A calculation Πi=0N−1e(R(i, 0), . . . , R(i, K−1)) where a calculation of K elements R(i, k)εGF(pm) of a finite field GF(pm) over a finite field is expressed as e(R(i, 0), . . . , R(i, K−1)) is efficiently performed. Polynomials poly(R(i, 0), . . . , R(i, K−1)) that express a d-th-order extension field of the finite field GF(pm), which are obtained by the calculations e(R(i, 0), . . . , R(i, K−1)) for different values of i, are multiplied by each other, and a cumulative multiplication of the products is performed, for example. The polynomial poly(R(i, 0), . . . , R(i, K−1)) is a mapping from the input elements of the finite field GF(pm), and the coefficients of at least some of the terms thereof are 0. The same process is performed for different sets of values of i, and the calculation Πi=0N−1e(R(i, 0), . . . , R(i, K−1)) is performed using the result.