A method and apparatus to square an element A when a defining polynomial of a finite field GF(2.sup.n) is expressed as.function..times..times. ##EQU00001## and the element A contained in the finite field is expressed as A=(a.sub.0,a.sub.1,a.sub.2, . . . ,a.sub.n-1).di-elect cons.GF(2.sup.n). The method determines coefficients m.sub.i, I.sub.ij, V.sub.0, V.sub.ij, and V such that the coefficient m.sub.i satisfies a predetermined condition with respect to k.sub.i when 1.ltoreq.i.ltoreq.t is a natural number, I.sub.ij depends on n, k.sub.i, and j when 2.ltoreq.j.ltoreq.m.sub.i, V.sub.0 and V.sub.ij of n bits, respectively, depend on n, I.sub.ij, and k.sub.i, and obtains the coefficient V with respect to m.sub.i according to the following formula.times..times..times..sym..times..times..sym..sym..times..sym..not- eq..times..times. ##EQU00002## determines a coefficient s.sub.i according to k.sub.i and n and cyclically shifts the coefficient V by s.sub.i; performing an XOR operation on the cyclically shifted coefficient V and the element A; and rewires a result of the XOR operation in a predetermined order and outputs results of the squaring.