The paper outlines methods for constructing telecommunication systems based on the principle of time division of channels and using factorial code in order to maintain the cyclic phase of receiver/transmitter and ensure information security. These systems provide integrated data protection (against errors in communication channel and attempts of unauthorized access to information), as well as the ability to allocate system resources (bandwidth) between its subscribers. The purpose of this work is to develop and research the approach of building telecommunication systems with multiple access to a common channel for collective use, based on the property of factorial codes to keep clock and frame synchronism with a working signal. The basic idea is to choose the permutations to transfer information with a single set of properties or attributes. This provides opportunities of dividing channel into subchannels, bandwidth sharing on transmission accuracy, and dividing plurality of network users into closed groups. The channel resource sharing procedure based on factorial coding is described. Examples of multiplex cycle organization and the order of occupying/releasing multiplex cycle time channels by users are given. The system load and the subchannel bandwidth are estimated. Copyright © 2020 Praise Worthy Prize - All rights reserved.

The paper proposes a new principle for the implementation of a three-pass cryptographic protocol. All operations implemented in it are performed on permutations. Such operations are the multiplication of permutations, raising to the power of their disjoint cycles, as well as the operation of finding the conjugate permutation. This avoids the problems associated with discrete logarithms, which can increase the cryptographic strength of the proposed protocol. The developed protocol can be used both for information transmission systems using factorial coding and for traditional systems.

FACTORIAL CODING WITH ERROR CORRECTION