lmat2450  2020-2021  Louvain-la-Neuve

Due to the COVID-19 crisis, the information below is subject to change, in particular that concerning the teaching mode (presential, distance or in a comodal or hybrid format).
5 credits
30.0 h + 15.0 h
We introduce the core concepts of modern cryptography, with a specific focus on the mathematical and algorithmic aspects. Historical problems and constructions will be discussed and serve as a basis for the introduction of the core security notions and cryptographic mechanisms that are in use to day, as well as for the development of methods for justifying the security of these mechanisms. The contents may include:
  • Information theoretic cryptography, perfect encryption.
  • Probabilistic algorithms, computational security, attacker models, elaboration of security proofs in cryptography.
  • Symmetric encryption: security definitions, basis constructions, block ciphers (AES, DES), cryptanalysis, operation modes.
  • Authentication codes, hash functions.
  • Asymmetric cryptography: Diffie-Hellman protocol, public key encryption (ElGamal, RSA, ...), signature (Schnorr, DSA/DSS, RSA hash-and-sign, ...), public key infrastructures.
  • Basic algorithmic number theory (modular arithmetic, primality testing, elliptic curves)
  • Protocols: challenge-response, identification, authentication, zero-knowledge
  • Standards and norms: discussion, practical concerns,
The balance between the various parts can vary from one year to another.
Teaching methods

Due to the COVID-19 crisis, the information in this section is particularly likely to change.

The class is organised around lectures and exercise sessions. Homeworks may also be proposed.
A specific attention is placed on the links between the theoretical concepts introduced in the class and the practical applications of cryptography.
Evaluation methods

Due to the COVID-19 crisis, the information in this section is particularly likely to change.

The evaluation is based on a written examination. Homeworks proposed during the semester may contribute to the final grade.
Answers can be provided in English or in French.
Online resources
Moodle website.
J. Katz et Y. Lindell, Introduction to Modern Cryptography, 2nd edition. (Chapman and Hall/CRC Press).
More references are available on Moodle.
Teaching materials
  • slides sur moodle
Faculty or entity

Programmes / formations proposant cette unité d'enseignement (UE)

Title of the programme
Master [120] in Mathematics

Master [120] in Computer Science and Engineering

Master [120] in Computer Science

Master [120] in Electrical Engineering

Additionnal module in Mathematics

Master [120] in Mathematical Engineering

Master [120] in Data Science Engineering

Master [120] in Data Science: Information Technology