On Second-Order Nonlinearities of Two Classes of Cubic Boolean Functions

Deep Singh; Maheshanand Bhaintwal

Quality, Reliability, Security and Robustness in Heterogeneous Networks. 9th International Conference, QShine 2013, Greader Noida, India, January 11-12, 2013, Revised Selected Papers

Research Article

On Second-Order Nonlinearities of Two Classes of Cubic Boolean Functions

Download

427 downloads

Cite: BibTeX Plain Text

@INPROCEEDINGS{10.1007/978-3-642-37949-9_49,
    author={Deep Singh and Maheshanand Bhaintwal},
    title={On Second-Order Nonlinearities of Two Classes of Cubic Boolean Functions},
    proceedings={Quality, Reliability, Security and Robustness in Heterogeneous Networks. 9th International Conference, QShine 2013, Greader Noida, India, January 11-12, 2013, Revised Selected Papers},
    proceedings_a={QSHINE},
    year={2013},
    month={7},
    keywords={Boolean functions Walsh-Hadamard transform Nonlinearity Reed-Muller codes},
    doi={10.1007/978-3-642-37949-9_49}
}

Deep Singh
Maheshanand Bhaintwal
Year: 2013
On Second-Order Nonlinearities of Two Classes of Cubic Boolean Functions
QSHINE
Springer
DOI: 10.1007/978-3-642-37949-9_49

Deep Singh¹^,*, Maheshanand Bhaintwal¹^,*

1: Indian Institute of Technology Roorkee

*Contact email: deepsinghspn@gmail.com, mahesfma@iitr.ernet.in

Abstract

The higher order nonlinearity of a Boolean function is a cryptographic criterion, which plays an important role in the design of secure block ciphers and stream ciphers. In this paper, we obtain lower bounds of second-order nonlinearities of two classes of highly nonlinear cubic Boolean functions of the form , for = 3 and = 5 by investigating the lower bounds of the first order nonlinearity of their derivatives.

Keywords: Boolean functions Walsh-Hadamard transform Nonlinearity Reed-Muller codes

Published: 2013-07-09

: http://dx.doi.org/10.1007/978-3-642-37949-9_49