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

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  • @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.