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An Introduction to the Theory of Elliptic Curves (PDF 104P)
Covered topics are: Elliptic Curves, The Geometry of Elliptic Curves, The Algebra of Elliptic Curves, Elliptic Curves Over Finite Fields, The Elliptic Curve Discrete Logarithm Problem, Height Functions, Canonical Heights on Elliptic Curves, Factorization Using Elliptic Curves, L-Series, Birch-Swinnerton-Dyer.
Author(s): Joseph H. Silverman
104 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 Curve Cryptography by Christian Wuthrich
Ellipticcurve cryptography is an approach to publickey cryptography based on the algebraic structure of elliptic curves over finite fields.
Author(s): Christian Wuthrich
98 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