7th Algorithmic Number Theory Symposium, 23 - 28 July 2006


The refereed Proceedings of ANTS VII are published in the Springer series Lecture Notes in Computer Science Volume 4076 and were handed to the participants when they check in. They are also available electronically.

The articles are organized into the chapters Invited Talks, Algebraic Number Theory, Analytic and Elementary Number Theory, Lattices, Curves and Varieties over Fields of Characteristic Zero, Curves over Finite Fields and Applications, and Discrete Logarithms. On this page you find slides of talks, source code of programs, errata, and other additional material.

Selfridge Prize in Computational Number Theory

[Communicated by Hugh Williams] In honour of the many contributions of John Selfridge to mathematics, the Number Theory Foundation has established a prize to be awarded to those individuals who have authored the best paper accepted for presentation at ANTS. The prize, called the Selfridge Prize, will normally be awarded every two years in an even numbered year. The prize winner(s) receive a cash award and a certificate. The successful paper will be selected by the ANTS Program Committee.

Werner Bley and Robert Boltje were awarded the Selfridge Prize in Computational Number Theory for their paper Computation of locally free class groups.

Invited Talks

Computing Pro-P Galois Groups
Nigel Boston and Harris Nover
The Elliptic Curve Database
John Cremona
Database, Errata, Talk
On the Computation of the Coefficients of a Modular Form
Bas Edixhoven
Cohen-Lenstra heuristics of quadratic number fields
Etienne Fouvry and Jürgen Klüners
(q-Hypergeometric Series and Modular Forms)
Don Zagier

Algebraic Number Theory

An algorithm for computing p-class groups of abelian number fields
Miho Aoki and Takashi Fukuda
Computation of locally free class groups
Werner Bley and Robert Boltje
Numerical Results on Class Groups of Imaginary Quadratic Fields
M.J. Jacobson, S. Ramachandran, H.C. Williams
Supplementary Tables
Cyclic polynomials arising from Kummer theory of norm algebraic tori
Masanari Kida
The totally real primitive number fields of discriminant at most 109
Gunter Malle
A Modular Method for Computing the Splitting Field of a Polynomial
Guénaël Renault and Kazuhiro Yokoyama

Analytic and Elementary Number Theory

The Density of Sums of Three Cubes
Jean-Marc Deshouillers, Francois Hennecart, Bernard Landreau
The Mertens Conjecture Revisited
Tadej Kotnik and And Herman te Riele
Talk, Errata: page 158, line -7, "by Theorem 1" should read: "by Theorem 2".
Fast Bounds on the Distribution of Smooth Numbers
Scott T. Parsell and Jonathan P. Sorenson
Use of Extended Euclidean Algorithm in Solving a System of Linear Diophantine Equations with Bounded Variables
Parthasarathy Ramachandran
The Pseudosquares Prime Sieve
Jonathan P. Sorenson
Doubly-Focused Enumeration of Pseudosquares and Pseudocubes
Kjell Wooding and H. C. Williams


Practical Lattice Basis Sampling Reduction
Johannes Buchmann and Christoph Ludwig
LLL on the average
Phong Q. Nguyen and Damien Stehlé
On the Randomness of Bits Produced by Sufficiently Regular Functions
Damien Stehlé

Curves and Varieties over Fields of Characteristic Zero

Computing a Lower Bound for the Canonical Height on Elliptic Curves over Q
John Cremona and Samir Siksek
Points of Low Height on Elliptic Curves and Surfaces I: Elliptic Surfaces over P1 with small d
Noam D. Elkies
Shimura Curves for Level-3 Subgroups of the (2, 3, 7) Triangle Group and Some Other Examples
Noam D. Elkies
The Asymptotics of Points of Bounded Height on Diagonal Cubic and Quartic Threefolds
Andreas-Stephan Elsenhans and Joerg Jahnel
Talk, C-Source for hashing package, C-Source for solving x4 + 2 y4 = z4 + 4 w4
Testing Equivalence of Ternary Cubics
Tom Fisher
Classification of Genus 3 Curves in Special Strata of the Moduli Space
Martine Girard, David Kohel
Heegner point computations via numerical p-adic integration
Matthew Greenberg
Symmetric Powers of Elliptic Curve L-Functions
Phil Martin and Mark Watkins
Determined sequences, continued fractions, and hyperelliptic curves
Alfred J. van der Poorten
Computing CM Points on Shimura Curves Arising from Cocompact Arithmetic Triangle Groups
John Voight

Curves over Finite Fields and Applications

Arithmetic of Generalized Jacobians
Isabelle Dechene
Hidden Pairings and Trapdoor DDH Groups
Alexander W. Dent and Steven D. Galbraith
Talk (PDF, PPT)
Constructing Pairing-Friendly Elliptic Curves with Embedding Degree 10
David Freeman
Fast bilinear maps from the Tate-Lichtenbaum pairing on hyperelliptic curves
Gerhard Frey and Tanja Lange
High Security Pairing-Based Cryptography Revisited
R. Granger, D. Page, and N.P. Smart
Efficiently Computable Endomorphisms for Hyperelliptic Curves
David R. Kohel, Benjamin A. Smith
Finding Points on Elliptic Curves in Deterministic Polynomial Time
Andrew Shallue and Christiaan van de Woestijne
Implementation for odd characteristic: ellpoint.magma, implementation.magma
20 years of ECM
Paul Zimmermann and Bruce Dodson

Discrete Logarithms

Index Calculus with Double Large Prime Variation in Class Groups of Plane Curves of Small Degree
Claus Diem
The density of sums of three cubes
Hard Instances of Constrained Discrete Logarithm Problem
Ilya Mironov, Anton Mityagin, Kobbi Nissim
Corrected Article, Talk (PDF, PPT)
Spectral Analysis of Pollard Rho Collisions
Stephen D. Miller and Ramarathnam Venkatesan
Signature Calculus and Discrete Logarithm Problems
Ming-Deh Huang and Wayne Raskind

Program Committee

Karim Belabas, Universite Bordeaux 1
Johannes Buchmann, Universität Darmstadt
John Cannon, University of Sydney
Gerhard Frey, Universität Duisburg-Essen
Istvan Gaal, University of Debrecen
Francois Morain, Ecole Polytechnique
Ken Nakamula, Tokyo Metropolitan University
Enric Nart, Universitat Autonoma de Barcelona
Takakazu Satoh, Tokyo Institute of Technology
Peter Stevenhagen, Universiteit Leiden
Fernando Villegas, University of Texas
Hugh Williams, University of Calgary

 Organizers: Florian Heß, Sebastian Pauli, Michael Pohst