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Recently, a new concept called multiplicative differential was introduced by Ellingsen et al. [7]. As an extension of the differential uniformity, it is theoretically appealing to determine the properties of c-differential uniformity and the corresponding c-differential spectrum. In this paper, based on certain quadratic character sums and two special elliptic curves over Fp, the (-1)-differential spectra of the following two classes of power functions over Fpn is completely determined: (1) f1(x)=xpn+32, where p>3 and p≡3(mod4); (2) f2(x)=xpn-3, where p>3. The obtained result shows that the (-1)-differential spectra of f1(x) and f2(x) can be expressed explicitly in terms of n. Moreover, an upper bound of the c-differential uniformity of f2(x) is given. © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2025.
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Applicable Algebra in Engineering, Communications and Computing
ISSN: 0938-1279
Year: 2025
0 . 6 0 0
JCR@2023
CAS Journal Grade:4
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ESI Highly Cited Papers on the List: 0 Unfold All
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