3 papers
math.DS2009
Dynamical Systems of Simplices in Dimension 2 or 3
Gerald Bourgeois, Sebastien Orange
Let T_0=(A_0,..,A_d) be a d-simplex, G_0 its centroid, S its circumsphere, O the center of S. Let (B_i) be the points where S intersects the lines (G_0A_i), T_1 the d-simplex (B_1,…
math.RA2007
Algebraic systems of matrices and Grobner basis
Gerald Bourgeois
One studies a particular algebraic system where the unknowns are matrices. We solve this system according to the parameters values thanks to the theory of Grobner basis.
cs.CR2006
Attaque algebrique de NTRU a l'aide des vecteurs de Witt
Gerald Bourgeois
One improves an algebraic attack of NTRU due to Silverman, Smart and Vercauteren; the latter considered the first 2 bits of a Witt vector attached to the research of the secret key…