The purpose of this article is to present a method for depersonalizing personal data based on the use of cellular automata. This method is the construction of a hash function with a secret key that performs transformations on a two-dimensional matrix in accordance with the transition rules for two-dimensional cellular automata. A new kind of transition rules for two-dimensional cellular automata related to the Moore neighborhood and the state of the cell is proposed. Additionally, these rules are based on the initial state of the matrix, which avoids the existence of insignificant bits that can lead to collisions. The proposed hashing method can be classified as universal. A computer program “HFCA-2D” is presented, designed not only to automate the process of hashing data using cellular automata, but also containing tools for testing hashing algorithms for speed and the presence of collisions when processing various types and amounts of data, in comparison with SHA algorithms. 256 and SHA-512. The test results showed that the developed data hashing method provides a high level of security and privacy protection