Zbrajanje i multiplikacija točaka na eliptičkim krivuljama

Abstract

U ovom radu smo definirali zbrajanje i multiplikaciju točaka na eliptičkim krivuljama, te proučavali složenosti istih operacija u različitim koordinatama. U prvom poglavlju smo definirali osnovne algebarske pojmove nužne za razumijevanje ostatka rada, specifično grupe, prstenove i polja. U drugom poglavlju smo definirali pojam eliptičke krivulje, te zbrajanje točaka i množenje skalarom. U trećem poglavlju smo obavili centralni dio ovog diplomskog rada, pokazali prikaz eliptičke krivulje u različitim koordinatnim sustavima, te analizirali složenost zbrajanja i multiplikacije skalarom.In this work we have defined addition and multiplication of points on elliptic curves and analysed complexity of said operations in different coordinates. First chapter was about defining basic algebraic notions necessary for understanding the rest of the work, those notions being groups, rings and fields. In second chapter we have defined the concept of elliptic curves along with point addition and scalar multiplication. Third chapter is the main part of this work. In it we have shown equation of elliptic curves in different coordinates and have analysed different complexities of addition and scalar multiplication