Algorithmic Number Theory: Second International Symposium, ANTS-II Talence, France, May 18–23, 1996 Proceedings

Leonard M. Adleman, Ming-Deh A. Huang (auth.), Henri Cohen (eds.)3540615814, 9783540615811

This book constitutes the refereed post-conference proceedings of the Second International Algorithmic Number Theory Symposium, ANTS-II, held in Talence, France in May 1996.
The 35 revised full papers included in the book were selected from a variety of submissions. They cover a broad spectrum of topics and report state-of-the-art research results in computational number theory and complexity theory. Among the issues addressed are number fields computation, Abelian varieties, factoring algorithms, finite fields, elliptic curves, algorithm complexity, lattice theory, and coding.

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Table of contents :
Counting rational points on curves and abelian varieties over finite fields….Pages 1-16
Computing cubic fields in quasi-linear time….Pages 17-25
Fast ideal arithmetic via lazy localization….Pages 27-34
A comparative study of algorithms for computing continued fractions of algebraic numbers….Pages 35-47
Computing ray class groups, conductors and discriminants….Pages 49-57
Computing l -isogenies using the p -torsion….Pages 59-65
On computing Hilbert class fields of prime degree….Pages 67-74
On the reduction of composed relations from the number field sieve….Pages 75-90
Checking the $$mathfrak{p}$$ -adic stark conjecture when $$mathfrak{p}$$ is archimedean….Pages 91-97
A multiple polynomial general number field sieve….Pages 99-114
Construction of high-rank elliptic curves over ℚ and ℚ( t ) with non-trivial 2-torsion….Pages 115-120
The height on an abelian variety….Pages 121-131
On lattices over number fields….Pages 133-139
Minimum discriminants of primitive sextic fields….Pages 141-143
A new algorithm and refined bounds for extended gcd computation….Pages 145-150
Application of thue equations to computing power integral bases in algebraic number fields….Pages 151-155
Computing S -integral points on elliptic curves….Pages 157-171
Probabilistic computation of the Smith normal form of a sparse integer matrix….Pages 173-186
Ray class field constructions of curves over finite fields with many rational points….Pages 187-195
Computing isogenies in $$mathbb{F}_{2^n } $$ ….Pages 197-212
A computational technique for determining relative class numbers of CM-fields….Pages 213-216
Old and new deterministic factoring algorithms….Pages 217-224
Efficient algorithms for computing the Jacobi symbol….Pages 225-239
The number field database on the World Wide web server http://hasse.mathematik.tu-muenchen.de/….Pages 241-242
An algorithm of subexponential type computing the class group of quadratic orders over principal ideal domains….Pages 243-257
Computational aspects of Kummer theory….Pages 259-272
On integral basis reduction in global function fields….Pages 273-282
Computational aspects of curves of genus at least 2….Pages 283-306
The complexity of approximate optima for greatest common divisor computations….Pages 307-322
Compact representation in real quadratic congruence function fields….Pages 323-336
Discrete logarithms: The effectiveness of the index calculus method….Pages 337-361
How difficult is it to solve a thue equation?….Pages 363-373
Elliptic congruence function fields….Pages 375-384
Algebraic geometry lattices and codes….Pages 385-389
Computing discrete logarithms with the general number field sieve….Pages 391-403