Research And Design Of Two Kinds Of General Secret Sharing Scheme

Secret sharing scheme is an important branch of modern cryptographyand research field of information security. The first secret sharing scheme is a (t,n)threshold secret sharing scheme. In the scheme, the dealer first splits the secret into ndifferent pieces, called shadows, which are given to the participants over a secretchannel. At least t or more participants can use their shadows to collaborativelyreconstruct the secret, but only t-1 or fewer participants will not be enough. Theassumption that every participant have the completely equal position and authority isadded to threshold scheme virtually, but the real world often can't meet the demand ofsuch assumption. Therefore, research of secret sharing scheme based on general accessstructure not only has important theory meaning but also have important realisticmeanings.This dissertation reviews the research advances and the current situation of generalsecret sharing, discovers that available documents has little research on general secretsharing scheme and some of that also has problems on the repeated use of shadow,member addition and deletion, member deception, scheme efficiency. Aiming at theseproblems, this paper presents design several relatively secure and efficiency generalsecret sharing schemes based on the known knowledge. Main contributions of this paperare summarized as follows:1. Analyzed security and efficiency of the special general secret sharing schemegiven by Liu Huanping et al, pointed out the flaws in security, applied ElGamalsignature scheme into this scheme, designed a special general secret sharing schemewhich can detect the deception of the participants, but there are still some problems inthis scheme, such as computational complexity, public parameters.2. Two special general secret sharing schemes based on the property of discretelogarithm and LUC crypto system was given. In these schemes, each participant's secretshadow was selected by the participant himself and even the dealer did not knowanything about his secret shadows. In the recovery phase, each participant was allowedto check whether another participant provided the true information or not. Eachparticipant can share many secrets with other participants by holding only one shadow. 3. Analyzed and proved the design flaws of the generalized (t,n)threshold secretsharing schemes, designed one (t₁,n₁;…;t_k,n_k)scheme, two t-(t₁,n₁;…;t_k,n_k)schemes. In these schemes, each participant is allowed to check whether anotherparticipant provided the true information or not, the shadows of participants can bereused, many secrets can be shared in one scheme and the security of the originalscheme cannot be descended.