Reinier Bröker

Brown University
Box 1917
151 Thayer Street
Providence, RI 02912
USA

Info and CV

Modular polynomials for genus 2, to appear in London Mathematical Society, Journal of Computation and Mathematics (with K. Lauter)
Constructing supersingular elliptic curves, to appear in Journal of Combinatorics and Number Theory
Evaluating large degree isogenies and applications to pairing based cryptography, Pairing 2008, published by Springer-Verlag in Lecture Notes in Computer Science 5209, pp. 100-112 (with D. Charles, K. Lauter)
Computing Hilbert Class Polynomials, Algorithmic Number Theory Symposium VIII, published by Springer-Verlag in Lecture Notes in Computer Science 5011, pp. 282-295 (2008) (with J. Belding, A. Enge, K. Lauter)
Constructing elliptic curves of prime order, Contemporary Mathematics 463, pp. 17-28 (2008) (with P. Stevenhagen)
A p-adic algorithm to compute the Hilbert class polynomial, Mathematics of Computation 77 (2008), pp. 2417-2435
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

Explicit CM-theory in dimension 2 (with D. Gruenewald, K. Lauter)
An explicit height bound for the classical modular polynomial (with A. V. Sutherland)
Evaluating Igusa functions (with K. Lauter)
p-adic class invariants
Abelian surfaces admitting an (l,l)-endomorphism, in preparation (with K. Lauter, M. Streng)
Computing modular polynomials with the Chinese remainder theorem, in preparation (with K. Lauter, A. V. Sutherland)

Computing modular polynomials, talk given at the Maine/Quebec Number Theorey Conference, October 2009
Explicit CM-computations in dimension 2, talk given at the Algebra Seminar of Boston University, October 2008
Computing Hilbert class polynomials, talk given at ANTS VIII, Banff, May 2008
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
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

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