Number Theory Algorithms in Public Key Cryptography

Cilj diplomskog rada je opis osnovnih pojmova i algoritama u teoriji brojeva s primjenom u kriptografiji javnog ključa. Opisuju se osnovni pojmovi kao što su djeljivost, kongruencija, Euklidov algoritam itd. kako bi mogli kreirati kompleksnije sustave koji se na njima temelje. Opisani su moderni kriptosustavi s javnim ključem kao i primjena, njihovi nedostatci te kako ih ispraviti. Krajnji rezultat je aplikacija koja objedinjuje bitne algoritme.The aim of this thesis is to describe essential and frequently used number theory terms and algorithms with the use in public-key cryptography. Basic concepts such as divisibility, congruence, Euclidean algorithm etc. are described in order to create complex systems based on them. Modern public-key cryptosystems have been described, as well as their application, their disadvantages and how to correct them. The final result is an application that integrates essential algorithms