Computer system, computer program, and addition method

An addition method used for adding two or more integers using a computer system that includes a memory unit and a processor, the addition method comprising steps of:

• a conversion step to cause the processor to generate elements belonging to a group G by implementing a power operation in the group G using each integer,
• an operation step to cause the processor to generate an operation value by implementing a basic operation other than addition using all the generated elements, and
• an inverse conversion step to cause the processor to generate a sum value of the integers by implementing, in the group G or a proper subgroup S of the group G, an inverse power operation on the operation value.

A computer program for adding two or more integers, the program, including:

• a conversion instruction set for generating elements belonging to a group G by implementing a power operation in the group G using each integer,
• an operation instruction set for generating an operation value by implementing a basic operation other than addition using all the generated elements, and
• an inverse conversion instruction set for generating a sum value of the integers by implementing, in the group G or a proper subgroup S of the group G, an inverse power operation on the operation value.