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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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