Partially APN Boolean functions and classes of functions that are not APN infinitely often
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Authors
Budaghyan, Lilya
Kaleyski, Nikolay
Kwon, Soonhak
Riera, Constanza
Stănică, Pantelimon
Subjects
Boolean function
almost perfect nonlinear (APN)
partial APN
Walsh-Hadamard coefficients.
almost perfect nonlinear (APN)
partial APN
Walsh-Hadamard coefficients.
Advisors
Date of Issue
2019
Date
2019
Publisher
Language
en_US
Abstract
In this paper we define a notion of partial APNness and find various characterizations and constructions of classes of functions satisfying this condition. We connect this notion to the known conjecture that APN functions modified at a point cannot remain APN. In the second part of the paper, we find conditions for some transformations not to be partially APN, and in the process, we find classes of functions that are never APN for infinitely many extensions of the prime field F2, extending some earlier results of Leander and Rodier.
Type
Preprint
Description
Series/Report No
Department
Applied Mathematics
Organization
Naval Postgraduate School (U.S.)
Identifiers
NPS Report Number
Sponsors
S.K. was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2016R1D1A1B03931912 and No. 2016R1A5A1008055). The research of the first two authors was supported by Trond Mohn foundation.
Funding
S.K. was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2016R1D1A1B03931912 and No. 2016R1A5A1008055). The research of the first two authors was supported by Trond Mohn foundation.
Format
24 p.
Citation
L. Budaghyan, N.S. Kaleyski, S. Kwon, C. Riera, P. Stanica, Partially APN Boolean functions and classes of functions that are not APN infinitely often, Cryptography & Communication - CCDS (2019), 1-19.
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.