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The second-order zero differential spectra of almost perfect nonlinear functions and the inverse function in odd characteristic

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Abstract

In a prior paper (Boukerrou et al. IACR Trans. Symmetric Cryptol. 2020(1), 331–362 2020), Boukerrou et al. introduced the Feistel Boomerang Connectivity Table (FBCT). FBCT is an important cryptanalytic technique on Feistel ciphers. In fact, the coefficients of FBCT are actually related to the second-order zero differential spectra of functions in even characteristic. In this paper, we push further the study initiated in Boukerrou et al. (IACR Trans. Symmetric Cryptol. 2020(1), 331–362 2020). Almost perfect nonlinear (APN) functions and the inverse function are interesting in cryptography and coding theory. In Boukerrou et al. (IACR Trans. Symmetric Cryptol. 2020(1), 331–362 2020), Boukerrou et al. determined the second-order zero differential spectra of APN functions and the inverse function in even characteristic. In order to derive further cryptographic properties of APN functions and the inverse function in odd characteristic, we calculate the second-order zero differential spectra of some APN functions and the inverse function in odd characteristic. In addition, these APN functions and the inverse function have low second-order zero differential uniformity.

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Authors and Affiliations

  1. Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 211100, People’s Republic of China

    Xia Li & Qin Yue

  2. State Key Laboratory of Cryptology, P. O. Box 5159, Beijing, 100878, People’s Republic of China

    Xia Li, Qin Yue & Deng Tang

  3. The School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China

    Deng Tang

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  1. Xia Li
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  2. Qin Yue
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  3. Deng Tang
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Correspondence to Qin Yue.

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The paper was supported by National Natural Science Foundation of China (No. 61772015), the Postgraduate Research & Practice Innovation Program of Jiangsu Province (No. SJKY19−0167).

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Li, X., Yue, Q. & Tang, D. The second-order zero differential spectra of almost perfect nonlinear functions and the inverse function in odd characteristic. Cryptogr. Commun. 14, 653–662 (2022). https://doi.org/10.1007/s12095-021-00544-5

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  • DOI: https://doi.org/10.1007/s12095-021-00544-5

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