Schoof's algorithm is an efficient algorithm to count points on elliptic curves over finite fields. The algorithm has applications in elliptic curve cryptography where it is important to know the number of points to judge the difficulty of solving the discrete logarithm problem in the group of points on an elliptic curve.
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.
Manfred Schoof is a German jazz trumpeter.
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 such as number theory, and more recently in cryptography and Digital Signature Authentication. While in number theory they have important consequences in the solving of Diophantine equations, with respect to cryptography, they enable us to make effective use of the difficulty of the discrete logarithm problem (DLP) for the group , of elliptic curves over a finite field , where q = pk and p is a prime. The DLP, as it has come to be known, is a widely used approach to public key cryptography, and the difficulty in solving this problem determines the level of security of the cryptosystem. This article covers algorithms to count points on elliptic curves over fields of large characteristic, in particular p > 3. For curves over fields of small characteristic more efficient algorithms based on p-adic methods exist.
In mathematics the division polynomials provide a way to calculate multiples of 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 in Schoof's algorithm.
Schoof is a Low Saxon surname. Its Standard German equivalent is Schoff. Schaub is a High German dialect variant. Related to the English verb to shove, it means a gathering of like things. For example, birds migrating together are said to fly in a Schoof. It is also related to the English noun sheaf, which is another specific meaning of the word Schoof.
Bibiane Schoofs, previously known as Bibiane Weijers, is a Dutch professional tennis player.
René Schoof is a mathematician from the Netherlands who works in Algebraic Number Theory, Arithmetic Algebraic Geometry, Computational Number Theory and Coding Theory.
Lauritz Schoof is a German rower. He was part of the German crew that won the gold medal in the men's quadruple sculls at the 2012 Summer Olympics in London. He also successfully defended the quadruple sculls title at the 2016 Rio Olympics as part of the German team.
Rob Schoofs is a Belgian footballer who currently plays for KV Mechelen in the Belgian Pro League. He is well known for his stint with AA Gent from 2016 until 2017.
Lucas Schoofs is a Belgian footballer plays as a defending midfielder for Heracles Almelo. He began his career in the youth teams of Lommel United in 2014.
Irene Schoof is a Dutch former cricketer. She played fifteen Women's One Day International matches for the Netherlands women's national cricket team. She was part of the Netherlands squad for the 1988 Women's Cricket World Cup.
The 2016 Slovak Open was a professional tennis tournament played on indoor hard courts. It was the 17th edition of the tournament which was part of the 2016 ATP Challenger Tour. It was also the 8th edition of the tournament which was part of the ITF Women's Circuit. It took place in Bratislava, Slovakia between 7 and 13 November 2016.
Mark Schoofs is an American Pulitzer Prize-winning journalist and was the editor-in-chief of BuzzFeed News. He is also a visiting professor at the USC Annenberg School for Communication and Journalism.
Anastasia Pavlyuchenkova was the defending champion, but chose to compete in Linz instead.
Sara Errani and Bibiane Schoofs were the defending champions, but Errani was unable to participate due to her doping suspension. Schoofs played alongside Desirae Krawczyk, but lost in the first round to Han Xinyun and Darija Jurak.
The 2019 Libéma Open was a tennis tournament played on outdoor grass courts. It was the 30th edition of the event, and part of the 250 Series of the 2019 ATP Tour, and of the WTA International tournaments of the 2019 WTA Tour. Both the men's and the women's events took place at the Autotron park in Rosmalen, 's-Hertogenbosch in the Netherlands, from June 10 through June 16, 2019.
Shuko Aoyama and Aleksandra Krunić defeated Lesley Kerkhove and Bibiane Schoofs in the final, 7–5, 6–3, to win the women's doubles tennis title at the 2019 Rosmalen Grass Court Championships.
The 2019 BGL BNP Paribas Luxembourg Open was a professional women's tennis tournament played on indoor hard courts sponsored by BNP Paribas. It was the 24th edition of the Luxembourg Open, and part of the WTA International tournaments category of the 2019 WTA Tour. It was held in Kockelscheuer, Luxembourg from 14 to 20 October 2019.
Jeļena Ostapenko won the title, defeating defending champion Julia Görges in the final, 6–4, 6–1.
