Mathematical Foundations of Cryptography

Content

This course aims at explaining the following mathematical concepts, which are important in modern-day cryptography:

• Groups, Rings, Fields
• Finite Fields
• Gröbner Bases
• Elliptic Curves
• Discrete Logarithm
• Lattices

Material

Date	Lecture (10:00–12:00)	Who
08.10.2020	Introduction L01 – Groups Proofs	LH
15.10.2020	L02 - Rings	LH
22.10.2020	L03 - Fields and Finite Fields	RL
29.10.2020	L04 - Elliptic Curves	RL
12.11.2020	L05 - Discrete Logarithm	LH
26.11.2020 & 03.12.2020	L06 & L07 - Gröbner Bases	RL
10.12.2020	L08 - Lattices	LH
17.12.2020	L09 - Lattices Crypto	LH
14.01.2020	Cube Attacks SIDH

Administrative Information

Previous Knowledge No specific knowledge required. Basic mathematical competence in Linear Algebra and Discrete Mathematics is of advantage. Prerequisites Curriculum See position in the curriculum. Objective In this course, you will ...

• ...discuss mathematical concepts behind modern cryptography.
• ...have hands-on opportunity to analyze these concepts.
• ...get insight into selected topics of cryptographic research.

Language English Teaching Method Lecturing, work on individual topics, collaborating, classroom discussions Registration See Course registration in TUGOnline.

Lecturers