Algorithmic Number Theory: Second International Symposium, ANTS-II Talence, France, May 18–23, 1996 Proceedings [1 ed.] 3540615814, 9783540615811

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