A New Upper Bound on the Order of Affine Sub-families of NFSRs

LIU Junying · ZHENG Qunxiong · LIN Dongdai

Journal of Systems Science & Complexity ›› 2020, Vol. 33 ›› Issue (1) : 196-214.

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Journal of Systems Science & Complexity ›› 2020, Vol. 33 ›› Issue (1) : 196-214. DOI: 10.1007/s11424-019-8072-9

A New Upper Bound on the Order of Affine Sub-families of NFSRs

  • LIU Junying · ZHENG Qunxiong · LIN Dongdai
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Abstract

Nonlinear feedback shift registers (NFSRs) are widely used as building blocks in the design of stream ciphers. Let NFSR(f) be an NFSR with the characteristic function f and let G(f) be the set of output sequences of NFSR(f). For a given NFSR(f), if there exists an affine Boolean function l such that G(l) 伜 G(f), then G(l) is called an affine sub-family of NFSR(f). In this paper, by skillfully combining previous ideas, the authors give a new upper bound on the order of affine sub-families of NFSR(f). Compared with the four known bounds, the bound is better than three of them, and in some cases is also better than the rest one.

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LIU Junying · ZHENG Qunxiong · LIN Dongdai. A New Upper Bound on the Order of Affine Sub-families of NFSRs. Journal of Systems Science and Complexity, 2020, 33(1): 196-214 https://doi.org/10.1007/s11424-019-8072-9
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