Dynamic Secret Sharing Scheme. Linear Code

The threshold secret sharing scheme based on Lagrange interpolotion polynomial was frist introduced by Shamir in 1979. Since then Shamir's scheme was reseached deeply by many experts and reseachers. In order to satisfy some special cases for secret sharing schemes of the real world, various kinds of schemes have been put forward, such as verifiable secret sharing scheme, dynamic secret sharing scheme, multi-secret sharing scheme, subkey periodically renewed secret sharing scheme, visual secret sharing scheme and so on. A secret sharing scheme based on Massey's scheme was proposed in this paper. The scheme has the following advantages compared with Massey's scheme:(1)Verification:The verification of the scheme can be realized by the RSA cryptosystem. In sharing phase, each participant's secret shadow was selected by himself, and the secret shadow can verify the information that published on the public board by the dealer. In reconstruction phase, the designated combiner can use the public information to verify the information transfered by each participant.(2) Dynamic:Due to the relationship between the linear codes and the access structure, a chain of linear codes was definited in this paper. The length of the linear code in the chain of linear codes can determinate the number of the participants, thus the participants can dynamically add and exit in the scheme. The secrets also can be updated dynamically, but each participant's shadow has no need to be changed, only the corresponding value has to be updated on the public board.(3) Multi-secrets:Only one secret shadow was hold by each participant, and the several secrets can be shared by the participants.In addition, the public board was used in this scheme, thus the information on the public board has no need to be transferred, so that the burden of the transmission and the participants" saving can be reduced. The transferred information was encrypted by the RSA cryptosystem, thus the transferred information didn't require the private channel. Compared with the threshold secret sharing schemes, the access structure of the sharing scheme in this paper is more interesting.