This book constitutes the refereed proceedings of the 9th International Algorithmic Number Theory Symposium, ANTS 2010, held in Nancy, France, in July 2010. The 25 revised full papers presented together with 5 invited papers were carefully reviewed and selected for inclusion in the book. The papers are devoted to algorithmic aspects of number theory, including elementary number theory, algebraic number theory, analytic number theory, geometry of numbers, algebraic geometry, finite fields, and cryptography.
Author(s): Henri Darmon (auth.), Guillaume Hanrot, François Morain, Emmanuel Thomé (eds.)
Series: Lecture Notes in Computer Science 6197 : Theoretical Computer Science and General Issues
Edition: 1
Publisher: Springer-Verlag Berlin Heidelberg
Year: 2010
Language: English
Pages: 397
Tags: Algorithm Analysis and Problem Complexity; Discrete Mathematics in Computer Science; Data Encryption; Symbolic and Algebraic Manipulation; Number Theory; Algorithms
Front Matter....Pages -
Putting the Hodge and Tate Conjectures to the Test....Pages 1-1
Curves of Genus 3 with a Group of Automorphisms Isomorphic to S 3 ....Pages 2-2
Learning with Errors over Rings....Pages 3-3
Lattices and Spherical Designs....Pages 4-5
Fixed Points for Discrete Logarithms....Pages 6-15
Explicit Coleman Integration for Hyperelliptic Curves....Pages 16-31
Smallest Reduction Matrix of Binary Quadratic Forms....Pages 32-49
Practical Improvements to Class Group and Regulator Computation of Real Quadratic Fields....Pages 50-65
On the Use of the Negation Map in the Pollard Rho Method....Pages 66-82
An O ( M ( n ) log n ) Algorithm for the Jacobi Symbol....Pages 83-95
New Families of ECM Curves for Cunningham Numbers....Pages 96-109
Visualizing Elements of Sha[3] in Genus 2 Jacobians....Pages 110-125
On Weil Polynomials of K 3 Surfaces....Pages 126-141
Class Invariants by the CRT Method....Pages 142-156
Short Bases of Lattices over Number Fields....Pages 157-173
On the Complexity of the Montes Ideal Factorization Algorithm....Pages 174-185
Congruent Number Theta Coefficients to 10 12 ....Pages 186-200
Pairing the Volcano....Pages 201-218
A Subexponential Algorithm for Evaluating Large Degree Isogenies....Pages 219-233
Huff’s Model for Elliptic Curves....Pages 234-250
Efficient Pairing Computation with Theta Functions....Pages 251-269
Small-Span Characteristic Polynomials of Integer Symmetric Matrices....Pages 270-284
Decomposition Attack for the Jacobian of a Hyperelliptic Curve over an Extension Field....Pages 285-300
Factoring Polynomials over Local Fields II....Pages 301-315
On a Problem of Hajdu and Tengely....Pages 316-330
Sieving for Pseudosquares and Pseudocubes in Parallel Using Doubly-Focused Enumeration and Wheel Datastructures....Pages 331-339
On the Extremality of an 80-Dimensional Lattice....Pages 340-356
Computing Automorphic Forms on Shimura Curves over Fields with Arbitrary Class Number....Pages 357-371
Improved Primality Proving with Eisenstein Pseudocubes....Pages 372-384
Hyperbolic Tessellations Associated to Bianchi Groups....Pages 385-396
Back Matter....Pages -
