Investigations on c-(Almost) Perfect Nonlinear Functions

In a prior paper (Ellingsen et al. , 2020), two of us, along with P. Ellingsen, P. Felke, and A. Tkachenko, defined a new (output) multiplicative differential and the corresponding <inline-formula> <tex-math notation="LaTeX">c </tex-math></inline-formula>-differenti...

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Bibliographic Details
Published in:IEEE transactions on information theory Vol. 67; no. 10; pp. 6916 - 6925
Main Authors: Mesnager, Sihem, Riera, Constanza, Stanica, Pantelimon, Yan, Haode, Zhou, Zhengchun
Format: Journal Article
Language:English
Published: New York IEEE 01.10.2021
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Institute of Electrical and Electronics Engineers
Subjects:
11T06
94A60
94D10
<italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">c -differential
<italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">p -ary function
Boolean function
Boolean functions
Ciphers
Cryptography
Data structures
differential uniformity
Gold
Mathematics
MSC 2000: 06E30
perfect and almost perfect <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">c -nonlinearity
Resistance
Transforms
Walsh transform
ISSN:0018-9448, 1557-9654
Online Access:Get full text
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Summary:In a prior paper (Ellingsen et al. , 2020), two of us, along with P. Ellingsen, P. Felke, and A. Tkachenko, defined a new (output) multiplicative differential and the corresponding <inline-formula> <tex-math notation="LaTeX">c </tex-math></inline-formula>-differential uniformity, which has the potential of extending differential cryptanalysis. Here, we continue the work by looking at some APN functions through the mentioned concept and showing that their <inline-formula> <tex-math notation="LaTeX">c </tex-math></inline-formula>-differential uniformity increases significantly in some cases.
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content type line 14
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2021.3081348