Abstract
Let \(m \ge 5\) 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.
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Acknowledgements
The authors are grateful to anonymous referees for careful reading and for many useful suggestions. Xiong’s research was supported by RGC No. 609513 from Hong Kong. Yan’s research was supported by National Cryptography Development Fund under Grant MMJJ20170119. Yuan’s research was supported by the NSF of China (Grant No. 11671153).
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Communicated by P. Charpin.
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Xiong, M., Yan, H. & Yuan, P. On a conjecture of differentially 8-uniform power functions. Des. Codes Cryptogr. 86, 1601–1621 (2018). https://doi.org/10.1007/s10623-017-0416-7
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DOI: https://doi.org/10.1007/s10623-017-0416-7