Schoof algorithm, Jernej Barbič

Abstract of the diploma thesis: In this thesis elliptic curves and elliptic groups are introduced. We give a detailed description of the basic Schoof algorithm for determining the cardinality of the group of rational points on an elliptic curve over a finite field. We demonstrate the cryptographic importance of the presented material and comment on the current development of the cryptographical science in this field. We also give an overview of the basic algebraic properties of finite field with implications to cryptography.

Keywords: elliptic curves, finite fields, computational number theory.
Math. subj. class (2000): primary 14H52, 11T71, 11Y16.