Enhanced Advanced Encryption Standard

The analysis of AES (Advanced Encryption Standard) including the byte substitution method, the permutation stage made by shifting the data matrix rows and the column mixing step, shows some of the weak points of this algorithm. We propose enhancing some features of AES by the mean of more powerful arrays and polynomials that make the algorithm more robust against various cryptographic attacks including the differential one. We analyze the algorithm over the Galois Field with 256 integer values, denoted as GF(256), and we propose to use Costas arrays for byte substitution and permutation, and a polynomial with primitive roots for mixing the columns of the data matrix, getting an enhanced version of the encryption algorithm, with better features and an increased degree of non-linearity.