Secure computation apparatus, system, method and program

A secure computation apparatus comprising:

• a share value storage apparatus that stores share values obtained by using (2, 3) threshold type RSS (Replicated Secret Sharing) with modulo 2 to the power of n;
• a decomposed share value storage apparatus that stores a sequence of share values obtained by using (2, 3) threshold type RSS with modulo 2;
• and
• a bit-decomposition secure computation apparatus including a first processor and a first memory storing program instructions executable by the first processor, wherein
• the first processor included in the bit-decomposition secure computation apparatus is configured to
• with respect to a value w, use r1, r2, and r3 satisfying w=r1+r2+r3 mod 2{circumflex over ( )}n (where mod is a modulo operation;
• n is an integer of 2 or more;
• and {circumflex over ( )} is a power operator) as share information of (2, 3) threshold type RSS stored in the share value storage apparatus, and execute
• a full adder secure computation process that performs secure computation of
• r12=r1+r2 mod 2{circumflex over ( )}n, and
• r123=r12+r3 mod 2{circumflex over ( )}n
• for each digit using secure computation of a full adder to store a computation result in the decomposed share value storage apparatus.

A secure computation method for three sets of secure computation apparatuses constituting a secure computation system, each of the secure computation apparatus comprising:

• a share value storage apparatus that stores share values obtained by using (2, 3) threshold type RSS (Replicated Secret Sharing) modulo the power of 2;
• and
• a decomposed share value storage apparatus that stores a sequence of share values obtained by using (2, 3) threshold type RSS with modulo 2, wherein the method comprises:
• the secure computation apparatus, with respect to a value w,
• using r1, r2, and r3 satisfying w=r1+r2+r3 mod 2{circumflex over ( )}n (where mod is a modulo operation, {circumflex over ( )} is a power operator) as share information of (2, 3) threshold type RSS stored in the share value storage apparatus;
• summing two values out of the share information by modulo 2{circumflex over ( )}n arithmetic;
• distributing the sum using (2, 3) threshold type RSS;
• and
• adding the share value of the sum of the two values and share information of one remaining value other than the two values for each digit by using secure computation of a full adder to store a computation results in the decomposed share value storage apparatus as bit-decomposed share values.

A non-transitory computer readable medium storing a program causing a computer apparatus comprising:

• a share value storage apparatus that stores share values obtained by using (2, 3) threshold type RSS (Replicated Secret Sharing) modulo the power of 2;
• and
• a decomposed share value storage apparatus that stores a sequence of share values obtained by using (2, 3) threshold type RSS with modulo 2 to execute processing comprising:
• with respect to a value w,
• using r1, r2, and r3 satisfying w=r1+r2+r3 mod 2{circumflex over ( )}n (where mod is a modulo operation;
• {circumflex over ( )} is a power operator) as share information of (2, 3) threshold type RSS stored in the share value storage apparatus, summing two values out of the share information by modulo 2{circumflex over ( )} n arithmetic;
• distributing the sum using (2, 3) threshold type RSS;
• and
• adding the share value of the sum of the two values and share information of one remaining value other than the two values for each digit by using secure computation of a full adder;
• and
• storing the computation results in the decomposed share value storage apparatus as bit-decomposed share values.