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. Secure signal processing is typically based on probabilistic and homomorphic encryption in public key cryptosystem. Based on related works, a composite method using binary representation and precomputation is implemented for efficient exponentiation of encrypted signals. A new scheme of secret sharing in the encrypted domain that makes use of the efficient exponentiation method is presented. Experimental results validate the suitability of the proposed method.