Secret Sharing in the Encrypted Domain with Secure Comparison

Secret sharing refers to the sharing and reconstruction of a secret among a group of participants. In light of a few disadvantages of the traditional secret sharing, it is desirable to reconstruct the secret directly from the encrypted shares to protect the secret and shares during secret reconstruction. This paper develops several useful techniques for processing encrypted data. A new secure comparison protocol based on the additive homomorphic property and a new scheme of secret sharing in the encrypted domain with secure comparison are proposed. In this scenario, secret reconstruction could be done on an untrusted device while comparison is performed in a trusted environment. Experimental results confirm the effectiveness of the proposed scheme and protocol.