On lower bounds on second--order nonliearities of bent functions obtained by using Niho power functions

Manish Garg; Sugata Gangopadhyay

Paper 2011/171

On lower bounds on second--order nonliearities of bent functions obtained by using Niho power functions

Manish Garg and Sugata Gangopadhyay

Abstract

In this paper we find a lower bound of the second-order nonlinearities of Boolean bent functions of the form $f (x) = T r_{1}^{n} (α_{1} x^{d_{1}} + α_{2} x^{d_{2}})$ ,where $d_{1}$ and $d_{2}$ are Niho exponents. A lower bound of the second-order nonlinearities of these Boolean functions can also be obtained by using a result proved by Li, Hu and Gao (eprint.iacr.org/2010 /009.pdf). It is demonstrated that for large values of $n$ the lower bound obtained in this paper are better than the lower bound obtained by Li, Hu and Gao.

Note: We have revised our paper. We are posting the revised version.

Metadata

Available format(s): PDF
Category: Secret-key cryptography
Publication info: Published elsewhere. Unknown where it was published
Contact author(s): gsugata @ gmail com
manishiitr8 @ gmail com
History: 2011-07-07: revised; 2011-04-04: received; See all versions
Short URL: https://ia.cr/2011/171
License: CC BY

BibTeX

@misc{cryptoeprint:2011/171,
      author = {Manish Garg and Sugata Gangopadhyay},
      title = {On lower bounds on second--order nonliearities of bent functions obtained by using Niho power functions},
      howpublished = {Cryptology {ePrint} Archive, Paper 2011/171},
      year = {2011},
      url = {https://eprint.iacr.org/2011/171}
}