The Properties of the FCSR-Based Self-Shrinking Sequence

摘要

In the construction of a no-linear key-stream generator, self-shrinking is an established way of getting the binary pseudo-random periodic sequences in cryptography design. In this paper, using the theoretical analysis, we mainly study the self-shrinking sequence based on the 1-sequence, and the theoretical results reflect its good cryptography properties accurately, such that it has the last period T = p~e(p - 1)/2 when T is an odd number, and the expected value of its autocorrelation belongs to {0,1/T} and the variance is O(T/ln~4 T). Furthermore, we find that the 2-adic complexity of the self-shrinking sequence based on the 1-sequence is large enough to resist the Rational Approximation attack.