| abstract |
Π i=0 n N-1 e(R(i,0), …, R(i,k-1)) is effectively calculated when it is assumed that an arithmetic on a finite field for an element R(i,k)ЄGF(p m ) of K finite fields GF(p m ) is represented by e(R(i,0), …, R(i,k-1)). Polynomials poly(R(i,0),…, R(i,k-1)) which represent a d-th order extension field of the finite field GF(p m ), which is obtained in the process of the calculation of e(R(i,0), …, R(i,k-1)) for each i, are multiplied, and the multiplication results are cumulatively multiplied. The polynomial poly(R(i,0),…, R(i,k-1))is a mapping from an element of the input finite field GF(p m ), and the coefficient of at least one term is 0. Similar operations are carried out for different combinations of i, and Π i=0 n N-1 e(R(i,0), …, R(i,k-1)) is calculated using the results of the operations. |