Polynomial Approach in a Secret Image Sharing Using Quadratic Residue

Abstract

Secret Image Sharing is a technique to share the secret among n participants. Each participant has meaningless, noise like shares. The secret image is revealed if any k of the shares are gathered. This scheme uses polynomial based (k, n) secret sharing approach proposed by Shamir in 1979. In 2007, Chen et al. proposed a new secret image sharing method that uses quadratic residues. Their scheme restricts the value of k, only (2, 2) scheme is realized with their algorithm. This prevents use of their method for any values of (k, n). In this work, we applied Shamir's polynomial approach with quadratic residues to generalize Chen's method. Proposed method is valid for any values of (k, n) as can be seen in the experimental results. Two methods (both lossy and lossless) are implemented, and their results are compared with respect to shares' size. As a result, lossless method is preferable for k values larger than two. Otherwise, lossy method is recommended.