Changing the Threshold in a Bivariate Polynomial Based Secret Image Sharing Scheme

Qindong Sun,Han Cao,Yanxiao Liu,Shancang Li,Houbing Song

doi:10.3390/math10050710

Abstract

Secret image sharing (SIS) is an important application of the traditional secret sharing scheme, which has become popular in recent years. In an SIS scheme, a confidential image is encrypted into a group of shadows. Any set of shadows that reaches the threshold can reconstruct the image; otherwise, nothing can be recovered at all. In most existing SIS schemes, the threshold on shadows for image reconstruction is fixed. However, in this work, we consider more complicated cases of SIS, such that the threshold is changeable according to the security environment. In this paper, we construct a (k↔h,n) threshold-changeable SIS (TCSIS) scheme using a bivariate polynomial, which provides h−k+1 possible thresholds, k,k+1,…,h. During image reconstruction, each participant can update their shadow according to the current threshold T based only on their initial shadow. Unlike previous TCSIS schemes, the proposed scheme achieves unconditional security and can overcome the information disclosure problem caused by homomorphism.

Highlights

The issue of image security has become important in recent years—for instance, in image steganography [1,2] and verification of visual consistency of images [3]
Visual cryptography-based Secret image sharing (SIS) uses the human visual system to recover an image, but the shadow size is greatly expanded from the original image, and the reconstructed image is of diminished quality; polynomial-based SIS is capable of recovering an image losslessly, and the shadow size is reduced from the original image, but the computation for image reconstruction is more complicated than in visual cryptography-based SIS
The model threshold-changeable SIS (TCSIS) scheme consists of two phases: shadow encryption phase and image reconstruction phase, which have the following steps

Summary

Introduction

The issue of image security has become important in recent years—for instance, in image steganography [1,2] and verification of visual consistency of images [3]. Secret image sharing (SIS) is an important topic in image security, which is meant to protect confidential images among multiple participants. Most SIS schemes satisfy a (k, n) threshold, such that an image is encrypted into n shadows: k or more shadows can reconstruct the image, but less than k shadows can do nothing. When an image has a huge number of pixels, the computations in shadow generation or image reconstruction may cause high time complexity. One can use the method of compressive sensing [16,17] to reduce image size, so that the time complexity for an SIS scheme can be reduced

Methods

Results

Conclusion