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Three classes of balanced vectorial semi-bent functions

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Abstract

Semi-bent functions play an important role in symmetric ciphers and sequence designs. So far, there are few studies related to the construction of vectorial semi-bent functions even though lots of work has been done on single-output semi-bent functions. In this paper, three classes of balanced vectorial semi-bent functions are presented with varying cryptographic properties. The classes denoted \({{\mathcal {D}}}{{\mathcal {C}}}\) and \({{\mathcal {D}}}{{\mathcal {S}}}\) are constructed using disjoint codes and disjoint spectra functions, respectively. The former class has a useful provable property that its component functions do not admit linear structures. It is shown that the number of output bits of the constructed n-variable \({{\mathcal {D}}}{{\mathcal {C}}}\) and \({{\mathcal {D}}}{{\mathcal {S}}}\) vectorial functions can respectively reach \((n+1)/2\) and n/3. In addition, a construction method of semi-bent functions from \({\mathbb {F}}_2^{3n} \rightarrow {\mathbb {F}}_2^n\) by using almost bent (AB) functions on \({\mathbb {F}}_2^n\) is given.

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Acknowledgements

WeiGuo Zhang is supported by the National Natural Science Foundation of China (No. 61972303). Enes Pasalic is supported in part by the Slovenian Research Agency (research program P1-0404 and research projects J1-9108, J1-1694, N1-0159, J1-2451).

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Authors and Affiliations

  1. State Key Laboratory of Integrated Services Networks, Xidian University, Xi’an, 710071, China

    WeiGuo Zhang & YuJuan Sun

  2. State Key Laboratory of Cryptology, P.O. Box 5159, Beijing, 100878, China

    WeiGuo Zhang & YuJuan Sun

  3. University of Primorska, FAMNIT & IAM, Koper, Slovenia

    Enes Pasalic

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  1. WeiGuo Zhang
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  2. YuJuan Sun
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Correspondence to WeiGuo Zhang.

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Communicated by C. Carlet.

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Zhang, W., Sun, Y. & Pasalic, E. Three classes of balanced vectorial semi-bent functions. Des. Codes Cryptogr. 89, 2697–2714 (2021). https://doi.org/10.1007/s10623-021-00943-y

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