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Elliptic curves in cryptography

Code: 130301
ECTS: 5.0
Lecturers in charge: prof. dr. sc. Filip Najman - Lectures
English level:


All teaching activities will be held in Croatian. However, foreign students in mixed groups will have the opportunity to attend additional office hours with the lecturer and teaching assistants in English to help master the course materials. Additionally, the lecturer will refer foreign students to the corresponding literature in English, as well as give them the possibility of taking the associated exams in English.

1. komponenta

Lecture typeTotal
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.

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)
  1. A. Dujella, M. Maretić: Kriptografija
  2. N. Koblitz: A Course in Number Theory and Cryptography
  3. J. H. Silverman, J. Tate: Rational Points on Elliptic Curves
  4. L. C. Washington: Elliptic Curves: Number Theory and Cryptography
  5. I. Blake, G. Seroussi, N. Smart: Elliptic Curves in Cryptography
  6. D. Hankerson, A. Menezes, S. Vanstone: Guide to Elliptic Curve Cryptography
1. semester
Izborni predmet 1, 2 - Regular study - Theoretical Mathematics

2. semester
Izborni predmet 1, 2 - Regular study - Theoretical Mathematics

3. semester
Izborni predmet 3, 4 - Regular study - Theoretical Mathematics

4. semester
Izborni predmet 3, 4 - Regular study - Theoretical Mathematics
Consultations schedule: