Algebraic Combinatorics
A.Y. 2025/2026
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.
Lesson period: First semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
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.
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.).
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.
Professor(s)