Algorithmic Number Theory

ANTS-IX was the ninth edition of the biennial International Symposium on Algorithmic Number Theory. The ?rst edition of this symposium was held at Cornell University in 1994. ANTS-IX was held July 19-23, 2010 at INRIA in Nancy, France. The ANTS-IX Program Committee consisted of 12 members whose names are listed on the next page. The selection of the accepted papers among the submissions was made from mid-January to end of March 2010. Each paper was thoroughly reviewed by at least two experts, including a Program Committee member. The Program Committee selected 25 high-quality articles, which are excellent representatives of the current state of the art in various areas of - gorithmic number theory. The Selfridge Prize in computational number theory was awarded to the authors of the best contributed paper presented at the c- ference. We gratefully thank the authors of all submitted papers for their hard work which made the selection of a varied program possible. We also thank the authors of the accepted papers for their cooperation in the timely production of the revised versions. Each submitted paper was presented by one of its co-authors at the c- ference. Besides contributed papers, the conference included ?ve invited talks by Henri Darmon (McGill University), Jean-Fran cois Mestre (Universit eParis 7), Gabriele Nebe (RWTH Aachen), Carl Pomerance (Dartmouth College), and Oded Regev (Tel-Aviv University).

Klappentext

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.

Inhalt
Invited papers.- Putting the Hodge and Tate Conjectures to the Test.- Curves of Genus 3 with a Group of Automorphisms Isomorphic to S3.- Learning with Errors over Rings.- Lattices and Spherical Designs.- Fixed Points for Discrete Logarithms.- Contributed papers.- Explicit Coleman Integration for Hyperelliptic Curves.- Smallest Reduction Matrix of Binary Quadratic Forms.- Practical Improvements to Class Group and Regulator Computation of Real Quadratic Fields.- On the Use of the Negation Map in the Pollard Rho Method.- An O(M(n) logn) Algorithm for the Jacobi Symbol.- New Families of ECM Curves for Cunningham Numbers.- Visualizing Elements of Sha[3] in Genus 2 Jacobians.- On Weil Polynomials of K3 Surfaces.- Class Invariants by the CRT Method.- Short Bases of Lattices over Number Fields.- On the Complexity of the Montes Ideal Factorization Algorithm.- Congruent Number Theta Coefficients to 1012.- Pairing the Volcano.- A Subexponential Algorithm for Evaluating Large Degree Isogenies.- Huff's Model for Elliptic Curves.- Efficient Pairing Computation with Theta Functions.- Small-Span Characteristic Polynomials of Integer Symmetric Matrices.- Decomposition Attack for the Jacobian of a Hyperelliptic Curve over an Extension Field.- Factoring Polynomials over Local Fields II.- On a Problem of Hajdu and Tengely.- Sieving for Pseudosquares and Pseudocubes in Parallel Using Doubly-Focused Enumeration and Wheel Datastructures.- On the Extremality of an 80-Dimensional Lattice.- Computing Automorphic Forms on Shimura Curves over Fields with Arbitrary Class Number.- Improved Primality Proving with Eisenstein Pseudocubes.- Hyperbolic Tessellations Associated to Bianchi Groups.