The Differential Spectrum of the Power Mapping x^p^n-3

08/06/2021

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by   Haode Yan, et al.

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Let n be a positive integer and p a prime. The power mapping x^p^n-3 over 𝔽_p^n has desirable differential properties, and its differential spectra for p=2, 3 have been determined. In this paper, for any odd prime p, by investigating certain quadratic character sums and some equations over 𝔽_p^n, we determine the differential spectrum of x^p^n-3 with a unified approach. The obtained result shows that for any given odd prime p, the differential spectrum can be expressed explicitly in terms of n. Compared with previous results, a special elliptic curve over 𝔽_p plays an important role in our computation for the general case p ≥ 5.