[2310.18568] On the second-order zero differential spectra of some power functions over finite fields
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Computer Science > Information Theory

arXiv:2310.18568 (cs)
[Submitted on 28 Oct 2023]

Title:On the second-order zero differential spectra of some power functions over finite fields

Authors:Yuying Man, Nian Li, Zejun Xiang, Xiangyong Zeng
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Abstract:Boukerrou et al. (IACR Trans. Symmetric Cryptol. 2020(1), 331-362) introduced the notion of Feistel Boomerang Connectivity Table (FBCT), the Feistel counterpart of the Boomerang Connectivity Table (BCT), and the Feistel boomerang uniformity (which is the same as the second-order zero differential uniformity in even characteristic). FBCT is a crucial table for the analysis of the resistance of block ciphers to power attacks such as differential and boomerang attacks. It is worth noting that the coefficients of FBCT are related to the second-order zero differential spectra of functions. In this paper, by carrying out certain finer manipulations of solving specific equations over the finite field $\mathbb{F}_{p^n}$, we explicitly determine the second-order zero differential spectra of some power functions with low differential uniformity, and show that our considered functions also have low second-order zero differential uniformity. Our study pushes further former investigations on second-order zero differential uniformity and Feistel boomerang differential uniformity for a power function $F$.
Subjects: Information Theory (cs.IT)
Cite as: arXiv:2310.18568 [cs.IT]
  (or arXiv:2310.18568v1 [cs.IT] for this version)
  https://doi.org/10.48550/arXiv.2310.18568

Submission history

From: Yuying Man [view email]
[v1] Sat, 28 Oct 2023 02:30:25 UTC (10 KB)
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