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author:

Liu, Q. (Liu, Q..) [1] | Huang, Z. (Huang, Z..) [2] | Chen, Z. (Chen, Z..) [3] | Jiang, R. (Jiang, R..) [4] | Zhang, L. (Zhang, L..) [5]

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Abstract:

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.

Keyword:

c-differential spectrum c-differential uniformity Elliptic curve Power function Quadratic character sum

Community:

  • [ 1 ] [Liu Q.]Key Laboratory of Information Security of Network Systems, College of Computer and Data Science, Fuzhou University, Fuzhou, 350116, China
  • [ 2 ] [Liu Q.]Hubei Key Laboratory of Applied Mathematics, Faculty of Mathematics and Statistics, Hubei University, Wuhan, 430062, China
  • [ 3 ] [Liu Q.]Yunnan Key Laboratory of Service Computing, Yunnan University of Finance and Economics, Kunming, 650221, China
  • [ 4 ] [Huang Z.]Key Laboratory of Information Security of Network Systems, College of Computer and Data Science, Fuzhou University, Fuzhou, 350116, China
  • [ 5 ] [Chen Z.]Fujian Key Laboratory of Financial Information Processing, Putian University, Putian, 351100, China
  • [ 6 ] [Jiang R.]Yunnan Key Laboratory of Service Computing, Yunnan University of Finance and Economics, Kunming, 650221, China
  • [ 7 ] [Zhang L.]School of Computer Science and Technology, Dongguan University of Technology, Dongguan, 523808, China

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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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