Arithmetic device, method, and program product

An arithmetic method for performing 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 method comprising:
• inputting input data that are elements of the group;
• when the input data are in the second representation, converting the input data into the first representation, and performing 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, performing 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
• performing arithmetic processing on the first converted data or the second converted data by using secret information.

A program product having a computer readable medium including programmed instructions for performing 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, and
• wherein the instructions, when executed by a computer, cause the computer to perform:
• inputting input data that are elements of the group;
• when the input data are in the second representation, converting the input data into the first representation, and performing 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, performing 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
• performing arithmetic processing on the first converted data or the second converted data by using secret information.