Elliptic Curve Cryptography by Christian Wuthrich

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 Curves by Pete L. Clark

An elliptic curve is an object defined over a ground field K. This PDF covers the following topics related to Elliptic Curves : What is an elliptic curve?, Mordell-Weil Groups, Background on Algebraic Varieties, The Riemann-Roch Express, Weierstrass Cubics, The l-adic Tate module, Elliptic Curves Over Finite Fields, The Mordell-Weil Theorem I: Overview, The Mordell-Weil Theorem II: Weak Mordell-Wei, The Mordell-Weil Theorem III: Height Functions, The Mordell-Weil Theorem IV: The Height Descent Theorem, The Mordell-Weil Theorem V: Finale, More On Heights, Diophantine Approximation, Siegel’s Theorems on Integral Points.

Author(s): Pete L. Clark

90 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