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Hardness Assumptions in Lattice-Based Cryptography

ECTS credits:



Course parameters:

Language: English

Level of course: PhD course

Time of year: April-May 2022

No. of contact hours/hours in total incl. preparation, assignment(s) or the like: 16h/90h

Capacity limits: 20 participants


Objectives of the course:

At the end of the course participants should be able to navigate through the landscape of hardness assumptions on lattices that are used in current cryptography.


Learning outcomes and competences:

At the end of the course, the student should be able to:

- understand basic notions of lattice theory (lattice, determinant, volume, dual, minima, Minkowski)

- know the most important worst-case problems on lattices (shortest vector problem, closest vector problem)

- know the most important average-case problems on lattices used in crypto (LWE + variants, SIS + variants)

- understand how they are used in cryptography (LWE encryption, SIS hash function/signature)

- understand how we can improve efficiency of the cryptographic construction by using structured lattice problems

- have a rough understanding what a good/standard hardness assumption is and what not


Compulsory programme:

Attendance to 80% of the hours; a report (or presentation) on some topic/research paper


Course contents:

Mainly lectures, at the end also some discussions



Interest and basic knowledge in mathematics (linear algebra, geometry, number theory) and at least one graduate-level course in cryptography


Name of lecturer:

Katharina Boudgoust


Type of course/teaching methods:

The course will mainly involve lectures. Towards the end, we will open the course for discussions



There will be lecture notes made available during the course with references therein.


Course homepage:



Course assessment:

Participants have to write a report (or give a presentation) on a research work in this domain that will be assessed.



Department of Computer Science


Special comments on this course:




Monday 25.04 & 02.05 & 09.05 & 16.05 & 23.05 from 11h00 to 12h30

Friday 29.04 & 6.05 & 20.05 from 9h00 to 10h30



5335-395 Nygaard Meeting Room



Deadline for registration is 20 April 2022. Information regarding admission will be sent out no later than 22 April 2022.

For registration: please send an e-mail to Katharina Boudgoust, katharina.boudgoust@cs.au.dk

If you have any questions, please contact Katharina Boudgoust, e-mail: katharina.boudgoust@cs.au.dk

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