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ANTS
2010
Springer
268views Algorithms» more  ANTS 2010»
15 years 8 months ago
Lattices and Spherical Designs
Gabriele Nebe
ANTS
2010
Springer
250views Algorithms» more  ANTS 2010»
15 years 8 months ago
A Subexponential Algorithm for Evaluating Large Degree Isogenies
An isogeny between elliptic curves is an algebraic morphism which is a group homomorphism. Many applications in cryptography require evaluating large degree isogenies between ellip...
David Jao, Vladimir Soukharev
ANTS
2010
Springer
246views Algorithms» more  ANTS 2010»
15 years 8 months ago
Visualizing Elements of Sha[3] in Genus 2 Jacobians
Abstract. Mazur proved that any element ξ of order three in the Shafarevich-Tate group of an elliptic curve E over a number field k can be made visible in an abelian surface A in...
Nils Bruin, Sander R. Dahmen
ANTS
2010
Springer
246views Algorithms» more  ANTS 2010»
15 years 8 months ago
On the Extremality of an 80-Dimensional Lattice
Abstract. We show that a specific even unimodular lattice of dimension 80, first investigated by Schulze-Pillot and others, is extremal (i.e., the minimal nonzero norm is 8). Thi...
Damien Stehlé, Mark Watkins
ANTS
2010
Springer
291views Algorithms» more  ANTS 2010»
15 years 8 months ago
Fixed Points for Discrete Logarithms
: We establish a conjecture of Brizolis that for every prime p > 3 there is a primitive root r and an integer t in the interval [1, p − 1] with logr t = t. Here, logr is the d...
Mariana Levin, Carl Pomerance, K. Soundararajan