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Dutta, Suman; Maitra, Subhamoy
Designs, codes, and cryptography, 03/2024, Letnik: 92, Številka: 3Journal Article
Aaronson defined Forrelation (2010) as a measure of correlation between a Boolean function f and the Walsh–Hadamard transform of another function g . In a recent work, we have studied different cryptographically important spectra of Boolean functions through the lens of Forrelation. In this paper, we explore a similar kind of correlation in terms of nega-Hadamard transform. We call it nega-Forrelation and obtain a more efficient sampling strategy for nega-Hadamard transform compared to the existing results. Moreover, we present an efficient sampling strategy for nega-crosscorrelation (and consequently nega-autocorrelation) spectra too, by tweaking the nega-Forrelation technique. Finally, we connect the hidden shift finding algorithm for bent functions (Rötteler, 2010) with the Forrelation algorithm and extend it for the negabent functions.
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