Secret Sharing And Application Of Secret Sharing In Digital Signature

Secret sharing scheme is one important branch of modern cryptography and important research field of information security. In a (t,n) threshold secret sharing scheme, the dealer first splits the secret into n different pieces,called shadows,which are given to the participants over a secret channel. At least t or more participants can use their shadows to collabrattively reconstruct the secret, but only t-1 or fewer participants will not be enough. Threshold signature schemes are integrated by the threshold secret sharing scheme with digital signature scheme. In a (t,n) threshold signature, t or more members of the group cooperate to generate a valid group signature (anonymously or publicly) on behalf of the group of n members.This dissertation reviews the research advances of secret sharing schemes and threshold signature, designs secure secret sharing schemes based on general access structure. And constructs secure and efficient threshold multi-secret sharing scheme. In addition, application of secret sharing in signature is studied and secure and efficient threshold signature schemes are proposed. The following are the main researching results:1. A general secret sharing scheme based on the intractability of discrete logarithm problem is proposed. A notice board is introduced in this scheme, so that when a new secret is shared in the system, the dealer do not require sends new shares to the participants, only changes the corresponding participants on the notices board. So the efficiency is improved.2. We analyzed and pointed out the weakness of the best so far threshold multi-secret sharing schemes based on the factorization problem. In the meanwhile, a new secure and efficient threshold verifiable multi-secret sharing scheme based on factorization problem and discrete logarithm modulo a large composite problem is given. The scheme can detect both the cheating by the dealer and that by any participant. And every participant keeps only one reusable shadow that can be used to reconstruct the multi-secret distributed by the dealer.3. We analyzed the weakness of three best so far threshold group signature schemes...