Introducing nega-Forrelation: quantum algorithms in analyzing nega-Hadamard and nega-crosscorrelation spectra

Article Type

Research Article

Publication Title

Designs Codes and Cryptography

Abstract

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.

First Page

863

Last Page

883

DOI

10.1007/s10623-023-01346-x

Publication Date

3-1-2024

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