On characteristics of a three-stage key generator with an alternating step modified with key generator "Stop-Forward"

The generator G named in the title of the paper consists of five binary linear feedback shift registers (LFSRs) of maximal periods divided into three cascades. The first cascade is a filter generator X based on a LFSR of a length n. Each of the second and third cascades consists of two LFSRs Y, Z and U, V of lengths m, ^ and r, p respectively. The registers Y, Z are controlled by the output x of the filter generator X, the registers U, V - by the sum y ф z of the outputs y,z of the registers Y, Z respectively. The control is made in such a way: if a controlling signal is 1, then one of the controlled registers shifts but another does not change its state; otherwise their behaviour is just opposite. The output of the generator G is the sum u ф v of the outputs of registers U, V. It is shown, that if the numbers n, m, r, p are relatively prime, then the period t of the sequence produced by G equals the product of the (maximal) periods of its registers. In the cyclic group of order t of the generator G, there is a linear subgroup of order (2^r - 1)(2^P - 1). Local exponents i, (p +1) - exp Г of the mixing digraph Г of G are equal to n + 2 if i G {1,..., n}, to max(m, +1 if i G {n + 1,..., n + m+and to max(r, p) if i G {n+m+^ + 1,... ,p +1} where p = n+m+^+r+p. Consequently, for G the length of "free running" is recommended to be at least max{n+2, max(m, ^) + 1, max(r, p)}.

Keywords

Authors

References