A comparison of Carlet's second-order nonlinearity bounds

Sihem Mesnager; Gavin McGrew; James Davis; Dayton Steele; Katherine Marsten

doi:10.1080/00207160.2015.1112002

A comparison of Carlet's second-order nonlinearity bounds

Sihem Mesnager, Gavin McGrew, James Davis, Dayton Steele, Katherine Marsten

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

Carlet provides two bounds on the second-order nonlinearity of Boolean functions. We construct a family of Boolean functions where the first bound (the presumed weaker bound) is tight and the second bound is strictly worse than the first bound. We show that the difference between the two bounds can be made arbitrarily large.

Original language	English (US)
Pages (from-to)	427-436
Number of pages	10
Journal	International Journal of Computer Mathematics
Volume	94
Issue number	3
DOIs	https://doi.org/10.1080/00207160.2015.1112002
State	Published - Mar 4 2017
Externally published	Yes

Bibliographical note

Funding Information:
G. McGrew was supported by NSF Grant EMSW21-MCTP 0636528. J. Davis was supported by NSF Grant EMSW21-MCTP 0636528. D. Steele was supported by NSF Grant EMSW21-MCTP 0636528. K. Marsten was supported by NSF Grant EMSW21-MCTP 0636528.

Publisher Copyright:
© 2016 Informa UK Limited, trading as Taylor & Francis Group.

Keywords

Boolean
concatenation
derivative
functions
Nonlinearity

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10.1080/00207160.2015.1112002

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A comparison of Carlet's second-order nonlinearity bounds

Abstract

Bibliographical note

Keywords

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