Research On Two Typical Secret Sharing Schemes

Secret sharing is an important concept in cryptography.The so-called secret sharing scheme is a method that a dealer distributes shares of a secret to participants such that only qualified subsets of the participants can recover the secret,while unqualified subsets can't get any information about the secret.The design idea of the modern cryptosystems is that the security of a system depends on the keys and the cryptographic algorithms are public in the meantime.In order to ensure the security of a secret system,the management of a key is very important.Secret sharing can be applied in secure storage and encryption of data,which ensures the security and accuracy of transmitted information.As an important tool to protect information,secret sharing schemes included threshold secret sharing schemes and general secret sharing schemes and so on.The secret sharing have become a cornerstone of cryptography.The main results of this dissertation are listed below.(1)In order to deal with the weakness in the scheme of Lin and Yeh,this dissertation proposes a dynamic multi-secret sharing scheme with verification based on the RSA cryptosystem,one-way hash functions and the XOR operation.In this scheme,each participant only need keep one master secret share which can reconstruct different master secrets according to the size of the threshold values.The scheme can add new secrets or update the secrets and remove or add participants freely.This scheme has verifiable property,which can avoid the fraud of the dealer and the participants.(2)We construct two-weight linear codes over finite field by using linear cods over a finite non-chain ring,then we prove that two-weight linear codes can be used to construct the secret sharing schemes and determine the access structures of secret sharing schemes.Compared with existing schemes,we determine the minimal codewords of linear codes by using different algebraic structure.Moreover,the construction method about the generator matrix G_k~? of the simplex codes S_k~? is simpler.