A novel linearly bounded secret sharing scheme that supports prioritization of shares

Secret Sharing is a technique of decomposing a secret into number of shares in such a manner that reconstruction of the secret is only possible by a subset of shares that has at least a specific minimum size. Adi Shamir and George Blackley individually proposed the idea of Secret Sharing for the first time, but high computational complexity and noise like shares are the main issues of these schemes. However, using current state of the art schemes it is possible to perform this task in linear time without producing noise like shares. Providing special privilege to a subset of shares is not supported by the existing schemes. It would be a novel concept if it is possible to assign special priority to a set of shares during decomposition of secrets. Hence a linear time bounded scheme is being proposed which decomposes any secret into N number of shares among which M (M≤N) of them are specially privileged. During reconstruction of the actual secret, a subset of shares with a minimum size K (M≤K≤N) which essentially contains all the specially privileged shares or mandatory shares is required.