Elementary Mathematics from an Advanced Standpoint 2

A.Y. 2016/2017
6
Max ECTS
47
Overall hours
SSD
MAT/04
Language
Italian
Learning objectives
Il corso propone un'introduzione con metodi elementari alla teoria dei numeri e alle sue applicazioni alla crittografia. I concetti di base sono introdotti nella parte A del corso, le applicazioni alla crittografia sono trattate nella parte B. L'obiettivo del corso è di coniugare conoscenze e abilità applicative.
Expected learning outcomes
Undefined
Course syllabus and organization

Single session

Responsible
Lesson period
Second semester
Course syllabus
A
Introduction
Unique factorization and the GDD
Some arithmetic functions
Congruences and the ring Zm.
Solution of congruences of degree n
Primitive roots
nth power residues
Quadratic residues and Legendre symbol
The law of quadratic reciprocity
Sum of squares
Some Diophantine equations
B
Intro to cryptography: Caesar's algorithm, substitution, transposition
Integer factorization
Primality tests
Public key cryptography: RSA
Rational points on curves
Introduction to elliptic curves: rational points and cryptography applications.
MAT/04 - MATHEMATICS EDUCATION AND HISTORY OF MATHEMATICS - University credits: 6
Laboratories: 12 hours
Lessons: 35 hours