2015
DOI: 10.1007/s11425-015-4996-2
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Further results on differentially 4-uniform permutations over $\mathbb{F}_{2^{2m} } $

Abstract: In this paper, we present several new constructions of differentially 4-uniform permutations over F 2 2m by modifying the values of the inverse function on some subsets of F 2 2m . The resulted differentially 4-uniform permutations have high nonlinearities and algebraic degrees, which provide more choices for the design of crytographic substitution boxes.

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Cited by 24 publications
(8 citation statements)
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“…Qu et al [QTTL13,QTLG16], Peng et al [PT16] and Tang et al [TCT15] proposed several families of differentially 4-uniform permutations with optimal algebraic degree from the inverse function by applying the powerful switching method. Later, Zha et al [ZHS14,ZHSS15] presented some more families of differentially 4-uniform permutations with optimal algebraic degree by applying affine transformations on the elements of some subfields of the inverse function. In [CTTL14], Carlet et al built a family of differentially 4-uniform permutations with optimal algebraic degree by concatenating two functions from F 2 n−1 to F 2 n for even n ≥ 6.…”
Section: Introductionmentioning
confidence: 99%
“…Qu et al [QTTL13,QTLG16], Peng et al [PT16] and Tang et al [TCT15] proposed several families of differentially 4-uniform permutations with optimal algebraic degree from the inverse function by applying the powerful switching method. Later, Zha et al [ZHS14,ZHSS15] presented some more families of differentially 4-uniform permutations with optimal algebraic degree by applying affine transformations on the elements of some subfields of the inverse function. In [CTTL14], Carlet et al built a family of differentially 4-uniform permutations with optimal algebraic degree by concatenating two functions from F 2 n−1 to F 2 n for even n ≥ 6.…”
Section: Introductionmentioning
confidence: 99%
“…The nonlinearity bound of these functions can be obtained by using Theorem 3.5 in [15]. By comparing our newly constructed functions with previous constructions in [17][18][19]25], we found that the differential spectrum or the nonlinearity of the functions in Table 1 are different from that in those papers (see Table 3 in [17], Tables 2 and 3 in [18], Tables III and IV in [19] and Table 2 in [25]), which implies that the functions in Table 1 are CCZ-inequivalent to all the functions in those papers. Unfortunately, our numerical results show that the construction in Theorem 3.2 does not provide a function with nonlinearity better than Construction 5.5 in [15], although our construction can get more differentially 4-uniform permutations polynomials.…”
Section: It Follows From Lemma 31 That Trmentioning
confidence: 99%
“…Compared to the numerical results in [15, 17-19, 21, 23-25], Table 2 presents new results on nonlinearities and differential spectra for n = 12, 6, 8. This implies that the differentially 4-uniform permutations defined in Theorems 4.4 and 4.8 are CCZ-inequivalent to all the functions in [15, 17-19, 21, 23-25] (see Table 2 in [15], Tables 2, 3 and 4 in [17], Tables 2 and 3 in [18],Tables II, III and IV in [19], Table 3 in [21], Table A.1 in [23], Tables 1 and 2 in [24] and Tables 1 and 3 in [25]).…”
Section: The Second Class Of Differentially 4-uniform Permutation Polmentioning
confidence: 99%
See 1 more Smart Citation
“…There are very few known APN functions, and they may have potential drawbacks. In recent years, increasing attention has been given to differentially 4/6-uniform permutations (see [2][3][4][5] and references therein). Another key property of vectorial functions is the nonlinearity, which is characterized by the Walsh transforms of the functions.…”
mentioning
confidence: 99%