Kriptografija temeljena na grafovima izogenija supersingularnih eliptičkih krivulja

The algorithms used in the present time for cryptographic purposes, can be broken in polynomial time if the development of a quantum computer becomes reality.Insecurity of data exchange on quantum computers would very easily become one of the global the problem of the future. In this master thesis, we are studying an algorithm that is believed to be quantum resistant, since no serious attacks against it have been found yet, and therefore can be used in post-quantum era, if this becomes a reality. It is called SIDH. It is a key exchange method based on Diffie-Hellmankey exchange, with security based on the dificulty of finding isogenies between supersingular elliptic curve. First chapter is defined as introduction to reader, from basic definition of cryptography to classic algorithms and why we should consider implementing a new ones. In second chapter one can find what are elliptic curves and how they behave on finite fields. Third chapter has focus on defining isogeny, isogeny graph and di erences between isomorphism and isogeny. In fourth chapter we are going through steps of SIDH algoritam, from key exchange to finding bases of torsion subgroups. There is subsection about complexity and security of SIDH algorithm.