Usage of hypercomplex numbers in a cryptographic key agreement protocol based on neural networks

We analyse the features of the structural and functional organisation of two interacting neural networks based on the known architecture in the form of a tree parity machine (TPM) using algebras of real and hypercomplex numbers. Such machines are used as an alternative to the Diffie – Hellman algorithm to generate a shared secret cryptographic key between two parties. The main elements of mathematical models of TPMs, operating on the basis of the listed algebras, are considered. The features of the software implementation of a system simulator based on interacting TРMs are described, and the results of using the developed tool for analysing the dynamics of processes in the system under consideration are presented. Mutual learning and data exchange of two TРMs are realised based on the transmission control and Internet protocols (TCP/IP). The synchronisation state of the networks is determined by the equality of the hashes that each party calculates based on the secure hash algorithm. A hash size of 512 bits are generated by transforming the string representation of the current input vector of neuron weights. The effectiveness of possible attempts by a third party to synchronise with two legitimate TPMs operating on the basis of algebras of hypercomplex numbers is assessed.