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International Association for Cryptologic Research (IACR)
Abstract
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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