Research On Verifiable Secret Sharing And It's Application In Threshold Signature

Secret sharing system is an important branch in the field of modern cryptography and an important research field in information security. Secret sharing is first proposed for the decentralized management of private key. The normal secret sharing scheme is that the shared secret is first divided into several parts (secret shadow) and then given the participants. 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 can prevent misuse of the over-centralization of power, and on the other hand it can warrant the security and wholeness of the shared secret. Secret sharing is extensively used in the field of keeping secret keys, data security, management of bank net and missile management and launching. Moreover, it is used to structure worthily cryptographic arithmetic in combination with digital signature and status authentication, which further expanded the application field of secret sharing system. Obviously, not only the research on secret sharing has the theory value regarding this, moreover has the widespread practical application value.In this paper, we introduced the background of secret sharing and its status quo in development, researched the problems and shortcomings of existing secret sharing scheme in practice. Aiming at these problems, we studied its application in threshold signature and designed two practical threshold signature schemes on the known knowledge, and made a detailed analysis of their security.In ID-based cryptography, the digital certificate could be replaced by any information about identity as public key, a trusted third party called private key generator (PKG) can generate a private key according to user information. From view point of the convenience and efficiency, ID-based cryptography could take the place of CA-based cryptography very well. We will give an ID-based proactive threshold signature scheme in chapter 5. At last, we implement a prototype system of the ( t ,n )- threshold signature scheme.