Research Of Veriifable And Renewable Secret Sharing Scheme

With wide application of information technology and network, much attentionhas been given to how to ensure information security. Secret sharing scheme is animportant branch of modern cryptography and research field of information security.The first secret sharing scheme is a ( t , n )threshold secret sharing scheme. In thescheme, 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 moreparticipants can use their shadows to reconstruct the secret collaboratively, but onlyt-1 1or fewer participants will not be enough to do so. Verifiable secret sharing is akind of secret sharing which can prevent the dealer and participants from cheating.As a kind of secret sharing scheme, verifiable secret sharing schemes are widelyused in many fields, such as distributed computing, e-commerce. In renewable secretsharing schemes, the secret shares of participants are updated at first. After that,each participant destroys the original secret shares that make the secret share got bythe attacker in the last period expires in the current period. Main contributions ofthis paper are summarized as follows.Firstly, a secret sharing scheme based on bilinear pairings is introduced andanalyzed, we point out that the scheme could not prevent participants from cheating.Based on this scheme, this paper proposes a verifiable and renewable thresholdsecret sharing scheme based on bilinear pairings. By setting up the equation which isverified by both the dealer and the participants，the scheme can identify the validityof the secret share provided by the participant. The dealer can regularly updateinterpolation polynomial using Hash function, so the secret share held by theparticipants can be regularly updated. Under the assumption of discrete logarithmdifferent problem in finite fields, the verification processes of the secret shares canprevent participants from cheating efficiently.Secondly, based on ElGamal cryptosystem, a verifiable dynamic general secret sharing scheme is proposed. In this scheme, each participant’s secret shadow isselected by the participant himself. No security channel exists between the dealerand the participants. Before the secret reconstructing, through setting up an equationwhich is verified by each participant, the scheme can distinguish if the dealer iscredible or not, after secret reconstructing, any participant only needs to compute theequation once that can confirm the existence of the cheater, the secret dealer canpoint out the identity of the cheater. In the scheme, the sub-secrets of participantscan be repeatedly used. The security of this scheme is based on the ElGamalcryptosystem and Shamir’s (t, n) threshold secret sharing scheme.Finally, the main contents are summarized and future research work is pointedout at the end of the thesis.