a multiplier circuit for multiplying first and second polynomials with coefficients over a Galois field to obtain their product; and

a Galois field transformer circuit for applying an irreducible polynomial of power n to said product including a partial result generator responsive to terms of power n and greater in said product for providing a folded partial result and a Galois field adder for combining said folded partial result and the terms less than power n in the product to obtain Galois field transform of power n of said product, said partial result generator including a look-up table that includes the folded partial results for the terms with the power of n or greater, the computing system used for error correction and/or encryption.