On generalized semi-bent (and partially bent) Boolean functions

Brajesh Kumar Singh

Paper 2013/166

On generalized semi-bent (and partially bent) Boolean functions

Brajesh Kumar Singh

Abstract

In this paper, we obtain a characterization of generalized Boolean functions based on spectral analysis. We investigate a relationship between the Walsh-Hadamard spectrum and $σ_{f}$ , the sum-of-squares-modulus indicator (SSMI) of the generalized Boolean function. It is demonstrated that $σ_{f} = 2^{2 n + s}$ for every $s$ -plateaued generalized Boolean function in $n$ variables. Two classes of generalized semi-bent Boolean functions are constructed.% and it is demonstrated that their SSMI is over generalized $s$ -plateaued Boolean functions is $2^{2 n + s}$ . We have constructed a class of generalized semi-bent functions in $(n + 1)$ variables from generalized semi-bent functions in $n$ variables and identify a subclass of it for which $σ_{f}$ and $△_{f}$ both have optimal value. Finally, some construction on generalized partially bent Boolean functions are given.

Metadata

Available format(s): PDF
Category: Secret-key cryptography
Publication info: Published elsewhere. Unknown where it was published
Keywords: Boolean functions generalized functions Walsh-Hadamard spectrum generalized bent Boolean functions generalized semi-bent functions sum-of-squares-modulus indicator modulus indicator
Contact author(s): bksingh0584 @ gmail com
History: 2013-03-28: received
Short URL: https://ia.cr/2013/166
License: CC BY

BibTeX

@misc{cryptoeprint:2013/166,
      author = {Brajesh Kumar Singh},
      title = {On generalized semi-bent (and partially bent) Boolean functions},
      howpublished = {Cryptology {ePrint} Archive, Paper 2013/166},
      year = {2013},
      url = {https://eprint.iacr.org/2013/166}
}