학술논문

Investigations on c-(Almost) Perfect Nonlinear Functions
Document Type
Periodical
Source
IEEE Transactions on Information Theory IEEE Trans. Inform. Theory Information Theory, IEEE Transactions on. 67(10):6916-6925 Oct, 2021
Subject
Communication, Networking and Broadcast Technologies
Signal Processing and Analysis
Boolean functions
Data structures
Ciphers
Gold
Transforms
Standards
Resistance
Boolean function
p<%2Fitalic>-ary+function%22">p-ary function
c<%2Fitalic>-differential%22">c-differential
Walsh transform
differential uniformity
c<%2Fitalic>-nonlinearity%22">perfect and almost perfect c-nonlinearity
MSC 2000: 06E30
11T06
94A60
94D10
Language
ISSN
0018-9448
1557-9654
Abstract
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 $c$ -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 $c$ -differential uniformity increases significantly in some cases.