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 l-sequence, and the theoretical results reflect its good cryptography properties accurately, such that it has the last period T = pe(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/ln4T). Furthermore, we find that the 2-adic complexity of the self-shrinking sequence based on the l-sequence is large enough to resist the Rational Approximation attack.

This paper studies the 2-adic complexity of the self-shrinking sequence under the relationship between 2-adic integers and binary sequences. Based on the linear complexity and the number of the sequences which have the same connection integer, we conclude that the 2-adic complexity of the self-shrinking sequence constructed by a binary m-sequence of order n has a lower bound 2n-2-1. Furthermore, it is shown that its 2-adic complexity has a bigger lower bound under some circumstances.