Algorithmic Number Theory

Invited Papers.- Running Time Predictions for Factoring Algorithms.- A New Look at an Old Equation.- Elliptic Curves Cryptology and Generalizations.- Abelian Varieties with Prescribed Embedding Degree.- Almost Prime Orders of CM Elliptic Curves Modulo p.- Efficiently Computable Distortion Maps for Supersingular Curves.- On Prime-Order Elliptic Curves with Embedding Degrees k?=?3, 4, and 6.- Arithmetic of Elliptic Curves.- Computing in Component Groups of Elliptic Curves.- Some Improvements to 4-Descent on an Elliptic Curve.- Computing a Lower Bound for the Canonical Height on Elliptic Curves over Totally Real Number Fields.- Faster Multiplication in GF(2)[x].- Integer Factorization.- Predicting the Sieving Effort for the Number Field Sieve.- Improved Stage 2 to P ± 1 Factoring Algorithms.- K3 Surfaces.- Shimura Curve Computations Via K3 Surfaces of Néron-Severi Rank at Least 19.- K3 Surfaces of Picard Rank One and Degree Two.- Number Fields.- Number Fields Ramified at One Prime.- An Explicit Construction of Initial Perfect Quadratic Forms over Some Families of Totally Real Number Fields.- Functorial Properties of Stark Units in Multiquadratic Extensions.- Enumeration of Totally Real Number Fields of Bounded Root Discriminant.- Point Counting.- Computing Hilbert Class Polynomials.- Computing Zeta Functions in Families of C a,b Curves Using Deformation.- Computing L-Series of Hyperelliptic Curves.- Point Counting on Singular Hypersurfaces.- Arithmetic of Function Fields.- Efficient Hyperelliptic Arithmetic Using Balanced Representation for Divisors.- Tabulation of Cubic Function Fields with Imaginary and Unusual Hessian.- Modular Forms.- Computing Hilbert Modular Forms over Fields with Nontrivial Class Group.- Hecke Operators and Hilbert Modular Forms.- Cryptography.- A Birthday Paradox for Markov Chains, with an Optimal Bound for Collision in the Pollard Rho Algorithm for Discrete Logarithm.- An Improved Multi-set Algorithm for the Dense Subset Sum Problem.- Number