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A Fibonacci View on the Galois NFSR Used in Trivium

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Abstract

Trivium is an international standard of lightweight stream ciphers (ISO/IEC 29192-3: 2012). In this paper, the Trivium-like NFSRs, a class of Galois NFSRs generalized from the Galois NFSR of Trivium, are studied from the perspective of Fibonacci NFSRs. It is shown that an n-stage Trivium-like NFSR cannot be equivalent to an n-stage Fibonacci NFSR, which is proved by showing the existence of “collision initial states”. As an intermediate conclusion, a necessary and sufficient condition for a kind of linear degeneracy of a Trivium-like NFSR is obtained from the persepective of interleaved sequences. Moreover, the smallest stage number of a Fibonacci NFSR that can generate all the output sequences of an n-stage Trivium-like NFSR is shown to be greater than n − 7 and this value is no less than 371 = 287 + min{93, 84, 111} specifically for the 288-stage Galois NFSR used in Trivium. These results contradict the existence of a equivalent Fibonacci model of Trivium NFSR of small stage, which implies that Trivium algorithm possesses a fair degree of immunity against “structure attack”.

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Authors and Affiliations

  1. PLA Strategic Support Force Information Engineering University, Zhengzhou, 450001, China

    Hongyu Wang, Qunxiong Zheng & Wenfeng Qi

Authors
  1. Hongyu Wang
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  2. Qunxiong Zheng
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  3. Wenfeng Qi
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Correspondence to Qunxiong Zheng.

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The authors declare no conflict of interest.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant Nos. 12371526, 61872383, 61802430, and 62202494.

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Wang, H., Zheng, Q. & Qi, W. A Fibonacci View on the Galois NFSR Used in Trivium. J Syst Sci Complex 37, 1326–1350 (2024). https://doi.org/10.1007/s11424-024-2295-0

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  • DOI: https://doi.org/10.1007/s11424-024-2295-0

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