Table of contents (35 papers)

  1. Front Matter
  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. Computing rates of growth of division fields on CM Abelian varieties
    Bruce A. Dodson, Matthew J. Haines
    Pages 41-41
  6. Algorithms for CM-Fields
    Sachar Paulus
    Pages 42-42
  7. Schoof's algorithm and isogeny cycles
    Jean-Marc Couveignes, François Morain
    Pages 43-58
  8. Integer points on rational elliptic curves
    Nelson Stephens
    Pages 59-59
  9. 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
  10. Decomposition of algebraic functions
    Dexter Kozen, Susan Landau, Richard Zippel
    Pages 80-92
  11. The function field sieve
    Leonard M. Adleman
    Pages 108-121
  12. Heegner point computations
    Noam D. Elkies
    Pages 122-133
  13. An analysis of the Gaussian algorithm for lattice reduction
    Hervé Daudé, Philippe Flajolet, Brigitte Vallée
    Pages 144-158
  14. Reducing lattice bases by means of approximations
    Johannes Buchmann
    Pages 160-168

About these proceedings


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.


Finite Fields Greatest Common Divisor (GCD) Größtter Gemeinsamer Teiler Integer Factorization Number theory Polynom-Faktorisierung Polynominal Factorization Siebmethoden Sieve Methods algorithms ants complexity

Bibliographic information

  • Copyright Information Springer-Verlag 1994
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-58691-3
  • Online ISBN 978-3-540-49044-9
  • Series Print ISSN 0302-9743
  • Series Online ISSN 1611-3349