Poorten A.J. van der, Stein A. (Eds.) Algorithmic Number Theory: 8th International Symposium, ANTS-VIII

Springer, 2008. — x, 454 p. — (Lecture Notes in Computer Science, 5011). — ISBN 3-540-79455-7, 978-3-540-79455-4, 978-3-540-79456-1.This book constitutes the refereed proceedings of the 8th International Algorithmic Number Theory Symposium, ANTS 2008, held in Banff, Canada, in May 2008. The conference included four invited talks, by Johannes Buchmann (TU Darmstadt), Andrew Granville (Université de Montréal), François Morain (École Polytechnique), and Hugh Williams (University of Calgary), a poster session, and 28 contributed talks in appropriate areas of number theory.
Each submitted paper was reviewed by at least two experts external to the Program Committee; the selection was made by the committee on the basis of those recommendations. The Selfridge Prize in computational number theory was awarded to the authors of the best contributed paper presented at the conference. The participants in the conference gratefully acknowledge the contribution made by the sponsors of the meeting.
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.Invited Papers
Running Time Predictions for Factoring Algorithms
Ernie Croot, Andrew Granville, Robin Pemantle, and Prasad Tetali
A New Look at an Old Equation
R.E. Sawilla, A.K. Silvester, and H.C. Williams
Elliptic Curves Cryptology and Generalizations
Abelian Varieties with Prescribed Embedding Degree
David Freeman, Peter Stevenhagen, and Marco Streng
Almost Prime Orders of CM Elliptic Curves Modulo p
Jorge Jiménez Urroz
Effciently Computable Distortion Maps for Supersingular Curves
Katsuyuki Takashima
On Prime-Order Elliptic Curves with Embedding Degrees k = 3, 4, and 6
Koray Karabina and Edlyn Teske
Arithmetic of Elliptic Curves
Computing in Component Groups of Elliptic Curves
J.E. Cremona
Some Improvements to 4-Descent on an Elliptic Curve
Tom Fisher
Computing a Lower Bound for the Canonical Height on Elliptic Curves over Totally Real Number Fields
Thotsaphon Thongjunthug
Faster Multiplication in GF(2)[x]
Richard P. Brent, Pierrick Gaudry, Emmanuel Thomé, and Paul Zimmermann
Integer Factorization
Predicting the Sieving Effort for the Number Field Sieve
Willemien Ekkelkamp
Improved Stage 2 to P±1 Factoring Algorithms
Peter L. Montgomery and Alexander Kruppa
K3 Surfaces
Shimura Curve Computations Via K3 Surfaces of Néron–Severi Rank at Least 19
Noam D. Elkies
K3 Surfaces of Picard Rank One and Degree Two
Andreas-Stephan Elsenhans and Jörg Jahnel
Number Fields
Number Fields Ramified at One Prime
John W. Jones and David P. Roberts
An Explicit Construction of Initial Perfect Quadratic Forms over Some Families of Totally Real Number Fields
Alar Leibak
Functorial Properties of Stark Units in Multiquadratic Extensions
Jonathan W. Sands and Brett A. Tangedal
Enumeration of Totally Real Number Fields of Bounded Root Discriminant
John Voight
Point Counting
Computing Hilbert Class Polynomials
Juliana Belding, Reinier Bröker, Andreas Enge, and Kristin Lauter
Computing Zeta Functions in Families of Ca,b Curves Using Deformation
Wouter Castryck, Hendrik Hubrechts, and Frederik Vercauteren
Computing L-Series of Hyperelliptic Curves
Kiran S. Kedlaya and Andrew V. Sutherland
Point Counting on Singular Hypersurfaces
Remke Kloosterman
Arithmetic of Function Fields
Effcient Hyperelliptic Arithmetic Using Balanced Representation for Divisors
Steven D. Galbraith, Michael Harrison, and David J. Mireles Morales
Tabulation of Cubic Function Fields with Imaginary and Unusual Hessian
Pieter Rozenhart and Renate Scheidler
Modular Forms
Computing Hilbert Modular Forms over Fields with Nontrivial Class Group
Lassina Dembélé and Steve Donnelly
Hecke Operators and Hilbert Modular Forms
Paul E. Gunnells and Dan Yasaki
Cryptography
A Birthday Paradox for Markov Chains, with an Optimal Bound for Collision in the Pollard Rho Algorithm for Discrete Logarithm
Jeong Han Kim, Ravi Montenegro, Yuval Peres, and Prasad Tetali
An Improved Multi-set Algorithm for the Dense Subset Sum Problem
Andrew Shallue
Number Theory
On the Diophantine Equation x² + 2ᵅ5ᵝ13ᵞ = yⁿ
Edray Goins, Florian Luca, and Alain Togbé
Non-vanishing of Dirichlet L-functions at the Central Point
Sami Omar
Author IndexTrue PDF