Described is an apparatus for performing a Galois field product computation on data. A first symbol data includes a plurality of symbols each being a bit sequence on which a product operation by a factor α is to be performed in a Galois field, where α is a primitive element of the Galois field, is acquired. A factor α computation is performed on the first symbol data by performing a bit shift operation on the first symbol data toward high-order bit position, generating first mask data from the first symbol data, generating first correction data by computing a logical AND of the first mask data and a first symbol correction value, generating a factor α computation result by computing a XOR of the second symbol data and the first correction data.