Rings and Finite Fields in Modern Cryptography
Year | Expected 2026 |
ECTS | 4 |
Course content |
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. |
Course objectives |
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. |
Invited lecturers |
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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 application scenarios and the need for cryptography
13:30-15.00: Introduction to cryptography
15:30-17:00: IoT, edge devices, and recent attack examples
18:00-22:00: Welcome reception with dinner
Tuesday morning: Various implementation technologies
9:00-11:15: ASIC, FPGA, CPUs, GPUs, HPC
11:30-12:30: Performance metrics, optimization techniques, trade-offs
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 Shuttle service to station Putten leaves at 12:45 in front of the hotel. |
Assessment |
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.
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