Algorithmic Number Theory: First International Symposium, ANTS-I Ithaca, NY, USA, May 6–9, 1994 Proceedings [1 ed.] 3540586911, 9783540586913

Table of contents :
On the difficulty of finding reliable witnesses....Pages 1-16
Density computations for real quadratic 2-class groups....Pages 17-17
Lattice sieving and trial division....Pages 18-27
A subexponential algorithm for discrete logarithms over the rational subgroup of the Jacobians of large genus hyperelliptic curves over finite fields....Pages 28-40
Computing rates of growth of division fields on CM Abelian varieties....Pages 41-41
Algorithms for CM-Fields....Pages 42-42
Schoof's algorithm and isogeny cycles....Pages 43-58
Integer points on rational elliptic curves....Pages 59-59
Counting the number of points on elliptic curves over finite fields of characteristic greater than three....Pages 60-70
Straight-line complexity and integer factorization....Pages 71-79
Decomposition of algebraic functions....Pages 80-92
A new modular interpolation algorithm for factoring multivariate polynomials....Pages 93-107
The function field sieve....Pages 108-121
Heegner point computations....Pages 122-133
Computing the degree of a modular parametrization....Pages 134-142
Galois representations from the cohomology of SL(3,ℤ)....Pages 143-143
An analysis of the Gaussian algorithm for lattice reduction....Pages 144-158
A fast variant of the Gaussian reduction algorithm....Pages 159-159
Reducing lattice bases by means of approximations....Pages 160-168
Analysis of a left-shift binary GCD algorithm....Pages 169-183
The complexity of greatest common divisor computations....Pages 184-193
Explicit formulas for units in certain quadratic number fields....Pages 194-208
Factorization of polynomials over finite fields in subexponential time under GRH....Pages 209-219
On orders of optimal normal basis generators....Pages 220-220
Computing in the jacobian of a plane algebraic curve....Pages 221-233
Under the assumption of the Generalized Riemann Hypothesis verifying the class number belongs to NP ∩ co-NP....Pages 234-247
Calculating the class number of certain Hilbert class fields....Pages 248-248
Efficient checking of computations in number theory....Pages 249-249
Constructing elliptic curves with given group order over large finite fields....Pages 250-263
Computing π(x), M(x) and Ψ(x)....Pages 264-264
On some applications of finitely generated semi-groups....Pages 265-279
Improved incremental prime number sieves....Pages 280-288
Polynomial time algorithms for discrete logarithms and factoring on a quantum computer....Pages 289-289
On dispersion and Markov constants....Pages 290-290
Open problems in number theoretic complexity, II....Pages 291-322