MPRI

- Error-correcting codes and applications to cryptography (24h, 3 ECTS)

Error-correcting codes and applications to cryptography (24h, 3 ECTS)

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: 2.12-1, 2.12-2, 2.30, 2.34.2 and 2.13.1.

Preliminary schedule year 2022-2023

Thursday, from 8:45 to 10:15, building Sophie Germain (Room 1002).

15/09	Alain Couvreur	Introduction
22/09	Anne Canteaut	Finite Fields basics Exercises
29/09	Alain Couvreur	Decoding problems, Shannon theory
06/10	Alain Couvreur	Bounds on the parameters of codes
13/10	Alain Couvreur	Duality, MacWilliams identity
20/10	Alain Couvreur	Reed-Solomon codes
27/10	no lecture
03/11	Alain Couvreur	Cyclic codes, BCH codes
10/11	Anne Canteaut	Exercises
17/11	Alain Couvreur	List decoding of Reed-Solomon codes, Guruswami-Sudan algorithm
01/12	mid-term exam
08/12	no lecture
15/12	Anne Canteaut	Reed-Muller codes, Boolean functions
05/01	Anne Canteaut	Algebraic attacks and statistical attacks on block ciphers
12/01	Anne Canteaut	Linear cryptanalysis
19/01	Anne Canteaut	Linearity of Sboxes
26/01	Anne Canteaut	Differential cryptanalysis
02/02	no lecture
09/02	Anne Canteaut	Diffusion in block ciphers
16/02	Thomas Debris	Public-key code-based cryptography I
23/02	Thomas Debris	Public-key code-based cryptography II
09/03	final exam

Exams

Partial exam: December 1. Lecture notes are allowed.
Final exam: March 9. 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.