1. A programmable data encryption engine interconnected between an input circuit and an output circuit for performing the cipher function of an advanced encryption standard (AES) algorithm, the engine comprising: a first parallel look-up table responsive to a first data block for implementing an AES selection function and executing the multiplicative inverse in GF-J(28) and applying an affine over GF(2) transformation to obtain a subbyte transformation; a second parallel look-up table for transforming said subbyte transformation to obtain a shift row transformation; and a Galois field multiplier for transforming said shift row transformation to obtain a mix column transformation and adding a round key resulting in an advanced encryption standard cipher function of said first data block, said Galois field multiplier including a multiplier circuit for multiplying two polynomials with coefficients over a Galois field to obtain their product; a Galois field linear transformer circuit responsive to said multiplier circuit for predicting the modulo remainder of the polynomial product for an irreducible polynomial; and a storage circuit for supplying to said Galois field linear transformer circuit a set of coefficients for predicting the modulo remainder for a predetermined irreducible polynomial.