List of Figures

List of Tables

Preface

Contributors

1 Visual Cryptography from Halftone Error Diffusion
Gonzalo R. Arce, Zhongmin Wang, and Giovanni Di Crescenzo

1.1 Introduction

1.1.1 Visual Cryptography

1.1.2 Halftone Visual Cryptography

1.1.3 Blue Noise Error Diffusion

1.2 Visual Secret Sharing

1.2.1 Notion and Formal Definitions

1.2.2 Construction of VSS Scheme

1.3 Halftone VSS Construction Using Error Diffusion

1.3.1 Share Structure

1.3.2 Distribution of SIPs and ABPs

1.3.3 Generation of Halftone Shares via Error Diffusion

1.4 Halftone VSS Construction Using Parallel Error Diffusion

1.5 Quality of Halftone Shares

1.6 Discussion

1.6.1 Improvement of Image Quality

1.6.2 Comparison with Other Methods

1.6.3 Image Decoding

1.7 Simulation Results

1.8 Conclusion

Bibliography

2 Visual Cryptography for Color Images
Stelvio Cimato, Roberto De Prisco, and Alfredo De Santis

2.1 Introduction

2.2 Color Superposition

2.2.1 Color Vision and Color Models

2.2.2 Lattices

2.2.3 The Darkening Problem

2.2.4 The Annihilator Color

2.2.5 The Identity Color

2.3 Formal Models for Colored VCS

2.3.1 The Models for B&W-VC

2.3.2 The Models for Color-VC

2.3.3 The SC, ND, and General Models

2.3.4 Base Matrices

2.4 Schemes for the SC Model

2.4.1 The VV Schemes

2.4.2 The BDD Schemes

2.4.3 The KY and YL Schemes

2.4.4 The CDD Schemes and a Lower Bound

2.5 Schemes for the ND Model

2.6 Schemes for the General Model

2.6.1 (2,2)-Threshold Schemes

2.6.2 The (2, n)-Threshold AS Schemes

2.7 Other Schemes

2.8 Conclusions

Bibliography

3 Visual Cryptography for Multiple Secrets
Shyong Jian Shyu

3.1 Introduction

3.2 Naor and Shamir’s Basic Visual Secret Sharing Scheme

3.3 Visual Two-Secret Sharing Schemes

3.3.1 Wu and Chen’s Scheme

3.3.2 Wu and Chang’s Scheme

3.4 Visual Multiple-Secret Sharing Schemes

3.4.1 Shyu et al.’s Scheme

3.4.1.1 Informal Description

3.4.1.2 Encoding Circle Share A

3.4.1.3 Encoding Circle Share B

3.4.1.4 General Algorithm

3.4.2 Feng et al.’s Scheme

3.4.3 Experimental Results

3.4.4 Comparison and Discussions

3.5 Concluding Remarks

Bibliography

4 Extended Visual Cryptography for Photograph Images
Yasushi Yamaguchi

4.1 Introduction

4.2 Basic Visual Cryptography Schemes

4.2.1 (k,n) Visual Secret Sharing Schemes

4.2.2 Extended Visual Cryptography Scheme

4.2.3 Random Grids

4.3 Fundamentals of Photograph Visual Cryptography

4.3.1 Digital Halftoning

4.3.2 Image Quality and Related Parameters

4.3.3 Photograph Visual Cryptography with Basic Schemes

4.4 Variations of Photograph Visual Cryptography

4.4.1 Approaches to Photograph Visual Cryptography

4.4.2 Random-Dot Shadow Images

4.4.3 Similar Shadow Images

4.4.4 Positive and Negative Shadow Images

4.4.5 Error and Secret Diffusion

4.4.6 Simultaneous Iterative Search

4.4.7 Tone Adjustment

4.4.8 Continuous-Tone Subpixel

4.5 Misalignment-Tolerant Photograph Visual Cryptography

4.5.1 Theory and Implementation

4.5.2 Results

4.6 Conclusions

Bibliography

5 Probabilistic Visual Cryptography Schemes
Stelvio Cimato, Roberto De Prisco, and Alfredo De Santis

5.1 Introduction

5.2 Visual Cryptography Schemes

5.2.1 The Deterministic Model

5.2.2 The Probabilistic Model

5.3 Canonical Probabilistic Schemes

5.4 Probabilistic Schemes with No Pixel Expansion

5.5 Trading Pixel Expansion with Probabilities

5.5.1 Probabilistic Schemes with Given Pixel Expansion

5.6 Constructing Probabilistic Schemes

5.6.1 (n, n)-Threshold Probabilistic Schemes with Any Pixel Expansion

5.6.2 (2, n)-Threshold Probabilistic Schemes with Any Pixel Expansion

5.7 Probabilistic Schemes with Boolean Operations

5.7.1 (2, n) Scheme for Binary Images (Wang)

5.7.2 (n, n) Scheme for Binary Images (Wang)

5.8 Conclusions and Open Problems

Bibliography

6 XOR-Based Visual Cryptography
Daoshun Wang and Lin Dong

6.1 Introduction

6.2 Preliminaries

6.3 Visual Cryptography Scheme Using the Polarization of Light

6.3.1 (2, n) Scheme

6.3.2 (n, n) Scheme

6.3.3 (k, n) Scheme

6.4 Visual Cryptography Scheme with Reversing

6.4.1 (k, n) VC Scheme Using Cyclic-Shift Operation

6.4.2 A Scheme for General Access Structure

6.5 Secret Sharing Scheme Using Boolean Operation

6.5.1 (2, n) Scheme

6.5.2 (n, n) Scheme

6.5.3 (k, n) Scheme

6.6 Conclusion

Bibliography

7 Visual Cryptography and Random Grids
Shyong Jian Shyu

7.1 Introduction

7.2 Random Grids

7.2.1 Random Pixel, Random Grid, and Average Light Transmission

7.2.2 Superimposition of Random Grids

7.3 Visual Cryptograms of Random Grids

7.3.1 Definition of VCRG

7.3.2 (2, 2)-VCRG Algorithms for Binary Images

7.3.3 Experiments for (2, 2)-VCRG

7.3.4 Definition of Light Contrast and Performance Evaluation

7.3.5 Algorithms of (n, n)-VCRG for Binary Images

7.3.6 Algorithms of (n, n)-VCRG for Gray-Level and Color Images

7.3.7 Experiments for (n, n)-VCRG

7.4 Concluding Remarks

Bibliography

8 Visual Cryptography and Contrast Bounds
Andreas Klein

8.1 Introduction

8.2 Preliminaries

8.3 Approximate Inclusion Exclusion

8.4 Designs and Codes

8.5 Optimal 3-out-of-n Schemes

8.6 Asymptotic Optimal k-out-of-n Schemes

8.7 Contrast Trade-Offs for Extended Visual Cryptography Schemes

8.8 Enhancing the Contrast by Nonstandard Models

8.9 Conclusion

Bibliography

9 Visual Cryptography Schemes with Reversing
Alfredo De Santis, Anna Lisa Ferrara, and Barbara Masucci

9.1 Introduction

9.2 Visual Cryptography Schemes

9.2.1 (k, k)-Threshold Visual Cryptography Schemes

9.2.2 Perfect Black Visual Cryptography Schemes

9.3 Almost Ideal Contrast VCS with Reversing

9.4 Ideal Contrast VCS with Reversing

9.4.1 A Construction Using a Binary Secret Sharing Scheme

9.4.2 Constructions Using Perfect Black VCSs

9.4.2.1 The Scheme by Cimato, De Santis, Ferrara, and Masucci

9.4.2.2 The Scheme by Hu and Tzeng

9.4.2.3 The Scheme by Yang, Wang, and Chen

9.4.2.4 Comparisons

9.4.3 A Construction Using a Nonperfect Black VCS

9.5 Conclusions

Bibliography

10 Cheating Prevention in Visual Cryptography
Yu-Chi Chen, Gwoboa Horng, and Du-Shiau Tsai

10.1 Introduction

10.2 Preliminaries

10.2.1 Visual Cryptography

10.2.2 Cheating in VC

10.3 Cheating Prevention Schemes

10.3.1 HCT1 and HCT2

10.3.2 HT

10.3.3 TCH

10.3.4 PS1 and PS2

10.4 Analysis of Cheating Prevention Schemes

10.5 Conclusions

Bibliography

11 Resolving the Alignment Problem in Visual Cryptography
Feng Liu

11.1 Introduction

11.2 Preliminaries

11.3 Misalignment with Integer Number of Subpixels

11.4 Misalignment with Less Than One Subpixel

11.4.1 Shares with Slightly Misalignment Can Still Recover the Secret Image

11.4.2 Large Subpixels Have Better Misalignment Tolerance

11.5 A Misalignment Tolerant VCS

11.5.1 The Algorithm

11.5.2 Simulations

11.6 Conclusions and Discussions

11.7 Acknowledgments

Bibliography

12 Applications of Visual Cryptography
Bernd Borchert and Klaus Reinhardt

12.1 Introduction

12.2 Trojan-Secure Confirmation of Transactions

12.3 Trojan-Secure Authentication Using a PIN

12.4 Security versus Multiple Use

12.5 Using Refraction

12.6 Technical Problems Concerning Adjustment and Parallaxes

12.7 Voting with a Receipt Based on visual cryptography

12.8 Conclusion

Bibliography

13 Steganography in Halftone Images
Oscar C. Au, Yuanfang Guo, and John S. Ho

13.1 Introduction

13.2 A Review of Error Diffusion

13.3 Data Hiding by Stochastic Error Diffusion (DHSED)

13.4 Data Hiding by Conjugate Error Diffusion (DHCED) 359

13.5 Performance Analysis

13.6 Summary

Bibliography

14 Image Secret Sharing
WeiQi Yan, Jonathan Weir, and Mohan S. Kankanhalli

14.1 Introduction

14.2 State of the Art

14.3 Approaches for Image Sharing

14.3.1 Shamir’s Secret Sharing Scheme

14.3.2 Color Image Sharing Based on the Lagrange Interpolation

14.3.3 Color Image Sharing Based on Moving Lines

14.3.4 Improved Algorithm

14.4 Experiment and Evaluation

14.5 Conclusion

Bibliography

15 Polynomial-Based Image Sharing
Shiuh-Jeng Wang, Chen-Hsing Yang, and Yu-Ting Chen

15.1 Introduction

15.2 Polynomial-Based Sharing Scheme

15.2.1 Shamir’s Secret Sharing Scheme

15.2.2 Lagrange Interpolation Scheme

15.3 Preliminaries and Related Works

15.3.1 Thien-Lin Scheme

15.3.2 Lin-Tsai Scheme

15.3.3 Yang et al.’s Scheme

15.3.4 Inverted Pattern LSB Scheme

15.3.5 Scalable Secret Image Sharing

15.4 Wang et al.’s Scheme

15.4.1 Secret Image Sharing

15.4.2 Set-Up Authentication

15.4.3 Main Algorithms

15.5 Experimental Results

15.5.1 Fidelity Analysis

15.5.2 Evaluating Authentication

15.6 Conclusions

Bibliography

16 Image Sharing with Steganography and Authentication
Zhao-Xia Yin, Chia-Chen Lin, and Chin-Chen Chang

16.1 Introduction

16.2 Related Work

16.2.1 Lin and Tsai’s Scheme

16.2.2 Yang et al.’s Scheme

16.2.3 Chang et al.’s Scheme

16.3 Adopted Techniques in the Proposed Scheme

16.3.1 Error Diffusion Technique

16.3.2 Interpolation Technique

16.3.3 Canny Edge Detector

16.3.4 Edge Lookup Inverse Halftoning Technique

16.3.5 Shamir Scheme for Secret Sharing

16.4 Proposed Scheme

16.4.1 Sharing and Embedding Phase

16.4.2 Reconstruction and Verifying Phase

16.5 Experimental Results

16.6 Conclusions

Bibliography

17 Two-Decoding-Option Image Sharing Method
Ching-Nung Yang, Chuei-Bang Ciou, and Tse-Shih Chen

17.1 Introduction

17.2 Preliminaries

17.2.1 PISSS

17.2.2 VCS

17.3 Previous Works

17.3.1 Jin et al.’s TiOISSS

17.3.2 Lin and Lin’s TiOISSS

17.4 A New (k, n)-TiOISSS

17.4.1 Design Concept

17.4.2 The Lossless TiOISSS

17.5 Experimental Results and Comparisons

17.6 Conclusion

Bibliography

Index