Implementations of Advanced Encryption Standard (AES) encryption and decryption processes are disclosed. In one embodiment of S-box processing, a block of 16 byte values is converted, each byte value being converted from a polynomial representation in GF(256) to a polynomial representation in GF((22)4). Multiplicative inverse polynomial representations in GF((22)4) are computed for each of the corresponding polynomial representations in GF((22)4). Finally corresponding multiplicative inverse polynomial representations in GF((22)4) are converted and an affine transformation is applied to generate corresponding polynomial representations in GF(256). In an alternative embodiment of S-box processing, powers of the polynomial representations are computed and multiplied together in GF(256) to generate multiplicative inverse polynomial representations in GF(256). In an embodiment of inverse-columns-mixing, the 16 byte values are converted from a polynomial representation in GF(256) to a polynomial representation in GF((24)2). A four-by-four matrix is applied to the transformed polynomial representation in GF((24)2) to implement the inverse-columns-mixing.