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Cryptographic functions with interesting properties from CCZ-equivalence

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Abstract

In the last decades, because of their significantly important applications, a large number of papers were devoted to constructing cryptographic functions with interesting properties by various methods. In this paper, our motivation is to construct more families of such functions up to EA-equivalence (extended affine equivalence) by using the properties of CCZ-equivalence (Carlet-Charpin-Zinoviev equivalence). To this end, we present two CCZ-equivalent forms, and show their applications on bent functions, vectorial functions having the maximum number of bent components, and vectorial plateaued functions with single amplitude, respectively.

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Acknowledgements

The authors are very grateful to the Editor-in-Chief Claude Carlet, the Associate Editor, the reviewers and another two anonymous experts for their valuable comments and suggestions that improved the presentation and quality of this paper highly.

Funding

This work was supported in part by the National Key Research and Development Program of China under Grant 2019YFB2101703; in part by the National Natural Science Foundation of China under Grants 61972258, 62272107 and U19A2066; in part by the Innovation Action Plan of Shanghai Science and Technology under Grants 20511102200 and 21511102200; in part by the Key Research and Development Program of Guangdong Province under Grant 2020B0101090001, in part by Scientific Research Fund of Hunan Provincial Education Department under Grant 19B485, and in part by Open Research Program of Shanghai Key Lab of Intelligent Information Processing under Grant IIPL201902.

Author information

Authors and Affiliations

  1. Institute of Statistics and Applied Mathematics, Anhui University of Finance and Economics, Bengbu, Anhui, 233030, China

    Yanjun Li

  2. Shanghai Key Laboratory of Intelligent Information Processing, School of Computer Science, Fudan University, Shanghai, 200433, China

    Haibin Kan

  3. Shanghai Engineering Research Center of Blockchain, Shanghai, 200433, China

    Haibin Kan

  4. Yiwu Research Institute of Fudan University, Yiwu City, 322000, China

    Haibin Kan

  5. Mathematics and Science College of Shanghai Normal University, Shanghai, 200234, China

    Jie Peng

  6. School of Mathematics and Physics, University of South China, Hengyang, Hunan, 421001, China

    Lijing Zheng

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  1. Yanjun Li
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  2. Haibin Kan
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  4. Lijing Zheng
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Yanjun Li and Jie Peng wrote the main manuscript text. All authors reviewed the manuscript.

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Correspondence to Jie Peng.

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Li, Y., Kan, H., Peng, J. et al. Cryptographic functions with interesting properties from CCZ-equivalence. Cryptogr. Commun. 15, 831–844 (2023). https://doi.org/10.1007/s12095-023-00646-2

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