Publicly Verifiable Secret Sharing Schemes Using Bilinear Pairings

A non-interactive, simple and efficient publicly verifiable secret sharing (PVSS) is constructed based on the bilinear pairing on elliptic curves, which has all advantages of Schoenmakers’ PVSS in [15]. Moreover, in the scheme’s distribution of shares phase, only using bilinearity of bilinear paring, anybody can verify that the participants received whether correct shares without implementing interactive or the non-interactive protocol and without construction so called witness of shares applying Fiat-Shamir’s technique. Subsequently, in the scheme’s reconstruction of secret phase, the released shares may be verified by anybody with the same method. Since the PVSS need not to implement non-interactive protocol and construct witness in order to prevent malicious players, hence it reduces the overhead of communication. Finally, the PVSS has been extensions to the case without a dealer (or without a trusted center). A distributive publicly verifiable secret sharing (DPVSS) is proposed, which also reduces the overhead of communication. Analysis shows that these schemes are more secure and effective than others, and it can be more applicable in special situation.