1,064 research outputs found
Balanced Symmetric Functions over
Under mild conditions on , we give a lower bound on the number of
-variable balanced symmetric polynomials over finite fields , where
is a prime number. The existence of nonlinear balanced symmetric
polynomials is an immediate corollary of this bound. Furthermore, we conjecture
that are the only nonlinear balanced elementary symmetric
polynomials over GF(2), where , and we prove various results in support of this conjecture.Comment: 21 page
Fast algebraic immunity of Boolean functions and LCD codes
Nowadays, the resistance against algebraic attacks and fast algebraic attacks
are considered as an important cryptographic property for Boolean functions
used in stream ciphers. Both attacks are very powerful analysis concepts and
can be applied to symmetric cryptographic algorithms used in stream ciphers.
The notion of algebraic immunity has received wide attention since it is a
powerful tool to measure the resistance of a Boolean function to standard
algebraic attacks. Nevertheless, an algebraic tool to handle the resistance to
fast algebraic attacks is not clearly identified in the literature. In the
current paper, we propose a new parameter to measure the resistance of a
Boolean function to fast algebraic attack. We also introduce the notion of fast
immunity profile and show that it informs both on the resistance to standard
and fast algebraic attacks. Further, we evaluate our parameter for two
secondary constructions of Boolean functions. Moreover, A coding-theory
approach to the characterization of perfect algebraic immune functions is
presented. Via this characterization, infinite families of binary linear
complementary dual codes (or LCD codes for short) are obtained from perfect
algebraic immune functions. The binary LCD codes presented in this paper have
applications in armoring implementations against so-called side-channel attacks
(SCA) and fault non-invasive attacks, in addition to their applications in
communication and data storage systems
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