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## CRIPTOGRAPHY AND CODE THEORY

CODE 34327 2020/2021 5 cfu during the 2nd year of 9011 MATEMATICA(LM-40) - GENOVA 5 cfu during the 1st year of 9011 MATEMATICA(LM-40) - GENOVA MAT/02 Italian GENOVA 2° Semester AULAWEB

## OVERVIEW

A large portion of the course will be devoted to the study of the mathematical theory of error-correcting codes, which enable us to control errors in data transmission over unreliable or noisy communication channels. We will also consider family of codes.

In the  second part of the course we  will turn to Cryptography, the study of mathematical techniques for secure communication. We will introduce classical cryptography, and we will give a general view  on modern cryptographic schemes.

## AIMS AND CONTENT

### LEARNING OUTCOMES

Aim of the course is to present  to the students the basic topics on Code Theory and Criptography.

### PREREQUISITES

Linear algebra and a basic algebra topics (e.g., modular arithmetic, Euclidean algorithm, polynomials, fields).

### TEACHING METHODS

Lessons and students seminar.

### SYLLABUS/CONTENT

Code Theory: Finite fields,  introduction to the problem of error-correction in data transmission, linear codes over finite fields, Hamming distance and minimum distance decoding Singleton and sphere-packing bounds, perfect and MDS codes, Hamming codes and syndrome decoding, codes constructions.

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

### EXAM DESCRIPTION

Oral exams and students seminar

### FURTHER INFORMATION

To attend the lessons is reccomended