Research Of Secure Secret Sharing And Its Applications

Secret sharing scheme is one important branch of modern cryptography and one important research field of information security. This dissertation reviews the research advances of secret sharing schemes, designs secure threshold secret sharing schemes, and constructs secure and efficient secret sharing schemes based on vector space access structure. In addition, applications of secret sharing in signature and multi-party decryption are studied, and secure and efficient crypto-algorithms are proposed.Firstly, by means of the intractability of discrete logarithm problem, a threshold secret sharing scheme with periodic renewing to identify cheaters is established. Shares are periodically renewed without changing the secret. Every participant is able to verify the share he receives and those other participants show. This scheme can efficiently prevent adversaries from getting the secret or shares, and prevent some participants from cheating others. Afterwards, the threshold secret sharing scheme with periodic renewing to identify cheaters is extended to the vector space access structure, and a vector space secret sharing scheme with periodic renewing to identify cheaters is proposed. The threshold scheme is actually a particular case of the vector space secret sharing scheme. Therefore the vector space secret sharing scheme can find more applications than the threshold scheme.In the above two schemes, every participant is required verifying the shares of the other participants, and the computation complexity is relatively high. Sometimes the schemes with low computation complexity that can detect cheaters are needed in practice. The secure threshold secret sharing scheme and the secure vector space secret sharing scheme proposed in the dissertation can meet this need. Both schemes can detect if cheaters exist. They are perfect secret sharing schemes. Their information rates are asymptotically optimal. And the probability of successfully cheating in these two schemes can be ignored.A threshold multiple secret sharing scheme and a dynamic (t, n) threshold secret sharing scheme based on certificate are proposed. The security of the threshold multiple secret sharing scheme is based on the security of RSA signature, i.e. the difficulty of factoring large integers. The dynamic (t, n) threshold secret sharing scheme based on certificate uses the key in the participant's certificate as his share. This scheme can assure that any t participants can calculate the secret value, but no group of t-1 participants can do so. In this scheme, the dealer doesn't require secretly sending anyinformation to any participant. Therefore no secure channel is required between the dealer and the participants. In the two schemes, the shares can be repeatedly used for the reconstruction of multiple secrets, and no information of the existing participants needs changing after a new participant joins.A vector space secret sharing-multisignature scheme is proposed based on vector space secret sharing scheme and multisignature scheme. The security of this scheme is analyzed. The group signature can be easily produced if an authorized subset of participants pool their secret shares and it is impossible for them to generate a group . signature if an unauthorized subset of participants pool their secret shares. The validity of the partial signature and the group signature can be verified by means of verification equations. A group signature of an authorized subset of participants cannot be impersonated by any other set of participants. Moreover the suspected forgery and the malicious participants can be found in this scheme. None of several possible attacks can successfully break this scheme. When there is not a trusted share distribution center, this dissertation gives a solution how the group signature is realized for vector space access structure, or constructs a vector space secret sharing-multisignature scheme without trusted share distribution center, and analyzes its security. The generalized-multisignature scheme is proposed based...