Secure selective product computation system, secure selective product computation method, secure computation apparatus, and program

A secure selective product computation method executed by a secure selective product computation system for receiving a sequence of share values [c0], . . . , [cn−1] of n conditions c0, . . . , cn−1 and a binary table including multipliers m0,0, m0,1, . . . , mn−1,0, and mn−1, 1 associating two multipliers of the multipliers with each of the conditions as inputs, and outputting a share value [A] of a total product of the multipliers selected according to the conditions, the secure selective product computation system including a plurality of secure computation apparatuses, the secure selective product computation method comprising:

• calculating, by processing circuitry of each secure computation apparatus of the plurality of secure computation apparatuses in cooperation with others of the plurality of secure computation apparatuses via communications including transmitting and receiving data over a network, share values [cici+1] obtained by multiplying the share values [ci] and the share values [ci+1] where i is an even number equal to or greater than 0 or smaller than n;
• generating, by the processing circuitry of each of the plurality of secure computation apparatuses, a 4-value table including m′00, m′01, m′10, and m′11 where m′00:=mi,0mi+1,0, m′01:=mi,0mi+1,1, m′10:=mi,1mi+1,0, and m′11:=mi,1mi+1,1 where i is an even number equal to or greater than 0 or smaller than n;
• generating, by the processing circuitry of each of the plurality of secure computation apparatuses, share values [ai] of values ai obtained by calculating [cici+1](m00+m11−m01−m10)+[ci](mi+1,0−mi,0)+[ci+1](mi,1−mi,0)+mi,0 where i is an even number i equal to or greater than 0 or smaller than n;
• calculating, by the processing circuitry of each secure computation apparatus of the plurality of secure computation apparatuses in cooperation with others of the plurality of secure computation apparatuses via communications including transmitting and receiving data over the network, a share value [A] of a value A obtained by multiplying all the share values [ai];
• and
• multiplying, by the processing circuitry of each secure computation apparatus of the plurality of secure computation apparatuses in cooperation with others of the plurality of secure computation apparatuses via communications including transmitting and receiving data over the network, the share value [A] by a multiplier selected from multipliers mn−1,1 and mn−1,0 according to a condition cn−1 when n is an odd number.