On the second-order nonlinearities of some bent functions

Tang, Deng; Carlet, Claude; Tang, Xiaohu

doi:10.1016/j.ins.2012.08.024

Cited by 16 publications

(2 citation statements)

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“…It can easily be seen that t = 0 or t = (a r + a) −3 are solutions of (24). So c = a and c = a + (a r + a) −3 are two solutions of (21). In total, c = 0, (a This completes the proof.…”

Section: 2mentioning

confidence: 55%

“…However, up to now, providing a tight lower bound on the second-order nonlinearity is also a difficult task for all values of n. In [4], by utilizing a recursive method to calculate the lower bound on the rth-order nonlinearity of a function f from the (r − 1)th-order nonlinearity of the derivatives of f , Carlet deduced the lower bounds on the secondorder nonlinearity of Welch function and inverse function. Inspired by Carlet's approach, much progress on determining the lower bounds on the second-order nonlinearity of cubic Boolean functions had been made, see [10,18,20,21,22] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

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The lower bounds on the second-order nonlinearity of three classes of Boolean functions

Liu¹

2023

AMC

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In this paper, by calculating the lower bounds on the nonlinearity of the derivatives of the following three classes of Boolean functions, we provide the tight lower bounds on the second-order nonlinearity of these Boolean functions:), where λ ∈ F * 2 r and n = 4r with even r;), where (x, y) ∈ F 2 n × F 2 , n = 2r with odd r. The results show that our bounds are better than previously known lower bounds in some cases.

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“…It can easily be seen that t = 0 or t = (a r + a) −3 are solutions of (24). So c = a and c = a + (a r + a) −3 are two solutions of (21). In total, c = 0, (a This completes the proof.…”

Section: 2mentioning

confidence: 55%