Abstract
\(\textit{HN}\)-transforms, which have been proposed as generalizations of Hadamard transforms, are constructed by tensoring Hadamard and nega-Hadamard kernels in any order. We show that all the \(2^n\) possible \(\textit{HN}\)-spectra of a Boolean function in n variables, each containing \(2^n\) elements (i.e., in total \(2^{2n}\) values in transformed domain) can be computed in \(O(2^{2n})\) time (more specific with little less than \(2^{2n+1}\) arithmetic operations). We propose a generalization of Deutsch-Jozsa algorithm, by employing \(\textit{HN}\)-transforms, which can be used to distinguish different classes of Boolean functions over and above what is possible by the traditional Deutsch-Jozsa algorithm.
S. Maitra is supported by the project “Cryptography & Cryptanalysis: How far can we bridge the gap between Classical and Quantum Paradigm”, awarded by the Scientific Research Council of the Department of Atomic Energy (DAE-SRC), the Board of Research in Nuclear Sciences (BRNS).
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Gangopadhyay, S., Maitra, S., Sinha, N., Stănică, P. (2017). Quantum Algorithms Related to \(\textit{HN}\)-Transforms of Boolean Functions. In: El Hajji, S., Nitaj, A., Souidi, E. (eds) Codes, Cryptology and Information Security. C2SI 2017. Lecture Notes in Computer Science(), vol 10194. Springer, Cham. https://doi.org/10.1007/978-3-319-55589-8_21
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