A compact Galois field parallel multiplier engine includes a multiplier circuit for multiplying together two polynomials with coefficients over a Galois field to obtain their product; a Galois field linear transformer circuit has a multiply input from the multiplier circuit for predicting the modulo remainder of the polynomial product for an irreducible polynomial; first and second polynomial inputs; the Galois field linear transformer circuit may include a plurality of cells configured in a matrix section and a unity matrix section wherein the unity matrix section cells represent the prediction of the remainder when the output of the multiplier circuit is a polynomial with a power less than the power of the irreducible polynomial.
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