In an arithmetic operation method and an arithmetic operation device arithmetic operations such as exponentiation or scalar multiplication can be performed at high speed. In the case where there exists a plurality of different elements Y and each element Y is represented by tuples in which a plurality of different elements X are combined with an operator, an arithmetic operation method for calculating each element Y by using an electronic computer, associates each element Y with the element X by setting each element X, sets temporary data having an index indicating whether or not each element Y has an identical element X for each element X, and represents each element Y by the temporary data combined with the operator. When there is a combination of temporary data which is common in plurality of elements Y in temporary data contained in each element Y, new temporary data is set by combining the common temporary data and each element Y consisting of each tuple is calculated using the new temporary data.