We present a realization of an LFSM that utilizes an LFSR. This is based on a well-known fact from linear algebra. This structure is used to show that a previous attempt at using a CA in place of an LFSR in constructing a stream cipher did not necessarily increase its security. We also give a general method for checking whether or not a nonlinear filter generator based on an LFSM allows reduction to one that is based on an LFSR and which is vulnerable to Anderson information leakage. Keywords : stream cipher, nonlinear filter model, LFSR, CA, Anderson information leakage.