Algorithmic Number Theory: 6th International Symposium, Ants-vi, Burlington, Vt, Usa, June 13-18, 2004, Proceedings

by Buell, Duncan A.

• ISBN13: 9783540221562
• ISBN10: 3540221565
• Format: Paperback
• Copyright: 2004-11-30
• Publisher: Springer-Verlag New York Inc

Summary

This book constitutes the refereed proceedings of the 6th International Algorithmic Number Theory Symposium, ANTS 2004, held in Burlington, VT, USA, in June 2004. The 30 revised full papers presented together with 3 invited papers were carefully reviewed and selected for inclusion in the book. Among the topics addressed are zeta functions, elliptic curves, hyperelliptic curves, GCD algorithms, number field computations, complexity, primality testing, Weil and Tate pairings, cryptographic algorithms, function field sieve, algebraic function field mapping, quartic fields, cubic number fields, lattices, discrete logarithms, and public key cryptosystems.

Table of Contents

Invited Talks
Computing Zeta Functions via p-Adic Cohomology	1	(17)
Kiran S. Kedlaya
Using Primitive Subgroups to Do More with Fewer Bits	18	(24)
K. Rubin
A. Silverberg
Elliptic Curves of Large Rank and Small Conductor	42	(15)
Noam D. Elkies
Mark Watkins
Contributed Papers
Binary GCD Like Algorithms for Some Complex Quadratic Rings	57	(15)
Saurabh Agarwal
Gudmund Skovbjerg Frandsen
On the Complexity of Computing Units in a Number Field	72	(15)
V. Arvind
Piyush P. Kurur
Implementing the Arithmetic of C3,4 Curves	87	(15)
Abdolali Basiri
Andreas Enge
Jean-Charles Faugere
Nicolas Gurel
Pseudocubes and Primality Testing	102	(15)
P. Berrizbeitia
S. Muller
H.C. Williams
Elliptic Curves with a Given Number of Points	117	(15)
Reinier Broker
Peter Stevenhagen
Rational Divisors in Rational Divisor Classes	132	(8)
N. Bruin
E. V. Flynn
Conjectures about Discriminants of Hecke Algebras of Prime Level	140	(13)
Frank Calegari
William A. Stein
Montgomery Scalar Multiplication for Genus 2 Curves	153	(16)
Sylvain Duquesne
Improved Weil and Tate Pairings for Elliptic and Hyperelliptic Curves	169	(15)
Kirsten Eisentrager
Kristin Lauter
Peter L. Montgomery
Elliptic Curves x3 + y3 = k of High Rank	184	(10)
Noam D. Elkies
Nicholas F. Rogers
Proving the Primality of Very Large Numbers with fastECPP	194	(14)
J. Franke
T. Kleinjung
F. Morain
T. Wirth
A Low-Memory Parallel Version of Matsuo, Chao, and Tsujii's Algorithm	208	(15)
Pierrick Gaudry
Eric Schost
Function Field Sieve in Characteristic Three	223	(12)
R. Granger
A.J. Holt
D. Page
N.P. Smart
F. Vercauteren
A Comparison of Ceilidh and XTR	235	(15)
R. Granger
D. Page
M. Stam
Stable Models of Elliptic Curves, Ring Class Fields, and Complex Multiplication	250	(13)
Jordi Guardia
Eugenia Torres
Montserrat Vela
An Algorithm for Computing Isomorphisms of Algebraic Function Fields	263	(9)
F. Hess
A Method to Solve Cyclotomic Norm Equations ƒ * ƒ	272	(8)
Nick Howgrave-Graham
Mike Szydlo
Imaginary Cyclic Quartic Fields with Large Minus Class Numbers	280	(13)
M.J. Jacobson, Jr.
H.C. Williams
K. Wooding
Nonic 3-adic Fields	293	(16)
John W. Jones
David P. Roberts
Montgomery Addition for Genus Two Curves	309	(9)
Tanja Lange
Numerical Evaluation at Negative Integers of the Dedekind Zeta Functions of Totally Real Cubic Number Fields	318	(9)
Stephane R. Louboutin
Salem Numbers of Trace --2 and Traces of Totally Positive Algebraic Integers	327	(11)
James McKee
Chris Smyth
Low-Dimensional Lattice Basis Reduction Revisited	338	(20)
Phong Q. Nguyen
Damien Stehle
Computing Order Statistics in the Farey Sequence	358	(9)
Corina E. Patrascu
Mihai Patrascu
The Discrete Logarithm in Logarithmic l-Class Groups and Its Applications in K-theory	367	(12)
Sebastian Pauli
Florence Soriano-Gafiuk
Point Counting on Genus 3 Non Hyperelliptic Curves	379	(16)
Christophe Ritzenthaler
Algorithmic Aspects of Cubic Function Fields	395	(16)
R. Scheidler
A Binary Recursive Gcd Algorithm	411	(15)
Damien Stehle
Paul Zimmermann
Lagrange Resolvents Constructed from Stark Units	426	(16)
Brett A. Tangedal
Cryptanalysis of a Divisor Class Group Based Public-Key Cryptosystem	442	(9)
Aaram Yun
Jaeheon Kim
Dong Hoon Lee
Author Index	451