Research Of (k,n) Threshold Secret Sharing Technology

Secret sharing is one important research field of information security and modern cryptography. The security of network communication is mainly decided by the security of secret shares. Secret sharing is an important tool in key management, which plays an important role in preventing key loss、leak and key safekeep. In this dissertation, we expound the background of secret sharing and the current situation of secret sharing, and mainly focus on all kinds of (k,n) threshold secret sharing schemes. The major contributions of this thesis are as follows:(1) We propose a new verifiable secret sharing scheme based on Shamir’s (k, n) secret sharing scheme. In this scheme, the size of share is smaller than the previous schems, which makes the scheme more efficient. In addition, we give two different ways of verification based on wether the dealer is honest.(2) We propose a more efficient verifiable (n,k,n) secret sharing scheme based on Harn’s scheme and then improve the proposed scheme to a multi-secret sharing scheme and a verifiable multi-secret sharing scheme respectively.(3) We review previous secret sharing schemes secure against cheating, and propose three new such schemes. The first one is based on the property of symmetry. In this scheme, the deal adopts a symmetric polynomial to sending shares, and the cheating detection is also based on the property of symmetry. The second one is based on the public information. In this scheme, deal will publish some information for cheating detection, and it would not release any information about the secret. The last one is based on majority voting. In this scheme, the cheating can be detected when the honest shareholders are majority.(4) With the inspiring of verifiable secret sharing and its method, we propose a verifiable key distribution scheme. In this scheme, all participants can collaborate to verify the invalidity of their shares without releasing them. According to different requirement on security and storage space, we give two different ways for verification.