A secure strong mapping computing system is a secure joining system including a plurality of secure computing apparatuses. The plurality of secure computing apparatuses include a first vector joining unit 11n, a first permutation calculation unit 12n, a first vector generation unit 13n, a second vector joining unit 14n, a first permutation application unit 15n, a second vector generation unit 16n, a first inverse permutation application unit 17n, and a first vector extraction unit 18n.