Threshold verifiable multi‐secret sharing based on elliptic curves and Chinese remainder theorem

Information Privacy Protection Based on Verifiable (t, n)-Threshold Multi-Secret Sharing Scheme

“…As shown in Table 1, our scheme is the most effective one compared to other schemes in the initialization and construction phases. The efficiency of our scheme is slightly higher than that of the schemes in [19], [25]- [27], and lower than that of the schemes in [28] and [29]. The computational costs of these seven schemes are almost the same in the recovery phase.…”

“…The computational costs of these seven schemes are almost the same in the recovery phase. Since we have added conformance tests to prevent cheating between dealer and participants, the verification phase of our new scheme requires more modular exponentiation than the schemes in [19], [25]- [27]. Such an increase in computational costs is necessary to prevent cheating on dealer and participants.…”

“…Table 2 shows that our new scheme has all the performance features. In [19], participants hold different shares in different rounds of multi-secret sharing, which increasing the storage space of the system. None of the schemes proposed in [25]- [27] can resist deceit between dishonest distributors and participants.…”

“…In a verifiable secret sharing scheme, participants can verify whether their shares are consistent and they can detect fraudulent behavior by dishonest traders. Verifiable secret sharing scheme is a basic tool in cryptographic research [19]. In order to solve the fraudulent behavior of the participants, we investigated deception immunity secret sharing [20]- [23] and publicly verifiable secret sharing [24].…”

“…Sheikhi-Garjan et al [19] proposed the threshold verifiable multi-secret sharing based on elliptic curves and Chinese remainder theorem. The challenge of this scheme is to solve equations.…”