Algorithmic Number Theory: 4th International Symposium, ANTS-IV Leiden, The Netherlands, July 2-7, 2000. Proceedings Author: Wieb Bosma Published by Springer Berlin Heidelberg ISBN: 978-3-540-67695-9 DOI: 10.1007/10722028 Table of Contents: The Complexity of Some Lattice Problems Rational Points Near Curves and Small Nonzero | x Coverings of Curves of Genus 2 Lattice Reduction in Cryptology: An Update Construction of Secure C Curves over Finite Fields with Many Rational Points Obtained by Ray Class Field Extensions New Results on Lattice Basis Reduction in Practice Baby-Step Giant-Step Algorithms for Non-uniform Distributions On Powers as Sums of Two Cubes Factoring Polynomials over ρ-Adic Fields Strategies in Filtering in the Number Field Sieve Factoring Polynomials over Finite Fields and Stable Colorings of Tournaments Computing Special Values of Partial Zeta Functions Construction of Tables of Quartic Number Fields Counting Discriminants of Number Fields of Degree up to Four On Reconstruction of Algebraic Numbers Dissecting a Sieve to Cut Its Need for Space Counting Points on Hyperelliptic Curves over Finite Fields Modular Forms for GL(3) and Galois Representations Modular Symbols and Hecke Operators