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

Abstract

The XOR operator is a simple yet crucial computation in computer science, especially in cryptography. In symmetric cryptographic schemes, particularly in block ciphers, the AddRoundKey transformation is commonly used to XOR an internal state with a round key. One method to enhance the security of block ciphers is to diversify this transformation. In this paper, we propose some straightforward yet highly effective techniques for generating t-bit random XOR tables. One approach is based on the Hadamard matrix, while another draws inspiration from the popular intellectual game Sudoku. Additionally, we introduce algorithms to animate the XOR transformation for generalized block ciphers. Specifically, we apply our findings to the AES encryption standard to present the key-dependent AES algorithm. Furthermore, we conduct a security analysis and assess the randomness of the proposed key-dependent AES algorithm using NIST SP 800-22, Shannon entropy based on the ENT tool, and min-entropy based on NIST SP 800-90B. Thanks to the key-dependent random XOR tables, the key-dependent AES algorithm have become much more secure than AES, and they also achieve better results in some statistical standards than AES.