Elliptic Curve Handbook

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

Tutorial on complex multiplication of elliptic curves

This note describes the following topics: Galois theory, separability, finite fields, Sum of two squares, Number fields and rings of integers, Inertia subgroups, Riemann surfaces, Modular functions, Elliptic functions, Algebraic theory of elliptic curves.

Author(s): Yihang Zhu and Rong Zhou

NA 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

Elliptic Curves and Number Theory

Aim of this note is to explain the connection between a simple ancient problem in number theory and a deep sophisticated conjecture about Elliptic Curves. Topics covered includes: Pythagorean Triples, Pythogoras Theorem, Fundamental Theorem of Arithmetic, Areas, Unconditional Results, Iwasawa theory

Author(s): R. Sujatha

120 Pages

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 Curve Handbook

This book covers the following topics: Projective coordinates, Cubic to Weierstrass, Formal Groups, The Mordell-Weil theorem, Twists, Minimal Weierstrass Equations, Isomorphisms of elliptic curves , Automorphisms and fields of definition, Kraus’s theorem.

Author(s): Ian Connell

327 Pages

Introduction to elliptic curves

This book covers the following topics: The group law, Elliptic curves over finite fields, Pairings, Travaux Diriges, Elliptic curves over finite fields, Number of points on elliptic curves over finite fields: theory and practice.

Author(s): Christophe Ritzenthaler

59 Pages

Elliptic Curves by David Loeffler

This note provides the explanation about the following topics: Definitions and Weierstrass equations, The Group Law on an Elliptic Curve, Heights and the Mordell-Weil Theorem, The curve, Completion of the proof of Mordell-Weil, Examples of rank calculations, Introduction to the P-adic numbers, Motivation, Formal groups, Points of finite order, Minimal Weierstrass Equations, Reduction mod pII and torsion points over algebraic extensions, Isogenies, Hasse’s Theorem and Galois cohomology.

Author(s): David Loeffler

74 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

Algebraic Theory of KP Equations

This note covers the following topics: The KP equation and elliptic functions, The spectral curve of a differential operator, Grassmannians and the geometric inverse scattering, Iso-spectral deformations and the KP system, Jacobian varieties as moduli of iso-spectral deformations, Morphisms of curves, Prym varieties and commuting partial differential operators.

Author(s): Motohico Mulase

61 Pages

Elliptic Curves and Formal Groups

This note explains many topics related to Elliptic Curves and Formal Groups.

Author(s): J. Lubin, J.P. Serre and J. Tate

NA Pages

Elliptic Curves by Jim Milne

Currently this section contains no detailed description for the page, will update this page soon.

Author(s): NA

NA Pages