An in-depth analysis of strong t-consistency on secret image sharing

The detection of an adversary in secret image sharing has been a problematic side in the reconstruction phase. Some of verifiable secret sharing solutions have been proposed to solve the problem. However, there is some computational limitation in the previous schemes. The purpose of this paper is to analyze the importance of consistency for detecting an adversary in a secure reconstruction phase. Strong t-consistency assures the correctness of reconstructed secret as long as participants P ∈ N and n(P) = t. Consistency is a solution for preventing the participant to be absent and helps the dealer to easily detect the adversary without an additional verification step.

This paper focuses on secure reconstruction, and uses two different approaches, namely, single-secret and multi-secret, to experiment the relationship between the given variable (t,m,n) and the adversaries by observing the quality test result, polynomial approach and visualization.

The results show that t and m are inversely proportional to the image quality without respect to the polynomial approach. The reconstruction phase is declared as securely conducted when m = 2t − 1, for both single- and multi-secret approaches.

The application of consistency is a considerable step for securing the secret from an adversary by combining the reconstruction phase and the consistency combination at once, removing the need for additional separate verification steps for decreasing the computational time, especially in secret image sharing.