Paper 2012/283

Some properties of q-ary functions based on spectral analysis

Deep Singh and Maheshanand Bhaintwal

Abstract

In this paper, we generalize some existing results on Boolean functions to the $q$-ary functions defined over $\BBZ_q$, where $q\geq 2$ is an integer, and obtain some new characterization of $q$-ary functions based on spectral analysis. We provide a relationship between Walsh-Hadamard spectra of two $p$-ary functions $f$ and $g$ (for $p$ a prime) and their derivative $D_{f, g}$. We provide a relationship between the Walsh-Hadamard spectra and the decompositions of any two $p$-ary functions. Further, we investigate a relationship between the Walsh-Hadamard spectra and the autocorrelation of any two $q$-ary functions.

Metadata
Available format(s)
PDF
Category
Secret-key cryptography
Publication info
Published elsewhere. Unknown where it was published
Keywords
Boolean functions$q$-ary functionsWalsh-Hadamard spectrumCrosscorrelation
Contact author(s)
deepsinghspn @ gmail com
History
2012-05-29: received
Short URL
https://ia.cr/2012/283
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2012/283,
      author = {Deep Singh and Maheshanand Bhaintwal},
      title = {Some properties of q-ary functions based on spectral analysis},
      howpublished = {Cryptology {ePrint} Archive, Paper 2012/283},
      year = {2012},
      url = {https://eprint.iacr.org/2012/283}
}
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