AN ALGORITHMIC FRAMEWORK FOR TEXT ENCRYPTION BASED ON A CLOSED KNIGHT’S TOUR ON OPTIMAL-SIZED BOARDS

Abstract

The application of knight's tour permutations to data encryption has been explored for media such as images and video, where algorithms typically operate on standardized, fixed-size blocks of data. This paper addresses a different and more fundamental challenge: the encryption of variable-length text, where no predefined block size exists. The primary contribution of this work is a novel algorithmic framework that determines the optimally sized rectangular board that admits a closed knight's tour and minimizes the padding required for a given text length. Using this framework, we develop a complete symmetric-key cryptosystem that combines a Vigenère-style XOR substitution for confusion with a knight’s tour-based permutation for diffusion. To improve robustness, we incorporate an iterative board-resizing mechanism to handle cases in which the tour-finding heuristic fails. The system's performance reveals an efficient board-finding process that both theoretically and empirically minimizes padding, along with a non-linear increase in encryption time for input length increases. Security analysis demonstrates that the cipher obfuscates plaintext statistics and has a large keyspace,; however, it exhibits a poor avalanche effect, consistent with its single-round architecture. This work lies at the intersection of graph theory, optimization, and cryptography, and it concludes by proposing a multi-round architecture with improved diffusion for future research.