5. ANTS 2002: Sydney, NSW, Australia

Claus Fieker, David R. Kohel (Eds.): Algorithmic Number Theory, 5th International Symposium, ANTS-V, Sydney, Australia, July 7-12, 2002, Proceedings. Lecture Notes in Computer Science 2369 Springer 2002, ISBN 3-540-43863-7

Invited Talks

Manjul Bhargava:
Gauss Composition and Generalizations. 1-8
John Coates:
Elliptic Curves - The Crossroads of Theory and Computation. 9-19
Antoine Joux:
The Weil and Tate Pairings as Building Blocks for Public Key Cryptosystems. 20-32
Bjorn Poonen:
Using Elliptic Curves of Rank One towards the Undecidability of Hilbert's Tenth Problem over Rings of Algebraic Integers. 33-41
Takakazu Satoh:
On p-adic Point Counting Algorithms for Elliptic Curves over Finite Fields. 43-66

Wieb Bosma, Bart de Smit:
On Arithmetically Equivalent Number Fields of Small Degree. 67-79
Henri Cohen, Francisco Diaz y Diaz, Michel Olivier:
A Survey of Discriminant Counting. 80-94
Graham Everest, Peter Rogers, Thomas Ward:
A Higher-Rank Mersenne Problem. 95-107
Takashi Fukuda, Keiichi Komatsu:
An Application of Siegel Modular Functions to Kronecker's Limit Formula. 108-119
Michael J. Jacobson Jr., Alfred J. van der Poorten:
Computational Aspects of NUCOMP. 120-133
Stéphane Louboutin:
Efficient Computation of Class Numbers of Real Abelian Number Fields. 134-147
Ulrich Vollmer:
An Accelerated Buchmann Algorithm for Regulator Computation in Real Quadratic Fields. 148-162

Roland Auer, Jaap Top:
Some Genus 3 Curves with Many Points. 163-171
Nils Bruin, Noam D. Elkies:
Trinomials ax and ax with Galois Groups of Order 168 and 8·168. 172-188
Enrique González-Jiménez, Josep González, Jordi Guàrdia:
Computations on Modular Jacobian Surfaces. 189-197
Andrew Kresch, Yuri Tschinkel:
Integral Points on Punctured Abelian Surfaces. 198-204
Tony Shaska:
Genus 2 Curves with (3, 3)-Split Jacobian and Large Automorphism Group. 205-218
Helena A. Verrill:
Transportable Modular Symbols and the Intersection Pairing. 219-233

Jean Marc Couveignes, Thierry Henocq:
Action of Modular Correspondences around CM Points. 234-243
Noam D. Elkies:
Curves Dy=x-x of Odd Analytic Rank. 244-251
Andreas Enge, François Morain:
Comparing Invariants for Class Fields of Imaginary Quadratic Fields. 252-266
William A. Stein, Mark Watkins:
A Database of Elliptic Curves - First Report. 267-275

Mireille Fouquet, François Morain:
Isogeny Volcanoes and the SEA Algorithm. 276-291
Hae Young Kim, Jung Youl Park, Jung Hee Cheon, Je Hong Park, Jae Heon Kim, Sang Geun Hahn:
Fast Elliptic Curve Point Counting Using Gaussian Normal Basis. 292-307
Jan Denef, Frederik Vercauteren:
An Extension of Kedlaya's Algorithm to Artin-Schreier Curves in Characteristic 2. 308-323

Steven D. Galbraith, Keith Harrison, David Soldera:
Implementing the Tate Pairing. 324-337
Carl Pomerance, Igor Shparlinski:
Smooth Orders and Cryptographic Applications. 338-348
Igor Shparlinski, Ron Steinfeld:
Chinese Remaindering for Algebraic Numbers in a Hidden Field. 349-356

Florian Hess:
An Algorithm for Computing Weierstrass Points. 357-371
Wen-Ching W. Li, Hiren Maharaj, Henning Stichtenoth, Noam D. Elkies:
New Optimal Tame Towers of Function Fields over Small Finite Fields. 372-389
Alfred J. van der Poorten, Xuan Chuong Tran:
Periodic Continued Fractions in Elliptic Function Fields. 390-404

Joshua Holden:
Fixed Points and Two-Cycles of the Discrete Logarithm. 405-415
Jeremy Horwitz, Ramarathnam Venkatesan:
Random Cayley Digraphs and the Discrete Logarithm. 416-430
Antoine Joux, Reynald Lercier:
The Function Field Sieve Is Quite Special. 431-445
Paul C. Leyland, Arjen K. Lenstra, Bruce Dodson, Alec Muffett, Samuel S. Wagstaff Jr.:
MPQS with Three Large Primes. 446-460
Kazuto Matsuo, Jinhui Chao, Shigeo Tsujii:
An Improved Baby Step Giant Step Algorithm for Point Counting of Hyperelliptic Curves over Finite Fields. 461-474
Peter Ebinger, Edlyn Teske:
Factoring N = pq with the Elliptic Curve Method. 475-490

Allan K. Steel:
A New Scheme for Computing with Algebraically Closed Fields. 491-505

J. Maurice Rojas:
Additive Complexity and Roots of Polynomials over Number Fields and \mathfrak{p} -adic Fields. 506-516

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