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Title: Constructions of q-ary functions with good global avalanche characteristics
Authors: Singh D.
Bhaintwal, Maheshanand
Singh B.K.
Published in: International Journal of Computer Mathematics
Abstract: In this paper, we construct two classes of q-ary balanced functions which have good global avalanche characteristics (GAC) measured in terms of sum-of-squares-modulus indicator (SSMI), modulus indicator(MI), and propagation criterion (PC). We show that the SSMI, MI, and PC of q-ary functions are invariant under affine transformations. Also, we give a construction of q-ary s-plateaued functions and obtain their SSMI. We provide a relationship between the autocorrelation spectrum of a cubic Boolean function and the dimension of the kernel of the bilinear form associated with the derivative of the function. Using this result, we identify several classes of cubic semi-bent Boolean functions which have good bounds on their SSMI and MI, and hence show good behaviour with respect to the GAC. © 2014, © 2014 Taylor & Francis.
Citation: International Journal of Computer Mathematics (2015), 92(2): 266-276
Issue Date: 2015
Publisher: Taylor and Francis Ltd.
Keywords: autocorrelation
q-ary bent and semi-bent functions
q-ary functions
Walsh–Hadamard transform
ISSN: 207160
Author Scopus IDs: 56311781600
Author Affiliations: Singh, D., Department of Mathematics, Central University of Jammu, Jammu, 180011, India
Bhaintwal, M., Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, 247667, India
Singh, B.K., Department of Mathematics, School of Allied Sciences, Graphic Era Hill University, Dehradun, Uttrakhand 248002, India
Corresponding Author: Singh, B.K.; Department of Mathematics, School of Allied Sciences, Graphic Era Hill UniversityIndia
Appears in Collections:Journal Publications [MA]

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