On Converting Secret Sharing Scheme to Visual Secret Sharing Scheme

Daoshun Wang,Feng Yi

doi:10.1155/2010/782438

Abstract

Traditional Secret Sharing (SS) schemes reconstruct secret exactly the same as the original one but involve complex computation. Visual Secret Sharing (VSS) schemes decode the secret without computation, but each share is m times as big as the original and the quality of the reconstructed secret image is reduced. Probabilistic visual secret sharing (Prob.VSS) schemes for a binary image use only one subpixel to share the secret image; however the probability of white pixels in a white area is higher than that in a black area in the reconstructed secret image. SS schemes, VSS schemes, and Prob. VSS schemes have various construction methods and advantages. This paper first presents an approach to convert (transform) a (k, k)-SS scheme to a (k, k)-VSS scheme for greyscale images. The generation of the shadow images (shares) is based on Boolean XOR operation. The secret image can be reconstructed directly by performing Boolean OR operation, as in most conventional VSS schemes. Its pixel expansion is significantly smaller than that of VSS schemes. The quality of the reconstructed images, measured by average contrast, is the same as VSS schemes. Then a novel matrix-concatenation approach is used to extend the greyscale (k, k)-SS scheme to a more general case of greyscale (k, n)-VSS scheme.

Highlights

A secret kept in a single information-carrier could be lost or damaged
Visual secret sharing (VSS) schemes [5] have been proposed to encode a secret image into n “shadow” (“share”) images to be distributed to n participants
This paper proposes an approach to convert a deterministic (k, k)-Secret Sharing (SS) scheme to a (k, k)-VSS scheme for greyscale images with maximum number of grey levels g

Summary

Introduction

A secret kept in a single information-carrier could be lost or damaged. Secret Sharing (SS) schemes, called (k, n) threshold schemes, have been proposed since the late 1970s to encode a secret into n pieces (“shadows” or “shares”) so that the pieces can be distributed to n participants at different locations [1, 2]. To further reduce pixel expansion, a number of probabilistic VSS schemes (Prob.VSS schemes) have been proposed in [14,15,16]. These schemes were designed for the case of g = 2, that is, for black and white images. Lin et al [20] presented an innovative approach to combine two VSS and SS scheme, the n shares are created for a given grey-valued secret image. Each share includes both SS and VSS scheme information, providing two options for decoding.

A Review of Probabilistic VSS Scheme

Result

4: Concatenate all n k as the resulting n

Findings

Conclusions