René Schoof

René Schoof, Oberwolfach 2009

René Schoof (born May 8, 1955 in Den Helder ) is a Dutch mathematician who deals with algebraic number theory, arithmetic algebraic geometry, algorithmic number theory and coding theory.

Schoof received his PhD in 1985 from the University of Amsterdam with Hendrik Lenstra ( Elliptic Curves and Class Groups ). He is a professor at the Tor Vergata University in Rome .

In 1985 Schoof found an algorithm that counted points on elliptic curves over finite bodies in polynomial time . This was important for the use of elliptic curves in cryptography . The algorithm was impractical in its original form and was improved by AOL Atkin (1992) and Noam Elkies (1990).

Schoof also wrote a book on the Catalan Conjecture .

Fonts

Counting points of elliptic curves over finite fields , Journal des Théories des Nombres de Bordeaux, Vol. 7, 1995, pp. 219-254, PDF file
With Gerard van der Geer , Ben Moonen (editor): Number fields and function fields - two parallel worlds , Birkhäuser 2005
Catalan's Conjecture , Universitext, Springer, 2008

Web links

References

^ René Schoof: Elliptic curves over finite fields and the calculation of square roots mod p , Mathematics of Computation, Vol. 44, 1985, pp. 483-494. The previously known procedures, such as a variant of Daniel Shanks ' Baby Step-Giant Step procedure , were exponential in time.

personal data
SURNAME	Schoof, René
BRIEF DESCRIPTION	Dutch mathematician
DATE OF BIRTH	May 8, 1955
PLACE OF BIRTH	The hero

[1] René Schoof: Elliptic curves over finite fields and the calculation of square roots mod p , Mathematics of Computation, Vol. 44, 1985, pp. 483-494. The previously known procedures, such as a variant of Daniel Shanks ' Baby Step-Giant Step procedure , were exponential in time.