Algorithmic Number Theory : 5th International Symposium, ANTSV, Sydney, Australia, July 712, 2002. Proceedings
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Format:  eBook 
Language:  English 
Published: 
Berlin, Heidelberg
Springer Berlin Heidelberg
2002, 2002

Edition:  1st ed. 2002 
Series:  Lecture Notes in Computer Science

Subjects:  
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 padic 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 HigherRank 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 ArtinSchreier 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 TwoCycles 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