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ANTS
2008
Springer
106views Algorithms» more  ANTS 2008»
13 years 9 months ago
Computing in Component Groups of Elliptic Curves
Let K be a p-adic local field and E an elliptic curve defined over K. The component group of E is the group E(K)/E0(K), where E0(K) denotes the subgroup of points of good reduction...
J. E. Cremona
ANTS
2008
Springer
103views Algorithms» more  ANTS 2008»
13 years 9 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
133views Algorithms» more  ANTS 2008»
13 years 9 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...
ANTSW
2008
Springer
13 years 8 months ago
Rigorous Analyses for the Combination of Ant Colony Optimization and Local Search
Abstract. Ant colony optimization (ACO) is a metaheuristic that produces good results for a wide range of combinatorial optimization problems. Often such successful applications us...
Frank Neumann, Dirk Sudholt, Carsten Witt
ANTS
2008
Springer
115views Algorithms» more  ANTS 2008»
13 years 9 months ago
Abelian Varieties with Prescribed Embedding Degree
We present an algorithm that, on input of a CM-field K, an integer k 1, and a prime r 1 mod k, constructs a q-Weil number OK corresponding to an ordinary, simple abelian variety ...
David Freeman, Peter Stevenhagen, Marco Streng