Section: New Results

Study of binary multiplication and dynamical approaches to the integer factorization

Participants : Sylvain Contassot-Vivier, Nazim Fatès.

In the context of a collaboration with Nazim Fatès over dynamical systems we have co-supervised the internship of Raphaël Rieu-Helft (student at the ENS Paris), during June and July 2014. The goal of this internship was to study the relevance of the dynamical systems formalism as an efficient way to express and solve two specific problems. The former one was the queens problem on chessboards of arbitrary size. This goal was to express a solving algorithm of the queens problem under the form of a cellular automaton. The second step was to extend the results obtained for the queens problem to a more complex and computationally expensive problem that is the integer factorization. Two dynamical systems (cellular automata) have been obtained for both problems and their respective efficiencies, either in terms of convergence speed or speed of solution reaching, have been experimentally evaluated.