On the Lower Bounds of the Second Order  Nonlinearity of some Boolean Functions

Sugata Gangopadhyay; Sumanta Sarkar; Ruchi Telang

Paper 2009/094

On the Lower Bounds of the Second Order Nonlinearity of some Boolean Functions

Sugata Gangopadhyay, Sumanta Sarkar, and Ruchi Telang

Abstract

The $r$ -th order nonlinearity of a Boolean function is an important cryptographic criterion in analyzing the security of stream as well as block ciphers. It is also important in coding theory as it is related to the covering radius of the Reed-Muller code $R (r, n)$ . In this paper we deduce the lower bounds of the second order nonlinearity of the two classes of Boolean functions of the form \begin{enumerate} \item with and where . \item where and is an integer such that , . \end{enumerate} For some , the first class gives bent functions whereas Boolean functions of the second class are all bent, i.e., they achieve optimum first order nonlinearity.

Metadata

Available format(s): PDF
Category: Secret-key cryptography
Publication info: Published elsewhere. Unknown where it was published
Keywords: Boolean functions second order nonlinearity
Contact author(s): gsugata @ gmail com
History: 2009-03-17: last of 4 revisions; 2009-03-02: received; See all versions
Short URL: https://ia.cr/2009/094
License: CC BY

BibTeX

@misc{cryptoeprint:2009/094,
      author = {Sugata Gangopadhyay and Sumanta Sarkar and Ruchi Telang},
      title = {On the Lower Bounds of the Second Order  Nonlinearity of some Boolean Functions},
      howpublished = {Cryptology {ePrint} Archive, Paper 2009/094},
      year = {2009},
      url = {https://eprint.iacr.org/2009/094}
}