Mathematical Foundations of Cryptography

Course Number 705103 | Wintersemester 2020/21

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.

Lecture Dates

Date Begin End Location Event Type Comment
2021/01/28 10:00 12:00 External Location (please check TUGRAZonline) Abhaltung SE fix/

Lecturers

Christian Rechberger
Christian
Rechberger

Professor

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Lukas Helminger
Lukas
Helminger

PhD Student

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Reinhard Lüftenegger
Reinhard
Lüftenegger

PhD Student

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