René Schoof (born 8 May 1955, Den Helder) is a mathematician from the Netherlands who works in algebraic number theory, arithmetic algebraic geometry, computational number theory and coding theory.
In 1985, Schoof discovered an algorithm which enabled him to count points on elliptic curves over finite fields in polynomial time. This was important for the use of elliptic curves in cryptography. The algorithms known before (e.g. the baby-step giant-step algorithm) were of exponential running time. His algorithm was improved by A. O. L. Atkin (1992) and Noam Elkies (1990).
He also wrote a book on Catalan's conjecture.
- Counting points of elliptic curves over finite fields, Journal des Théories des Nombres de Bordeaux, No. 7, 1995, 219–254, pdf
- With Gerard van der Geer, Ben Moonen (editors): Number fields and function fields – two parallel worlds, Birkhäuser 2005
- Catalan´s Conjecture, Universitext, Springer, 2008
- R.J. Schoof, 1955 - at the University of Amsterdam Album Academicum website
- René Schoof, Mathematics Genealogy Project
- R. Schoof's homepage, University Tor Vergata
- René Schoof: Elliptic curves over finite fields and the calculation of square roots mod p, Mathematics of Computation, No. 44, 1985, 483–494.