14 citations · 18 across the 5 of their papers we have counts for
4 papers · 1 filter
Explicit computations in Iwasawa theory
Reinier Broker, David Hubbard, Lawrence C. Washington
We give two algorithms to compute layers of the anticyclotomic -extension of an imaginary quadratic field. The first is based on complex multiplication techniques for no…
Genus-2 curves and Jacobians with a given number of points
Reinier Bröker, Everett W. Howe, Kristin E. Lauter +1
We study the problem of efficiently constructing a curve C of genus 2 over a finite field F for which either the curve C itself or its Jacobian has a prescribed number N of F-ratio…
Constructing elliptic curves of prime order
Reinier Broker, Peter Stevenhagen
We present a very efficient algorithm to construct an elliptic curve E and a finite field F such that the order of the point group E(F) is a given prime number N. Heuristically, th…
Constructing elliptic curves in almost polynomial time
Reinier Broker, Peter Stevenhagen
We present an algorithm that, on input of a positive integer N together with its prime factorization, constructs a finite field F and an elliptic curve E over F for which E(F) has…