3. ANTS 1998: Portland, Oregon, USA

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 M. Gordon, Eugene R. Rodemich:
  Dense Admissible Sets. 216-225
  
• 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
  
• Adam L. Young, Moti Yung:
  Finding Length-3 Positive Cunningham Chains. 289-298
  

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
  
• Edlyn Teske, Hugh C. Williams:
  A Problem Concerning a Character Sum - Extended Abstract. 351-357
  
• 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
  
• David S. Dummit, Brett A. Tangedal:
  Computing the Lead Term of an Abelian L-function. 400-411
  
• John W. Jones, David P. Roberts:
  Timing Analysis of Targeted Hunter Searches. 412-423
  
• 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
  
• Alice Gee, Peter Stevenhagen:
  Generating Class Fields using Shimura Reciprocity. 441-453
  
• 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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