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When establishing a cryptographic key between two users, the asymmetric cryptography scheme is generally used to send it through an insecure channel. However, given that the algorithms that use this scheme, such as RSA, have already been compromised, it is imperative to research for new methods of establishing a cryptographic key that provide security when they are sent. To solve this problem, a new branch known as neural cryptography was born, using a modified artificial neural network called Tree Parity Machine or TPM. Its purpose is to establish a private key through an insecure channel. This article proposes the analysis of an optimal structure of a TPM network that allows generating and establishing a private cryptographic key of 512-bit length between two authorized parties. To achieve this, the combinations that make possible to generate a key of that length were determined. In more than 15 million simulations that were executed, we measured synchronization times, the number of steps required, and the number of times in which an attacking TPM network manages to imitate the behaviour of the two networks. The simulations resulted in the optimal combination, minimizing the synchronization time and prioritizing security against the attacking network. Finally, the model was validated by applying a heuristic rule.

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