668 research outputs found
Cryptographic properties of Boolean functions defining elementary cellular automata
In this work, the algebraic properties of the local transition functions of elementary cellular automata (ECA) were analysed. Specifically, a classification of such cellular automata was done according to their algebraic degree, the balancedness, the resiliency, nonlinearity, the propagation criterion and the existence of non-zero linear structures. It is shown that there is not any ECA satisfying all properties at the same time
Revisiting LFSMs
Linear Finite State Machines (LFSMs) are particular primitives widely used in
information theory, coding theory and cryptography. Among those linear
automata, a particular case of study is Linear Feedback Shift Registers (LFSRs)
used in many cryptographic applications such as design of stream ciphers or
pseudo-random generation. LFSRs could be seen as particular LFSMs without
inputs.
In this paper, we first recall the description of LFSMs using traditional
matrices representation. Then, we introduce a new matrices representation with
polynomial fractional coefficients. This new representation leads to sparse
representations and implementations. As direct applications, we focus our work
on the Windmill LFSRs case, used for example in the E0 stream cipher and on
other general applications that use this new representation.
In a second part, a new design criterion called diffusion delay for LFSRs is
introduced and well compared with existing related notions. This criterion
represents the diffusion capacity of an LFSR. Thus, using the matrices
representation, we present a new algorithm to randomly pick LFSRs with good
properties (including the new one) and sparse descriptions dedicated to
hardware and software designs. We present some examples of LFSRs generated
using our algorithm to show the relevance of our approach.Comment: Submitted to IEEE-I
Cellular Automata and Randomization: A Structural Overview
The chapter overviews the methods, algorithms, and architectures for random number generators based on cellular automata, as presented in the scientific literature. The variations in linear and two-dimensional cellular automata model and their features are discussed in relation to their applications as randomizers. Additional memory layers, functional nonuniformity in space or time, and global feedback are examples of such variations. Successful applications of cellular automata random number/signal generators (both software and hardware) reported in the scientific literature are also reviewed. The chapter includes an introductory presentation of the mathematical (ideal) model of cellular automata and its implementation as a computing model, emphasizing some important theoretical debates regarding the complexity and universality of cellular automata
Cellular Automata
Modelling and simulation are disciplines of major importance for science and engineering. There is no science without models, and simulation has nowadays become a very useful tool, sometimes unavoidable, for development of both science and engineering. The main attractive feature of cellular automata is that, in spite of their conceptual simplicity which allows an easiness of implementation for computer simulation, as a detailed and complete mathematical analysis in principle, they are able to exhibit a wide variety of amazingly complex behaviour. This feature of cellular automata has attracted the researchers' attention from a wide variety of divergent fields of the exact disciplines of science and engineering, but also of the social sciences, and sometimes beyond. The collective complex behaviour of numerous systems, which emerge from the interaction of a multitude of simple individuals, is being conveniently modelled and simulated with cellular automata for very different purposes. In this book, a number of innovative applications of cellular automata models in the fields of Quantum Computing, Materials Science, Cryptography and Coding, and Robotics and Image Processing are presented
A reversible system based on hybrid toggle radius-4 cellular automata and its application as a block cipher
The dynamical system described herein uses a hybrid cellular automata (CA)
mechanism to attain reversibility, and this approach is adapted to create a
novel block cipher algorithm called HCA. CA are widely used for modeling
complex systems and employ an inherently parallel model. Therefore,
applications derived from CA have a tendency to fit very well in the current
computational paradigm where scalability and multi-threading potential are
quite desirable characteristics. HCA model has recently received a patent by
the Brazilian agency INPI. Several evaluations and analyses performed on the
model are presented here, such as theoretical discussions related to its
reversibility and an analysis based on graph theory, which reduces HCA security
to the well-known Hamiltonian cycle problem that belongs to the NP-complete
class. Finally, the cryptographic robustness of HCA is empirically evaluated
through several tests, including avalanche property compliance and the NIST
randomness suite.Comment: 34 pages, 12 figure
Predicting Non-linear Cellular Automata Quickly by Decomposing Them into Linear Ones
We show that a wide variety of non-linear cellular automata (CAs) can be
decomposed into a quasidirect product of linear ones. These CAs can be
predicted by parallel circuits of depth O(log^2 t) using gates with binary
inputs, or O(log t) depth if ``sum mod p'' gates with an unbounded number of
inputs are allowed. Thus these CAs can be predicted by (idealized) parallel
computers much faster than by explicit simulation, even though they are
non-linear.
This class includes any CA whose rule, when written as an algebra, is a
solvable group. We also show that CAs based on nilpotent groups can be
predicted in depth O(log t) or O(1) by circuits with binary or ``sum mod p''
gates respectively.
We use these techniques to give an efficient algorithm for a CA rule which,
like elementary CA rule 18, has diffusing defects that annihilate in pairs.
This can be used to predict the motion of defects in rule 18 in O(log^2 t)
parallel time
Pseudo-random Sequences Generated by Cellular Automata
International audienceGeneration of pseudo random sequences by cellular automata, as well as by hybrid cellular automata is surveyed. An application to the fast evaluation and FPGA implementation of some classes of boolean functions is sketched out
- âŠ