Schoof-Elkies-Atkin algorithm

Schoof-Elkies-Atkin algorithm

The Schoof-Elkies-Atkin algorithm (SEA) is an algorithm used for finding the order of or calculating the number of points on an elliptic curve over a finite field. Its primary application is in elliptic curve cryptography. The algorithm is an extension of Schoof's algorithm by Noam Elkies and A. O. L. Atkin to significantly improve its efficiency.

External links

* [ article on Mathworld]
* [ "Remarks on the Schoof-Elkies-Atkin algorithm"]
* [ "The Schoof-Elkies-Atkin Algorithm in Characteristic 2"]

Wikimedia Foundation. 2010.

Look at other dictionaries:

  • Schoof's algorithm — Schoof s algorithm, first described by R. Schoof in 1985, allows one to calculate the number of points on an elliptic curve over a finite field and is used mostly in elliptic curve cryptography.From Hasse s theorem on elliptic curves the number… …   Wikipedia

  • Noam Elkies — Noam David Elkies Noam Elkies en 2007 à Oberwolfach Naissance 25 août 1966 New York (États Unis) Nationalité Américaine Isr …   Wikipédia en Français

  • Noam Elkies — in 2007 Born August 25, 1966 (1966 08 25 …   Wikipedia

  • A. O. L. Atkin — Arthur Oliver Lonsdale Atkin (July 31, 1925 – December 28, 2008), who published under the name A. O. L. Atkin, was a Professor Emeritus of mathematics at the University of Illinois at Chicago. As an undergraduate during World War II, he worked at …   Wikipedia

  • Counting points on elliptic curves — An important aspect in the study of elliptic curves is devising effective ways of counting points on the curve. There have been several approaches to do so, and the algorithms devised have proved to be useful tools in the study of various fields… …   Wikipedia

  • List of mathematics articles (S) — NOTOC S S duality S matrix S plane S transform S unit S.O.S. Mathematics SA subgroup Saccheri quadrilateral Sacks spiral Sacred geometry Saddle node bifurcation Saddle point Saddle surface Sadleirian Professor of Pure Mathematics Safe prime Safe… …   Wikipedia

  • Elliptic curve cryptography — (ECC) is an approach to public key cryptography based on the algebraic structure of elliptic curves over finite fields. The use of elliptic curves in cryptography was suggested independently by Neal Koblitz[1] and Victor S. Miller[2] in 1985.… …   Wikipedia

  • Riemann surface — For the Riemann surface of a subring of a field, see Zariski–Riemann space. Riemann surface for the function ƒ(z) = √z. The two horizontal axes represent the real and imaginary parts of z, while the vertical axis represents the real… …   Wikipedia

  • Plane curve — In mathematics, a plane curve is a curve in a Euclidean plane (cf. space curve). The most frequently studied cases are smooth plane curves (including piecewise smooth plane curves), and algebraic plane curves. A smooth plane curve is a curve in a …   Wikipedia

  • Moduli of algebraic curves — In algebraic geometry, a moduli space of (algebraic) curves is a geometric space (typically a scheme or an algebraic stack) whose points represent isomorphism classes of algebraic curves. It is thus a special case of a moduli space. Depending on… …   Wikipedia