Secret Sharing Scheme And It's Application In Threshold Signature

secret sharing is an important branch in modern cryptography and animportant research field in information. Secret sharing is first proposed for thedecentralized management of private key. The normal secret sharing scheme is thatthe shared secret is first divided in to several parts (secret shadow) and then given theparticipants. Only the qualified class of participants can recover the secret, any otherclass of participants can't obtain any information about the shared secret.Secret sharing scheme is very useful in key management, on the one hand it canprevent misuse of the over-centralization of power, and on the other hand it can warrantthe security and wholeness of the shared secret. Secret sharing is extensively used in thefield of keeping secret keys,data security,management of bank net and missilemanagement and launching. Moreover, it is used to structure worthily cryptographicarithmetic in combination with digital signature and status authentication, whichexpanded secret sharing schemes' application. Obviously, not only the research onsecret sharing has the theory value regarding this, moreover has the widespreadpractical application value.In this paper, the concept of secret sharing and its development and broadcast areintroduced, the shortcomings of existing secret sharing scheme in practice. Aiming atthese problems, we designed two practical secret sharing schemes and studied itsapplication in threshold group signature on the known knowledge. Main contributionsof this paper are summarized as follows:1. By means of RSA signature, a secret sharing scheme is proposed, its security isbased on the RSA signature, i.e. the difficulty of factoring large integers.2. A publicly verifiable secret sharing scheme is proposed. Its security is on thebasic of ELGamal system, i. e. the difficulty of discrete logarithm problem.3. By the means of designed group signature using signal signature scheme, athreshold group-signature scheme with multi-party is proposed. And in this scheme, wecan assure the anonymity of the participants and detect the ID of participants aftersignature. 4. On the basic of threshold group-signature scheme with multi-party, a new IDbased threshold group signature is proposed. This scheme is an ID based signature andit can satisfy the require of threshold signature.