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## CRIPTOGRAPHY AND CODE THEORY

CODE 34327 2021/2022 5 credits during the 1st year of 9011 Mathematics (LM-40) GENOVA MAT/02 GENOVA (Mathematics) 2° Semester AULAWEB

## OVERVIEW

This is an introductory course in Coding Theory and Cryptography.

A large part will be dedicated to the mathematical aspects of Coding Theory which studies the problem of correcting errors in messages transmitted through a non secure channel with noise.

In the last part we will present a short introduction to Cryptography, which studies mathematical techniques in order to secure the communication in presence of third parties.

## AIMS AND CONTENT

### LEARNING OUTCOMES

The aim of the course is to present the basic topics of Coding Theory and Criptography.

### AIMS AND LEARNING OUTCOMES

At the end of the course students will be able to:

- recognise the main classes of error correcting codes;
- master the main constructions of linear codes;
- recognise the principal decoding algorithms;
- master basic tools of modern cryptography and related algorithms.

### PREREQUISITES

Necessary prerequisites are the following: vector spaces, groups, fields.

The courses "Algebra Lineare e Geometria Analitica" and "Algebra 2" are recommended.

### TEACHING METHODS

Lectures and students' seminar.

### SYLLABUS/CONTENT

Coding Theory:

- introduction to the problem of error-correction in data transmission;
- linear codes over finite fields;
- Hamming distance and minimum distance decoding;
- perfect and MDS codes;
- Hamming codes;
- codes constructions;
- cyclic codes;
- Goppa codes

Cryptography:

- introduction to classical cryptography;
- some modern cryptographic schemes.

J.H Van Lint - Introduction to coding theory

Neal Koblitz - A Course in Number Theory and Cryptography

Douglas R. Stinson - Cryptography. Theory and Practice

## TEACHERS AND EXAM BOARD

### Exam Board

EMANUELA DE NEGRI (President)

ALDO CONCA

ALESSIO CAMINATA (President Substitute)

## LESSONS

### LESSONS START

The class will start according to the academic calendar.

### Class schedule

All class schedules are posted on the EasyAcademy portal.

## EXAMS

Oral exam.

### ASSESSMENT METHODS

Questions of the oral exam will concern the main topics presented during the lectures. The aim is to establish not only whether students will have reached an appropriate level of knowledge, but also whether they can analize and approach problems related to Coding Theory and Cryptography.

### FURTHER INFORMATION

Attendance is recommended.