Some properties of q-ary functions based on spectral analysis

Deep Singh; Maheshanand Bhaintwal

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 functions Walsh-Hadamard spectrum Crosscorrelation
Contact author(s): deepsinghspn @ gmail com
History: 2012-05-29: received
Short URL: https://ia.cr/2012/283
License: 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}
}