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» A Study of the Genus of a Group
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JCT
2006
100views more  JCT 2006»
13 years 7 months ago
Enumeration of unrooted maps of a given genus
Let Ng(f ) denote the number of rooted maps of genus g having f edges. An exact formula for Ng(f ) is known for g = 0 (Tutte, 1963), g = 1 (Arques, 1987), g = 2,3 (Bender and Canf...
Alexander Mednykh, Roman Nedela
JCT
2010
112views more  JCT 2010»
13 years 6 months ago
Annular embeddings of permutations for arbitrary genus
In the symmetric group on a set of size 2n, let P2n denote the conjugacy class of involutions with no fixed points (equivalently, we refer to these as “pairings”, since each ...
I. P. Goulden, William Slofstra
CHES
2004
Springer
148views Cryptology» more  CHES 2004»
14 years 1 months ago
Aspects of Hyperelliptic Curves over Large Prime Fields in Software Implementations
We present an implementation of elliptic curves and of hyperelliptic curves of genus 2 and 3 over prime fields. To achieve a fair comparison between the different types of groups,...
Roberto Maria Avanzi
SMI
2005
IEEE
111views Image Analysis» more  SMI 2005»
14 years 1 months ago
Rational Spherical Splines for Genus Zero Shape Modeling
Traditional approaches for modeling a closed manifold surface with either regular tensor-product or triangular splines (defined over an open planar domain) require decomposing th...
Ying He 0001, Xianfeng Gu, Hong Qin
WAIFI
2010
Springer
158views Mathematics» more  WAIFI 2010»
13 years 5 months ago
On the Efficiency and Security of Pairing-Based Protocols in the Type 1 and Type 4 Settings
Abstract. We focus on the implementation and security aspects of cryptographic protocols that use Type 1 and Type 4 pairings. On the implementation front, we report improved timing...
Sanjit Chatterjee, Darrel Hankerson, Alfred Meneze...