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Algorithmic Number Theory

First International Symposium, ANTS-I, Ithaca, NY, USA, May 6 - 9, 1994. Proceedings

  • Conference proceedings
  • © 1994

Overview

Editors:
  1. Leonard M. Adleman
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  2. Ming-Deh Huang
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Part of the book series: Lecture Notes in Computer Science (LNCS, volume 877)

Included in the following conference series:

Conference proceedings info: ANTS 1994.

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Table of contents (35 papers)

  1. Front Matter

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  2. On the difficulty of finding reliable witnesses

    • W. R. Alford, Andrew Granville, Carl Pomerance
    Pages 1-16

  3. Density computations for real quadratic 2-class groups

    • Wieb Bosma, Peter Stevenhagen
    Pages 17-17

  4. Lattice sieving and trial division

    • Roger A. Golliver, Arjen K. Lenstra, Kevin S. McCurley
    Pages 18-27

  5. A subexponential algorithm for discrete logarithms over the rational subgroup of the Jacobians of large genus hyperelliptic curves over finite fields

    • Leonard M. Adleman, Jonathan DeMarrais, Ming-Deh Huang
    Pages 28-40

  6. Computing rates of growth of division fields on CM Abelian varieties

    • Bruce A. Dodson, Matthew J. Haines
    Pages 41-41

  7. Algorithms for CM-Fields

    • Sachar Paulus
    Pages 42-42

  8. Schoof's algorithm and isogeny cycles

    • Jean-Marc Couveignes, François Morain
    Pages 43-58

  9. Integer points on rational elliptic curves

    • Nelson Stephens
    Pages 59-59

  10. Counting the number of points on elliptic curves over finite fields of characteristic greater than three

    • Frank Lehmann, Markus Maurer, Volker Müller, Victor Shoup
    Pages 60-70

  11. Straight-line complexity and integer factorization

    • Richard J. Lipton
    Pages 71-79

  12. Decomposition of algebraic functions

    • Dexter Kozen, Susan Landau, Richard Zippel
    Pages 80-92

  13. A new modular interpolation algorithm for factoring multivariate polynomials

    • Ronitt Rubinfeld, Richard Zippel
    Pages 93-107

  14. The function field sieve

    • Leonard M. Adleman
    Pages 108-121

  15. Heegner point computations

    • Noam D. Elkies
    Pages 122-133

  16. Computing the degree of a modular parametrization

    • J. E. Cremona
    Pages 134-142

  17. Galois representations from the cohomology of SL(3,ℤ)

    • Mark McConnell
    Pages 143-143

  18. An analysis of the Gaussian algorithm for lattice reduction

    • Hervé Daudé, Philippe Flajolet, Brigitte Vallée
    Pages 144-158

  19. A fast variant of the Gaussian reduction algorithm

    • Michael Kaib
    Pages 159-159

  20. Reducing lattice bases by means of approximations

    • Johannes Buchmann
    Pages 160-168
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About this book

This volume presents the refereed proceedings of the First Algorithmic Number Theory Symposium, ANTS-I, held at Cornell University, Ithaca, NY in May 1994.
The 35 papers accepted for inclusion in this book address many current issues of algorithmic, computational and complexity-theoretic aspects of number theory and thus report the state-of-the-art in this exciting area of research; the book also contributes essentially to foundational research in cryptology and coding.
Of particular value is a collection entitled "Open Problems in Number Theoretic Complexity, II" contributed by Len Adleman and Kevin McCurley. This survey presents on 32 pages 36 central open problems and relates them to the literature by means of some 160 references.

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