Aller au menu Aller au contenu
Une voie, plusieurs choix
Informatique et Mathématiques appliquées
Une voie, plusieurs choix

> Formation > Cursus ingénieur

Codes: Cryptography, Compression, Error Correction - 4MMCRY6

A+Augmenter la taille du texteA-Réduire la taille du texteImprimer le documentEnvoyer cette page par mail Partagez cet article Facebook Twitter Linked In Google+ Viadeo
  • Number of hours

    • Lectures : 15.0
    • Tutorials : 15.0
    • Laboratory works : 3.0
    ECTS : 3.0

Goals

The goal is to acquire the foundations of code theory (computer science and mathematics) that provide provable guarantees on confidentiality, inetgrity and authentication for digital communications. This course presents the theory of codes, its mathematical foundation and its applications in cryptography,
compression and error-correction. It gives the bases required to implement and use coding protocols.

Contact Jean-Marc BROSSIER

Content

1. Binary information coding. Entropy.
2. The group Zn*; Euler function and Chinese remainder theorem. Polynomials and finite fields.
3. Symmetric cipher – Vernam cipher on a group. AES, crypt
4. Asymmetric cryptography. Diffie-Hellman. RSA: security and attacks.
5. Chaining modes. CSPRNG. Hash functions. Digital signature. DSA
6. Lossless data compression. Huffman tree; Lempel-Ziv. Zlib /zip
7. Codes and Hamming distance. Codes for error detection: CRC
8. Linear codes and Reed-Solomon codes. Unique and list decoding.
9. Cyclic codes and shortened variants.



Prerequisites

Applied Probability 1 and 2 (1st year). Algorithms and cost analysis (Algorithms 2 and 3). Basic knowledge in linear
algebra (linear system solving by Gaussian elimination) and in integer and polynomial arithmetic (primality and gcd).

Tests

NORMAL SESSION:
Written exam
Duration : 3h
Authorized documents: all handwritten or photocopy documents
Prohibited documents: books
Electronic computers (including mobile phones, ...) are prohibited.



1 examen écrit de 2 heures (documents autorisés) (E).
N1=E1
N2=E2

Additional Information

Curriculum->Information Systems Engineering->Semester 8
Curriculum->Embedded Systems & Connect. Devices->Semester 8
Curriculum->Math. Modelling, Image & Simulation->Semester 8

Bibliography

S. Arora, B. Barak, Computaional complexity: a modern approach, 2009
JG Dumas, JL Roch, E Tannier, S Varrette, Théorie des Codes, Dunod Sc.iences Sup., 2ème édition, 2009.
James Massey. Applied Digital Information Theory (vol I et II) ETZH. University.

A+Augmenter la taille du texteA-Réduire la taille du texteImprimer le documentEnvoyer cette page par mail Partagez cet article Facebook Twitter Linked In Google+ Viadeo

Date of update January 15, 2017

Grenoble INP Institut d'ingénierie Univ. Grenoble Alpes