Improving methods for generating encryption keys using strange attractors

Abstract

The urgency of the work is determined by the need to transfer confidential information through open communication channels. Such information can be of two types: symmetric encryption keys and directly informational messages that are encrypted with encryption keys. The article deals with the problem of improving the transmission of closed information over open channels using the Diffie- Hellman algorithm. The improvement is due to the introduction of a new type of one-sided function based on the numerical solution of the system of ordinary differential equations describing the dynamics of the phase coordinate movement of the strange attractor. For this purpose, the classic Diffie-Hellman algorithm based on the one-sided function of the discrete logarithm was considered. The required properties of one-sided functions in the general case were considered. Next, the peculiarities of algorithm modification in the case of transition to a one-sided function based on the use of a strange attractor were considered. It is assumed that at the beginning of the operation of the modified algorithm, through a secret channel, the exchange parties (agents) exchange information regarding the properties of the strange attractor to be used, namely, the definition of the differential equations describing the dynamics of a strange attractor, the values of the parameters of the equations, the initial integration conditions and the integration step (for methods with a constant step of integration). After that, all exchanges are conducted exclusively through open channels. The paper also considers the case of information exchange between more than two agents, in particular, the approach of hiding the number of agents participating in the exchange. Approbation of the method is carried out and intermediate and final results of the one-sided function based on strange attractors are given. Possibilities regarding partial disclosure by agents of certain parameters of the use of one-way functions are discussed. But at the same time, the safety of revealing such information is justified in the general case (both in the classical and in the modified Diffie-Hellman method). It was determined that depending on the needs of users, the complexity of the encryption keys can be increased by changing the initial parameters of the attractor, which will also allow controlling speed of key generation and encryption in general. The software that implements the proposed modified algorithm is implemented in three programming languages, C#, Python, and MatLab. This made it possible to perform a comparative analysis of the results and consciously choose the programming language of individual parts of the software to optimize the encryption key generation process for specific conditions.