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Designs, Codes and Cryptography
Published in: Designs, Codes and Cryptography 9/2019

09-01-2019

Transparency order for Boolean functions: analysis and construction

Authors: Qichun Wang, Pantelimon Stănică

Published in: Designs, Codes and Cryptography | Issue 9/2019

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Abstract

The notion of transparency order, proposed by Prouff (DPA attacks and S-boxes, FSE 2005, LNCS 3557, Springer, Berlin, 2005) and then redefined by Chakraborty et al. (Des Codes Cryptogr 82:95–115, 2017), is a property that attempts to characterize the resilience of cryptographic algorithms against differential power analysis attacks. In this paper, we give a tight upper bound on the transparency order in terms of nonlinearity, inferring the worst possible transparency order of those functions with the same nonlinearity. We also give a lower bound between transparency order and nonlinearity. We study certain classes of Boolean functions for their transparency order and find that this parameter for some functions of low algebraic degree can be determined by their nonlinearity. Finally, we construct two infinite classes of balanced semibent Boolean functions with provably relatively good transparency order (this is the first time that an infinite class of highly nonlinear balanced functions with provably good transparency order is given).
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Metadata
Title
Transparency order for Boolean functions: analysis and construction
Authors
Qichun Wang
Pantelimon Stănică
Publication date
09-01-2019
Publisher
Springer US
Published in
Designs, Codes and Cryptography / Issue 9/2019
Print ISSN: 0925-1022
Electronic ISSN: 1573-7586
DOI
https://doi.org/10.1007/s10623-019-00604-1

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