Bit decomposition secure computation apparatus, bit combining secure computation apparatus, method and program

A bit decomposition secure computation system comprising:

• a share value storage apparatus to store share values obtained by applying (2, 3) type RSS (Replication type Secret Sharing) using modulo of power of 2 arithmetic;
• a decomposed share value storage apparatus to store a sequence of share values obtained by applying (2, 3) type RSS using modulo 2 arithmetic;
• and
• a bit decomposition secure computation apparatus including:
• a processor;
• and a memory storing a program executable by the processor, wherein the processor is configured to perform
• with respect to sharing of a value w,
• r1, r2, and r3 satisfying w=r1+r2+r3 mod 2{circumflex over ( )}n, where mod is a modulo operator, {circumflex over ( )}n is a power operator and n is a preset positive integer, being used as share information by the (2, 3) type RSS stored in the share value storage apparatus,
• a full adder secure computation process that performs secure computation of r12=r1+r2 mod 2{circumflex over ( )}n and secure computation of r123=r12+r3 mod 2{circumflex over ( )}n, for each digit, by using secure computation of a full adder, and stores the computation result in the decomposed share value storage apparatus.

A bit combining secure computing system comprising:

• a share value storage apparatus to store share values obtained by applying (2, 3) type RSS (Replication type Secret Sharing) using modulo of power of 2 arithmetic;
• a decomposed share value storage apparatus to store a sequence of share values obtained by applying (2, 3) type RSS using modulo 2 arithmetic;
• and
• a bit combining secure computation apparatus including:
• a processor;
• and a memory storing a program executable by the processor, wherein the processor is configured to perform
• with respect to sharing of a value w_i,
• r_{1, i}, r_{2, i}, r_{3, i} satisfying w_i=r {1, i}+r {2, i}+r_{3, i} mod 2, for i=1 to n, where w_i, r_{1, i}, r_{2, i}, and r_{3, i} indicate respectively an i-th digit bit of w, r1, r2, and r3, and mod is a modulo operator, being used as a sequence of n items of share information by the (2, 3) type RSS stored in the decomposed share value storage apparatus,
• a full adder secure computation process that performs secure computation of r12=r_{1, n}∥ . . . ∥r_{1, 1}+r_{2, n}∥ . . . ∥r_{2, 1} mod 2{circumflex over ( )}n, where a symbol ∥ is a concatenation operator, {circumflex over ( )} is a power operator and n is a preset positive integer, and performs secure computation of r123=r12+r_{3, n}∥ . . . ∥r_{3, 1} mod 2{circumflex over ( )}n, for each digit, by using secure computation of a full adder, and stores the computation result in the share value storage apparatus.