Secure computation apparatus, secure computation method, and program

A secure computation device that curbs overflow in secure computations, wherein x is a real number, [μ] is a secret share value of μ, n is an integer equal to or greater than 1, t=0, . . . , n−1, u=1, . . . , n−1, ft(x) is a function of the real number x, f′t(x) is an approximation function of the function ft(x), a secret share value [f′0(x)] of an approximation function f′0(x) is [f′0(x)]=c0,0+c0,1[x], a secret share value [f′u(x)] of an approximation function f′u(x) is [f′u(x)]=cu,0+cu,1[x]+cu,2[f0(x)]+ . . . +cu,u+1[fu−1(x)], ct,0 is a public value, and ct,1, . . . , ct,n+1 are coefficients, the secure computation device comprising:

• first secure computation circuitry configured to obtain a secret share value [ft(x)−f′t(x)] of ft(x)−f′t(x) through secure computation using a secret share value [x] of the real number x;
• and
• second secure computation circuitry configured to obtain a secret share value [ft(x)−f′t(x)]r of (ft(x)−f′t(x))r obtained by right-shifting ft(x)−f′t(x) by the number of bits predetermined through secure computation using the secret share value [ft(x)−f′t(x)],
• wherein the secret share value [x], the secret share value [ft(x)−f′t(x)], and the secret share value [ft(x)−f′t(x)]r are fixed-point real numbers which are implemented in the first secure computation circuitry and the second secure computation circuitry, and the secure computation device curbs overflow in the first secure computation circuitry and the second secure computation circuitry.