title:
Error-Correcting Codes and Applications to Cryptography
Codes correcteurs d'erreurs et applications à la cryptographie
manager:
Anne Canteaut
ects:
3
period:
1-2
periodpref:
1 and 2
format:
16 x 1.5h over 2 periods
hours:
24
weeks:
16
hours-per-week:
1.5
language:
French by default
lang:
track:
C
themes:
Cryptography, Discrete Math/Graphs
number:
2.13.2
year:
2024, 2025, 2026

Instructors: Anne Canteaut (responsable), Alain Couvreur, Thomas Debris

Objectives
The aim of this course is to present common issues essential to the theory of error-correcting codes and to cryptology (symmetric cryptography and public-key cryptosystems), with algorithmic and computational aspects.

English Policy
Lectures will be in French, but could be in English if some student asks for it.
Lecture notes are in English.

Prerequisite
First-year master level in standard algebra, algorithms and cryptology.

Sister courses: CRYPTALG, LCRYPT, SECURE, QCC.

**Preliminary schedule year 2026-2027**

Wednesday, from 8:45 to 10:15, building Sophie Germain, Room 1002

16/09 Thomas Debris Introduction
23/09 no lecture
30/09 Anne Canteaut Finite Fields basics Exercises
07/10 Alain Couvreur Decoding problems, Shannon theory
14/10 Alain Couvreur Bounds on the parameters of codes
21/10 no lecture
04/11 Alain Couvreur Duality, MacWilliams identity
11/11 no lecture
18/11 Alain Couvreur Cyclic codes, BCH codes
25/11 Anne Canteaut Exercises
02/12 mid-term exam
09/12 Alain Couvreur Reed-Solomon codes
16/12 Thomas Debris Decoding as an intractable problem
06/01 Thomas Debris Random codes and generic decoding algorithms
13/01 Thomas Debris Code-based encryption schemes
20/01 Anne Canteaut Reed-Muller codes, Boolean functions
27/01 Anne Canteaut Algebraic attacks and statistical attacks on block ciphers
03/02 Anne Canteaut Linear cryptanalysis
10/02 Anne Canteaut Linearity of Sboxes
17/02 Anne Canteaut Differential cryptanalysis
24/02 Anne Canteaut Diffusion in block ciphers
10/03 final exam

**Exams**

Lecture notes are allowed.

The final grade is defined as the maximum between the grade of the final exam and the average of the grades of the partial exam and of the final exam.

Lecture Notes

Training

TBA

Annals

Internships & Theses

TBA