d-Functions in V _k (F₂) and self-decimation of m-sequences

Abstract

With the purpose of generating, by the help of a single clock-controlled LFSR, a large class of binary sequences strong enough for cryptographic application, an extension class of key-specifiable transfer functions is proposed and analyzed. When tapped as feedforward networks to the LFSR under consideration, these functions will control the stepping of the latter in such a way that its output signals will be decimated pseudo-randomly at a pre-assigned rate. The decimation rate and the length of the LFSR are then suitably selected so that the resulting sequence will have, among others, a large prime period and a linear complexity comparable in order of magnitude to the period. Some conclusions concerning the average and maximal implementable decimation rates are also given.