LINEAR RECURRENT RELATIONS IN THE SYSTEM OF SYMMETRIC ENCRYPTION ALGORITHMS

Abstract

The article proposes the principles of functioning of symmetric encryption based on a gamma cipher obtained by gen- erating linear recurrence relations. The influence of a linear recurrence relation on the cryptographic stability of algorithms is investigated, and examples of practical application of recurrent models in ensuring the encryption process are also given. The encrypted text obtained by the gamma method based on a linear recurrence relation is quite laborious to reveal if the gamma cipher does not contain repeated bit sequences and changes randomly for each encrypted word. If the gamma period exceeds the length of the entire encrypted text and no part of the original text is known, then the cipher can be revealed only by direct search of the set of probable key values, in this case, the cryptographic stability is determined by the size of the key. The extent to which the formed gamma meets the security requirements in most cases depends on the initial data on the basis of which the linear recurrence relation is generated. The maximum value of the sequence period depends entirely on the depth of the linear recurrence relation and the relation that sets it, and the specific values – on the initial state of the sequence. The cryptographic strength of the algorithm can be increased by combining several different linear recurrence relations in the context of LFSRs and/or by using nonlinear functions in the register feedback, nonlinear logic and filtering of the register contents. The symmet- ric encryption algorithm based on the linear recurrence relation allows for both software and hardware implementation. From the point of view of practicality, software implementation allows for greater flexibility in use. However, the implementation of encryption algorithms in the main program code provokes numerous security risks associated mainly with unauthorized access and message confidentiality issues. To solve such a problem, it is appropriate to apply the practice of removing encryption and/ or decryption functions to separate modules or libraries, as well as transmitting the protected key using only protected channels. The article describes how a linear recurrence relation functions based on establishing dependencies between members of an unknown sequence and an index. The current method has found wide application in algorithm analysis, digital signal processing, economics, and in the context of cryptography it is often used within the framework of symmetric encryption. The article defines that a modular approach involves dividing software into logically independent parts, each of which performs a separate function. When converting a module into a dynamic library, the main program will only call the function, when necessary, completely hiding access to the algorithm code. Thus, cryptographic operations will be implemented in isolation, which will reduce the risk of unauthorized access to the encryption algorithm.