The Short Share Secret Sharing Agreement with Matrix Factorization

To make up the limitation of traditional secret sharing schemes that the length of secret can not be extremely great, we use the theory of Jordan matrix factorization and combine with the formulary of Lagrange putting forward an algorithm of (r, n) threshold secret sharing with short share and high efficiency. The length of secret share that each participator needs to conserve has no relation with the length of the secret. So our scheme has a very high space, computation and communication efficiency. It has a very important application when the secret is a big privacy file, a big message transmitting in an insecurity channel, a secret data base shared by several participant or magnanimity data in distributed storage.