Unified Byte Permutations for the Block Cipher 3D

3D is a 512-bit block cipher whose design is inspired from the Advanced Encryption Standard (AES). Like the AES, each round of 3D is composed of 4 transformations including a round-key addition, a byte-wise substitution, a byte-wise shuffle and an MDS matrix multiplication. In 3D, two distinct byte-wise permutations are employed for odd and even rounds. In this paper, using concepts from graph theory, we design a unified byte permutation for both odd and even rounds with the same diffusion property as the original cipher. The main advantage of this new transformation is in hardware implementation of the cipher where with less resources we can speed up the encryption/decryption process.