Secret Sharing in the Encrypted Domain

Secret sharing refers to dividing a secret into pieces or shares and allocating the shares among a group of participants. The secret can be reconstructed only when a sufficient number of shares are combined. To protect each share during secret reconstruction, it is desirable to reconstruct the secret directly from the encrypted shares. A composite algorithm using binary representation and precomputation is developed for efficient exponentiation of encrypted data. A new scheme of secret sharing in the encrypted domain is proposed that makes use of the efficient exponentiation algorithm. Experimental results verify the effectiveness of the efficient exponentiation algorithm and the scheme of secret sharing in the encrypted domain.