Glavni cilj ovog rada je predstaviti ElGamalovu shemu potpisa i neke njene varijante. Rad je podijeljen na sedam poglavlja, uključujući uvodni dio. Nakon što dobijemo kratak uvid u to što je digitalni potpis i koja je njegova primjena u našoj svakodnevnici, u drugom poglavlju ćemo se osvrniti na osnovne pojmove iz teorije brojeva i kriptografije radi boljeg razumijevanja sadržaja rada. Treće i četvrto poglavlje bazira se na ozbiljnijim problemima koji mogu narušiti sigurnost digitalnog potpisa te načinima na kojima se isti mogu spriječiti. Peto poglavlje predstavlja matematički problem koji se javlja u mnogim područjima pa tako i modulo p, a to je problem diskretnog logaritma. Kroz šesto poglavlje prvo ćemo se upoznati s ElGamalovom shemom potpisa objavljenom u radu 1985., zatim osvrnuti na njenu sigurnosti. Kako bi nam shema bila jasnija proći ćemo kroz nekoliko primjera. Posljednje poglavlje rada bavi se varijantama ElGamalove sheme potpisa, a to su Schnorrova shema potpisa predložena 1989. i Algoritam digitalnog potpisa prvi puta predložen 1991.

The main purpose of this paper is to present ElGamal’s signature scheme and some of its variants. The work is divided into seven chapters, including the introductory part. After we get a brief insight into what the digital signature is and what its application is in our everyday life, for a better understanding of the content of the work the second chapter will cover the basic concepts from the theory of numbers and cryptography. The third and fourth chapters are based on more serious issues that can violate the security of the digital signature and the ways in which it can be prevented. The fifth chapter represents a mathematical problem that occurs in many areas, such as modulo p, which is the problem of discrete logarithm. Through the sixth chapter, we will first get acquainted with ElGamal’s signature scheme published in 1985, and then consider its security. In order to make the scheme clearer, we will go through several examples. The last chapter deals with the variants of the ElGamal signature scheme, which are the Schnorra signature scheme proposed in 1989 and the Digital Signature Algorithm for the first time suggested in 1991.