In reversible image secret sharing (RISS), the cover image can be recovered to some degree, and a share can be comprehensible rather than noise-like. Reversible cover images play an important role in law enforcement and medical diagnosis. The comprehensible share can not only reduce the suspicion of attackers but also improve the management efficiency of shares. In this paper, we first provide a formal definition of RISS. Then, we propose an RISS algorithm for a $(k,n)$ -threshold based on the principle of the Chinese remainder theorem-based ISS (CRTISS). In the proposed RISS, the secret image is losslessly decoded by a modular operation, and the original cover image is recovered by a binarization operation, both of which are just simple operations. Theoretical analyses and experiments are provided to validate the proposed definition and algorithm.

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Reversible Image Secret Sharing

In this paper, a novel visual secret sharing (VSS) scheme based on QR code (VSSQR) with (k, n) threshold is investigated. Our VSSQR exploits the error correction mechanism in the QR code structure, to generate the bits corresponding to shares (shadow images) by VSS from a secret bit in the processing of encoding QR. Each output share is a valid QR code that can be scanned and decoded utilizing a QR code reader, which may reduce the likelihood of attracting the attention of potential attackers. Due to different application scenarios, two different recovered ways of the secret image are given. The proposed VSS scheme based on QR code can visually reveal secret image with the abilities of stacking and XOR decryptions as well as scan every shadow image, i.e., a QR code, by a QR code reader. The secret image could be revealed by human visual system without any computation based on stacking when no lightweight computation device. On the other hand, if the lightweight computation device is available, the secret image can be revealed with better visual quality based on XOR operation and could be lossless revealed when sufficient shares are collected. In addition, it can assist alignment for VSS recovery. The experiment results show the effectiveness of our scheme.

Visual secret sharing scheme for (k, n) threshold based on QR code with multiple decryptions

Chinese remainder theorem-based two-in-one image secret sharing with three decoding options

( k , n ) progressive secret image sharing (PSIS) schemes were discussed frequently in recent years. A ( k , n ) PSIS scheme consists of sharing phase and reconstruction phase. During sharing phase, a secret image is encrypted into n image-shadows; while during reconstruction phase, k to n image-shadows can progressively recover the image; fewer than k image-shadows get no information on the image. Most previous PSIS schemes can be divided into two categories, polynomial based PSIS schemes and visual cryptography based PSIS schemes. Polynomial based schemes can recover high quality image with complicated cryptographic computations; visual cryptography based PSIS schemes can reconstruct image using human visual system without any cryptographic computation, however, the size of image shadow expands largely from the image and the recovered image is quality-distortion. The motivation of this work is to solving the problems in existing PSIS schemes. Thus, in this paper, we adopt three Boolean operations: bit-level XOR, C O V ( 1 , 7 , 3 ) from ( 7 , 4 ) Hamming code and C O V ( 2 , 8 , 4 ) from ( 8 , 4 ) shortened Hamming code to propose three ( k , n ) PSIS schemes. In our schemes, k to n image-shadows can decrypt randomly partial pixels on entire image, and reconstruct image progressively. Comparing with previous PSIS schemes, our schemes has smaller image-shadow size and higher quality of recovered image than visual cryptography based PSIS schemes. On the other hand, our schemes has much more efficient operations in sharing procedure and image reconstruction procedure than polynomial based PSIS schemes.

Progressive (k,n) secret image sharing schemes based on Boolean operations and covering codes

Classic secret image sharing (SIS) including polynomial-based SIS, visual secret sharing (VSS), linear congruence (LC)-based SIS and so on, generally has the shortcoming of “all-or-nothing”, which is mainly caused by that most of their ideas are borrowed from secret data sharing designed for data rather than image. Progressive secret image sharing (PSIS) has the feature that the more shadows the better recovered secret image quality. In this paper, we introduce a general PSIS construction method with no pixel expansion from classic “all-or-nothing” SIS. Based on our PSIS construction method, three PSIS algorithms with selective progressive thresholds are extended from classic SIS schemes, respectively. Experiments are provided to demonstrate the efficiency of our method in terms of illustrations and analyses.

A general progressive secret image sharing construction method

Visual secret sharing (VSS) for general access structure (GAS) owns wider applications than (k, n) threshold VSS. VSS with multiple decryptions realizes the functionalities of both OR-based VSS (OVSS) and XOR-based VSS (XVSS), which can broaden the applications as well compared to one recovery method-based VSS. In this paper, we propose a progressive VSS (PVSS) scheme for GAS with the features of both OR and XOR decryptions based on random grid (RG). The different regions of the secret image and corresponding genearted random bits are employed to gain progressive property as well as GAS with OR and XOR decryptions. For the qualified sets, if we have a copy machine, we can reconstruct the secret by stacking. On the other hand, if a device with XOR operation is available, we can improve the visual quality of the recovered secret image as well as we can reconstruct the secret image losslessly when we collect all the n shares. In addition, our scheme has neither pixel expansion nor codebook design due to RG. The effectiveness of the proposed scheme are shown in terms of experimental results and analyses.

Progressive Visual Secret Sharing for General Access Structure with Multiple Decryptions

In comparison with Shamir’s original polynomial-based secret image sharing (SIS), Chinese remainder theorem-based SIS (CRTSIS) overall has the advantages of lossless recovery, low recovery computation complexity and no auxiliary encryption. Traditional CRTSIS methods generally suffer from no (k, n) threshold, lossy recovery, ignoring the image characteristics and auxiliary encryption. Based on the analysis of image characteristics and SIS, in this paper we propose a CRTSIS method for (k, n) threshold, through dividing the gray image pixel values into two intervals corresponding to two available mapping intervals. Our method realizes (k, n) threshold and lossless recovery for gray image without auxiliary encryption. Analysis and experiments are provided to indicate the effectiveness of the proposed method.

Chinese Remainder Theorem-Based Secret Image Sharing for ( k , n ) Threshold

In this paper, homomorphic visual cryptographic scheme HVCS is proposed. The proposed HVCS inherits the good features of traditional VCS, such as, loss-tolerant e.g., k, n threshold and simply reconstructed method, where simply reconstructed method means that the decryption of the secret image is based on human visual system HVS without any cryptographic computation. In addition, the proposed HVCS can support signal processing in the encrypted domain SPED, e.g., homomorphic operations and authentication, which can protect the user's privacy as well as improve the security in some applications, such as, cloud computing and so on. Both the theoretical analysis and simulation results demonstrate the effectiveness and security of the proposed HVCS.

Exploiting the Homomorphic Property of Visual Cryptography

Lossless﻿recovery﻿is﻿important﻿for﻿the﻿transmission﻿and﻿storage﻿of﻿image﻿data.﻿In﻿polynomial-based﻿ secret﻿ image﻿ sharing,﻿ despite﻿ many﻿ previous﻿ researchers﻿ attempted﻿ to﻿ achieve﻿ lossless﻿ recovery,﻿ none﻿of﻿the﻿proposed﻿work﻿can﻿simultaneously﻿satisfy﻿an﻿efficiency﻿execution﻿and﻿at﻿no﻿cost﻿of﻿some﻿ storage﻿capacity.﻿This﻿article﻿proposes﻿a﻿secret﻿sharing﻿scheme﻿with﻿fully﻿lossless﻿recovery﻿based﻿on﻿ polynomial-based﻿scheme﻿and﻿modular﻿algebraic﻿recovery.﻿The﻿major﻿difference﻿between﻿the﻿proposed﻿ method﻿and﻿polynomial-based﻿scheme﻿is﻿that,﻿instead﻿of﻿only﻿using﻿the﻿first﻿coefficient﻿of﻿sharing﻿ polynomial,﻿this﻿article﻿uses﻿the﻿first﻿two﻿coefficients﻿of﻿sharing﻿polynomial﻿to﻿embed﻿the﻿pixels﻿as﻿ well﻿as﻿guarantee﻿security.﻿Both﻿theoretical﻿proof﻿and﻿experimental﻿results﻿are﻿given﻿to﻿demonstrate﻿ the﻿effectiveness﻿of﻿the﻿proposed﻿scheme. KeywoRDS Lossless Recovery, Modulo Algebra, Polynomial-Based Secret Sharing, Secret Image Sharing

Wanmeng Ding

Papers

Progressive Visual Secret Sharing for General Access Structure with Multiple Decryptions

Chinese Remainder Theorem-Based Secret Image Sharing for ( k , n ) Threshold

Exploiting the Homomorphic Property of Visual Cryptography

Polynomial-Based Secret Image Sharing Scheme with Fully Lossless Recovery

Period-assisted adaptive parameterized wavelet dictionary and its sparse representation for periodic transient features of rolling bearing faults