Research On Threshold Secret Sharing Scheme And Its Applications

With the rapid development of computer science and internet techniques, it’s more and more important to keep information’s security and integrity. Threshold secret sharing scheme provides an effective approach for this issue. It plays an important role in the field of modern cryptography and is a major subject of information security. Study on secret sharing scheme not only is of great significance, but aslo enjoys the bright prospect of extensive applications. In this dissertation, the background, progress and significance of threshold secret sharing are reviewed. Based on multi-secret sharing scheme, hierarchical secret sharing scheme, and threshold changeable secret sharing scheme, we deeply research the threshold secret sharing scheme and its applications. The main contributions are summarized as follows:(1) A reusable multi-attribute hierarchical threshold scheme based on Tassa’s hierarchical secret sharing scheme and Mignotte’s secret sharing scheme, is proposed. In this scheme participants are divided into different partitions according to multiple attributes. Based on Yang et al.’s multi-secret sharing scheme and Tassa’s hierarchical secret sharing scheme, we propose a hierarchical multi-secret sharing scheme. In this scheme, multi-secrets can be shared in one secret sharing procedure.(2) Based on Birkhoff interpolation and two-variable, one-way function, we propose two modified threshold-changeable schemes:(tmin←t�'tmax,n) threshold-changeable scheme and ([t1,…tm],n) threshold-changeable scheme. In the (tmin←t�'tmax,n) threshold-changeable scheme, the dealer can change the threshold up to tmax or down to tmin before the recovery phase. In the ([t1,…tm],n) threshold-changeable scheme, no subset of participants can recover the shared secret unless the dealer broadcasts the threshold’s active information before the recovery phase. Compared with other ([t1,…tm],n) threshold-changeable schemes, our scheme needs less storage and broadcasts less information, moreover the secret shares of participants can be reused.(3) We propose a traceable, group-oriented, signature scheme based on Hsu et al.’s multi-secret sharing scheme and the modified ElGamal digital-signature scheme. In this scheme, each authorized subset of participants’ groups can generate a unique group signature, which makes it easy for the outsider to trace the signers (4) Based on Shamir’s secret sharing scheme and Bao et al.’s self-healing key distribution scheme, we propose a modified self-healing key distribution scheme in wireless sensor networks. Self-healing key distribution schemes are used to ensure that, even if the message packets that are broadcast in some sessions get lost, the group nodes can still recover the lost session keys simply by using their personal secret keys and broadcast messages that have been received without requesting additional transmissions from the group manager. Our scheme uses only one secret polynomial and modified access polynomials, which achieve constant storage and lower communication overhead.