New results of 0-APN power functions over 𝔽_2^n

10/05/2022

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by   Yan-Ping Wang, et al.

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Partially APN functions attract researchers' particular interest recently. It plays an important role in studying APN functions. In this paper, based on the multivariate method and resultant elimination, we propose several new infinite classes of 0-APN power functions over 𝔽_2^n. Furthermore, two infinite classes of 0-APN power functions x^d over 𝔽_2^n are characterized completely where (2^k-1)d≡ 2^m-1 ( mod 2^n-1) or (2^k+1)d≡ 2^m+1 ( mod 2^n-1) for some positive integers n, m, k. These infinite classes of 0-APN power functions can explain some examples of exponents of Table 1 in <cit.>.