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
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
  • Error-Correcting Codes and Applications to Cryptography
    Codes correcteurs d'erreurs et applications à la cryptographie
  • Language:
  • Period:
  • 1-2.
  • Duration:
  • 24h (1.5h/week).
  • ECTS:
  • 3.
  • Manager:
  • Anne Canteaut.

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 2025-2026**

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

17/09 Alain Couvreur Introduction
24/09 Anne Canteaut Finite Fields basics
01/10 Alain Couvreur Decoding problems, Shannon theory
08/10 Alain Couvreur Bounds on the parameters of codes
15/10 Alain Couvreur Duality, MacWilliams identity
22/10 Alain Couvreur Cyclic codes, BCH codes
05/11 Alain Couvreur Reed-Solomon codes
12/11 Anne Canteaut Exercises
19/11 Thomas Debris Decoding as an intractable problem
26/11 mid-term exam
10/12 Thomas Debris Random codes and generic decoding algorithms
17/12 Thomas Debris Code-based encryption schemes
07/01 no lecture
14/01 Anne Canteaut Reed-Muller codes, Boolean functions
21/01 Anne Canteaut Algebraic attacks and statistical attacks on block ciphers
28/01 Anne Canteaut Linear cryptanalysis
04/02 no lecture
11/02 Anne Canteaut Linearity of Sboxes
18/02 Anne Canteaut Differential cryptanalysis
25/02 Anne Canteaut Diffusion in block ciphers
11/03 final exam

**Exams**

  • Partial exam: November 26. Lecture notes are allowed.
  • Final exam: March 11. The final exam will rely on a research paper given to the students 3 weeks in advance. The day of the exam, a list of questions related to the paper is handed.

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

Annals

Internships & Theses

TBA