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

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.

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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.

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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.

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