Patent ID: 8649511

Claim:
A method for dealing with Galois Field computation, comprising: providing an operating circuit which has at least a multiplicative inverse unit; and using the multiplicative inverse unit to execute at least a plurality of isomorphism maps for deriving a multiplicative inverse of an input data on a specific Galois Field, wherein the plurality of isomorphism maps comprise at least a change of basis, wherein providing the operating circuit comprises selecting coefficients of an irreducible polynomial for designing the multiplicative inverse unit, wherein the coefficients are selected according to a Hamming weight, a power operation matrix, and the plurality of isomorphism maps, wherein the irreducible polynomial is m(x)=x 2 +λx+ρ and wherein λ and ρ are the coefficients of the irreducible polynomial, wherein the step of deriving the multiplicative inverse of the input data on the specific Galois Field comprises: executing a first isomorphism map for transferring the input data from a polynomial basis over the specific Galois Field GF(2 K ) to a polynomial basis over a composite field GF(2 L ) M , wherein K=L*M; executing a second isomorphism map for transferring from the polynomial basis over the composite field GF(2 L ) M to a normal basis over the specific Galois Field (2 K ); executing a power operation at the normal basis over the specific Galois Field GF(2 K ) for deriving a predetermined power of the input data; executing a third isomorphism map for transferring the predetermined power of the input data to the polynomial basis over the composite field GF(2 L ) M ; deriving a product of the input data after processing by the first isomorphism map, and the predetermined power of the input data after processing by the third isomorphism map; deriving a multiple inverse of the product at a ground field GF (2 L ); deriving a product of the input data after processing by the third isomorphism map and the multiplicative inverse of the product for deriving a multiple inverse of the input data over the basic field GF(2 L ); and executing a fourth isomorphism map for transferring the multiple inverse over the basic field GF(2 L ) from the polynomial basis over the composite field GF(2 L ) M to the polynomial basis over the specific Galois Field GF(2 K ).