1,861 research outputs found
On the Derivative Imbalance and Ambiguity of Functions
In 2007, Carlet and Ding introduced two parameters, denoted by and
, quantifying respectively the balancedness of general functions
between finite Abelian groups and the (global) balancedness of their
derivatives , (providing an
indicator of the nonlinearity of the functions). These authors studied the
properties and cryptographic significance of these two measures. They provided
for S-boxes inequalities relating the nonlinearity to ,
and obtained in particular an upper bound on the nonlinearity which unifies
Sidelnikov-Chabaud-Vaudenay's bound and the covering radius bound. At the
Workshop WCC 2009 and in its postproceedings in 2011, a further study of these
parameters was made; in particular, the first parameter was applied to the
functions where is affine, providing more nonlinearity parameters.
In 2010, motivated by the study of Costas arrays, two parameters called
ambiguity and deficiency were introduced by Panario \emph{et al.} for
permutations over finite Abelian groups to measure the injectivity and
surjectivity of the derivatives respectively. These authors also studied some
fundamental properties and cryptographic significance of these two measures.
Further studies followed without that the second pair of parameters be compared
to the first one.
In the present paper, we observe that ambiguity is the same parameter as
, up to additive and multiplicative constants (i.e. up to rescaling). We
make the necessary work of comparison and unification of the results on ,
respectively on ambiguity, which have been obtained in the five papers devoted
to these parameters. We generalize some known results to any Abelian groups and
we more importantly derive many new results on these parameters
ICLabel: An automated electroencephalographic independent component classifier, dataset, and website
The electroencephalogram (EEG) provides a non-invasive, minimally
restrictive, and relatively low cost measure of mesoscale brain dynamics with
high temporal resolution. Although signals recorded in parallel by multiple,
near-adjacent EEG scalp electrode channels are highly-correlated and combine
signals from many different sources, biological and non-biological, independent
component analysis (ICA) has been shown to isolate the various source generator
processes underlying those recordings. Independent components (IC) found by ICA
decomposition can be manually inspected, selected, and interpreted, but doing
so requires both time and practice as ICs have no particular order or intrinsic
interpretations and therefore require further study of their properties.
Alternatively, sufficiently-accurate automated IC classifiers can be used to
classify ICs into broad source categories, speeding the analysis of EEG studies
with many subjects and enabling the use of ICA decomposition in near-real-time
applications. While many such classifiers have been proposed recently, this
work presents the ICLabel project comprised of (1) an IC dataset containing
spatiotemporal measures for over 200,000 ICs from more than 6,000 EEG
recordings, (2) a website for collecting crowdsourced IC labels and educating
EEG researchers and practitioners about IC interpretation, and (3) the
automated ICLabel classifier. The classifier improves upon existing methods in
two ways: by improving the accuracy of the computed label estimates and by
enhancing its computational efficiency. The ICLabel classifier outperforms or
performs comparably to the previous best publicly available method for all
measured IC categories while computing those labels ten times faster than that
classifier as shown in a rigorous comparison against all other publicly
available EEG IC classifiers.Comment: Intended for NeuroImage. Updated from version one with minor
editorial and figure change
C-DIFFERENTIALS AND GENERALIZED CRYPTOGRAPHIC PROPERTIES OF VECTORIAL BOOLEAN AND P-ARY FUNCTIONS
This dissertation investigates a newly defined cryptographic differential, called a c-differential, and its relevance to the nonlinear substitution boxes of modern symmetric block ciphers. We generalize the notions of perfect nonlinearity, bentness, and avalanche characteristics of vectorial Boolean and p-ary functions using the c-derivative and a new autocorrelation function, while capturing the original definitions as special cases (i.e., when c=1). We investigate the c-differential uniformity property of the inverse function over finite fields under several extended affine transformations. We demonstrate that c-differential properties do not hold in general across equivalence classes typically used in Boolean function analysis, and in some cases change significantly under slight perturbations. Thus, choosing certain affine equivalent functions that are easy to implement in hardware or software without checking their c-differential properties could potentially expose an encryption scheme to risk if a c-differential attack method is ever realized. We also extend the c-derivative and c-differential uniformity into higher order, investigate some of their properties, and analyze the behavior of the inverse function's second order c-differential uniformity. Finally, we analyze the substitution boxes of some recognizable ciphers along with certain extended affine equivalent variations and document their performance under c-differential uniformity.Commander, United States NavyApproved for public release. Distribution is unlimited
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