Generation of Binary Sequences with Controllable Complexity and Ideal r-Tupel Distribution

A key stream generator is analyzed which consists of a single linear feedback shift register (LFSR) with a primitive connection polynomial and a nonlinear feedforward logic. It is shown. how, for arbitrary integers n and r and a binary LFSR of length L = n • r the linear complexity of the generated keystream can be determined for a large class of nonlinear feedforward logics. Moreover, a simple condition imposed on these logics ensures an ideal r-tupel distribution for these keystreams. Practically useful solutions exist where the keystream has linear complexity n • rn−1 together with an ideal r-tupel distribution.