Abstract: A new class of variable length, nonlinear feedback shift registers (NLFSR's) is disclosed that uses data-dependent dynamically allocated taps to filter digital information reversibly, flexibly, and rapidly. This class of NLFSR's has been succinctly realized in terms of a multi-parameter family of nonlinear, discrete difference equations that operate on digital data of variable length. Each individual NLFSR is characterized by a collection of integer `parameter functions` and `boundary condition functions` denoted .PI..sub.T for an integer T.gtoreq.1. A concrete description of an exemplary set .PI..sub.T is given in the text. Given an input sequence to the NLFSR, the final output sequence is another sequence defined by the values of the parameter and boundary condition functions, and a new reversible (or invertible) nonlinear mathematical rule that transforms a sequence of integers into a different sequence of integers.