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Characterizing differential support of vectorial Boolean functions using the Walsh transform

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  1. 1

    Biham E, Shamir A. Differential cryptanalysis of DES-like cryptosystems. J Cryptol, 1991, 4: 3–72

  2. 2

    Qu L J, Tan Y, Tan C H, et al. Constructing differentially 4-uniform permutations over F22k via the switching method. IEEE Trans Inform Theor, 2013, 59: 4675–4686

  3. 3

    Tang D, Carlet C, Tang X. Differentially 4-uniform bijections by permuting the inverse function. Des Codes Cryptogr, 2015, 77: 117–141

  4. 4

    Tu Z, Zeng X, Zhang Z. More permutation polynomials with differential uniformity six. Sci China Inf Sci, 2018, 61: 038104

  5. 5

    Zha Z B, Hu L, Sun S W, et al. Further results on differentially 4-uniform permutations over F22m. Sci China Math, 2015, 58: 1577–1588

  6. 6

    Matsui L. Linear cryptanalysis method for DES cipher. In: Advances in Cryptology–EUROCRYPT’93. Berlin: Springer, 1994. 386–397

  7. 7

    Chabaud F, Vaudenay S. Links between differential and linear cryptanalysis. In: Proceedings of EUROCRYPT’94, 1995. 950: 356–365

  8. 8

    Carlet C. Characterizations of the differential uniformity of vectorial functions by the Walsh transform. IEEE Trans Inform Theor, 2018, 64: 6443–6453

  9. 9

    Blondeau C, Canteaut A, Charpin P. Differential properties of power functions. In: Proceedings of the 2010 IEEE International Symposium on Information Theory, Austin, 2010. 10: 2478–2482

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This work was supported by National Natural Science Foundation of China (Grant Nos. 61672355, 61672166, U19A2066), National Key Research & Development Plan(Grant No. 2019YFB2101703), Shanghai Excellent Academic Leader (Grant No. 16XD1400200), and Shanghai Innovation Plan of Science & Technology (Grant No. 16JC1402700).

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Correspondence to Haibin Kan.

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Peng, J., Gao, J. & Kan, H. Characterizing differential support of vectorial Boolean functions using the Walsh transform. Sci. China Inf. Sci. 63, 139108 (2020). https://doi.org/10.1007/s11432-018-9614-3

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