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Thursday, October 8, 2020 | History

6 edition of Elliptic Curves found in the catalog.

Elliptic Curves

Diophantine Analysis (Grundlehren der mathematischen Wissenschaften)

by S. Lang

  • 11 Want to read
  • 9 Currently reading

Published by Springer .
Written in English

    Subjects:
  • Mathematics,
  • General,
  • Mathematics / General,
  • Mathematics-General,
  • Science / General,
  • Science

  • The Physical Object
    FormatHardcover
    Number of Pages280
    ID Numbers
    Open LibraryOL9054034M
    ISBN 103540084894
    ISBN 109783540084891

    $\bullet$ Elliptic Curves: Number Theory and Cryptography by Lawrence C. Washington. This is a very nice book about the mathematics of elliptic curves. It contains proofs of many of the main theorems needed to understand elliptic curves, but at a slightly more elementary level than, say, Silverman’s book. 2 Chapter 1. Introduction to elliptic curves to be able to consider the set of points of a curve C/Knot only over Kbut over all bestwesternkitchenerwaterloo.comicular,wesimplycallaK¯-rationalpoint,apointofC. Thecondition∆ 6= 0 bestwesternkitchenerwaterloo.comheckthisinthecase.

    Jun 19,  · Elliptic Curves over Finite Fields. The elliptic curve cryptography (ECC) uses elliptic curves over the finite field 𝔽p (where p is prime and p > 3) or 𝔽2m (where the fields size p = 2_m_). This means that the field is a square matrix of size p x p and the points on the curve are limited to integer coordinates within the field only. All. Jan 01,  · Elliptic curves have played an increasingly important role in number theory and related fields over the last several decades, most notably in areas such as cryptography, factorization, and the proof of Fermat's Last Theorem/5(16).

    This book is an introduction to the theory of elliptic curves, ranging from its most elementary aspects to current research. The first part, which grew out of Tate's Haverford lectures, covers the elementary arithmetic theory of elliptic curves over the bestwesternkitchenerwaterloo.coms: 1. The theory of elliptic curves is distinguished by its long history and by the diversity of the methods that have been used in its study. This book treats the arithmetic theory of elliptic curves in its modern formulation, through the use of basic algebraic number theory and algebraic geometry.


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Elliptic Curves by S. Lang Download PDF EPUB FB2

The book is short (less than pages), so most of the mathematical proofs of the main results are omitted. The authors instead concentrate on the mathematics needed to implement elliptic curve cryptography. The book is written for the reader with some experience in cryptography and one who has some background in the theory of elliptic curves.

Sep 21,  · Elliptic curves are so ubiquitous in mathematics and science and such beautiful objects that no author who expounds on them would do a bad job. This book is no exception to this axiom, and even though short the author, a noted expert on the subject, gives the reader important insights into the main properties of elliptic curves/5(3).

Although the formal definition of an elliptic curve is fairly technical and requires some background in algebraic geometry, it is possible to describe some features of elliptic curves over the real numbers using only introductory algebra and geometry.

In this context, an elliptic curve is a plane curve defined by an equation of the form = + + where a and b are real numbers. I am currently doing a self study on algebraic geometry but my ultimate goal is to study more on elliptic curves.

Which are the most recommended textbooks I can use to study. I need something not so technical for a junior graduate student but at the same time I would wish to get a book with authority on elliptic curves.

Thanks. Indeed, the book is affordable (in fact, the most affordable of all references on the subject), but also a high quality work and a complete introduction to the rich theory of the arithmetic of elliptic curves, with numerous examples and exercises for the reader, many interesting remarks and an updated bibliography.

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.

Dec 26,  · Elliptic Curves: Number Theory and Cryptography; by Lawrence C. Washington. This is a very nice book about the mathematics of elliptic curves. It contains proofs of many of the main theorems needed to understand elliptic curves, but at a slightly more elementary level than, say, Silverman’s book.

In mathematics, an elliptic surface is a surface that has an elliptic fibration, in other words a proper morphism with connected fibers to an algebraic curve such that almost all fibers are smooth curves of genus 1.

(Over an algebraically closed field such as the complex numbers, these fibers are elliptic curves, perhaps without a chosen origin.)This is equivalent to the generic fiber being a.

Apr 03,  · Like its bestselling predecessor, Elliptic Curves: Number Theory and Cryptography, Second Edition develops the theory of elliptic curves to provide a basis for both number theoretic and cryptographic applications. With additional exercises, this edition offers more comprehensive coverage of the fundamental theory, techniques, and applicationCited by: This wonderful book is an excellent introduction to elliptic curves over the rational numbers.

It is self-contained and easily accessible, but still takes the reader quite far, thus giving an undergraduate reader some exciting glimpes of deeper mathematics/5(4). The theory of elliptic curves is distinguished by its long history and by the diversity of the methods that have been used in its study.

This book treats the arithmetic theory of elliptic curves in its modern formulation, through the use of basic algebraic number theory and algebraic geometry. TheBrand: Springer-Verlag New York.

The two subjects--elliptic curves and modular forms--come together in Eichler-Shimura theory, which constructs elliptic curves out of modular forms of a special kind.

The converse, that all rational elliptic curves arise this way, is called the Taniyama-Weil Conjecture and is. The converse, that all rational elliptic curves arise this way, is called the Taniyama-Weil Conjecture and is known to imply Fermat's Last Theorem.

Elliptic curves and the modeular forms in the Eichler- Shimura theory both have associated L functions, and it is a consequence of the theory that the two kinds of L. Elliptic Curves Points on Elliptic Curves † Elliptic curves can have points with coordinates in any fleld, such as Fp, Q, R, or C.

† Elliptic curves with points in Fp are flnite groups. † Elliptic Curve Discrete Logarithm Prob-lem (ECDLP) is the discrete logarithm problem for the group of points on an elliptic curve over a flnite fleld. The subject of elliptic curves is one of the jewels of nineteenth-century mathematics, originated by Abel, Gauss, Jacobi, and Legendre.

This book presents an introductory account of the subject in the style of the original discoverers, with references to and comments about more recent and Cited by: Dec 01,  · “Introduction to Elliptic Curves,” by Álvaro Lozano-Robledo. This is an overview of the theory of elliptic curves, discussing the Mordell-Weil theorem, how to compute the torsion subgroup of.

Cryptography/Elliptic curve. From Wikibooks, open books for an open world Because elliptic curves are mathematical functions, This page or section of the Cryptography book is a stub.

You can help Wikibooks by expanding it. Retrieved from "https. This book is an introduction to the theory of elliptic curves, ranging from elementary topics to current research. The first chapters, which grew out of Tate's Haverford Lectures, cover the arithmetic theory of elliptic curves over the field of rational numbers.

This book uses the beautiful theory of elliptic curves to introduce the reader to some of the deeper aspects of number theory. It assumes only a knowledge of the basic algebra, complex analysis, and topology usually taught in advanced undergraduate or first-year graduate courses.

It is possible to write endlessly on elliptic curves. (This is not a threat.) We deal here with diophantine problems, and we lay the foundations, especially for the theory of integral points. We review briefly the analytic theory of the Weierstrass function, and then deal with the arithmeticBrand: Springer-Verlag Berlin Heidelberg.

V of the book is devoted to explaining these results. The first three chapters of the book develop the basic theory of elliptic curves. Elliptic curves have been used to shed light on some important problems that, at first sight, appear to have nothing to do with elliptic curves. I mention three such problems.

Fast factorization of integers.May 28,  · Elliptic curves have played an increasingly important role in number theory and related fields over the last several decades, most notably in areas such as cryptography, factorization, and the proof of Fermat's Last Theorem.

However, most books on the subject assume a rather high level of mathematical sophistication, and few are truly accessible to5/5(1).May 04,  · I agree on "A course in number theory and cryptography" by Neal Koblitz for a first introduction; then “Elliptic Curves: Number Theory and Cryptography” by Lawrence C.

Washington gives more insight (but contains much heavier mathematics).