Tools in Analyzing Linear Approximation for Boolean Functions Related to FLIP

Maitra, Subhamoy; Mandal, Bimal; Martinsen, Thor; Roy, Dibyendu; Stănică, Pantelimon

doi:10.1007/978-3-030-05378-9_16

Cited by 9 publications

(1 citation statement)

References 6 publications

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“…Nowadays, the concept of biased inputs are used to analyze the cryptographic properties of some symmetric ciphers. For example, Maitra et al [15,16] analyzed the bias of Walsh-Hadamard transform of the filter function of FLIP [1,2] over a restricted domain where input vectors are not independent and identically distributed. They showed in Table IV [16,Section IV.A] that the bounds provided by the biased Walsh-Hadamard transforms are better than those obtained by Carlet et al [2].…”

Section: Introductionmentioning

confidence: 99%

A note on generalization of bent boolean functions

Mandal¹,

Gangopadhyay²

2021

Advances in Mathematics of Communications

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Suppose that µp is a probability measure defined on the input space of Boolean functions. We consider a generalization of Walsh-Hadamard transform on Boolean functions to µp-Walsh-Hadamard transforms. In this paper, first, we derive the properties of µp-Walsh-Hadamard transformation for some classes of Boolean functions and specify a class of nonsingular affine transformations that preserve the µp-bent property. We further derive the results on µp-Walsh-Hadamard transform of concatenation of Boolean functions and provide some secondary constructions of µp-bent functions. Finally, we discuss the µp-bentness for Maiorana-McFarland class of bent functions.

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