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Informatique et Mathématiques appliquées

# Codes: Cryptography, Compression, Error Correction - 4MMCRY6

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• #### 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

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.

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Date of update January 15, 2017

École nationale supérieure d'informatique et de mathématiques appliquées
681, rue de la passerelle - Domaine universitaire - BP 72
38402 SAINT MARTIN D'HERES