1. A circuit design method executed by a computer for designing a processing circuit for processing on a finite field comprising: a first step of obtaining a first primitive root &agr; 1 on the basis of a first polynomial for a first extension from a first finite field to a second finite field; a second step of obtaining a second primitive root &agr; 2 on the basis of a second polynomial for a second extension from said second finite field to a third finite field, in which a coefficient of a 0-th term is defined using said first primitive root &agr; 1 obtained in said first step and the coefficient of the 0-th term of said first polynomial; a third step of defining the processing on said third finite field using a base expressed using said second primitive root &agr; 2 obtained in said second step; and a fourth step of designing a processing circuit for the related processing on the basis of the processing defined in said third step.