Source and Channel Models for Secret-key Agreement Based on Catalan Numbers and the Lattice Path Combinatorial Approach

This paper presents a solution to secret key sharing protocol problem that establishes cryptographically secured communication between two entities. We propose a new symmetric cryptographic key exchange scenario based on the specific properties of Catalan numbers and the Lattice Path combinatorics. Our scenario consists of three phases: generating Catalan values, defining the Lattice Path movement space and defining the key equalization rules. In the experimental part of this study, we have merged our scenario with the Maurer’s protocol, while in the information-theoretical approach to the key exchange we have presented how a partially split bit sequence can become the secret key that both parties in communication can use. Maurer’s satellite scenario model for the exchange of the Catalan key is discussed in detail and its application is proposed. Security analysis of the protocol and testing for channel capacity or key generation speed is also suggested.