A verifiable essential secret image sharing scheme based on HLRs (VESIS-(t, s, k, n))

In traditional secret image sharing schemes, a secret image is shared among shareholders who have the same position. But if the shareholders have two different positions, essential and non-essential, it is necessary to use essential secret image sharing schemes. In this article, a verifiable essential secret image sharing scheme based on HLRs is proposed. Shareholder's share consists of two parts. The first part is produced by the shareholders, which prevents the fraud of dealers. The second part is a shadow image that is produced by using HLRs and the first part of share. The verification of the first part of the shares is done for the first time by using multilinear and bilinear maps. Also, for verifying shadow images, Bloom Filters are used for the first time. The proposed scheme is more efficient than similar schemes, and for the first part of the shares, has formal security.