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

A secure computation apparatus sharing a tripartite share of a concealed input vector between a first secure computation apparatus and a second other secure computation apparatus, the secure computation apparatus comprising:

• a processor;
• and
• a memory storing program instructions that cause the processor to:
• convert its own tripartite share into a bipartite share with the second secure computation apparatus;
• randomly determine a first permutation and a second permutation such that synthetic mapping between the first permutation and the second permutation is its own permutation;
• randomly determine a first vector and a second vector having the same size as its own bipartite share;
• calculate a third vector obtained by subtracting a result of applying the second permutation to the first vector, and the second vector from a result of applying the permutation to its own bipartite share;
• transmit the third vector and the second permutation to the first secure computation apparatus;
• and
• transmit the first permutation, the first vector, and the second vector to the second secure computation apparatus.

A method for use in a secure computation system including a first secure computation apparatus, a second secure computation apparatus, and a third secure computation apparatus each having a tripartite share of a concealed input vector.

• wherein the first secure computation apparatus executes
• converting its own tripartite share into a bipartite share with the third secure computation apparatus;
• calculating a third vector obtained by subtracting, from a result of applying its own permutation to its own bipartite share, a result of applying a second permutation determined according to the permutation to a first vector determined by a predetermined method and a second vector determined by a predetermined method;
• and
• transmitting the third vector and the second permutation to the second secure computation apparatus,
• the third secure computation apparatus executes
• converting its own tripartite share into a bipartite share with the first secure computation apparatus;
• calculating a fourth vector obtained by adding the first vector to a result of applying a first permutation determined according to the permutation to its own bipartite share;
• transmitting the fourth vector to the third secure computation apparatus;
• setting the second vector as a bipartite share with the second secure computation apparatus of a result of applying the permutation to the input vector, and
• the second secure computation apparatus executes setting a vector obtained by adding a result of applying the second permutation to the fourth vector to the third vector, as a bipartite share with the third secure computation apparatus of the result of applying the permutation to the input vector.