This book constitutes the refereed proceedings of the 8th International Algorithmic Number Theory Symposium, ANTS 2008, held in Banff, Canada, in May 2008.
The 28 revised full papers presented together with 2 invited papers were carefully reviewed and selected for inclusion in the book. The papers are organized in topical sections on elliptic curves cryptology and generalizations, arithmetic of elliptic curves, integer factorization, K3 surfaces, number fields, point counting, arithmetic of function fields, modular forms, cryptography, and number theory.
Author(s): Ernie Croot, Andrew Granville, Robin Pemantle, Prasad Tetali (auth.), Alfred J. van der Poorten, Andreas Stein (eds.)
Series: Lecture Notes in Computer Science 5011 : Theoretical Computer Science and General Issues
Edition: 1
Publisher: Springer-Verlag Berlin Heidelberg
Year: 2008
Language: English
Pages: 458
Tags: Algorithm Analysis and Problem Complexity; Discrete Mathematics in Computer Science; Data Encryption; Symbolic and Algebraic Manipulation; Number Theory; Algorithms
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 -
