Cryptography & Graphs

• Computational aspects of elliptic and hyperelliptic curves.


• Cryptography in computationally restricted devices.


• Secure electronic voting.


• Privacy-preserving social network data analysis.


• Extremal (di) graphs and eccentric (di) graphs.

   The world is more interconnected every day and needs to have, increasingly, design of optimal interconnection networks. One of the goals is to get the maximum number of nodes given the maximum number of links of a node and the maximum delay in the transmission of information between nodes. The modeling of these networks using digraphs, where nodes and links are represented by vertices and edges of the digraph, respectively, suggests the formulation of certain optimization problems as the degree/diameter problem, and more generally, the study of so-called dense digraphs.

   Our work focuses on modeling these problems in matrix terms and studying them by using combinatorial, algebraic and algorithmic techniques. In addition we also work on the study of so-called eccentric digraphs, because many practical applications arise questions about distances that can be formulated in terms of metric or eccentricities in digraphs.