Algorithmic Number Theory: 8th International Symposium, ANTS-VIII Banff, Canada, May 17-22, 2008 Proceedings

Front Matter....Pages -
Running Time Predictions for Factoring Algorithms....Pages 1-36
A New Look at an Old Equation....Pages 37-59
Abelian Varieties with Prescribed Embedding Degree....Pages 60-73
Almost Prime Orders of CM Elliptic Curves Modulo p ....Pages 74-87
Efficiently Computable Distortion Maps for Supersingular Curves....Pages 88-101
On Prime-Order Elliptic Curves with Embedding Degrees k  = 3, 4, and 6....Pages 102-117
Computing in Component Groups of Elliptic Curves....Pages 118-124
Some Improvements to 4-Descent on an Elliptic Curve....Pages 125-138
Computing a Lower Bound for the Canonical Height on Elliptic Curves over Totally Real Number Fields....Pages 139-152
Faster Multiplication in GF(2)[ x ]....Pages 153-166
Predicting the Sieving Effort for the Number Field Sieve....Pages 167-179
Improved Stage 2 to P ± 1 Factoring Algorithms....Pages 180-195
Shimura Curve Computations Via K3 Surfaces of Néron–Severi Rank at Least 19....Pages 196-211
K3 Surfaces of Picard Rank One and Degree Two....Pages 212-225
Number Fields Ramified at One Prime....Pages 226-239
An Explicit Construction of Initial Perfect Quadratic Forms over Some Families of Totally Real Number Fields....Pages 240-252
Functorial Properties of Stark Units in Multiquadratic Extensions....Pages 253-267
Enumeration of Totally Real Number Fields of Bounded Root Discriminant....Pages 268-281
Computing Hilbert Class Polynomials....Pages 282-295
Computing Zeta Functions in Families of C a,b Curves Using Deformation....Pages 296-311
Computing L -Series of Hyperelliptic Curves....Pages 312-326
Point Counting on Singular Hypersurfaces....Pages 327-341
Efficient Hyperelliptic Arithmetic Using Balanced Representation for Divisors....Pages 342-356
Tabulation of Cubic Function Fields with Imaginary and Unusual Hessian....Pages 357-370
Computing Hilbert Modular Forms over Fields with Nontrivial Class Group....Pages 371-386
Hecke Operators and Hilbert Modular Forms....Pages 387-401
A Birthday Paradox for Markov Chains, with an Optimal Bound for Collision in the Pollard Rho Algorithm for Discrete Logarithm....Pages 402-415
An Improved Multi-set Algorithm for the Dense Subset Sum Problem....Pages 416-429
On the Diophantine Equation x 2  + 2 α 5 β 13 γ  =  y n ....Pages 430-442
Non-vanishing of Dirichlet L -functions at the Central Point....Pages 443-453
Back Matter....Pages -