I. D. Gorkov

Efficiency of cryptographic methods of protection of the information that are used in information-telecommunication systems is defined appreciably by the construction of the cryptographic schemes. Consecutive connections of the independent finite automata (the operating block) and the on-line automata (the generating block) are often used in cryptographic schemes as generators of sequences. Thus the sequence developed by operating block (operating scale), defines the law of clock-controlled movement of the information in the generating block. Studying of so-called σ-periodic sequences, that are the sequences breaking into pieces of identical length, so that the sum of elements of sequence of each piece is identical, represents the interest for research of generators with clock-controlled movement (generators of "- steps" and generators with alternating step). The property of σ-periodicity must be considered as generalization of the property of periodicity. Properties of σ-periodic sequences are investigated in the article. For periodic sequence it is proved that length of the σ-period divides length of the period. For linear recurrent sequence with the period of the maximum length it is proved that lengths of the σ-period and of the period coincide. It is established that the length of the σ-period of de Bruijn-s sequence of the n-order is equal to 2r, (r

Pages: 34-37

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