Algebraic Combinatorics

A.Y. 2025/2026
6
Max ECTS
42
Overall hours
SSD
MAT/02
Language
Italian
Learning objectives
The course gives an introduction to Elliptic Curve Cryptography.
Expected learning outcomes
Knowledge of the basic notions and techniques of Elliptic Curve Cryptography.
Single course

This course can be attended as a single course.

Course syllabus and organization

Single session

Responsible
Lesson period
First semester
Course syllabus
Introduction to Cryptography:
public and private key systems; discrete logarithm and Diffie-Hellman; factorization and RSA; digital signature.

Introduction to Elliptic Curve Cryptography:
elliptic curves, group structure, torsion points; Weil and Tate-Lichtenbaum pairings; elliptic curves over finite fields, trace of Frobenius and Hasse's theorem; Schoof's algorithm; elliptic curve cryptographic systems; Lenstra's factorization algorithm.
Prerequisites for admission
Basic knowledge of Algebra (Algebra 1 and Algebra 2).
Teaching methods
Blackboard lectures.
Teaching Resources
J. Hoffstein, J. Pipher, J. H. Silverman: An Introduction to Mathematical Cryptography.

L. C. Washington: Elliptic Curves: Number Theory and Cryptography.

N. Koblitz: A Course in Number Theory and Cryptography.

J. H. Silverman: The Arithmetic of Elliptic Curves (2nd Ed.).
Assessment methods and Criteria
The final examination consists of a written exam and an oral discussion, to be given in the same session. It is not allowed to use notes, books or calculators.
MAT/02 - ALGEBRA - University credits: 6
Lessons: 42 hours
Professor: Venerucci Rodolfo
Professor(s)