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...
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 ...
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,...
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...
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...