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- W4313650788 abstract "In this paper, we study the boomerang spectrum of the power mapping $$F(x)=x^{k(q-1)}$$ over $${mathbb {F}}_{q^2}$$ , where $$q=p^m$$ , p is a prime, m is a positive integer and $$gcd (k,q+1)=1$$ . We first determine the differential spectrum of F(x) and show that F(x) is locally-APN. This extends a result of (IEEE Trans. Inf. Theory 57(12):8127-8137, 2011) from $$(p,k)=(2,1)$$ to general (p, k). We then determine the boomerang spectrum of F(x) by making use of its differential spectrum, which shows that the boomerang uniformity of F(x) is 4 if $$p=2$$ and m is odd and otherwise it is 2. Our results not only generalize the results in Hasan et al. (Des Codes Cryptogr 89:2627–2636, 2021) and Yan et al. (Adv Math Commun 16(4):1111–1120, 2022) but also extend the example $$x^{45}$$ over $${mathbb F}_{2^8}$$ in Hasan et al. (Des Codes Cryptogr 89:2627–2636, 2021) into an infinite class of power mappings with boomerang uniformity 2." @default.
- W4313650788 created "2023-01-07" @default.
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- W4313650788 date "2023-01-06" @default.
- W4313650788 modified "2023-09-25" @default.
- W4313650788 title "The differential spectrum and boomerang spectrum of a class of locally-APN functions" @default.
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- W4313650788 doi "https://doi.org/10.1007/s10623-022-01161-w" @default.
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