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Journal of Information Science and Engineering, Vol. 37 No. 2, pp. 469-482

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

1Department of Computer Sciences
University of Novi Pazar
Novi Pazar, 36300 Serbia

2Faculty of Informatics and Computing
Singidunum University
Belgrade, 11000 Serbia

3Faculty of Computer Sciences
Megatrend University
Belgrade, 11000 Serbia

4Faculty of Informatics
International Vision University
Gostivar, 1230 North Macedonia

5HTM School of Professional Studies in Trstenik
Trstenik, 37240 Serbia
E-mail: muzafers@uninp.edu.rs; sadamovic@singidunum.ac.rs;
macek.nemanja@gmail.com; aybeyan@vizyon.edu.mk; selverp@gmail.com

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.

Keywords: cryptography, secret key sharing protocol, Catalan numbers, Lattice path, Maurer’s satellite scenario

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