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Elliptic Curves by J.S. Milne
This note explains the following topics: Plane Curves, Rational Points on Plane Curves, The Group Law on a Cubic Curve, Functions on Algebraic Curves and the Riemann-Roch Theorem, Reduction of an Elliptic Curve Modulo p, Elliptic Curves over Qp, Torsion Points, Neron Models, Elliptic Curves over the Complex Numbers, The Mordell-Weil Theorem: Statement and Strategy, The Tate-Shafarevich Group; Failure Of The Hasse Principle, Elliptic Curves Over Finite Fields, The Conjecture of Birch and Swinnerton-Dyer, Elliptic Curves and Sphere Packings, The Conjecture of Birch and Swinnerton-Dyer, Algorithms for Elliptic Curves.
Author(s): J.S. Milne
163 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 Elliptic-Curve Cryptography, Efficient Implementation, Introduction to Pairing, Pairing-Based Cryptography, Sample Application—ECDSA 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, Landen’s 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
Elliptic-curve cryptography is an approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields.
Author(s): Christian Wuthrich
98 Pages