COMPREHENSIVE REVIEW OF CATALAN NUMBER-BASED CRYPTOGRAPHIC SYSTEMS IN MODERN ENCRYPTION FOCUSING ON SECURITY, PERFORMANCE, AND IMPLEMENTATION CHALLENGES

The rapid evolution of digital technologies has heightened the demand for cryptographic systems that are both secure and adaptable. Catalan number-based cryptography has recently attracted attention for its ability to leverage combinatorial structures in the design of block ciphers and encryption protocols. This review presents a critical analysis of the current state of the field, examining core algorithms such as tweakable ciphers, polygon triangulation schemes, and variable-length block mechanisms from both theoretical and practical perspectives. Particular emphasis is placed on their resistance to advanced cryptanalytic methods and their potential applicability to quantum-resilient security. At the same time, the review identifies key challenges, including efficiency optimization, interoperability with established standards, and the need for systematic benchmarking. By integrating mathematical foundations with implementation-oriented insights, this article highlights the promise of Catalan numbers as a basis for cryptographic innovation while outlining the gaps and future directions necessary for their broader adoption.