On a conjecture of differentially 8-uniform power functions |
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| Authors: | Maosheng Xiong Haode Yan Pingzhi Yuan |
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| Institution: | 1.Department of Mathematics,The Hong Kong University of Science and Technology,Kowloon,Hong Kong;2.School of Mathematics,Southwest Jiaotong University,Chengdu,China;3.School of Mathematics,South China Normal University,Guangzhou,China |
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| 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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