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On a conjecture of differentially 8-uniform power functions. (English) Zbl 1402.11149
Summary: Let $$m \geq 5$$ be an odd integer. For $$d=2^m+2^{(m+1)/2}+1$$ or $$d=2^{m+1}+3$$, Blondeau et al. conjectured that the power function $$F_d=x^d$$ over $$\mathrm {GF}(2^{2m})$$ is differentially 8-uniform in which all values $$0, 2, 4, 6, 8$$ appear. In this paper, we confirm this conjecture and compute the differential spectrum of $$F_d$$ for both values of $$d$$.

##### MSC:
 11T06 Polynomials over finite fields 94A60 Cryptography 11T71 Algebraic coding theory; cryptography (number-theoretic aspects) 11L05 Gauss and Kloosterman sums; generalizations
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