Enhancing Shamir’s Secret Sharing Using Gaussian Elimination Based on Hybrid Transform (Integer WT-DCT)

Abstract

A secret sharing is an important tool to share the secret key among N users in a secure manner with the need to treat the main problems of increment shares volume and sharing control. Based on the hybrid transformations, a new technique of sharing scheme with excellent sharing-control flexibility is suggested to share a secret image into multiple shadow pictures (for N users) utilizing a scheme of Shamir’s threshold beside a method for solving a system of linear equations by Gaussian Elimination to remade the secret. This scheme applied a hybrid I-WT and DCT firstly to de-correlate image pixels for more reduction in image size; then it employs the modifying Shamir’s (k, n) sharing scheme to generate the shadow images. A quality refinement of the recouped picture is accomplished by the information collected from the threshold (k) of share images, and each of one has no data about the secret image. The shadow image size for everyone is smaller than [1/3.5*(v / k- 0.1)] of the secret image (where v=2,3,.., according to k value) and any number of shadow pictures that is not as much as k or larger uncovers no data about the secret. This technique is secure for image sharing with excellent time execution and gives fantastic (PSNR) value rate [greater than 34 db] as shown in result table using integer WT and DPCM that keeps an image quality good, however, much is still expected.