An Ideal Multi-Secret Sharing Scheme with Verification

The ( ) , t n threshold secret sharing scheme proposed by Shamir (1979) encodes the secret key into n shares and those shares are distributed among the participants. Each share incorporates an x-value uniquely designated for every single participant. If the shares are distributed on insecure (or public) channels, malicious users may acquire a few (or all) shares. If the number of shares obtained by the malicious users is t or more ( n ≤ ), then malicious users can reconstruct the secret. Chattopadhyay, et al. (2016) proposed a scheme for the distribution of shares with RSA to encrypt the x-values at insecure channel along with verification, such that the secrecy of shares and secret both are maintained. A verifiable ( ) , , t k n − threshold multi-secret sharing scheme is proposed in this paper which extends the work proposed by Chattopadhyay, et al. (2016). The proposed scheme is ideal as the sizes of the shares are of same as that of the secrets.