Essential secret image sharing scheme with small and equal sized shadows

Abstract

In the literature of secret sharing, the property of essential secret sharing scheme ensures that no set of participants, missing at least one essential participant, should be able to get any information regarding the secret. However, there are essential secret image sharing schemes available in the literature in which we have shown mathematically as well as through experiments that any k or more non-essential participants together can get information about the secret image. It is true that in most of these schemes, preprocessing steps such as random permutations or chaotic maps are used on the secret image to avoid this problem. But that will surely introduce an overhead to the schemes. Moreover, the security of these schemes mainly depends on the preprocessing step and not on the secret sharing schemes. However, our proposed (t,k,n)-ESIS scheme for grayscale images over the finite field GF(pm) does not require any preprocessing step to secure the scheme. Though, the proposed scheme over GF(pm) with pm>28 is little lossy, it has the advantage over most of the ESIS schemes in the sense that the scheme works fine, even if the number of participants is more than 255. Most importantly, our proposed scheme over GF(28) is completely lossless. Moreover, our proposed scheme, does not have the limitations such as different size of shadows, concatenation of sub-shadows, use of derivative polynomials etc. Finally, our scheme has reduced share size and work fine without any preprocessing steps on secret image, making our scheme efficient.