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

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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.

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Acknowledgements

The authors like to acknowledge the anonymous reviewers for the detailed comments that improved the technical as well as editorial quality of this paper.

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  1. Indian Statistical Institute, Kolkata, India

    Suman Dutta & Subhamoy Maitra

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  1. Suman Dutta
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  2. Subhamoy Maitra
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Correspondence to Subhamoy Maitra.

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This is one of several papers published in Designs, Codes and Cryptography comprising the “Special Issue: Coding and Cryptography 2022”.

This is an extended and revised version of the paper presented in WCC 2022. Section 5 contains additional results over the workshop version.

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Dutta, S., Maitra, S. Introducing nega-Forrelation: quantum algorithms in analyzing nega-Hadamard and nega-crosscorrelation spectra. Des. Codes Cryptogr. 92, 863–883 (2024). https://doi.org/10.1007/s10623-023-01346-x

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