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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.