Data Encryption for Internet of Things Applications Based on Catalan Objects and Two Combinatorial Structures

This article presents a novel data encryption technique suitable for Internet of Things (IoT) applications. The cryptosystem is based on the application of a Catalan object (as a cryptographic key) that provides encryption based on combinatorial structures with noncrossing or nonnested matching. The experimental part of this article includes a comparative analysis of the proposed encryption method with the Catalan numbers and data encryption standard (DES) algorithm, which is performed with machine learning-based identification of the encryption method using ciphertext only. These tests showed that it is much more difficult to recognize ciphertext generated with the Catalan method than one made with the DES algorithm. System reliability depends on the quality of the key, therefore, statistical testing proposed by National Institute of Standards and Technology was also performed. Twelve standard tests, the approximate entropy measurement, and random digression complexity analysis are applied in order to evaluate the quality of the generated Catalan key. A proposal for applying this method in e-Health IoT is also given. Possibilities of applying this method in the IoT applications for smart cities data storage and processing are provided.