一类置换多项式的c-差分均匀度与回旋镖均匀度

doi:10.12677/AAM.2024.138374

期刊菜单

一类置换多项式的c-差分均匀度与回旋镖均匀度
The c-Differential Uniformity and Boomerang Uniformity of a Class of Permutation Polynomials

DOI: 10.12677/AAM.2024.138374, PDF,
作者: 陈艺文：西北师范大学数学与统计学院，甘肃兰州
关键词: 置换多项式；c-差分均匀度；回旋镖均匀度；Weil和；Permutation Polynomial； c-Differential Uniformity； Boomerang Uniformity； Weil Sums

摘要: S盒是分组密码算法中的一个重要组成部分。为抵抗已有的差分攻击、回旋镖攻击等各种攻击，一个理想的S盒通常应该具有低差分均匀度、低回旋镖均匀度等良好的密码学性质。本文利用Weil 和技巧证明了一类已知置换多项式具有较低的 c- 差分均匀度，并计算出了这类置换多项式的回旋镖均匀度。

Abstract: S-box is an important component of block cipher algorithms. In order to resist various attacks such as differential attacks and boomerang attacks, an ideal S-box is required to have low differential uniformity and low boomerang uniformity. In this paper, we propose a class of known permutation polynomials with low c-differential uniformity by employing Weil sums. Furthermore, we calculate the boomerang uniformity of this function.

文章引用：陈艺文. 一类置换多项式的c-差分均匀度与回旋镖均匀度[J]. 应用数学进展, 2024, 13(8): 3925-3935. https://doi.org/10.12677/AAM.2024.138374

参考文献

[1]	Biham, E. and Shamir, A. (1991) Differential Cryptanalysis of DES-Like Cryptosystems. Jour- nal of Cryptology, 4, 3-72. https://doi.org/10.1007/bf00630563
[2]	% Nyberg, K. (1994) Differentially Uniform Mappings for Cryptography. In: Helleseth, T., Ed., Lecture Notes in Computer Science, Springer, 55-64. https://doi.org/10.1007/3-540-48285-7 6
[3]	Borisov, N., Chew, M., Johnson, R. and Wagner, D. (2002) Multiplicative Differentials. In: Daemen, J. and Rijmen, V., Eds., Lecture Notes in Computer Science, Springer, 17-33. https://doi.org/10.1007/3-540-45661-9 2
[4]	Ellingsen, P., Felke, P., Riera, C., Staˇnicˇa, P. and Tkachenko, A. (2020) C-Differentials, Multi- plicative Uniformity, and (Almost) Perfect c-Nonlinearity. IEEE Transactions on Information Theory, 66, 5781-5789. https://doi.org/10.1109/tit.2020.2971988
[5]	Wu, Y., Li, N. and Zeng, X. (2021) New PcN and APcN Functions over Finite Fields. Designs, Codes and Cryptography, 89, 2637-2651. https://doi.org/10.1007/s10623-021-00946-9
[6]	Hasan, S.U., Pal, M. and Staˇnicˇa, P. (2022) The c-Differential Uniformity and Boomerang Uniformity of Two Classes of Permutation Polynomials. IEEE Transactions on Information Theory, 68, 679-691. https://doi.org/10.1109/tit.2021.3123104
[7]	Jeong, J., Koo, N. and Kwon, S. (2023) On Non-Monomial APcN Permutations over Finite Fields of Even Characteristic. Finite Fields and Their Applications, 89, Article 102196. https://doi.org/10.1016/j.ffa.2023.102196
[8]	Liu, Q., Huang, Z., Xie, J., Liu, X. and Zou, J. (2023) The c-Differential Uniformity and Boomerang Uniformity of Three Classes of Permutation Polynomials over F2n . Finite Fields and Their Applications, 89, Article 102212. https://doi.org/10.1016/j.ffa.2023.102212
[9]	Mesnager, S., Mandal, B. and Msahli, M. (2021) Survey on Recent Trends Towards Generalized Differential and Boomerang Uniformities. Cryptography and Communications, 14, 691-735. https://doi.org/10.1007/s12095-021-00551-6
[10]	Wagner, D. (1999) The Boomerang Attack. In: Knudsen, L., Ed., Lecture Notes in Computer Science, Springer, 156-170. https://doi.org/10.1007/3-540-48519-8 12
[11]	Cid, C., Huang, T., Peyrin, T., Sasaki, Y. and Song, L. (2018) Boomerang Connectivity Table: A New Cryptanalysis Tool. In: Nielsen, J. and Rijmen, V., Eds., Lecture Notes in Computer Science, Springer International Publishing, 683-714. https://doi.org/10.1007/978-3-319-78375-8 22
[12]	Boura, C. and Canteaut, A. (2018) On the Boomerang Uniformity of Cryptographic Sboxes. IACR Transactions on Symmetric Cryptology, No. 3, 290-310. https://doi.org/10.46586/tosc.v2018.i3.290-310
[13]	Li, K., Qu, L., Sun, B. and Li, C. (2019) New Results about the Boomerang Uniformity of Permutation Polynomials. IEEE Transactions on Information Theory, 65, 7542-7553. https://doi.org/10.1109/tit.2019.2918531
[14]	Lidl, R. and Niederreiter, H. (1997) Finite Fields, Encyclopedia of Mathematics and Its Ap- plications. Vol. 20, Cambridge University Press.
[15]	Helleseth, T. and Kholosha, A. (2006) Monomial and Quadratic Bent Functions over the Finite Fields of Odd Characteristic. IEEE Transactions on Information Theory, 52, 2018- 2032. https://doi.org/10.1109/tit.2006.872854
[16]	Charpin, P. and Kyureghyan, G.M. (2008) On a Class of Permutation Polynomials over F2n . In: Golomb, S.W., Parker, M.G., Pott, A. and Winterhof, A., Eds., Lecture Notes in Computer Science, Springer, 368-376. https://doi.org/10.1007/978-3-540-85912-3 32
[17]	Roy, S. (2012) Generalization of Some Results on Gold and Kasami-Welch Functions. Finite Fields and Their Applications, 18, 894-903. https://doi.org/10.1016/j.ffa.2012.06.006

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