Transparency order for Boolean functions: analysis and construction
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Authors
Wang, Qichun
Stănică, Pantelimon
Subjects
Transparency order
Boolean function
Nonlinearity
Boolean function
Nonlinearity
Advisors
Date of Issue
2019
Date
2019
Publisher
Springer
Language
en_US
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 cryp- tographic 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).
Type
Article
Description
The article of record as published may be found at https://doi.org/10.1007/s10623-019-00604-1
Series/Report No
Department
Applied Mathematics
Organization
Naval Postgraduate School (U.S.)
Identifiers
NPS Report Number
Sponsors
The first author would like to thank the financial support from the National Natural Science Foundation of China (Grant No. 61572189).
Funder
The first author would like to thank the financial support from the National Natural Science Foundation of China (Grant No. 61572189).
Format
17 p.
Citation
Q. Wang, P. Stanica, Transparency order for Boolean functions: analysis and construction, Designs, Codes and Cryptography 87:9 (2019), 2043-2059.
Distribution Statement
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.