Welcome to the resource topic for 2004/248
Title:
Classification of Boolean Functions of 6 Variables or Less with Respect to Cryptographic Properties
Authors: An Braeken, Yuri Borissov, Svetla Nikova, Bart Preneel
Abstract:This paper presents an efficient approach for classification of
the affine equivalence classes of cosets of the first order
Reed-Muller code with respect to cryptographic properties such as
correlation-immunity, resiliency and propagation characteristics.
First, we apply the method to completely classify all the 48
classes into which the general affine group AGL(2,5) partitions
the cosets of RM(1,5). Second, we describe how to find the affine
equivalence classes together with their sizes of Boolean functions in 6 variables.
We perform the same classification for these classes. Moreover, we
also determine the classification of RM(3,7)/RM(1,7).
We also study the algebraic immunity of the corresponding affine equivalence classes.
Moreover, several relations are derived between the algebraic immunity
and other cryptographic properties.
Finally, we introduce two new indicators which can be used to distinguish
affine inequivalent Boolean functions when the known criteria are
not sufficient. From these indicators a method can be derived for
finding the affine relation between two functions (if such
exists). The efficiency of the method depends on the structure of
the Walsh or autocorrelation spectrum.
ePrint: https://eprint.iacr.org/2004/248
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