3,030 research outputs found
Linear solutions for cryptographic nonlinear sequence generators
This letter shows that linear Cellular Automata based on rules 90/150
generate all the solutions of linear difference equations with binary constant
coefficients. Some of these solutions are pseudo-random noise sequences with
application in cryptography: the sequences generated by the class of shrinking
generators. Consequently, this contribution show that shrinking generators do
not provide enough guarantees to be used for encryption purposes. Furthermore,
the linearization is achieved through a simple algorithm about which a full
description is provided
Broadcasting Automata and Patterns on Z^2
The Broadcasting Automata model draws inspiration from a variety of sources
such as Ad-Hoc radio networks, cellular automata, neighbourhood se- quences and
nature, employing many of the same pattern forming methods that can be seen in
the superposition of waves and resonance. Algorithms for broad- casting
automata model are in the same vain as those encountered in distributed
algorithms using a simple notion of waves, messages passed from automata to au-
tomata throughout the topology, to construct computations. The waves generated
by activating processes in a digital environment can be used for designing a
vari- ety of wave algorithms. In this chapter we aim to study the geometrical
shapes of informational waves on integer grid generated in broadcasting
automata model as well as their potential use for metric approximation in a
discrete space. An explo- ration of the ability to vary the broadcasting radius
of each node leads to results of categorisations of digital discs, their form,
composition, encodings and gener- ation. Results pertaining to the nodal
patterns generated by arbitrary transmission radii on the plane are explored
with a connection to broadcasting sequences and ap- proximation of discrete
metrics of which results are given for the approximation of astroids, a
previously unachievable concave metric, through a novel application of the
aggregation of waves via a number of explored functions
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
Randomized Cellular Automata
We define and study a few properties of a class of random automata networks.
While regular finite one-dimensional cellular automata are defined on periodic
lattices, these automata networks, called randomized cellular automata, are
defined on random directed graphs with constant out-degrees and evolve
according to cellular automaton rules. For some families of rules, a few
typical a priori unexpected results are presented.Comment: 13 pages, 7 figure
The application of cellular automata to weather radar
A possible cellular automaton approach to weather (and in particular rainfall) modelling is considered. After posing a paradigm problem in a manner reminiscent of a numerical PDE solver and showing that the general approach appears to be valid, we consider some more detailed modelling and comment on how this could be used to construct a genuine finite-state cellular automaton
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