3. ANTS 1998: Portland, Oregon, USA
Joe Buhler (Ed.): Algorithmic Number Theory, Third International Symposium, ANTS-III, Portland, Oregon, USA, June 21-25, 1998, Proceedings. Springer 1998 Lecture Notes in Computer Science ISBN 3-540-64657-4
Invited Talk 1
- Noam D. Elkies: Shimura Curve Computations. 1-47
Invited Talk 2
- Dan Boneh: The Decision Diffie-Hellman Problem. 48-63
GCD Algorithms
- Giovanni Cesari: Parallel Implementation of Schönhage's Integer GCD Algorithm. 64-76
- Brigitte Vallée: The Complete Analysis of the Binary Euclidean Algorithm. 77-94
Primality
- Preda Mihailescu: Cyclotomy Primality Proving - Recent Developments. 95-110
- François Morain: Primality Proving Using Elliptic Curves: An Update. 111-127
Factoring
- Daniel J. Bernstein: Bounding Smooth Integers. 128-130
- Zhang Mingzhi: Factorization of the Numbers of the Form m3+c2m2+c1m+c0. 131-136
- Brian Murphy: Modelling the Yield of Number Field Sieve Polynominals. 137-150
- Phong Q. Nguyen: A Montgomery-Like Square Root for the Number Field Sieve. 151-168
Sieving
- William F. Galway: Robert Bennion's ``Hopping Sieve''. 169-178
- Jonathan Sorenson: Trading Time for Space in Prime Number Sieves. 179-195
Analytic Number Theory
- Jean-Marc Deshouillers, François Hennecart, Bernard Landreau: Do Sums of 4 Biquadrates Have a Positive Density? 196-203
- Jean-Marc Deshouillers, Herman te Riele, Yannick Saouter: New Experimental Results Concerning the Goldbach Conjecture. 204-215
- Daniel Panario, Xavier Gourdon, Philippe Flajolet: An Analytic Approach to Smooth Polynominals over Finite Fields. 226-236
Cryptography
- Dan Boneh, Jeremy Horwitz: Generating a Product of Three Primes with an Unknown Factorization. 237-251
- Erik De Win, Serge Mister, Bart Preneel, Michael J. Wiener: On the Performance of Signature Schemes Based on Elliptic Curves. 252-266
- Jeffrey Hoffstein, Jill Pipher, Joseph H. Silverman: NTRU: A Ring-Based Public Key Cryptosystem. 267-288
Linear Algebra, Lattices
- Stefan Neis: Reducing Ideal Arithmetic to Linear Algebra Problems. 299-310
- Igor A. Semaev: Evaluation of Linear Relations between Vectors of a Lattice in Euclidean Space. 311-322
- Susanne Wetzel: An Efficient Parallel Block-Reduction Algorithm. 323-337
Series, Sums
- Bruno Haible, Thomas Papanikolaou: Fast Multiprecision Evaluation of Series of Rational Numbers. 338-350
- Alfred J. van der Poorten: Formal Power Series and Their Continued Fraction Expansion. 358-371
Algebraic Number Fields
- Henri Cohen, Francisco Diaz y Diaz, Michel Olivier: Imprimitive Octic Fields with Small Discriminants. 372-380
- Henri Cohen, Francisco Diaz y Diaz, Michel Olivier: A Table of Totally Complex Number Fields of Small Discriminants. 381-391
- Bart de Smit: Generating Arithmetically Equivalent Number Fields with Elliptic Curves. 392-399
- Jacques Martinet: On Successive Minima of Rings of Algebraic Integers. 424-432
Class Groups and Fields
- Henri Cohen, Francisco Diaz y Diaz, Michel Olivier: Computation of Relative Quadratic Class Groups. 433-440
- Joshua Holden: Irregularity of Prime Numbers over Real Quadratic Fields. 454-462
- Michael J. Jacobson Jr.: Experimental Results on Class Groups of Real Quadratic Fields. 463-474
- Stéphane Louboutin: Computation of Relative Class Numbers of Imaginary Cyclic Fields of 2-power Degrees. 475-481
Curves
- Antonia W. Bluher: Formal Groups, Elliptic Curves, and Some Theorems of Couveignes. 482-501
- Z. Djabri, Nigel P. Smart: A Comparison of Direct and Indirect Methods for Computing Selmer Groups of an Elliptic Curve. 502-513
- Ming-Deh A. Huang, Yiu-Chung Wong: An Algorithm for Approximate Counting of Points on Algebraic Sets over Finite Fields. 514-527
- Attila Pethö, E. Herrmann, Horst Günter Zimmer: S-integral Points on Elliptic Curves and Fermat's Triple Equations. 528-540
- Edlyn Teske: Speeding Up Pollard's Rho Method for Computing Discrete Logarithms. 541-554
Function Fields
- Harald Niederreiter, Chaoping Xing: A General Method of Constructing Global Function Fields. 555-566
- Sachar Paulus: Lattice Basis Reduction in Function Fields. 567-575
- Sachar Paulus, Andreas Stein: Comparing Real and Imaginary Arithmetics for Divisor Class Groups of Hyperelliptic Curves. 576-591
- Renate Scheidler, Andreas Stein: Unit Computation in Purely Cubic Function Fields of Unit Rank 1. 592-606
- Andreas Stein, Hugh C. Williams: An Improved Method of Computing the Regulator of a Real Quadratic Function Field. 607-620
- Robert J. Zuccherato: The Equivalence Between Elliptic Curve and Quadratic Function Field Discrete Logarithms in Characteristic 2. 621-638
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