Enhancing block cipher security with key-dependent random XOR tables generated via hadamard matrices and Sudoku game

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In this paper, we propose several efficient methods to generate t-bit random XOR tables. Specifically, we propose two methods, one based on the Hadamard matrix and the other inspired by the famous intellectual game Sudoku. Furthermore, we propose dynamic block cipher algorithms based on animating key-dependent random XOR tables. We implement and test the algorithms and statistical record for several 4-bit XOR tables. In particular, we choose the AES-128 block cipher as a specific example to apply our dynamic block cipher algorithms. We conduct a comprehensive security analysis of the key-dependent AES block cipher. We evaluate the randomness of the proposed block cipher through the NIST SP 800-22 standards as well as using a 2-level evaluation using tests for short sequences. Furthermore, we evaluate the change in Shannon entropy and min-entropy over each round of the proposed dynamic block cipher using the ENT tool and estimators in SP 800-90B. The results show that the proposed dynamic AES block cipher is more secure than the regular AES block cipher, and its statistical randomness properties are either better or equal to those of AES. This demonstrates the significance of our proposed dynamic approach based on random XOR tables, enhancing the security of the AES block cipher. In future research directions, we will explore methods to make other components of the AES block cipher dynamic.

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