Algebraic Combinatorics
A.Y. 2026/2027
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 cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
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 an oral discussion.
MATH-02/A - Algebra - University credits: 6
Lessons: 42 hours
Professor:
Venerucci Rodolfo
Shifts:
Turno
Professor:
Venerucci RodolfoProfessor(s)
Reception:
Wednesday from 3 to 5 p.m. (by prior e-mail contact).
Department of Mathematics - Room 2094 (second floor).