A novel fast and provably secure (t,n)-threshold secret sharing construction for digital images

We propose a novel verifiable (t,n)-threshold secret sharing construction using simple cryptographic building blocks. The proposed construction provides an extremely low computational cost with respect to most of existing schemes, since the sharing algorithm has a linear time complexity with respect to the number of participants and the size of the share, when the reconstruction algorithm complexity is constant with respect to the threshold t. Furthermore, the proposed construction is provably secure, and has been shown to be robust, confidential, ideal and traceable. An instance of the proposed construction is implemented using a combination of the CRT-based sharing scheme and the Salsa20 stream cipher. Experimental results and comparisons with existing approaches shows that the proposed approach provides very competitive performances, hence is very suitable to share large sized secrets such like digital images.