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

• #### Number of hours

• Lectures 15.0
• Projects -
• Tutorials 15.0
• Internship -
• Laboratory works 3.0
• Written tests -

ECTS 3.0

## Goal(s)

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.

Responsible(s)

Clement PERNET, Jean-Guillaume DUMAS

## Content(s)

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).

Test

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

Calendar

The course exists in the following branches:

see the course schedule for 2023-2024