A processing unit transforms first input information into first nonlinear transformed information that is transformed into first linear transformed information, and transforms second input information into second nonlinear transformed information that is transformed into second linear transformed information. An exclusive-or section performs an exclusive-or operation based on the first and second linear transformed information. When the first nonlinear and linear transformed information are expressed as a first and second sequence vector, respectively, and the second nonlinear and linear transformed information are expressed as a third and fourth sequence vector, respectively, then a first row vector chosen from a first inverse matrix of a first matrix that transforms the first sequence vector to the second sequence vector, and a second row vector chosen from a second inverse matrix of a second matrix that transforms the third sequence vector to the fourth sequence vector, are linearly independent.