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...

counting (geology) A problem in the theory of elliptic curves, see Counting points on elliptic curves An evaluation system in bridge, see Hand evaluation...

Elliptic-curve cryptography (ECC) is an approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields. ECC...

an efficient algorithm to count points on elliptic curves over finite fields. The algorithm has applications in elliptic curve cryptography where it is...

From this definition it follows that elliptic curves are hyperelliptic curves of genus 1. In hyperelliptic curve cryptography K {\displaystyle K} is often...

points on elliptic curves and to study the fields generated by torsion points. They play a central role in the study of counting points on elliptic curves...

the GP function ellap. "Schoof: Counting points on elliptic curves over finite fields" article on Mathworld "Remarks on the Schoof-Elkies-Atkin algorithm"...

was the first deterministic polynomial time algorithm for counting points on elliptic curves. The algorithms known before (e.g. the baby-step giant-step...

elliptic curves over Q {\displaystyle \mathbb {Q} } . In order to obtain a reasonable notion of 'average', one must be able to count elliptic curves E...

In mathematics, elliptic curve primality testing techniques, or elliptic curve primality proving (ECPP), are among the quickest and most widely used methods...

methods for counting points on elliptic curves and hyperelliptic curves, that have applications to elliptic curve cryptography, hyperelliptic curve cryptography...

mathematician Sir Andrew Wiles of a special case of the modularity theorem for elliptic curves. Together with Ribet's theorem, it provides a proof for Fermat's Last...

rational and elliptic curves. Such curves defined over the rational numbers, by Faltings's theorem, can have only a finite number of rational points, and they...

(1992). Rational Points on Elliptic Curves. Springer-Verlag. ISBN 0-387-97825-9. John Tate (1974). "The arithmetic of elliptic curves". Inventiones Mathematicae...

distinguished point), such a curve is called an elliptic curve. While this model is the simplest way to describe hyperelliptic curves, such an equation will...

n(n−1) on the class of a curve of degree n. The class may be computed exactly by counting the number and type of singular points on C (see Plücker formula)...

certain particular examples of elliptic curves over finite fields having complex multiplication have their points counted by means of cyclotomy. For the...

S2CID 121520625. Zbl 0657.14018. Masser, David W. (1989). "Counting points of small height on elliptic curves". Bull. Soc. Math. France. 117 (2): 247–265. doi:10...

81–95. Smyth (2008) p.327 Masser, D.W. (1989). "Counting points of small height on elliptic curves". Bull. Soc. Math. Fr. 117 (2): 247–265. doi:10.24033/bsmf...

group; it is central to the theory of many fractals, modular forms, elliptic curves and Pellian equations. Möbius transformations can be more generally...

its efficiency Schoof's algorithm, efficient algorithm to count points on elliptic curves over finite fields This page lists people with the surname...

most, two points. A non-singular plane cubic defines an elliptic curve, over any field K for which it has a point defined. Elliptic curves are now normally...

manifold of complex points). For example, the definition of elliptic curve from algebraic geometry is connected non-singular projective curve of genus 1 with...

for curves of genus 1 is measured by the Tate–Shafarevich group. If X is a curve of genus 1 with a k-rational point p0, then X is called an elliptic curve...

rank of all elliptic curves over Q (when ordered by height) is bounded. Proof that most hyperelliptic curves over Q have no rational points. In 2015, Manjul...

1 of his Principia in 1687, where he claims that two curves have a number of intersection points given by the product of their degrees. However, Newton...

mathematics, the Cayley–Bacharach theorem is a statement about cubic curves (plane curves of degree three) in the projective plane P2. The original form states:...

Birch and Swinnerton-Dyer conjecture on elliptic curves postulates a connection between the rank of an elliptic curve and the order of pole of its Hasse–Weil...

characteristic (REC) Curves and the Regression ROC (RROC) curves. In the latter, RROC curves become extremely similar to ROC curves for classification,...

coefficients of the products of the periods therefore counts the number of points on these elliptic curves, and as a byproduct he proves the analog of the Riemann...