Efficient Multi-secret Sharing Scheme Using Room Square

In 1979, secret sharing scheme was first proposed by Shamir. In a secret sharing scheme, each participant receives a secret share in such a way that only authorized subsets can reconstruct the secret. Compare with Shamir´s scheme, Juan and Huang proposed an efficient secret sharing scheme from room square in 2005. Their scheme gave a practical algorithm to reduce the computation complexity by using room square, and obtained as (n - 1, n)-threshold secret sharing scheme. However, there is not any (t, n)-threshold secret sharing scheme for t les n - 2 with more efficient than Shamir´s scheme has been proposed. For this reason, this paper utilizes the characteristic of cycle to design four (t, n)-threshold secret sharing schemes for t = n - 2. These proposed schemes are not only more efficient than previous related works in the computational complexity, but also with the information rate is approximated optimal value 1. In addition, we combine the proposed scheme and the property of room square to present a new multi-secret sharing scheme in this paper.