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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
Modelling Nonlinear Sequence Generators in terms of Linear Cellular Automata
In this work, a wide family of LFSR-based sequence generators, the so-called
Clock-Controlled Shrinking Generators (CCSGs), has been analyzed and identified
with a subset of linear Cellular Automata (CA). In fact, a pair of linear
models describing the behavior of the CCSGs can be derived. The algorithm that
converts a given CCSG into a CA-based linear model is very simple and can be
applied to CCSGs in a range of practical interest. The linearity of these
cellular models can be advantageously used in two different ways: (a) for the
analysis and/or cryptanalysis of the CCSGs and (b) for the reconstruction of
the output sequence obtained from this kind of generators.Comment: 15 pages, 0 figure
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Pseudorandom number generation with self programmable cellular automata
In this paper, we propose a new class of cellular automata – self programming cellular automata (SPCA) with specific application to pseudorandom number generation. By changing a cell's state transition rules in relation to factors such as its neighboring cell's states, behavioral complexity can be increased and utilized. Interplay between the state transition neighborhood and rule selection neighborhood leads to a new composite neighborhood and state transition rule that is the linear combination of two different mappings with different temporal dependencies. It is proved that when the transitional matrices for both the state transition and rule selection neighborhood are non-singular, SPCA will not exhibit non-group behavior. Good performance can be obtained using simple neighborhoods with certain CA length, transition rules etc. Certain configurations of SPCA pass all DIEHARD and ENT tests with an implementation cost lower than current reported work. Output sampling methods are also suggested to improve output efficiency by sampling the outputs of the new rule selection neighborhoods
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