This book constitutes the refereed proceedings of the 7th International Algorithmic Number Theory Symposium, ANTS 2006, held in Berlin, Germany in July 2006.
The 37 revised full papers presented together with 4 invited papers were carefully reviewed and selected for inclusion in the book. The papers are organized in topical sections on algebraic number theory, analytic and elementary number theory, lattices, curves and varieties over fields of characteristic zero, curves over finite fields and applications, and discrete logarithms.
Author(s): Nigel Boston, Harris Nover (auth.), Florian Hess, Sebastian Pauli, Michael Pohst (eds.)
Series: Lecture Notes in Computer Science 4076
Edition: 1
Publisher: Springer-Verlag Berlin Heidelberg
Year: 2006
Language: English
Pages: 599
Tags: Algorithm Analysis and Problem Complexity; Discrete Mathematics in Computer Science; Data Encryption; Symbolic and Algebraic Manipulation; Number Theory; Algorithms
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 -
