Elliptic Curves Over Finite Fields

Balagopalan, Sonia (2010) Elliptic Curves Over Finite Fields. Masters thesis, National University of Ireland Maynooth.

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This thesis provides a self-contained introduction to elliptic curves accessible to advanced undergraduates and graduate students in mathematics, with emphasis on the the theory of elliptic curves over finite fields. In Chapter 1, affine and projective planes are introduced. Chapter 2 introduces the theory of algebraic curves and the Weierstrass Normal Form of a cubic curve is derived. In Chapter 3 we define derivations on arbitrary polynomial rings, and prove the group law for elliptic curves. Chapter 4 discusses elliptic curves over finite fields and proves some results on counting points.

Item Type: Thesis (Masters)
Keywords: Elliptic Curves; Finite Fields;
Academic Unit: Faculty of Science and Engineering > Mathematics and Statistics
Item ID: 2250
Depositing User: IR eTheses
Date Deposited: 17 Nov 2010 15:13

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