Geodesic
Inverse dynamical systems with variable dimension of phase space in problems of cryptographic information transformation
Prikladnaâ diskretnaâ matematika, no. 2 (2008), pp. 39-44.

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The paper considers modern algorithms of information protection based on discrete inverse dynamical systems. The effect of dynamical degradation of transformation system is identified. The attraction of trajectories to invariant sets of smaller dimension results in resistance decrease of corresponding algorithms. To compensate for this effect the method of phase space dimension regulation is proposed. For a Lorenz system, the transition from the prototype system to its automaton analogue specified by equations over a finite ring or a Galois field is described. For such an automaton an algorithm for controlling the state space and input space dimensions by means of introduction of certain predicates is described. It is proved that the obtained automaton might be considered us a subautomaton of some infinite automaton over the algebraic extension of the initial Galois field. 
@article{PDM_2008_2_a8,
     author = {A. M. Kovalev and V. A. Kozlovskii and V. F. Shcherbak},
     title = {Inverse dynamical systems with variable dimension of phase space in problems of cryptographic information transformation},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {39--44},
     publisher = {mathdoc},
     number = {2},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2008_2_a8/}
}
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A. M. Kovalev; V. A. Kozlovskii; V. F. Shcherbak. Inverse dynamical systems with variable dimension of phase space in problems of cryptographic information transformation. Prikladnaâ diskretnaâ matematika, no. 2 (2008), pp. 39-44. http://geodesic.mathdoc.fr/item/PDM_2008_2_a8/