A secure computation apparatus (1 n used in a secure conjugate gradient method computation system adapted to obtain, the secure conjugate gradient method computation system being implemented using fixed-point numbers, letting X be a set of values for computing a product of a d-dimensional real symmetric positive definite matrix A and a d-dimensional vector, b → be a d-dimensional vector, f be a function for computing Ax → based on a matrix X and a d-dimensional vector x →, k be an integer of d or less, i be each of integers from 1 to k, x → 0 be a d-dimensional vector for which a suitable value is set, and D be chosen to be equal to 1/d, an approximate solution x → k of a solution x → * of Ax → = b~ with secret values of the set X and a secret value of the vector b → used as inputs, the secure computation apparatus comprising: an initialization unit adapted to compute the following expression using secure computation, and generate secret values of vectors p → 0 and r → 0 and a value ρ 0; p → 0 = r → 0 = b → − ƒ X x → 0, ρ 0 = r → 0 T r → 0 a first computation unit adapted to compute the following expression using secure computation, and generate a secret value of a vector a → i-1; a → i − 1 = D × ƒ X p → i − 1 a second computation unit adapted to compute the following expression using secure computation, and generate a secret value of a value γ i-1; γ i − 1 = D × p → i − 1 T a → i − 1 a third computation unit adapted to compute the following expression using secure computation, and generate a secret value of a value α i-1; α i − 1 = ρ i − 1 γ i − 1 a fourth computation unit adapted to compute the following expression using secure computation, and generate a secret value of a vector d → i; d → i = D × α i − 1 p → i − 1 a fifth computation unit adapted to compute the following expression using secure computation, and generate a secret value of a vector x → i; x → i = x → i − 1 + d → i a sixth computation unit adapted to compute the following expression using secure computation, and generate a secret value of a vector r → i; r → i = r → i − 1 − α i − 1 a → i − 1 a seventh computation unit adapted to compute the following expression using secure computation, and generate a secret value of a value ρ i; ρ i = D × r → i T r → i an eighth computation unit adapted to compute the following expression using secure computation, and generate a secret value of a value β i; β i = ρ i ρ i − 1 a ninth computation unit adapted to compute the following expression using secure computation, and generate a secret value of a vector p → i. p → i = r → i − β i p → i − 1 an initialization unit adapted to compute the following expression using secure computation, and generate secret values of vectors p → 0 and r → 0 and a value ρ 0; p → 0 = r → 0 = b → − ƒ X x → 0, ρ 0 = r → 0 T r → 0 a first computation unit adapted to compute the following expression using secure computation, and generate a secret value of a vector a → i-1; a → i − 1 = D × ƒ X p → i − 1 a second computation unit adapted to compute the following expression using secure computation, and generate a secret value of a value γ i-1; γ i − 1 = D × p → i − 1 T a → i − 1 a third computation unit adapted to compute the following expression using secure computation, and generate a secret value of a value α i-1; α i − 1 = ρ i − 1 γ i − 1 a fourth computation unit adapted to compute the following expression using secure computation, and generate a secret value of a vector d → i; d → i = D × α i − 1 p → i − 1 a fifth computation unit adapted to compute the following expression using secure computation, and generate a secret value of a vector x → i; x → i = x → i − 1 + d → i a sixth computation unit adapted to compute the following expression using secure computation, and generate a secret value of a vector r → i; r → i = r → i − 1 − α i − 1 a → i − 1 a seventh computation unit adapted to compute the following expression using secure computation, and generate a secret value of a value ρ i; ρ i = D × r → i T r → i an eighth computation unit adapted to compute the following expression using secure computation, and generate a secret value of a value β i; β i = ρ i ρ i − 1 a ninth computation unit adapted to compute the following expression using secure computation, and generate a secret value of a vector p → i. p → i = r → i − β i p → i − 1