Algorithmic Number Theory : 5th International Symposium, ANTS-V, Sydney, Australia, July 7-12, 2002. Proceedings

Corporate Author: SpringerLink (Online service)
Other Authors: Fieker, Claus (Editor), Kohel, David R. (Editor)
Format: eBook
Published: Berlin, Heidelberg Springer Berlin Heidelberg 2002, 2002
Edition:1st ed. 2002
Series:Lecture Notes in Computer Science
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • Invited Talks
  • Gauss Composition and Generalizations
  • Elliptic Curves — The Crossroads of Theory and Computation
  • The Weil and Tate Pairings as Building Blocks for Public Key Cryptosystems
  • Using Elliptic Curves of Rank One towards the Undecidability of Hilbert’s Tenth Problem over Rings of Algebraic Integers
  • On p-adic Point Counting Algorithms for Elliptic Curves over Finite Fields
  • Number Theory
  • On Arithmetically Equivalent Number Fields of Small Degree
  • A Survey of Discriminant Counting
  • A Higher-Rank Mersenne Problem
  • An Application of Siegel Modular Functions to Kronecker’s Limit Formula
  • Computational Aspects of NUCOMP
  • Efficient Computation of Class Numbers of Real Abelian Number Fields
  • An Accelerated Buchmann Algorithm for Regulator Computation in Real Quadratic Fields
  • Arithmetic Geometry
  • Some Genus 3 Curves with Many Points
  • Trinomials ax 7 + bx + c and ax 8 + bx + c with Galois Groups of Order 168 and 8 · 168
  • Computations on Modular Jacobian Surfaces
  • Integral Points on Punctured Abelian Surfaces
  • Genus 2 Curves with (3, 3)-Split Jacobian and Large Automorphism Group
  • Transportable Modular Symbols and the Intersection Pairing
  • Elliptic Curves and CM
  • Action of Modular Correspondences around CM Points
  • Curves Dy 2 = x 3 — x of Odd Analytic Rank
  • Comparing Invariants for Class Fields of Imaginary Quadratic Fields
  • A Database of Elliptic Curves — First Report
  • Point Counting
  • Isogeny Volcanoes and the SEA Algorithm
  • Fast Elliptic Curve Point Counting Using Gaussian Normal Basis
  • An Extension of Kedlaya’s Algorithm to Artin-Schreier Curves in Characteristic 2
  • Cryptography
  • Implementing the Tate Pairing
  • Smooth Orders and Cryptographic Applications
  • Chinese Remaindering for Algebraic Numbers in a Hidden Field
  • Function Fields
  • An Algorithm for Computing Weierstrass Points
  • New Optimal Tame Towers of Function Fields over Small Finite Fields
  • Periodic Continued Fractions in Elliptic Function Fields
  • Discrete Logarithms and Factoring
  • Fixed Points and Two-Cycles of the Discrete Logarithm
  • Random Cayley Digraphs and the Discrete Logarithm
  • The Function Field Sieve Is Quite Special
  • MPQS with Three Large Primes
  • An Improved Baby Step Giant Step Algorithm for Point Counting of Hyperelliptic Curves over Finite Fields
  • Factoring N = pq 2 with the Elliptic Curve Method
  • Gröbner Bases
  • A New Scheme for Computing with Algebraically Closed Fields
  • Complexity
  • Additive Complexity and Roots of Polynomials over Number Fields and -adic Fields