Ognjen Milivojević,  Boris Damjanović 

Pan-European University “Apeiron”, Faculty for Information Technologies, vojvode Pere Krece, 78000 Banja Luka, Bosnia and Herzegovina, ognjenmili1993@gmail.com   

PROFESSIONAL PAPER

ISSN 2637-2150
e-ISSN 2637-2614
UDC 514.112/.113:316.647.5
DOI 10.7251/STED2302084M
COBISS.RS-ID 13942988

 
Paper Submited: 03.10.2023.
Paper Accepted: 17.11.2023.
Paper Published: 29.11.2023.
http://stedj-univerzitetpim.com  

Corresponding Author: Ognjen Milivojević, Pan-European University “Apeiron”, Faculty for Information Technologies, vojvode Pere Krece, 78000 Banja Luka, Bosnia and Herzegovina, ognjenmili1993@gmail.com

Copyright © 2022 Ognjen Milivojević & Boris Damjanović; published by UNIVERSITY PIM. This work licensed under the Creative Commons Attribution-NonCommercial-NoDerivs 4.

ABSTRACT

Understanding elliptic curves contributed to solving mathematical problems in number theory that had been unsolved for centuries. Elliptic curves were also used in solving one of the millennial problems, which is Fermat’s last theorem. They are also connected with many hypotheses and problems in mathematics that have yet to be solved. Elliptic curves defined over finite fields are widely used in public key cryptography, since they have proven to be groups that have the best properties for implementing the Diffie-Hellman protocol. This article provides an overview of the theoretical assumptions that are necessary for the development of cryptographic algorithms based on elliptic curve cryptography, which includes defining elliptic curves, defining the properties of arithmetic operations on elliptic curves used in cryptography with reference to curves defined over finite fields.

Keywords:  elliptic curve, Weierstrass form, finite fields, groups