Study On Theory And Application Of Multi-Secret Sharing

Secret sharing scheme provides an effective approach to saving securely and utilizing legally important information. It is a major subject of information security, and plays an important role in the field of modern cryptography. Study on theory of secret sharing not only is significant, but also enjoys the bright prospect of extensive applications. In this dissertation, the research background and advances of secret sharing are reviewed, and the strength and weakness of multi-secret sharing schemes in applications are analyzed. Based on these overviews, this dissertation concentrates on how to design secure and effective multi-secret sharing schemes, and proposes corresponding methods. Then, we discuss the application of multi-secret sharing technology to digital signatures, and several threshold signature schemes are designed: The main achievements are as follows:(1) In order to solve shortcomings of most existing threshold multi-secret schemes, some new methods are studied as follows: ① Based on systematic block codes, a new threshold multi-secret scheme is proposed, which avoids that the system efficiency is affected greatly by the number of secrets.② Based on Shamir's threshold scheme, another threshold multi-secret scheme is given, which also avoids that the system efficiency is affected greatly by the number of secrets. ③ Based on cellular automata, a multi-secret sharing scheme is represented, which reduces the amount of computation for sharing multiple secrets. ④ Based on the Chinese remainder theorem, a changeable threshold multi-secret sharing scheme was proposed. This scheme can share multiple groups of secrets in one sharing session, which improves the efficiency of sharing multiple groups of secrets. ⑤ An improved threshold multistage secret sharing scheme is presented, which needs less public values than the original one does. Analyses show that the proposed schemes avoid the shortcomings of existing schemes, and improve the efficiency of multi-secret sharing.(2) Based on Shamir's scheme, a multi-secret sharing scheme with general access structure is proposed. In this scheme, multiple secrets can be shared in one sharing session, and each participant needs to keep only one reusable secret shadow. This scheme needs less amount of computation than the existing ones. Then we give an alternative implementation of the previous one. The new one avoids that the system efficiency is affected greatly by the number of secrets, and uses less public values than the previous one. So it is especially suitable for occasions where the efficiency of communication is low. Through above studying,we generalize threshold multi-secret sharing schemes to general access structures, and extend the application of multi-secret sharing schemes.(3) The construction of secure multi-secret sharing schemes is studied in the dissertation. (D A LUC-based multiple secrets sharing scheme against cheating with general access structures is proposed. In this scheme, participants are allowed to choose their secret shadows by themselves;messages can be delivered as plaintext;cheating by participants can be checked out;shadows of participants can be reused for sharing multiple secrets. It is especially suitable for occasions where there exists no secure channel between participants. (2) An improved verifiable threshold multi-secret sharing scheme is given, which prevents the cheating by any malicious participant, reduces the number of modular exponentiations for preventing all kinds of cheating, and improves the system performance. (3) To solve the problem of new member expansion in threshold schemes, a verifiable protocol for member expansion is designed. In this protocol, the new member can verify the authenticity of the new share by using exponential computation, which makes the protocol defend against active attacks. In above schemes, some methods to prevent cheating by participants or the dealer are given, which can improve the security of secret sharing schemes.(4) In order to overcome the shortcoming of the fixed threshold in most existing threshold signature schemes, we give two solutions: ? A dynamic threshold signature scheme is constructed based on the changeable threshold multi-secret sharing scheme, in which different threshold values can be chose flexibly to sign documents depending on their significance. This scheme overcomes the shortcoming of the fixed threshold, and can protect the signature from allied cheating, ? Based on the previous scheme, a dynamic threshold group signature scheme without a trusted center is proposed, which has the same advantage as the previous one. Furthermore, no trust center is needed for managing secret keys of signers, and no secure channel is maintained. So this scheme is easier in key management and provides greater capabilities for applications.Finally, a summary of the dissertation research is made and some problems remained to be further studied are discussed.