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Elliptic curve

About: Elliptic curve is a(n) research topic. Over the lifetime, 13928 publication(s) have been published within this topic receiving 255355 citation(s).
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Journal ArticleDOI
TL;DR: The question of primitive points on an elliptic curve modulo p is discussed, and a theorem on nonsmoothness of the order of the cyclic subgroup generated by a global point is given.
Abstract: We discuss analogs based on elliptic curves over finite fields of public key cryptosystems which use the multiplicative group of a finite field. These elliptic curve cryptosystems may be more secure, because the analog of the discrete logarithm problem on elliptic curves is likely to be harder than the classical discrete logarithm problem, especially over GF(2'). We discuss the question of primitive points on an elliptic curve modulo p, and give a theorem on nonsmoothness of the order of the cyclic subgroup generated by a global point.

5,001 citations


Journal ArticleDOI
Abstract: We provide a framework for the analysis of a large class of discontinuous methods for second-order elliptic problems. It allows for the understanding and comparison of most of the discontinuous Galerkin methods that have been proposed over the past three decades for the numerical treatment of elliptic problems.

3,039 citations


5


Book
01 Jan 1993-
TL;DR: The first seven chapters guide readers to the heart of current research in computational algebraic number theory, including recent algorithms for computing class groups and units, as well as elliptic curve computations, while the last three chapters survey factoring and primality testing methods.
Abstract: A description of 148 algorithms fundamental to number-theoretic computations, in particular for computations related to algebraic number theory, elliptic curves, primality testing and factoring. The first seven chapters guide readers to the heart of current research in computational algebraic number theory, including recent algorithms for computing class groups and units, as well as elliptic curve computations, while the last three chapters survey factoring and primality testing methods, including a detailed description of the number field sieve algorithm. The whole is rounded off with a description of available computer packages and some useful tables, backed by numerous exercises. Written by an authority in the field, and one with great practical and teaching experience, this is certain to become the standard and indispensable reference on the subject.

2,680 citations


Journal ArticleDOI
Abstract: In this paper, we show that the single smooth coefficient of the elliptic operator LY = v yv can be determined from knowledge of its Dirichlet integrals for arbitrary boundary values on a fixed region 2 C R', n ? 3. From a physical point of view, we show that an isotropic conductivity can be determined by steady state measurements at the boundary.

1,493 citations


Journal ArticleDOI
Abstract: On etudie la regularite limite des solutions faibles de l'equation divA(x,u,Du)+B(x,u,Du)=0 avec des conditions aux limites conormales et de Dirichlet

1,167 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202212
2021564
2020608
2019623
2018590
2017590

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Topic's top 5 most impactful authors

Igor E. Shparlinski

72 papers, 1K citations

Filip Najman

33 papers, 284 citations

Kristin E. Lauter

29 papers, 466 citations

Karl Rubin

29 papers, 910 citations

Andrew V. Sutherland

24 papers, 311 citations