1. A system, comprising: a memory unit that stores key data for a cryptographic processing; a processing unit configured to perform an encryption of the cryptographic processing or a decryption of the cryptographic processing, the processing unit configured to transform first input information into first nonlinear transformed information, and to transform the first nonlinear transformed information into first linear transformed information, the processing unit configured to transform second input information into second nonlinear transformed information, and to transform the second nonlinear transformed information into second linear transformed information; and an exclusive-or section that performs an exclusive-or operation based on the second linear transformed information and the first linear transformed information, wherein, when the first nonlinear transformed information is expressed as a first sequence vector, the first linear transformed information is expressed as a second sequence vector, the second nonlinear transformed information is expressed as a third sequence vector, and the second linear transformed information is expressed as a fourth sequence vector, 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.