The second-order zero differential uniformity of the swapped inverse functions over finite fields

• URL: http://arxiv.org/abs/2405.16784v2
• Date: Wed, 16 Oct 2024 07:21:46 GMT
• Title: The second-order zero differential uniformity of the swapped inverse functions over finite fields
• Authors: Jaeseong Jeong, Namhun Koo, Soonhak Kwon,
• Abstract summary: We investigate the second-order zero differential uniformity of the swapped inverse functions. This paper is the first result to characterize classes of non-power functions with the second-order zero differential uniformity equal to 4, in even characteristic.
• Score: 2.2120851074630177
• License:
• Abstract: The Feistel Boomerang Connectivity Table (FBCT) was proposed as the feistel counterpart of the Boomerang Connectivity Table. The entries of the FBCT are actually related to the second-order zero differential spectrum. Recently, several results on the second-order zero differential uniformity of some functions were introduced. However, almost all of them were focused on power functions, and there are only few results on non-power functions. In this paper, we investigate the second-order zero differential uniformity of the swapped inverse functions, which are functions obtained from swapping two points in the inverse function. We also present the second-order zero differential spectrum of the swapped inverse functions for certain cases. In particular, this paper is the first result to characterize classes of non-power functions with the second-order zero differential uniformity equal to 4, in even characteristic.

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