The Properties of the FCSR-Based Self-Shrinking Sequence

Huijuan WANG  Qiaoyan WEN  Jie ZHANG  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E96-A   No.2   pp.626-634
Publication Date: 2013/02/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E96.A.626
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Cryptography and Information Security
Keyword: 
FCSR,  self-shrinking,  period,  autocorrelation,  complexity,  

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Summary: 
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.