Introductory Essentials to Elliptic Curves
Seddik Abdelalim
LMFA, FSAC, University Hassan II of Casablanca, Morocco.
Ilias Elmouki *
LMFA, FSAC, University Hassan II of Casablanca, Morocco.
Noreddine Abghour
LIS Labs, FSAC, University Hassan II of Casablanca, Morocco.
*Author to whom correspondence should be addressed.
Abstract
This study starts with some generalities on elliptic curves through the definitions of theWeierstrass equation and groups laws. Then, we provide our proof to Hasse’s theorem and we discuss its consequences. Finally, we discuss some applications of elliptic curves and their contributions to signatures, and the chapter introduces seventeen exercises on this topic.
Keywords: Elliptic curves, Hasse theorem, isogeny, Schoof algorithm, signature