Research On Verifiable Secret Sharing And Its Applications

Secure multiparty protocols play an important role in the area of information security. Oneof the fundamental notions and tools in the design of secure multiparty protocols isverifiable secret sharing (VSS for short). Many researchers have been studying themethods of VSS since the birth of its concept. Some secure and efficient VSS schemeshave been presented. The applications of verifiable secret sharing in fields such asthreshold cryptography, key escrow, secure multiparty computation, and electroniccommerce have also been studied.. Based on VSS, some protocols of practical value havebeen proposed for threshold signature, key escrow, secure multiparty computation,electronic auction, electronic voting, and fair exchange etc..But there are still several severe drawbacks in the research on verifiable secret sharingand its applications. The first one is there are not enough secure and efficient VSS schemes.What is more, there are hardly any VSS schemes that can withstand active attacks.Secondly, only a little attention has been paid to verifiable secret sharing with generalaccess structures (generalized VSS) whose applicability is much wider. And in the existingliteratures, there is no efficient and practical generalized VSS protocol. Thirdly, no one hasstudied the application of VSS in the threshold generation of authenticated encryption(signcryption). Lastly, the applications of generalized VSS in group oriented cryptgraphysuch as distributed digital signature, key escrow, and key generation based on generalaccess structures have not been mentioned in the literature available. Based on a detailedsummarization and analysis of related literatures, in this thesis, a further research on VSSand its applications is done aiming at the drawbacks presented above, and the followingresults are gotten:1.With respect to secure and efficient threshold VSS schemes, a threshold VSSscheme based on secret sharing matrix is presented. This breaks'through thelimitation that existing secure and efficient VSS schemes are all based on Shamir'ssecret sharing system. What is more, the problem of how to prevent active attacksin VSS is studied for the first time, and a method of constructing VSS schemes thatcan withstand active attacks using signcryption is proposed.2.Generalized VSS on vector space access structures is studied for the first time. Acomputational secure generalized VSS protocol and an information theoreticsecure one on this kind of access structures are given.3.With respect to VSS on arbitrary access structures, a computational securegeneralized VSS protocol as well as an information theoretic secure one applicableto arbitrary access structures are presented.4.A generalized verifiable multi-secret sharing scheme applicable to arbitrary accessstructures is presented for the first tir.5.Threshold generation of signcryption based on VSS is studied for the first timewith a secure and efficient protocol presented.6.Distributed key generation based on general access structures is studied with a keygeneration protocol applicable to arbitrary access structures proposed.7.The applications of VSS in electronic commerce are studied. The method ofconstructing VSS schemes using signcryption is applied to the design of a secureand efficient multi-round electronic auction scheme, and an optimistic fairexchange protocol with a distributed semi-trusted third party based on VSS ispresented.