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ANTS
2008
Springer
93views Algorithms» more  ANTS 2008»
11 years 1 months ago
Faster Multiplication in GF(2)[x]
Abstract. In this paper, we discuss an implementation of various algorithms for multiplying polynomials in GF(2)[x]: variants of the window methods, Karatsuba's, Toom-Cook...
Richard P. Brent, Pierrick Gaudry, Emmanuel Thom&e...
ANTS
2008
Springer
111views Algorithms» more  ANTS 2008»
11 years 1 months ago
Computing L-Series of Hyperelliptic Curves
We discuss the computation of coefficients of the L-series associated to a hyperelliptic curve over Q of genus at most 3, using point counting, generic group algorithms, and p-adic...
Kiran S. Kedlaya, Andrew V. Sutherland
ANTS
2008
Springer
133views Algorithms» more  ANTS 2008»
11 years 1 months ago
Efficient Hyperelliptic Arithmetic Using Balanced Representation for Divisors
We discuss arithmetic in the Jacobian of a hyperelliptic curve C of genus g. The traditional approach is to fix a point P C and represent divisor classes in the form E - d(P) wher...
Steven D. Galbraith, Michael Harrison, David J. Mi...
ANTS
2008
Springer
115views Algorithms» more  ANTS 2008»
11 years 1 months ago
Computing Hilbert Modular Forms over Fields with Nontrivial Class Group
In previous work, the first author developed an algorithm for the computation of Hilbert modular forms. In this paper, we extend this to all totally real number fields of even degr...
Lassina Dembélé, Steve Donnelly
ANTS
2008
Springer
105views Algorithms» more  ANTS 2008»
11 years 1 months ago
Number Fields Ramified at One Prime
John W. Jones, David P. Roberts
ANTS
2008
Springer
110views Algorithms» more  ANTS 2008»
11 years 1 months ago
Computing Hilbert Class Polynomials
We present and analyze two algorithms for computing the Hilbert class polynomial HD. The first is a p-adic lifting algorithm for inert primes p in the order of discriminant D < ...
Juliana Belding, Reinier Bröker, Andreas Enge...
ANTS
2008
Springer
83views Algorithms» more  ANTS 2008»
11 years 1 months ago
Hecke Operators and Hilbert Modular Forms
Paul E. Gunnells, Dan Yasaki
ANTS
2008
Springer
103views Algorithms» more  ANTS 2008»
11 years 1 months ago
On Prime-Order Elliptic Curves with Embedding Degrees k = 3, 4, and 6
Abstract. We further analyze the solutions to the Diophantine equations from which prime-order elliptic curves of embedding degrees k = 3, 4 or 6 (MNT curves) may be obtained. We g...
Koray Karabina, Edlyn Teske
ANTS
2008
Springer
83views Algorithms» more  ANTS 2008»
11 years 1 months ago
Enumeration of Totally Real Number Fields of Bounded Root Discriminant
We enumerate all totally real number fields F with root discriminant F 14. There are 1229 such fields, each with degree [F : Q] 9. In this article, we consider the following prob...
John Voight
ANTS
2008
Springer
67views Algorithms» more  ANTS 2008»
11 years 1 months ago
Running Time Predictions for Factoring Algorithms
Ernie Croot, Andrew Granville, Robin Pemantle, Pra...
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