There are no formal prerequisites. It would be desirable that the students passed the course Number Theory from the undergraduate mathematics study programme as well as one of the courses Algebraic curves (theoretical mathematics programme) or Cryptography and network security (computer science and mathematics programme).
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.
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.
Public key cryptography. The idea of the public key. Cryptosystems based on factorization and the discrete logarithm problem in a finite group. Digital signatures..
Cryptosystems based on elliptic curves. Analogues of El-Gamal and DSA cryptosystem. Comparisons with other public key cryptosystems. The discrete logarithm problem on elliptic curves. Parameter choices in the cryptosystem.
Other applications of elliptic curves. Elliptic curve factorization method by Lenstra. Primality proving using elliptic curves.
(in pdf format; in Croatian)
Cryptography - Undergraduate course
Number Theory - Undergraduate course
Algorithms for Elliptic Curves - Graduate course (2008/2009)
Number Theory in Cryptography - Graduate course (2003/2004)
Recommended readings in number theory
PARI/GP home page
PARI/GP in browser
Number Theory and PARI/GP