Algorithmic Number Theory

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.