A Multiple Secret Sharing Scheme based on Matrix Projection

Abstract

In [3], Bai et al. have proposed a multiple secret sharing scheme based on matrix projection. It is an elegant scheme with several advantages such as small share size and dynamic to secret changes. However,one of its disadvantages is that the secrets are organized in a square matrix and hence the number of secrets must be a square. So there is often a necessity to stuff dummy secrets into the secret matrix if the number of secrets is not a square.We present a new scheme based on matrix projection method that can share any number of secrets and make full use of every element of the secret matrix. The proposed scheme is as secure as Bai's scheme. Besides, the proposed scheme can also take advantage of the proactive characteristic of the matrix projection method to update shares periodically to improve security. Our scheme increases the potential range of the threshold. The increment of the threshold range is even more when we are using the proactive feature of the scheme. It also further reduces the share size to a constant (equal to that of a single secret). As with Bai's scheme, our scheme is partially verifiable based on the properties of the projection matrix. The paper also summarizes and classifies typical existing secret sharing schemes.