COM-102 / coefficient 7

Teacher: Gastpar Michael Christoph

Language: 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 modeling and probability. Entropy. Source coding and compression. Entropy to analyze algorithms.

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

III. Protecting information. Channel modeling. A few finite fields. Vector spaces. Hamming distance. Linear codes. Reed-Solomon codes.

## Keywords

Entropy

Data compression

Number theory

Cryptography

RSA cryptosystem

Linear codes

Reed-Solomon codes

## 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%

## Bibliography

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

## In the programs

• Semester: Spring
• Exam form: Written (summer session)
• Subject examined: Advanced information, computation, communication II
• Lecture: 4 Hour(s) per week x 14 weeks
• Exercises: 2 Hour(s) per week x 14 weeks
• Type: mandatory
• Semester: Spring
• Exam form: Written (summer session)
• Subject examined: Advanced information, computation, communication II
• Lecture: 4 Hour(s) per week x 14 weeks
• Exercises: 2 Hour(s) per week x 14 weeks
• Type: mandatory

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