A Secret Sharing Scheme to Reduce the Total Data Size

Secret sharing schemes have been proposed to prevent the loss or theft of secret data such as secret keys and files including highly private information. In the schemes, for given integer numbers of$n$and k (n ≥ k), n data called shares are constructed from the secret data so that the sharing conditions are satisfied, where the conditions are (i) the secret data can be reconstructed from arbitrary$k$or more shares and (ii) it can not be reconstructed from arbitrary less than$k$shares. However, the total data size (the number of bytes) to store all the shares is$n$times as large as the size of the secret data because the size of each share is equal to that of the secret data. In this paper, we propose a secret sharing scheme to reduce the total data size. In our proposed scheme, we partition the secret data into$n$blocks, and we construct each share from n-k+1 blocks so that the sharing conditions are satisfied. Our proposed scheme can reduce the total data size by a maximum of 2/n of the previous schemes when n = k.