Overview

This volume presents the refereed proceedings of the 1st Algorithmic Number Theory Symposium, ANTS-I, held at Cornell University, New York, in May 1994. The 35 papers accepted for inclusion in this book address many issues of the algorithmic, computational and complexity-theoretic aspects of number theory. The book also contributes to foundational research in cryptology and coding. Of particular value is a collection entitled ""Open Problems in Number Theoretic Complexity"", which presents 36 central open problems and relates them to the literature by means of some 160 references.

Full Product Details

Author:   Leonard M. Adleman ,  Ming-Deh Huang
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   1994 ed.
Volume:   877
Dimensions:   Width: 21.60cm , Height: 1.80cm , Length: 27.90cm
Weight:   1.070kg
ISBN:  

9783540586913

ISBN 10:   3540586911
Pages:   320
Publication Date:   15 November 1994
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

On the difficulty of finding reliable witnesses.- Density computations for real quadratic 2-class groups.- Lattice sieving and trial division.- A subexponential algorithm for discrete logarithms over the rational subgroup of the Jacobians of large genus hyperelliptic curves over finite fields.- Computing rates of growth of division fields on CM Abelian varieties.- Algorithms for CM-Fields.- Schoof's algorithm and isogeny cycles.- Integer points on rational elliptic curves.- Counting the number of points on elliptic curves over finite fields of characteristic greater than three.- Straight-line complexity and integer factorization.- Decomposition of algebraic functions.- A new modular interpolation algorithm for factoring multivariate polynomials.- The function field sieve.- Heegner point computations.- Computing the degree of a modular parametrization.- Galois representations from the cohomology of SL(3,?).- An analysis of the Gaussian algorithm for lattice reduction.- A fast variant of the Gaussian reduction algorithm.- Reducing lattice bases by means of approximations.- Analysis of a left-shift binary GCD algorithm.- The complexity of greatest common divisor computations.- Explicit formulas for units in certain quadratic number fields.- Factorization of polynomials over finite fields in subexponential time under GRH.- On orders of optimal normal basis generators.- Computing in the jacobian of a plane algebraic curve.- Under the assumption of the Generalized Riemann Hypothesis verifying the class number belongs to NP ? co-NP.- Calculating the class number of certain Hilbert class fields.- Efficient checking of computations in number theory.- Constructing elliptic curves with given group order over large finite fields.- Computing ?(x), M(x) and ?(x).- On some applications of finitely generated semi-groups.- Improved incremental prime number sieves.- Polynomial time algorithms for discrete logarithms and factoring on a quantum computer.- On dispersion and Markov constants.- Open problems in number theoretic complexity, II.

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