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The 4-adic complexity of interleaved quaternary sequences of even period with optimal autocorrelation

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Abstract

Su, Yang, Zhou, and Tang proposed several new classes of optimal autocorrelation interleaved quaternary sequences with period 2n from the twin-prime sequence pairs or GMW sequence pairs. In this paper, we determine the 4-adic complexity of these quaternary sequences by using the correlation function. Our results show that the 4-adic complexity of these quaternary sequences exceeds \(\frac{2n-16}{6}\), so that they are safe enough to resist the attack of the rational approximation algorithm.

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Funding

This work is supported by the N.S.F.(11971381, 12371007) of P. R. China and Shaanxi Fundamental Science Research Project for Mathematics and Physics(Grant No. 22JSY007).

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  1. Research Center for Number Theory and Its Applications, Northwest University, Xi’an, 710127, China

    Xiaoyan Jing & Zhefeng Xu

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  1. Xiaoyan Jing
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  2. Zhefeng Xu
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All authors wrote the main manuscript text and reviewed the manuscript.

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Correspondence to Zhefeng Xu.

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Jing, X., Xu, Z. The 4-adic complexity of interleaved quaternary sequences of even period with optimal autocorrelation. Cryptogr. Commun. 16, 613–628 (2024). https://doi.org/10.1007/s12095-023-00690-y

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  • DOI: https://doi.org/10.1007/s12095-023-00690-y

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