A secure aggregate order system comprising a plurality of secure computation apparatuses (1 1,..., 1 N), m being an integer equal to or greater than 2, [v]: = [v 0],..., [v m-1] being a share obtained by secret sharing a cross tabulation v: = v 0,..., v m-1 in which the number of records of each group when a table including a key attribute and a value attribute is grouped based on a value of the key attribute is set at elements corresponding to the number of groups from the head, and {{σ}} being a share obtained by secret sharing a permutation σ which moves elements so that last elements of each group are sequentially arranged from beginning when the table is grouped based on the value of the key attribute, each of the secure computation apparatuses comprising: an inverse permutating part configured to generate a share [u]: = [σ -1 (v)] which becomes an inversely permutated cross tabulation u: = σ -1 (v) obtained by inversely applying the permutation σ to the cross tabulation v, when reconstructed, using the share [v] and the share {{σ}}; a partial summing part configured to generate a share [s] which becomes a vector s: = s 0,..., s m-1 ∈ F, when reconstructed, by setting a sum from [u 0] to [u i] at [s i] for each integer i equal to or greater than 0 and equal to or less than m-1 using the share [u]; and an order computing part configured to generate a share [x] which becomes a vector x: = x 0,..., x m-1 representing ascending order within a group, when reconstructed, by setting [x i]: = [i-s i-1] for each integer i equal to or greater than 1 and equal to or less than m-1 and setting [x 0]: = using the share [s]. m being an integer equal to or greater than 2, [v]: = [v 0],..., [v m-1] being a share obtained by secret sharing a cross tabulation v: = v 0,..., v m-1 in which the number of records of each group when a table including a key attribute and a value attribute is grouped based on a value of the key attribute is set at elements corresponding to the number of groups from the head, and {{σ}} being a share obtained by secret sharing a permutation σ which moves elements so that last elements of each group are sequentially arranged from beginning when the table is grouped based on the value of the key attribute, each of the secure computation apparatuses comprising: an inverse permutating part configured to generate a share [u]: = [σ -1 (v)] which becomes an inversely permutated cross tabulation u: = σ -1 (v) obtained by inversely applying the permutation σ to the cross tabulation v, when reconstructed, using the share [v] and the share {{σ}}; a partial summing part configured to generate a share [s] which becomes a vector s: = s 0,..., s m-1 ∈ F, when reconstructed, by setting a sum from [u 0] to [u i] at [s i] for each integer i equal to or greater than 0 and equal to or less than m-1 using the share [u]; and an order computing part configured to generate a share [x] which becomes a vector x: = x 0,..., x m-1 representing ascending order within a group, when reconstructed, by setting [x i]: = [i-s i-1] for each integer i equal to or greater than 1 and equal to or less than m-1 and setting [x 0]: = using the share [s]. an inverse permutating part configured to generate a share [u]: = [σ -1 (v)] which becomes an inversely permutated cross tabulation u: = σ -1 (v) obtained by inversely applying the permutation σ to the cross tabulation v, when reconstructed, using the share [v] and the share {{σ}}; a partial summing part configured to generate a share [s] which becomes a vector s: = s 0,..., s m-1 ∈ F, when reconstructed, by setting a sum from [u 0] to [u i] at [s i] for each integer i equal to or greater than 0 and equal to or less than m-1 using the share [u]; and an order computing part configured to generate a share [x] which becomes a vector x: = x 0,..., x m-1 representing ascending order within a group, when reconstructed, by setting [x i]: = [i-s i-1] for each integer i equal to or greater than 1 and equal to or less than m-1 and setting [x 0]: = using the share [s].