15 lecture including break, 11:30-12:30 hands-on work session.
Afternoon sessions: 13:30-15:45 lecture including break, 16:00-17:00 hands-on work session.
Monday afternoon: Various implementation technologies
Tuesday morning: Various application scenarios and the need for cryptography
Tuesday afternoon: Mathematical background
Wednesday morning: Symmetric-key cryptography including authenticated encryption
Wednesday afternoon: Public-key cryptography including an excursus on post-quantum security
Thursday morning: Advanced primitives I: homomorphic encryption
Thursday afternoon: Advanced primitives II: zero-knowledge proofs
Friday morning: Advanced primitives III: secure multi-party computation
|ASCI students will be evaluated on 3 small assignments, to be partially completed during the in-class hands-on sessions (and should be finalized after the course completion), as well as a short essay where they link the knowledge obtained in this course with their field of research. Both the essay, and the hands-on related assignments are due 3 weeks after the completion of course.