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Mathematical Foundations of Elliptic Curve Cryptography (PDF 113P)
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 
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 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
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
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
Mathematical Foundations of Elliptic Curve Cryptography (PDF 113P)
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
Current Topics in Complex Algebraic Geometry(1995)
This note covers the following topics: Fundamental Groups of Smooth Projective Varieties, Vector Bundles on Curves and Generalized Theta Functions: Recent Results and Open Problems, The Schottky Problem, Spectral Covers, Torelli Groups and Geometry of Moduli Spaces of Curves.
Author(s): Herbert Clemens and Janos Kollar
NA Pages
This course note aims to give a basic overview of some of the main lines of study of elliptic curves, building on the student's knowledge of undergraduate algebra and complex analysis, and filling in background material where required (especially in number theory and geometry). Particular aims are to establish the link between doubly periodic functions, Riemann surfaces of genus 1, plane cubic curves, and associated Diophantine problems.
Author(s): Miles Reid
NA Pages