THE SERIAL TEST FOR A NONLINEAR PSEUDORANDOM NUMBER GENERATOR

Let M = 2(w), and G(M) = {1, 3,..., M - 1}. A sequence {y(n)}, y(n) is an element of G(M), is obtained by the formula y(n+1) = a (y) over ba r(n) + b + cy(n) mod M. The sequence {x(n)}, x(n), = y(n)/M, is a sequ ence of pseudorandom numbers of the maximal period length M/2 if and o nly if a + c = 1 (mod 4), b = 2 (mod 4). In this note, the uniformity is investigated by the 2-dimensional serial test for the sequence. We follow closely the method of papers by Eichenauer-Herrmann and Niederr eiter.