1. An arithmetic device that performs arithmetic processing on elements of a group by using secret information, wherein the elements of the group are expressed at least in a first representation and in a second representation, in which an element expressed by the first representation is constituted by a plurality of components each including a plurality of subcomponents, and one element of the group expressed in the second representation has a plurality of corresponding first representations, and an element expressed in the first representation obtained by performing arithmetic operation on an element expressed in the first representation by using an operand having the same group structure as a component included in the first representation represents the same element of the group as that before the arithmetic operation using the operand, the arithmetic device comprising: an input unit configured to input input data that are elements of the group; a converting unit configured to: when the input data are in the second representation, convert the input data into the first representation, and perform arithmetic operation on the converted first representation by using the operand in the first representation in which at least one subcomponent is a zero element to convert the converted first representation into first converted data expressed in the first representation, and when the input data are in the first representation, perform arithmetic operation on the input data by using the operand in the first representation in which at least one subcomponent is a zero element to convert the input data into second converted data expressed in the first representation; and an operating unit configured to perform arithmetic processing on the first converted data or the second converted data by using secret information.