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

Kiran S. Kedlaya (auth.), Duncan Buell (eds.)3540221565, 9783540221562, 9783540248477

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 e?ort of number theorists from around the world. There were four invited talks at ANTS VI, by Dan Bernstein of the Univ- sity of Illinois at Chicago, Kiran Kedlaya of MIT, Alice Silverberg of Ohio State University, and Mark Watkins of Pennsylvania State University. Thirty cont- 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 Universit´eB- 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.

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Table of contents :
Front Matter….Pages –
Computing Zeta Functions via p -Adic Cohomology….Pages 1-17
Using Primitive Subgroups to Do More with Fewer Bits….Pages 18-41
Elliptic Curves of Large Rank and Small Conductor….Pages 42-56
Binary GCD Like Algorithms for Some Complex Quadratic Rings….Pages 57-71
On the Complexity of Computing Units in a Number Field….Pages 72-86
Implementing the Arithmetic of C 3,4 Curves….Pages 87-101
Pseudocubes and Primality Testing….Pages 102-116
Elliptic Curves with a Given Number of Points….Pages 117-131
Rational Divisors in Rational Divisor Classes….Pages 132-139
Conjectures about Discriminants of Hecke Algebras of Prime Level….Pages 140-152
Montgomery Scalar Multiplication for Genus 2 Curves….Pages 153-168
Improved Weil and Tate Pairings for Elliptic and Hyperelliptic Curves….Pages 169-183
Elliptic Curves x 3 + y 3 = k of High Rank….Pages 184-193
Proving the Primality of Very Large Numbers with fastECPP….Pages 194-207
A Low-Memory Parallel Version of Matsuo, Chao, and Tsujii’s Algorithm….Pages 208-222
Function Field Sieve in Characteristic Three….Pages 223-234
A Comparison of CEILIDH and XTR….Pages 235-249
Stable Models of Elliptic Curves, Ring Class Fields, and Complex Multiplication….Pages 250-262
An Algorithm for Computing Isomorphisms of Algebraic Function Fields….Pages 263-271
A Method to Solve Cyclotomic Norm Equations $f * bar{f}$ ….Pages 272-279
Imaginary Cyclic Quartic Fields with Large Minus Class Numbers….Pages 280-292
Nonic 3-adic Fields….Pages 293-308
Montgomery Addition for Genus Two Curves….Pages 309-317
Numerical Evaluation at Negative Integers of the Dedekind Zeta Functions of Totally Real Cubic Number Fields….Pages 318-326
Salem Numbers of Trace -2 and Traces of Totally Positive Algebraic Integers….Pages 327-337
Low-Dimensional Lattice Basis Reduction Revisited….Pages 338-357
Computing Order Statistics in the Farey Sequence….Pages 358-366
The Discrete Logarithm in Logarithmic l -Class Groups and Its Applications in K-theory….Pages 367-378
Point Counting on Genus 3 Non Hyperelliptic Curves….Pages 379-394
Algorithmic Aspects of Cubic Function Fields….Pages 395-410
A Binary Recursive Gcd Algorithm….Pages 411-425
Lagrange Resolvents Constructed from Stark Units….Pages 426-441
Cryptanalysis of a Divisor Class Group Based Public-Key Cryptosystem….Pages 442-450
Back Matter….Pages –