Secure computation system, secure computation device, secure computation method, and program

A secure computation device configured to be implemented in a secure computation system comprising three or more secure computation devices, wherein it is assumed that a, b, c and d are non-negative integers, a is a frequency on a first row and a first column of a 2×2 contingency table, b is a frequency on the first row and a second column of the contingency table, c is a frequency on a second row and the first column of the contingency table, d is a frequency on the second row and the second column of the contingency table, [a], [b], [c] and [d] are secure texts of the respective frequencies a, b, c and d, and N is an upper bound satisfying a+b+c+d≤N,

• the secure computation device comprises circuitry configured to:
• receive, over a network, an input of the secure texts ([a], [b], [c], [d]), wherein the original respective frequencies a, b, c and d are concealed from the secret computation devices in the secure computation system;
• compute a secure text ([a0], [b0], [c0], [d0]) of a combination of reference frequencies (a0, b0, c0, d0) which are integers satisfying a0, b0=a+b, c0+d0=c+d, a0+c0=a+c, and b0+d0=b+d;
• determine integers h0 and h1 satisfying h0≤h1;
• and
• compute [ai]=[a0]+i, [bi]=[b0]−i, [ci]=[c0]−i and [di]=[d0]+i for i=h0, . . . , h1, and obtain a set S={([ai], [bi], [ci], [di])}i of secure texts of combinations of frequencies (ai, b1, ci, di).

A secure computation method implemented in a secure computation system comprising three or more secure computation devices, wherein it is assumed that a, b, c and d are non-negative integers, a is a frequency on a first row and a first column of a 2×2 contingency table, b is a frequency on the first row and a second column of the contingency table, c is a frequency on a second row and the first column of the contingency table, d is a frequency on the second row and the second column of the contingency table, [a], [b], [c] and [d] are secure texts of the respective frequencies a, b, c and d, and N is an upper bound satisfying a+b+c+d≤N,

• the secure computation method comprising by circuitry of each secure computation device:
• receiving, over a network, an input of the secure texts ([a], [b], [c], [d]), wherein the original respective frequencies a, b, c and d are concealed from each of the secret computation devices;
• computing a secure text ([a0], [b0], [c0], [d0]) of a combination of reference frequencies (a0, b0, c0, d0) which are integers satisfying a0+b0=a+b, c0+d0=c+d, a0+c0=a+c, and b0+d0=b+d,
• determining integers h0 and h1 satisfying h0≤h1 by the circuitry of the secure computation device, and
• computing [ai]=[a0]+i, [bi]=[b0]−i, [c0]=[c0]−i and [di]=[d0]+i for i=h0, . . . , h1, and obtaining a set S={([ai], [bi], [ci], [di])}i of secure texts of combinations of frequencies (ai, bi, ci, di) by the circuitry of the secure computation device.

A non-transitory computer readable medium including computer executable instructions that make a secure computation device perform a method, the secure computation device being configured to be implemented in a secure computation system comprising three or more secure computation devices,

• wherein it is assumed that a, b, c and d are non-negative integers, a is a frequency on a first row and a first column of a 2×2 contingency table, b is a frequency on the first row and a second column of the contingency table, c is a frequency on a second row and the first column of the contingency table, d is a frequency on the second row and the second column of the contingency table, [a], [b], [c] and [d] are secure texts of the respective frequencies a, b, c and d, and N is an upper bound satisfying a+b+c+d<N,
• the method comprising:
• receiving, over a network, an input of the secure texts ([a], [b], [c], [d]), wherein the original respective frequencies a, b, c and d are concealed from the secret computation devices in the secure computation system;
• computing a secure text ([a0], [b0], [c0], [d0]) of a combination of reference frequencies (a0, b0, c0, d0) which are integers satisfying a0+b0=a+b, c0+d0=c+d, a0+c0=a+c, and b0+d0=b+d,
• determining integers h0 and h1 satisfying h0≤h1;
• and
• computing [ai]=[a0]+i, [bi]=[b0]−i, [ci]=[c0]−i and [di]=[d0]+i for i=h0, . . . , h1, and obtaining a set S={([ai], [bi], [ci], [di])}i of secure texts of combinations of frequencies (ai, bi, ci, di).