Algorithmic Number Theory: 7th International Symposium, ANTS-VII, Berlin, Germany, July 23-28, 2006. Proceedings

Front Matter....Pages -
Computing Pro- P Galois Groups....Pages 1-10
The Elliptic Curve Database for Conductors to 130000....Pages 11-29
On the Computation of the Coefficients of a Modular Form....Pages 30-39
Cohen–Lenstra Heuristics of Quadratic Number Fields....Pages 40-55
An Algorithm for Computing p -Class Groups of Abelian Number Fields....Pages 56-71
Computation of Locally Free Class Groups....Pages 72-86
Numerical Results on Class Groups of Imaginary Quadratic Fields....Pages 87-101
Cyclic Polynomials Arising from Kummer Theory of Norm Algebraic Tori....Pages 102-113
The Totally Real Primitive Number Fields of Discriminant at Most 10 9 ....Pages 114-123
A Modular Method for Computing the Splitting Field of a Polynomial....Pages 124-140
On the Density of Sums of Three Cubes....Pages 141-155
The Mertens Conjecture Revisited....Pages 156-167
Fast Bounds on the Distribution of Smooth Numbers....Pages 168-181
Use of Extended Euclidean Algorithm in Solving a System of Linear Diophantine Equations with Bounded Variables....Pages 182-192
The Pseudosquares Prime Sieve....Pages 193-207
Doubly-Focused Enumeration of Pseudosquares and Pseudocubes....Pages 208-221
Practical Lattice Basis Sampling Reduction....Pages 222-237
LLL on the Average....Pages 238-256
On the Randomness of Bits Generated by Sufficiently Smooth Functions....Pages 257-274
Computing a Lower Bound for the Canonical Height on Elliptic Curves over ℚ....Pages 275-286
Points of Low Height on Elliptic Curves and Surfaces I: Elliptic Surfaces over  ${\mathbb P}^1$ with Small  d ....Pages 287-301
Shimura Curves for Level-3 Subgroups of the (2,3,7) Triangle Group, and Some Other Examples....Pages 302-316
The Asymptotics of Points of Bounded Height on Diagonal Cubic and Quartic Threefolds....Pages 317-332
Testing Equivalence of Ternary Cubics....Pages 333-345
Classification of Genus 3 Curves in Special Strata of the Moduli Space....Pages 346-360
Heegner Point Computations Via Numerical p -Adic Integration....Pages 361-376
Symmetric Powers of Elliptic Curve L-Functions....Pages 377-392
Determined Sequences, Continued Fractions, and Hyperelliptic Curves....Pages 393-405
Computing CM Points on Shimura Curves Arising from Cocompact Arithmetic Triangle Groups....Pages 406-420
Arithmetic of Generalized Jacobians....Pages 421-435
Hidden Pairings and Trapdoor DDH Groups....Pages 436-451
Constructing Pairing-Friendly Elliptic Curves with Embedding Degree 10....Pages 452-465
Fast Bilinear Maps from the Tate-Lichtenbaum Pairing on Hyperelliptic Curves....Pages 466-479
High Security Pairing-Based Cryptography Revisited....Pages 480-494
Efficiently Computable Endomorphisms for Hyperelliptic Curves....Pages 495-509
Construction of Rational Points on Elliptic Curves over Finite Fields....Pages 510-524
20 Years of ECM....Pages 525-542
An Index Calculus Algorithm for Plane Curves of Small Degree....Pages 543-557
Signature Calculus and Discrete Logarithm Problems....Pages 558-572
Spectral Analysis of Pollard Rho Collisions....Pages 573-581
Hard Instances of the Constrained Discrete Logarithm Problem....Pages 582-598
Back Matter....Pages -