1. komponenta

Lecture type	Total
Lectures	45

* Load is given in academic hour (1 academic hour = 45 minutes)

COURSE AIMS AND OBJECTIVES: The objective of this course is to introduce students with basic concepts, facts and algorithms concerning elliptic curves over the rational numbers and finite fields and their applications in cryptography and algorithmic number theory.

COURSE DESCRIPTION AND SYLLABUS:
1. Elliptic curves over the field of rational numbers. Addition of points on elliptic curves.The Mordell-Weil group of the elliptic curve over the field of rational numbers. Algorithms for computing the torsion group and rank. (2-3 weeks)
2. Elliptic curves over finite fields. Efficient implementation of basic operations on elliptic curves.Elliptic curves over the field of characteristic 2. Algorithms for cumputing the order of the group of points on elliptic curves. (2-3 weeks)
3. Public key cryptography. The idea of the public key. Cryptosystems based on factorization and the discrete logarithm problem in a finite group. Digital signatures. (2-3 weeks)
4. Cryptosystems based on elliptic curves. Analogues of El-Gamals and the DSA cryptosystem. Comparisons of other public key cryptosystems. The discrete logarithm problem on elliptic curvres. Parameter choice in the cryptosystem (2-3 weeks)
5. Other applications of elliptic curves. Elliptic curve factorization method of Lenstra. Primality proving using elliptic curvrs. (2-3 weeks)

Izborni predmet 1, 2 - Regular study - Theoretical Mathematics

Izborni predmet 1, 2 - Regular study - Theoretical Mathematics

Izborni predmet 3, 4 - Regular study - Theoretical Mathematics

Izborni predmet 3, 4 - Regular study - Theoretical Mathematics