
For FullText PDF, please login, if you are a member of IEICE,
or go to Pay Per View on menu list, if you are a nonmember of IEICE.

A Lower Bound on the SecondOrder Nonlinearity of the Generalized MaioranaMcFarland Boolean Functions
Qi GAO Deng TANG
Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Vol.E101A
No.12
pp.23972401 Publication Date: 2018/12/01
Online ISSN: 17451337
DOI: 10.1587/transfun.E101.A.2397
Type of Manuscript: Special Section LETTER (Special Section on Signal Design and Its Applications in Communications) Category: Cryptography and Information Security Keyword: Boolean function, secondorder nonlinearity, bent function, differential uniformity,
Full Text: PDF(312KB) >>Buy this Article
Summary:
Boolean functions used in stream ciphers and block ciphers should have high secondorder nonlinearity to resist several known attacks and some potential attacks which may exist but are not yet efficient and might be improved in the future. The secondorder nonlinearity of Boolean functions also plays an important role in coding theory, since its maximal value equals the covering radius of the secondorder ReedMuller code. But it is an extremely hard task to calculate and even to bound the secondorder nonlinearity of Boolean functions. In this paper, we present a lower bound on the secondorder nonlinearity of the generalized MaioranaMcFarland Boolean functions. As applications of our bound, we provide more simpler and direct proofs for two known lower bounds on the secondorder nonlinearity of functions in the class of MaioranaMcFarland bent functions. We also derive a lower bound on the secondorder nonlinearity of the functions which were conjectured bent by Canteaut and whose bentness was proved by Leander, by further employing our bound.

