In a secret sharing process based on an improved threshold scheme, secret data is shared as shared data parts equal to or greater than a threshold value in number such that the secret data cannot be reconstructed from shared data parts less than the threshold value in number. Each of the shared data pieces is created essentially from a different combination of the secret data pieces and the data pieces for secret sharing computation. The secret sharing process allows an algorithm desired by the user to be freely incorporated, and can prevent the secret data to be easily reconstructed even when more shared data parts than the threshold value are acquired by a third party.