A Cipher Based on Prefix Codes

A prefix code, a P-code, is a code where no codeword is a prefix of another codeword. In this paper, a symmetric cipher based on prefix codes is proposed. The simplicity of the design makes this cipher usable for Internet of Things applications. Our goal is to investigate the security of this cipher. A detailed analysis of the fundamental properties of P-codes shows that the keyspace of the cipher is too large to mount a brute-force attack. Specifically, in this regard we will find bounds on the number of minimal P-codes containing a binary word given in advance. Furthermore, the statistical attack is difficult to mount on such cryptosystem due to the attacker’s lack of information about the actual words used in the substitution mapping. The results of a statistical analysis of possible keys are also presented. It turns out that the distribution of the number of minimal P-codes over all binary words of a fixed length is Gaussian.

METAGRAMMATICAL MODEL AND METHOD OF DECODING THE VIDEOGRAPHICAL INFORMATION WITH PREFIX COMPRESSION CODES

In the article, a metagrammatic model and the local-frequency decoding method are proposed to solve the problem of decoding videographic information with prefix compression codes. The metagrammatic model is presented as a five – level stochastic metagrammatics that allows us to take into account the structural and statistical features of prefix coded data and use them to improve the decoding efficiency. It is shown that only regular Chomsky grammars can be used in the proposed stochastic metagrammatics. The model uses a combined metagrammatics scheme with matching rules such as “terminal – initial symbol” (TS) and “terminal – product label” (TP). It is shown that structuring the model in the form of stochastic metagrammatics can significantly reduce the total number of products in metagrammatics and simplify its modification when solving problems of decoding promising prefix compression codes. The features of the local-frequency method of decoding videographic information with prefix compression codes focused on this metagrammatic model are considered. To implement one of the main and time-consuming procedures of this method, related to the search in local code tables and translation of uneven prefix codes, a local-private procedure for searching code words is proposed. The features of the software implementation of the proposed method are considered. The results of experimental testing of the method on the example of real arrays of non-uniform prefix codes are presented.