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Block cipher is a cryptographic field that is now widely applied in various domains. Besides its security, deployment issues, implementation costs, and flexibility across different platforms are also crucial in practice. From an efficiency perspective, the linear layer is often the slowest transformation and requires significant implementation costs in block ciphers. Many current works employ lookup table techniques for linear layers, but they are quite costly and do not save memory storage space for the lookup tables. In this paper, we propose a novel lookup table technique to reduce memory storage when executing software. This technique is applied to the linear layer of block ciphers with recursive Maximum Distance Separable (MDS) matrices, Hadamard MDS matrices, and circulant MDS matrices of considerable sizes (e.g. sizes of 16, 32, 64, and so on). The proposed lookup table technique leverages the recursive property of linear matrices and the similarity in elements of Hadamard or circulant MDS matrices, allowing the construction of a lookup table for a submatrix instead of the entire linear matrix. The proposed lookup table technique enables the execution of the diffusion layer with unchanged computational complexity (number of XOR operations and memory accesses) compared to conventional lookup table implementations but allows a substantial reduction in memory storage for the pre-computed tables, potentially reducing the storage needed by 4 or 8 times or more. The memory storage will be reduced even more as the size of the MDS matrix increases. For instance, analysis shows that when the matrix size is 64, the memory storage ratio with the proposed lookup table technique decreases by 87.5% compared to the conventional lookup table technique. This method also allows for more flexible software implementations of large-sized linear layers across different environments. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]