Course Overview

In this course we will discuss several aspects of algorithmic number
theory closely related to cryptography.

Learning Achievement

Competence

Course prerequisites

> Applicants should:

- Have completed, with good results, a Bachelor of science degree in
Mathematics or equivalent.
- Have thorough proficiency in written and spoken English.

Grading Philosophy

Exams take place in December.

Course schedule

> The course will be organized as follows:

-  In the first part we will discuss classical algorithms for
primality and factorisation.

- The second part will be an introduction to quantum algorithms, in
view of a discussion of Shor quantum algorithm for factorization and
discrete log problem, which are of (quantum) polynomial complexity.
- In the third part, we will discuss Euclidean lattices, and their
recent applications to cryptography that (conjecturally) resist
quantum algorithms.

> The course will be illustrated by programming sessions using SAGE.

> Bibliography:

- J. von zur Gathen and J. Gerhard: Modern computer algebra,
Cambridge University Press, New York,1999.
- A. M. Childs and W. van Dam: Quantum algorithms for
algebraicproblems, Reviews of Modern Physics, 2010
- C. Peikert: A Decade of Lattice Cryptography
[https://web.eecs.umich.edu/~cpeikert/pubs/lattice-survey.pdf], 2016.

Course type

> Lectures and practical work: - 48 course hours. - 120 hours of personal study.

Online Course Requirement

Instructor

Other information

- This course is part of the ALGANT Joint Master Program.

- For further information on the program structure, partner
institutions, scholarship opportunities, etc., please visit: ALGANT
Erasmus Mundus. [http://algant.eu/]

Duration: 12 weeks (Fall Semester)

Language of instruction: English
Mode of delivery: Face-to-face teaching

Site for Inquiry