Elliptic Curves by Samuele Anni

Lectures on Moduli Spaces of Elliptic Curves

The goal of these notes is to introduce orbifolds and stacks through the example of elliptic curves. This note contains below topics, Elliptic Curves and the Moduli Problem, Families of Elliptic Curves and the Universal Curve, The Orbifold and Modular Forms.

Author(s): Richard Hain

80 Pages

Elliptic Curves An Introduction

This note describes the following topics, Solving cubic equations in two variables, Group law on the cubic curve, Theta functions, Rank two vector bundles on elliptic curves.

Author(s): University of Limerick

99 Pages

Elliptic Curves by Zhiyuan Bai

This note covers fermats method of infinite descent, Some remarks on algebraic curves, Weierstrass equations, The group law, Isogeny, The invariant differential, Elliptic curves over finite fields, Formal groups, Elliptic curves over local fields, Elliptic curves over number fields, Kummer theory, Mordell weil theorem, Heights, Dual isogenies and weil pairing, Galois cohomology, Descent by cyclic isogeny.

Author(s): Zhiyuan Bai

41 Pages

Elliptic Curve Cryptography by Abhijit Das

This note explains the following topics, Arithmetic of Elliptic Curves, Classical EllipticCurve Cryptography, Efficient Implementation, Introduction to Pairing, PairingBased Cryptography, Sample ApplicationECDSA Batch Verification.

Author(s): Abhijit Das

137 Pages

Elliptic Functions An Elementary Text Book for Students of Mathematics

This note explains the following topics, Elliptic Integrals, Elliptic Functions, Periodicity of the Functions, Landens Transformation, Complete Functions, Development of Elliptic Functions into Factors, Elliptic Integrals of the Second Order, Numerical Calculations.

Author(s): Arthur L. Bake

147 Pages

Elliptic Curves by Samuele Anni

This note explains the following topics, Plane curves, Projective space and homogenisation, Rational points on curves, BachetMordell equation, Congruent number curves, Elliptic curves and group law, Integer Factorization Using Elliptic Curves, Isomorphisms and jinvariant, Elliptic curves over C, Endomorphisms of elliptic curves, Elliptic Curves over finite fields, The MordellWeil Theorem, Elliptic Curve Cryptography.

Author(s): Samuele Anni

126 Pages

The elliptic modular functions associated with the elliptic norm curve E7

This note covers the following topics, The Groups Connected With E7, The Quadrigs On E7, The Interpretation Of The Forms F and F2, The Loci In S3.

Author(s): Roscoe Woods

106 Pages

Mathematical Foundations of Elliptic Curve Cryptography

This note covers the following topics, algebraic curves, elliptic curves, elliptic curves over special fields, more on elliptic divisibility sequences and elliptic nets, elliptic curve cryptography, computational aspects, elliptic curve discrete logarithm.

Author(s): Prof. Dipl-Ing, Dr. techn. Michael Drmota

113 Pages