A programmable data encryption engine for performing the cipher function of an advanced encryption standard AES algorithm comprising: a first parallel look-up table system responsive in a first mode to a first data block for executing the multiplicative inverse in GF -1 (2 8) and applying an affine over GF transformation to obtain a subbyte transformation result; and wherein the first parallel look-up table system is responsive in a second mode to said subbyte transformation result to obtain a shift row transformation; and the programmable data encryption engine further comprises: a Galois field multiplier for transforming said shift row transformation result to obtain a mix column transformation result 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 (110, 112, 114, 116) circuit responsive to said multiplier circuit for predicting the modulo remainder of the polynomial product for an irreducible polynomial; 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. a first parallel look-up table system responsive in a first mode to a first data block for executing the multiplicative inverse in GF -1 (2 8) and applying an affine over GF transformation to obtain a subbyte transformation result; and wherein the first parallel look-up table system is responsive in a second mode to said subbyte transformation result to obtain a shift row transformation; and the programmable data encryption engine further comprises: a Galois field multiplier for transforming said shift row transformation result to obtain a mix column transformation result 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 (110, 112, 114, 116) circuit responsive to said multiplier circuit for predicting the modulo remainder of the polynomial product for an irreducible polynomial; 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. a Galois field multiplier for transforming said shift row transformation result to obtain a mix column transformation result 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 (110, 112, 114, 116) circuit responsive to said multiplier circuit for predicting the modulo remainder of the polynomial product for an irreducible polynomial; 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.