Information protection problems of factorial numbers

Abstract

The article discusses the method of protecting data based on permutations for the simultaneous protection of data from unauthorized access and interference. Assigning a permutation, in which the elements are independent of each other and with large cipher lengths are close to equiprobable, is proposed for each message. In this case, the statistics of the protected messages will not affect the cipher, which will complicate their decryption. Another advantage of the proposed method is possibility to combine the protection of information from unauthorized access with its noise-resistant coding. This is due to the fact that permutations contain redundant information that makes possible to detect and correct errors in the transmitted messages. For implementation of the proposed method the conversion of the original message to the corresponding permutation of characters is required. In the work factorial numbers are used for this conversion. Forming permutations based on the factorial numbers makes it possible not only to obtain permutations, but also to perform various arithmetic operations on them. These transformations make the ciphers considered repeatable and homogeneous, thereby achieving homogeneity and noise immunity of encryption devices. The structure of the data transmission system on permutations obtained using factorial number systems, in which the problems posed in the work are solved, is shown. The main properties and characteristics of factorial number systems are listed. A detailed description of the method steps for message encryption with permutations is given. It is shown that in order to increase the efficiency of the considered method, it is necessary to introduce a special key that would not depend on the transformation algorithm. Such a key can be the second factorial number that will be added to the number obtained after converting the original message. If this key is dynamic, in the form of a pseudo-random factorial number, then deciphering such a cipher will be much more difficult, especially with increasing permutation length. It is harder, especially with increasing length of permutations. Thus, the purpose of the article is to develop a noise-resistant method of perfect encryption with a high-speed operation that is sufficient for practical tasks. The novelty of the work lies in the method of perfect Shannon-based encryption based on the platform of permutations using factorial numbers to obtain them.