# Coursebooks

## Advanced information, computation, communication II

Rimoldi Bixio

English

#### Summary

Text, sound, and images are examples of information sources stored in our computers and/or communicated over the Internet. How do we measure, compress, and protect the informatin they contain?

#### Content

I. How to measure information. Source and probability. Entropy per symbol. Source coding.

II. Cryptography and information security. Modular arithmetic, modern algebra and number theory. The Chinese remainder theorem and RSA.

III. Protecting information. A few finite fields. Linear speaces. Hamming distance. Linear codes. Reed-Solomon codes.

#### Keywords

Shannon's entropy

Linear codes

Reed-Solomon codes

Number theory

Asymmetric Cryptography, RSA

#### Learning Outcomes

By the end of the course, the student must be able to:
• Understand Shannon's entropy
• Construct an optimal code
• Understand elementary number theory
• Know what an abelian group is
• Recognize a hidden isomorphism
• Know how RSA works
• Know a few linear codes on simple finite fields

#### Transversal skills

• Take feedback (critique) and respond in an appropriate manner.
• Assess one's own level of skill acquisition, and plan their on-going learning goals.

#### Teaching methods

Ex cathedrra with exercises

#### Expected student activities

Homework (written and grades) ever week.

#### Assessment methods

Continuous evaluations 10% and final exam 90%

#### Resources

##### Bibliography

"Sciences de l'information", J.-Y. Le Boudec, R. Urbanke et P. Thiran, online

### Reference week

MoTuWeThFr
8-9
9-10
10-11
11-12
12-13
13-14
14-15
15-16
16-17
17-18
18-19
19-20
20-21
21-22
Under construction

Lecture
Exercise, TP
Project, other

### legend

• Autumn semester
• Winter sessions
• Spring semester
• Summer sessions
• Lecture in French
• Lecture in English
• Lecture in German