8. ANTS 2008: Banff, Canada

Alfred J. van der Poorten, Andreas Stein (Eds.): Algorithmic Number Theory, 8th International Symposium, ANTS-VIII, Banff, Canada, May 17-22, 2008, Proceedings. Lecture Notes in Computer Science 5011 Springer 2008, ISBN 978-3-540-79455-4

Invited Papers

Ernie Croot, Andrew Granville, Robin Pemantle, Prasad Tetali:
Running Time Predictions for Factoring Algorithms. 1-36
Reginald E. Sawilla, A. K. Silvester, Hugh C. Williams:
A New Look at an Old Equation. 37-59

Elliptic Curves Cryptology and Generalizations

David Freeman, Peter Stevenhagen, Marco Streng:
Abelian Varieties with Prescribed Embedding Degree. 60-73
Jorge Jiménez Urroz:
Almost Prime Orders of CM Elliptic Curves Modulo p. 74-87
Katsuyuki Takashima:
Efficiently Computable Distortion Maps for Supersingular Curves. 88-101
Koray Karabina, Edlyn Teske:
On Prime-Order Elliptic Curves with Embedding Degrees k = 3, 4, and 6. 102-117

Arithmetic of Elliptic Curves

J. E. Cremona:
Computing in Component Groups of Elliptic Curves. 118-124
Tom Fisher:
Some Improvements to 4-Descent on an Elliptic Curve. 125-138
Thotsaphon Thongjunthug:
Computing a Lower Bound for the Canonical Height on Elliptic Curves over Totally Real Number Fields. 139-152
Richard P. Brent, Pierrick Gaudry, Emmanuel Thomé, Paul Zimmermann:
Faster Multiplication in GF(2)[x]. 153-166

Integer Factorization

Willemien Ekkelkamp:
Predicting the Sieving Effort for the Number Field Sieve. 167-179
Peter L. Montgomery, Alexander Kruppa:
Improved Stage 2 to P±1 Factoring Algorithms. 180-195

K3 Surfaces

Noam D. Elkies:
Shimura Curve Computations Via K3 Surfaces of Néron-Severi Rank at Least 19. 196-211
Andreas-Stephan Elsenhans, Jörg Jahnel:
K3 Surfaces of Picard Rank One and Degree Two. 212-225

Number Fields

John W. Jones, David P. Roberts:
Number Fields Ramified at One Prime. 226-239
Alar Leibak:
An Explicit Construction of Initial Perfect Quadratic Forms over Some Families of Totally Real Number Fields. 240-252
Jonathan W. Sands, Brett A. Tangedal:
Functorial Properties of Stark Units in Multiquadratic Extensions. 253-267
John Voight:
Enumeration of Totally Real Number Fields of Bounded Root Discriminant. 268-281

Point Counting

Juliana Belding, Reinier Bröker, Andreas Enge, Kristin Lauter:
Computing Hilbert Class Polynomials. 282-295
Wouter Castryck, Hendrik Hubrechts, Frederik Vercauteren:
Computing Zeta Functions in Families of Ca, b. 296-311
Kiran S. Kedlaya, Andrew V. Sutherland:
Computing L-Series of Hyperelliptic Curves. 312-326
Remke Kloosterman:
Point Counting on Singular Hypersurfaces. 327-341

Arithmetic of Function Fields

Steven D. Galbraith, Michael Harrison, David J. Mireles Morales:
Efficient Hyperelliptic Arithmetic Using Balanced Representation for Divisors. 342-356
Pieter Rozenhart, Renate Scheidler:
Tabulation of Cubic Function Fields with Imaginary and Unusual Hessian. 357-370

Modular Forms

Lassina Dembélé, Steve Donnelly:
Computing Hilbert Modular Forms over Fields with Nontrivial Class Group. 371-386
Paul E. Gunnells, Dan Yasaki:
Hecke Operators and Hilbert Modular Forms. 387-401

Cryptography

Jeong Han Kim, Ravi Montenegro, Yuval Peres, Prasad Tetali:
A Birthday Paradox for Markov Chains, with an Optimal Bound for Collision in the Pollard Rho Algorithm for Discrete Logarithm. 402-415
Andrew Shallue:
An Improved Multi-set Algorithm for the Dense Subset Sum Problem. 416-429

Number Theory

Edray Goins, Florian Luca, Alain Togbé:
On the Diophantine Equation x²+2^alpha5^beta13^gamma=yⁿ. 430-442
Sami Omar:
Non-vanishing of Dirichlet L-functions at the Central Point. 443-453

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