An efficient cheating-detectable secret image sharing scheme with smaller share sizes

As a new approach to image protection, polynomial-based secret image sharing (PSIS) has attracted a lot of attention from many researchers in recent decades. When SIS technology is applied in practice, it is inevitably subject to various types of attacks, with cheating being the most likely to occur. To deal with the cheating problem in the process of secret image reconstruction, several effective (k, n)-PSIS schemes have been proposed. However, most previous schemes need to sacrifice the size of the share to achieve cheating detection capability. To address this issue, an efficient cheating-detectable (k, n)-PSIS scheme with smaller share sizes is designed based on the singularity of square matrix in this paper. In comparison with previous schemes, the proposed one can not only detect the complicity of up to k - 1 cheaters, but also reduce the size of shares to [1/k] times of the secret image. Moreover, the secret image can be recovered without loss, and it does not need to be scrambled before sharing, which could reduce the complexity of the scheme. Theoretical proofs and experiments show that the contrast and security conditions of the proposed scheme are satisfied, and the cheating detection capability is available as well.