OPERATIONAL METHOD AND APPARATUS OVER GF(2M) USING A SUBFIELD GF (2M/2)

An operation method and apparatus over Galois Field GF(2.sup.m) using a subfield GF(2.sup.m/2). The operation apparatus includes a conversion circuit for converting the elements represented by a basis of GF(2.sup.m) into the elements represented by a basis of GF(2.sup.m/2); an operation circuit for performing an operation over GF(2.sup.m/2) with respect to the elements represented by the basis of GF(2.sup.m/2); and a reversion circuit for reverting the operated elements represented by the basis of GF(2.sup.m/2) to the elements represented by the basis of GF(2.sup.m), thereby performing high speed operation and simplifying circuit construction.