Algorithmic Number Theory: 6th International Symposium, ANTS-VI, Burlington, VT, USA, June 13-18, 2004, Proceedings

456 Pages·2004·20.35 MB·English

by  Kiran S. Kedlaya (auth.)

Lecture Notes in Computer Science 3076
Commenced Publication in 1973
Founding and Former Series Editors:
Gerhard Goos, Juris Hartmanis, and Jan van Leeuwen
Editorial Board
Takeo Kanade
Carnegie Mellon University, Pittsburgh, PA, USA
Josef Kittler
University of Surrey, Guildford, UK
Jon M. Kleinberg
Cornell University, Ithaca, NY, USA
Friedemann Mattern
ETH Zurich, Switzerland
John C. Mitchell
Stanford University, CA, USA
Moni Naor
Weizmann Institute of Science, Rehovot, Israel
Oscar Nierstrasz
University of Bern, Switzerland
C. Pandu Rangan
Indian Institute of Technology, Madras, India
Bernhard Steffen
University of Dortmund, Germany
Madhu Sudan
Massachusetts Institute of Technology, MA, USA
Demetri Terzopoulos
New York University, NY, USA
Doug Tygar
University of California, Berkeley, CA, USA
Moshe Y. Vardi
Rice University, Houston, TX, USA
Gerhard Weikum
Max-Planck Institute of Computer Science, Saarbruecken, Germany
Springer
Berlin
Heidelberg
New York
Hong Kong
London
Milan
Paris
Tokyo
Duncan Buell (Ed.)
Algorithmic
Number Theory
6th International Symposium, ANTS-VI
Burlington, VT, USA, June 13-18, 2004
Proceedings
Springer
eBook ISBN: 3-540-24847-1
Print ISBN: 3-540-22156-5
©2005 Springer Science + Business Media, Inc.
Print©2004Springer-Verlag
Berlin Heidelberg
All rights reserved
No part of this eBook maybe reproducedor transmitted inanyform or byanymeans,electronic,
mechanical, recording, or otherwise, without written consent from the Publisher
Created in the United States of America
Visit Springer's eBookstore at: http://ebooks.springerlink.com
and the Springer Global Website Online at: http://www.springeronline.com
Preface
The sixth Algorithmic Number Theory Symposium was held at the University
of Vermont, in Burlington, from 13–18 June 2004. The organization was a joint
effort of number theorists from around the world.
There were four invited talks at ANTS VI, by Dan Bernstein of the Univer-
sity of Illinois at Chicago, Kiran Kedlaya of MIT, Alice Silverberg of Ohio State
University, and Mark Watkins of Pennsylvania State University. Thirty contri-
buted talks were presented, and a poster session was held. This volume contains
the written versions of the contributed talks and three of the four invited talks.
(Not included is the talk by Dan Bernstein.)
ANTS in Burlington is the sixth in a series that began with ANTS I in 1994
at Cornell University, Ithaca, New York, USA and continued at Université Bor-
deaux I, Bordeaux, France (1996), Reed College, Portland, Oregon, USA (1998),
the University of Leiden, Leiden, The Netherlands (2000), and the University
of Sydney, Sydney, Australia (2002). The proceedings have been published as
volumes 877, 1122, 1423, 1838, and 2369 of Springer-Verlag’s Lecture Notes in
Computer Science series.
The organizers of the 2004 ANTS conference express their special gratitude
and thanks to John Cannon and Joe Buhler for invaluable behind-the-scenes
advice.
June 2004 Duncan Buell
This page intentionally left blank
ANTS VI Organizing Committee
Duncan Buell (University of South Carolina)
David S. Dummit (University of Vermont)
David Joyner (United States Naval Academy)
Blair Kelly III (United States Department of Defense)
Jonathan W. Sands (University of Vermont)
Program Committee
Duncan Buell (University of South Carolina, USA, Chair)
Eric Bach (University of Wisconsin, USA)
Johannes Buchmann (Darmstadt University, Germany)
Richard Brent (Oxford University, UK)
Henri Cohen (Université de Bordeaux I, France)
Everett Howe (Center for Communications Research, La Jolla,
California, USA)
David Joyner (United States Naval Academy, USA)
Bjorn Poonen (University of California at Berkeley, USA)
Renate Scheidler (University of Calgary, Alberta, Canada)
Igor Shparlinski (Macquarie University, Sydney, Australia)
Jonathan Sorenson (Butler University, Indianapolis, Indiana, USA)
This page intentionally left blank
Table of Contents
Invited Talks
Computing Zeta Functions via Cohomology 1
Kiran S. Kedlaya
Using Primitive Subgroups to Do More with Fewer Bits 18
K. Rubin, A. Silverberg
Elliptic Curves of Large Rank and Small Conductor 42
Noam D. Elkies, Mark Watkins
Contributed Papers
Binary GCD Like Algorithms for Some Complex Quadratic Rings 57
Saurabh Agarwal, Gudmund Skovbjerg Frandsen
On the Complexity of Computing Units in a Number Field 72
V. Arvind, Piyush P. Kurur
Implementing the Arithmetic of Curves 87
Abdolali Basiri, Andreas Enge, Jean-Charles Faugère,
Nicolas Gürel
Pseudocubes and Primality Testing 102
P. Berrizbeitia, S. Müller, H.C. Williams
Elliptic Curves with a Given Number of Points 117
Reinier Bröker, Peter Stevenhagen
Rational Divisors in Rational Divisor Classes 132
N. Bruin, E. V. Flynn
Conjectures about Discriminants of Hecke Algebras of Prime Level 140
Frank Calegari, William A. Stein
Montgomery Scalar Multiplication for Genus 2 Curves 153
Sylvain Duquesne
Improved Weil and Tate Pairings for Elliptic
and Hyperelliptic Curves 169
Kirsten Eisenträger, Kristin Lauter, Peter L. Montgomery
Elliptic Curves of High Rank 184
Noam D. Elkies, Nicholas F. Rogers