A secret sharing system characterized by comprising: a sharing apparatus; Σ α=1 L h(α) share management apparatuses PA(α, h(α)) where α = 1,..., L, L ≥ 2, h(α) = 1,..., H(α), H(α) ≥ 2; and an acquisition apparatus; wherein the sharing apparatus includes secret sharing units (114-α) adapted to generate shares SH(α, h(α)) by secret sharing of secret information with a secret sharing scheme separately for respective subsets SUB(α) each of which is formed of H(α) share management apparatuses PA(α, 1),..., PA(α, H(α)), and to output the shares SH(α, h(α)); the share management apparatuses PA(α, h(α)) include shared secret value generators (124-α-h(α)) adapted to generate shared secret values DSH(α, h(α)) and to output the shared secret values DSH(α, h(α)) respectively, each of the shared secret values DSH(α, h(α)) being generated by performing a common operation to one of the shares SH(α, h(α)) and common information containing one of common values σ(α), each of the common values σ(α) being shared in each of the subsets SUB(α), the common information used by the share management apparatuses PA(α, h(α)) belonging to same one of subsets SUB(α) being the same, and the share management apparatuses PA(α, h(α)) belonging to the same one of subsets SUB(α) performing the same common operation; the acquisition apparatus includes: reconstruction units (134-α) adapted to generate reconstructed secret values SUBSK(α) corresponding to the subsets SUB(α) respectively, each of the reconstructed secret values SUBSK(α) being generated by performing reconstruction processing with the secret sharing scheme for each of the subsets SUB(α), using a plurality of the shared secret values DSH(α, h(α)) corresponding to the same one of the subsets SUB(α); and a composition unit adapted to generate generation information SK by using the reconstructed secret values SUBSK(α) and to output the generation information SK. a sharing apparatus; Σ α=1 L h(α) share management apparatuses PA(α, h(α)) where α = 1,..., L, L ≥ 2, h(α) = 1,..., H(α), H(α) ≥ 2; and an acquisition apparatus; wherein the sharing apparatus includes secret sharing units (114-α) adapted to generate shares SH(α, h(α)) by secret sharing of secret information with a secret sharing scheme separately for respective subsets SUB(α) each of which is formed of H(α) share management apparatuses PA(α, 1),..., PA(α, H(α)), and to output the shares SH(α, h(α)); the share management apparatuses PA(α, h(α)) include shared secret value generators (124-α-h(α)) adapted to generate shared secret values DSH(α, h(α)) and to output the shared secret values DSH(α, h(α)) respectively, each of the shared secret values DSH(α, h(α)) being generated by performing a common operation to one of the shares SH(α, h(α)) and common information containing one of common values σ(α), each of the common values σ(α) being shared in each of the subsets SUB(α), the common information used by the share management apparatuses PA(α, h(α)) belonging to same one of subsets SUB(α) being the same, and the share management apparatuses PA(α, h(α)) belonging to the same one of subsets SUB(α) performing the same common operation; the acquisition apparatus includes: reconstruction units (134-α) adapted to generate reconstructed secret values SUBSK(α) corresponding to the subsets SUB(α) respectively, each of the reconstructed secret values SUBSK(α) being generated by performing reconstruction processing with the secret sharing scheme for each of the subsets SUB(α), using a plurality of the shared secret values DSH(α, h(α)) corresponding to the same one of the subsets SUB(α); and a composition unit adapted to generate generation information SK by using the reconstructed secret values SUBSK(α) and to output the generation information SK. reconstruction units (134-α) adapted to generate reconstructed secret values SUBSK(α) corresponding to the subsets SUB(α) respectively, each of the reconstructed secret values SUBSK(α) being generated by performing reconstruction processing with the secret sharing scheme for each of the subsets SUB(α), using a plurality of the shared secret values DSH(α, h(α)) corresponding to the same one of the subsets SUB(α); and a composition unit adapted to generate generation information SK by using the reconstructed secret values SUBSK(α) and to output the generation information SK.