Symmetric stream and finite automaton ciphersystems

The following statements are proved in the paper: 1) stream ciphersystems with the indistinguishable key stream generators are indistinguishable themselves; 2) the output function of the encryption automaton in any finite automaton ciphersystem is injective one for any its state and key being fixed; 3) the classes of the stream and of the finite automaton ciphersystems are functionally equivalent; 4) every selfsynchronizing with a delay $\tau$ finite automaton ciphersystem with the strongly connected projections of the encryption automaton is indistinguishable from a ciphersystem built on the base of a shiftregister of the length $\tau$. Besides, a descriptive and a constructive definitions of the selfsynchronizing stream ciphersystem are introduced, and the equivalence between them are stated.