Abstract— An algorithm is proposed for the efficient multiplication of a vector by an n x n MDS matrix defined on Fq or by its inverse. The algorithm is based on the multiplication of two polynomials modulo a polynomial of degree n Reed-Solomon code generator and has complexity O(nlog2log2(nlog2q)). The algorithm only needs to store n values of the Fq field for the multiplication of a vector by an n x n MDS matrix and 2n values for the multiplication of the vector by the inverse matrix.