787 research outputs found
Fast Algebraic Attacks and Decomposition of Symmetric Boolean Functions
Algebraic and fast algebraic attacks are power tools to analyze stream
ciphers. A class of symmetric Boolean functions with maximum algebraic immunity
were found vulnerable to fast algebraic attacks at EUROCRYPT'06. Recently, the
notion of AAR (algebraic attack resistant) functions was introduced as a
unified measure of protection against both classical algebraic and fast
algebraic attacks. In this correspondence, we first give a decomposition of
symmetric Boolean functions, then we show that almost all symmetric Boolean
functions, including these functions with good algebraic immunity, behave badly
against fast algebraic attacks, and we also prove that no symmetric Boolean
functions are AAR functions. Besides, we improve the relations between
algebraic degree and algebraic immunity of symmetric Boolean functions.Comment: 13 pages, submitted to IEEE Transactions on Information Theor
Constructions of Almost Optimal Resilient Boolean Functions on Large Even Number of Variables
In this paper, a technique on constructing nonlinear resilient Boolean
functions is described. By using several sets of disjoint spectra functions on
a small number of variables, an almost optimal resilient function on a large
even number of variables can be constructed. It is shown that given any ,
one can construct infinitely many -variable ( even), -resilient
functions with nonlinearity . A large class of highly
nonlinear resilient functions which were not known are obtained. Then one
method to optimize the degree of the constructed functions is proposed. Last,
an improved version of the main construction is given.Comment: 14 pages, 2 table
Implementing Symmetric Cryptography Using Sequence of Semi-Bent Functions
Symmetric cryptography is a cornerstone of everyday digital security, where two parties must share a common key to communicate. The most common primitives in symmetric cryptography are stream ciphers and block ciphers that guarantee confidentiality of communications and hash functions for integrity. Thus, for securing our everyday life communication, it is necessary to be convinced by the security level provided by all the symmetric-key cryptographic primitives. The most important part of a stream cipher is the key stream generator, which provides the overall security for stream ciphers. Nonlinear Boolean functions were preferred for a long time to construct the key stream generator. In order to resist several known attacks, many requirements have been proposed on the Boolean functions. Attacks against the cryptosystems have forced deep research on Boolean function to allow us a more secure encryption. In this work we describe all main requirements for constructing of cryptographically significant Boolean functions. Moreover, we provide a construction of Boolean functions (semi-bent Boolean functions) which can be used in the construction of orthogonal variable spreading factor codes used in code division multiple access (CDMA) systems as well as in certain cryptographic applications
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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