Reinier Bröker

Microsoft Research
One Microsoft Way, 99/2975
Redmond, WA 98052
USA

Info and CV

Computing Hilbert Class Polynomials, to appear in Algorithmic Number Theory Symposium VIII, published by Springer-Verlag in Lecture Notes in Computer Science series, 2008 (with J. Belding, A. Enge, K. Lauter)
Constructing elliptic curves of prime order, to appear in Contemporary Mathematics, AMS Special Session on Computational Arithmetic Geometry (with P. Stevenhagen)
A p-adic algorithm to compute the Hilbert class polynomial, to appear in Mathematics of Computation
Efficient CM-constructions of elliptic curves over finite fields, Mathematics of Computation 76 (2007), pp. 2161-2179 (with P. Stevenhagen)
Elliptic curves with a given number of points, Algorithmic Number Theory Symposium VI, published by Springer-Verlag in Lecture Notes in Computer Science 3076, pp. 117-131 (2004) (with P. Stevenhagen)
PhD-thesis: Constructing elliptic curves of prescribed order, Universiteit Leiden, 2006

Modular polynomials for genus 2, talk given at Number Theory Seminar of the University of Washington, April 2008
p-adic class invariants, talk given at the Quebec-Vermont Number Theory Seminar, February 2007
A fast multi-prime approach to compute the Hilbert class polynomial, talk given at the Discrete Math Seminar in Calgary, January 2007
p-adic class invariants, talk given at workshop on Algebraic Curves in Toronto, October 2006
Constructing elliptic curves for cryptogaphy, talk given at ECC in Toronto, September 2006
Constructing elliptic curves with a given number of points, talk given at the DIAMANT/Eidma symposium, November 2005
Class invariants in a non-archimedean setting, talk given at the Journées Arithmétiques in Marseille, July 2005

The mathematics behind cryptography, course notes I wrote in 2007 for an undergraduate course in Calgary