A Lossless Linear Algebraic Secret Image Sharing Scheme

A (k, n)-threshold secret image sharing scheme is any method of distributing a secret image amongst n participants in such a way that any k participants are able to use their shares collectively to reconstruct the secret image, while fewer than k shares do not reveal any information about the secret image. In this work, we propose a lossless linear algebraic (k, n)-threshold secret image sharing scheme. The scheme associates a vector v(i) to the ith participant in the vector space F-2(k)alpha, where the vectors v(i) satisfy some admissibility conditions. The ith share is simply a linear combination of the vectors v(i) with coefficients from the secret image. Simulation results demonstrate the effectiveness and robustness of the proposed scheme compared to standard statistical attacks on secret image sharing schemes. Furthermore, the proposed scheme has a high level of security, error-resilient capability, and the size of each share is 1/k the size of the secret image. In comparison with existing work, the scheme is shown to be very competitive.