Elliptic-curve Diffie-Hellman for Key Exchange

U ovome je radu obrađena tema eliptičkih krivulja u kriptografiji i njihova primjena za razmjenu ključeva preko nesigurnog kanala metodom ECDH (engl. Elliptic-curve Diffie-Hellman). Opisani su korišteni matematički postupci, pravila i operacije uključujući i modularnu aritmetiku i cikličke grupe. U radu je dan uvod u simetričnu i asimetričnu kriptografiju te uvod u kriptoanalizu. Budući da se ECDH temelji na problemu diskretnog logaritma, isti je detaljno opisan. Implementacija samog ECDH algoritma je izvršena u programskom jeziku Python.This thesis elaborates on elliptic curves in cryptography and their application for key exchange over an insecure channel using the ECDH (Elliptic-Curve Diffie-Hellman) method. The thesis describes mathematical principles, rules, and operations, including modular arithmetic and cyclic groups. An introduction to symmetric and asymmetric cryptography is given as well as the basics of cryptanalysis. Since ECDH is based on the discrete logarithm problem, it is described in detail in the thesis. The implementation of the ECDH algorithm was done in the Python programming language