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Please use this identifier to cite or link to this item: http://repository.iitr.ac.in/handle/123456789/5822
Title: On the lower bounds of the second order nonlinearities of some Boolean functions
Authors: Gangopadhyay, Sugata
Sarkar S.
Telang R.
Published in: Information Sciences
Abstract: The rth 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 nonlinearities of the following two types of Boolean functions:. 1.f? (x) = Tr1n (? xd) with d = 22 r + 2r + 1 and ? ? F2n*, where n = 6 r.2.f (x, y) = Tr1t (xy2i + 1), where x, y ? F2t, n = 2 t, n ? 6 and i is an integer such that 1 ? i < t, gcd (2t - 1, 2i + 1) = 1. For some ?, the functions of the first type are bent functions, whereas Boolean functions of the second type are all bent functions, i.e., they possess the maximum first order nonlinearity. It is demonstrated that in some cases our bounds are better than the previously obtained bounds. © 2009 Elsevier Inc. All rights reserved.
Citation: Information Sciences (2010), 180(2): 266-273
URI: https://doi.org/10.1016/j.ins.2009.09.006
http://repository.iitr.ac.in/handle/123456789/5822
Issue Date: 2010
Keywords: Boolean functions
Derivative
Second order nonlinearity
ISSN: 200255
Author Scopus IDs: 55999031500
55246597400
35093495000
Author Affiliations: Gangopadhyay, S., Mathematics Department, Indian Institute of Technology Roorkee, 247 667 Uttarakhand, India
Sarkar, S., Projet SECRET, INRIA, B.P. 105, 78153 Le Chesnay Cedex, France
Telang, R., Mathematics Department, Indian Institute of Technology Roorkee, 247 667 Uttarakhand, India
Corresponding Author: Gangopadhyay, S.; Mathematics Department, Indian Institute of Technology Roorkee, 247 667 Uttarakhand, India; email: gsugata@gmail.com
Appears in Collections:Journal Publications [CS]

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