SHARED INFORMATION GENERATING APPARATUS AND RECOVERING APPARATUS

There is disclosed a system for identifying falsified secret information shares included in k secret information shares used to recover secret information according to a (k,n)-threshold secret sharing scheme, and producing falsified secret information shares of reduced size. A shared information generating apparatus generates cheater identifying information Ai(i=1, 2, . . . , n) using n secret information shares Vi generated according to the (k,n)-threshold secret sharing scheme and random polynomials. A recovering apparatus detects cheated secret information shares using the arbitrary k secret information shares and k cheater identifying information, and recovers the secret information from the k secret information shares if it detects no cheated secret information shares.