623 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
On -Variable Symmetric Boolean Functions with Maximum Algebraic Immunity
Algebraic immunity of Boolean function is defined as the minimal degree
of a nonzero such that or . Given a positive even integer
, it is found that the weight distribution of any -variable symmetric
Boolean function with maximum algebraic immunity is determined by
the binary expansion of . Based on the foregoing, all -variable symmetric
Boolean functions with maximum algebraic immunity are constructed. The amount
is $(2\wt(n)+1)2^{\lfloor \log_2 n \rfloor}
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
The Fourier Spectral Characterization for the Correlation-Immune Functions over Fp
The correlation-immune functions serve as an important metric for measuring
resistance of a cryptosystem against correlation attacks. Existing literature
emphasize on matrices, orthogonal arrays and Walsh-Hadamard spectra to
characterize the correlation-immune functions over (
is a prime). %with prime . Recently, Wang and Gong investigated the Fourier
spectral characterization over the complex field for correlation-immune Boolean
functions. In this paper, the discrete Fourier transform (DFT) of non-binary
functions was studied. It was shown that a function over is
th-order correlation-immune if and only if its Fourier spectrum vanishes at
a specific location under any permutation of variables. Moreover, if is a
symmetric function, is correlation-immune if and only if its Fourier
spectrum vanishes at only one location
Properties and constructions of coincident functions
Extensive studies of Boolean functions are carried in many fields. The Mobius
transform is often involved for these studies. In particular, it plays a
central role in coincident functions, the class of Boolean functions invariant
by this transformation. This class -- which has been recently introduced -- has
interesting properties, in particular if we want to control both the Hamming
weight and the degree. We propose an innovative way to handle the Mobius
transform which allows the composition between several Boolean functions and
the use of Shannon or Reed-Muller decompositions. Thus we benefit from a better
knowledge of coin-cident functions and introduce new properties. We show
experimentally that for many features, coincident functions look like any
Boolean functions
On the Immunity of Rotation Symmetric Boolean Functions Against Fast Algebraic Attacks
In this paper, it is shown that an -variable rotation symmetric Boolean function with even but not a power of 2 admits a rotation symmetric function of degree at most such that the product has degree at most
Constructing -variable Boolean functions with optimal algebraic immunity based on polar decomposition of
Constructing -variable Boolean functions with optimal algebraic immunity
based on decomposition of additive group of the finite field
seems to be a promising approach since Tu and Deng's
work. In this paper, we consider the same problem in a new way. Based on polar
decomposition of the multiplicative group of , we propose
a new construction of Boolean functions with optimal algebraic immunity. By a
slight modification of it, we obtain a class of balanced Boolean functions
achieving optimal algebraic immunity, which also have optimal algebraic degree
and high nonlinearity. Computer investigations imply that this class of
functions also behave well against fast algebraic attacks.Comment: 20 page
Design of a New Stream Cipher: PALS
In this paper, a new stream cipher is designed as a clock-controlled one, but
with a new mechanism of altering steps based on system theory in such a way
that the structures used in it are resistant to conventional attacks. Our
proposed algorithm (PALS) uses the main key with the length of 256 bits and a
32-bit message key. The most important criteria considered in designing the
PALS are resistance to known attacks, maximum period, high linear complexity,
and good statistical properties. As a result, the output keystream is very
similar to the perfectly random sequences and resistant to conventional attacks
such as correlation attacks, algebraic attack, divide & conquer attack,
time-memory tradeoff attack and AIDA/cube attacks. The base structure of the
PALS is a clock-controlled combination generator with memory and we obtained
all the features according to design criteria with this structure. PALS can be
used in many applications, especially in financial cryptography due to its
proper security feature
Search Space Reduction of Asynchrony Immune Cellular Automata by Center Permutivity
We continue the study of asynchrony immunity in cellular automata (CA), which
can be considered as a weaker version of correlation immunity in the context of
vectorial Boolean functions. The property could have applications as a
countermeasure for side-channel attacks in CA-based cryptographic primitives,
such as S-boxes and pseudorandom number generators. We first give some
theoretical results on the necessary conditions that a CA rule must satisfy in
order to meet asynchrony immunity, the most important one being center
permutivity. Next, we perform an exhaustive search of all asynchrony immune CA
rules of neighborhood size up to , leveraging on the discovered theoretical
properties to greatly reduce the size of the search space.Comment: 12 pages, 2 figures, extended version of the paper "Asynchrony Immune
Cellular Automata" by L. Mariot presented at ACA 2016. Corrected small typos
from previous version and added three bibliographical reference
Symmetric Boolean Function with Maximum Algebraic Immunity on Odd Number of Variables
To resist algebraic attack, a Boolean function should possess good algebraic
immunity (AI). Several papers constructed symmetric functions with the maximum
algebraic immunity . In this correspondence we prove
that for each odd , there is exactly one trivial balanced -variable
symmetric Boolean function achieving the algebraic immunity . And we also obtain a necessary condition for the algebraic
normal form of a symmetric Boolean function with maximum algebraic immunity
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