Visual Cryptography and Secret Image Sharing

1.1 Block diagram for binary error diffusion. The pixel f (m, n) is passed through a quantizer to obtain the corresponding pixel of the halftone g(m, n). The difference between these two pixels is diffused to the neighboring pixels by means of the filter h(k, l). (Reprinted with permission from IEEE Trans. Inf. Forensics Security, vol. 4, no. 3, pp. 383–396, Sep. 2009 ©IEEE 2009) 3

1.2 Floyd-Steinberg error filter. • indicates the current pixel. The weights are given by: h(0,1) = 7/16, h(1, −1) = 3/16, h(1, 0) = 5/16 and h(1, 1) = 1/16. (Reprinted with permission from IEEE Trans. Inf. Forensics Security, vol. 4, no. 3, pp. 383–396, Sep. 2009 ©IEEE 2009) 4

1.3 In a 2-out-of-2 scheme, a secret pixel is encoded into 2 subpixels in each of the two shares. (Reprinted with permission from IEEE Trans. Inf. Forensics Security, vol. 4, no. 3, pp. 383–396, Sep. 2009 ©IEEE 2009) 6

1.4 Example of 2-out-of-2 scheme. The secret image (a) is encoded into two shares (b)-(c) showing random patterns. The decoded image (d) shows the secret image with 50% contrast loss. (Reprinted with permission from IEEE Trans. Inf. Forensics Security, vol. 4, no. 3, pp. 383–396, Sep. 2009 ©IEEE 2009). 7

1.5 Example of halftone cells in a 2-out-of-2 scheme using the first method. The 1st and the 2nd pixels in both shares are SIPs. The 3rd pixel in share 1 and the 4th pixel in share 2 are ABPs. Others (”X”) are assigned to carry visual information. (Reprinted with permission from IEEE Trans. Inf. Forensics Security, vol. 4, no. 3, pp. 383–396, Sep. 2009 ©IEEE 2009). 10

1.6 Upper left: distributions Z_i, i = 0,1,…, 3. □ indicates pixels within Z₀; •_i indicates pixels within Z_i. Upper right: distribution of SIPs and ABPs in share 1. Down left: distribution of SIPs and ABPs in share 2. Down right: distribution of SIPs and ABPs in share 3. •_i indicates ABP and Δ indicates pixels used to carry share visual information. (Reprinted with permission from IEEE Trans. Inf. Forensics Security, vol. 4, no. 3, pp. 383–396, Sep. 2009 ©IEEE 2009). 13

1.7 Composition of shares. □ indicates SIPs; 1 indicates ABPs; Δ indicates pixels to carry the share visual information. Reprinted with permission from IEEE Trans. Inf. Forensics Security, vol. 4, no. 3, pp. 383–396, Sep. 2009 ©IEEE 2009). 14

1.8 Block diagram of halftone VSS using the first method. Depending on the secret image and VSS scheme chosen, the SIP assignment block outputs the SIPs. If g_i(m,n) is a SIP or ABP, its value is prefixed. Otherwise, g_i(m,n) is determined by the output of the thresholding block. (Reprinted with permission from IEEE Trans. Inf. Forensics Security, vol. 4, no. 3, pp. 383–396, Sep. 2009 ©IEEE 2009) 15

1.9 (a) Grayscale image Lena. (b) Part of the distribution of SIPs and ABPs. The gray pixels indicate SIPs and the black pixels indicate ABPs. (Reprinted with permission from IEEE Trans. Inf. Forensics Security, vol. 4, no. 3, pp. 383-396, Sep. 2009 ©IEEE 2009). 20

1.10 (a)–(c) Shares of the 3-out-of-3 scheme using the first method, q = 9. The perceived errors are 1.73 × 10¹⁰, 8.45 × 10⁹, and 5.46 × 10⁹, respectively. (d) Decoded image by shares (a)-(c), α = 1/9. (Reprinted with permission from IEEE Trans. Inf. Forensics Security, vol. 4, no. 3, pp. 383–396, Sep. 2009 ©IEEE 2009). 22

1.11 (a)–(c) Shares of the 3-out-of-3 scheme using the first method, q = 16. The perceived errors are 7.1 × 10⁹, 3.48 × 10⁹, and 2. 27 × 10⁹, respectively. (d) Decoded image by shares (a)-(c), α = 1/16. (Reprinted with permission from IEEE Trans. Inf. Forensics Security, vol. 4, no. 3, pp. 383–396, Sep. 2009 ©IEEE 2009) 23

1.12 (a)–(c) Shares of the 3-out-of-3 scheme using the second method, q = 16. (d) Decoded image by shares (a)–(c), α = 1 / 16. (Reprinted with permission from IEEE Trans. Inf. Forensics Security, vol. 4, no. 3, pp. 383–396, Sep. 2009 ©IEEE 2009) 24

1.13 (a)–(c) Another set of shares generated by the second method, q = 16, depicting more pronounced artifacts. (Reprinted with permission from IEEE Trans. Inf. Forensics Security, vol. 4, no. 3, pp. 383–396, Sep. 2009 ©IEEE 2009) 25

2.1 Pixels superposition: black and white (left) and colored (right) 33

2.2 Electromagnetic spectrum 33

2.3 Additive color model with primaries red, green, and blue 34

2.4 Subtractive color model with primaries cyan, magenta, and yellow 35

2.5 Examples of pixels superposition 37

2.6 More examples of pixels superposition 37

2.7 Lattice for the RGB and CMY color models 38

2.8 The darkening problem 39

2.9 The VV trick for the case of 4 colors. Subpixels with different colors are never superposed 45

3.1 Implementation results of visual one-secret sharing in two shares: (a) P, (b) S₁, (c) S₂, (d) S₁ ⊗ S₂ 61

3.2 Encoding S₁ in Wu and Chen’s scheme: (a) Four triangle-like areas. (b) Indexing the blocks in each of the four areas. (c) Blocks to be assigned. 64

3.3 Example for illustrating the idea of Wu and Chen [12]: (a) P₁, (b) P₂, (c) S₁, (d) S₂, (e) S₁ ⊗ S₂, $(f) S_{1}^{90 °}, (g) S_{1}^{90 °}$ ⊗ S₂ 65

3.4 2 × 2 sector blocks for A in Wu and Chang’s approach: (a) 2 × 2 sector blocks for A, (b) prev(s) and next(s) of sector block s 66

3.5 Decomposing circle shares A and B into chords, which are further divided into blocks: (a) A, (b) B 70

3.6 Elementary blocks for circle share A for sharing 3 secrets: (a) $S_{A}^{1}, (b) S_{A}^{2} (c) S_{A}^{3}$ 71

3.7 Subpixels in 2 × 3 elementary block s and permute(s, Σ): (a) a certain ordering of the subpixels in s, (b) the ordering of those in permute(s, Σ) where Σ = (3, 5,1, 6, 2, 4) 71

3.8 Encoding the first three blocks in each of the three chords by Σ₁ in A: (a) A, (b) A¹²⁰°, (c) A²⁴⁰° 72

3.9 Absolute location of block [1, j], [2, j], and [3, j] 73

3.10 Elementary blocks of share B for sharing 3 secrets: $(a) s_{B}^{0}, (b) s_{B}^{1}, (c) s_{B}^{2}, (d) s_{B}^{3}, (e) s_{B}^{4}, (f) s_{B}^{5}, (g) s_{B}^{6}, (h) s_{B}^{7}$ 74

3.11 Instances of the first three pixels of the three strips in (a) P₁, (b) P₂, and (c) P₃ 75

3.12 Encoding $b_{1}^{1}$ in B 75

3.13 Encoding $b_{1}^{2}$ in B 77

3.14 Encoding $b_{1}^{3}$ in B 79

3.15 Results of (a) A ⊗ B, (b) A¹²⁰° ⊗ B, and (c) A²⁴⁰° ⊗ B 79

3.16 Elementary block for x secrets 80

3.17 Elementary blocks in $E_{A}^{4} : (a) s_{A}^{1}, (b) s_{A}^{2}, (c) s_{A}^{3}, (d) s_{A}^{4}$ 81

3.18 Elementary blocks in $E_{B}^{4} : (a) s_{B}^{0}, (b) s_{B}^{1}, (c) s_{B}^{2}, (d) s_{B}^{3}, (e) s_{B}^{4}, (f) s_{B}^{5}, (g) s_{B}^{6}, (h) s_{B}^{7}, (i) s_{B}^{8}, (j) s_{B}^{9}, (k) s_{B}^{10}, (l) s_{B}^{11}, (m) s_{B}^{12}, (n) s_{B}^{13}, (o) s_{B}^{14}, (p) s_{B}^{15}$ 82

3.19 Stacking results of the chosen visual patterns for Feng et al.’s scheme. 84

3.20 Implementation results for the proposed visual 3-secret sharing scheme: (a) P₁, (b) P₂, (c) P₃, (d) A, (e) B, (f) A ⊗ B, (g) A¹²⁰° ⊗ B, (h) A²⁴⁰° ⊗ B, (i) A⁸⁵° ⊗ B 86

3.21 Implementation results for the proposed visual 3-secret sharing scheme with a different starting encoding position: (a) A′, (b) B′, (c) A′ ⊗ B′, (d) (A′)⁸⁵° ⊗ B′, (e) (A′)²⁰⁵° ⊗ B′, (f) (A′)³²⁵° ⊗ B′ 88

3.22 Results of computer implementation for 4-secret sharing: (a) P₁, (b) P₂, (c) P₃, (d) P₄, (e) A, (f) B, (g) A⊗B, (h) A⁹⁰° ⊗ B, (i) A¹⁸⁰° ⊗ B (j) A²⁷⁰° ⊗ B 89

3.23 Transforming circle shares (a) and (b) into cylinder counterparts (c) and (d), respectively 90

3.24 Shares (based upon Experiment 1) with supplementary lines to ease the alignments: (a) A with three markers, (b) B with one marker 92

4.1 Six possible patterns of subpixel arrangements with 50% gray. 97

4.2 An example of visual secret sharing scheme (VSSS) 98

4.3 An example of extended visual cryptography scheme (EVCS). 101

4.4 An example of random grid (RG) 102

4.5 Samples of ordered dither matrices 104

4.6 Point process and error diffusion 105

4.7 Error filters for error diffusion 106

4.8 Iterative and search-based method 106

4.9 Dither matrices for similar shadow scheme proposed in [32] 112

4.10 The conjugate error diffusion algorithm proposed in [9] 113

4.11 Examples of subpixel arrangements with enhanced misalignment tolerance 116

4.12 Variation of subpixel arrangement having the same transparency 117

4.13 An example of difference maximization 118

4.14 The possible pattern combinations of subpixel arrangements 118

4.15 Physical implementation of the concentric subpixel arrangements using square patterns 119

4.16 Input images 120

4.17 Examples of resulting images 121

4.18 Examples of the output with density pattern using 3 × 3 122

5.1 A construction for (2,n) Boolean probabilistic VCS 148

5.2 Ulutas et al. [18] construction for (2,n) Boolean probabilistic VCS 149

5.3 A construction for (n, n) Boolean probabilistic VCS 149

7.1 Implementation results of Algorithms 1, 2, and 3 for encrypting binary image B: (a) B; (b), (c), and (d) two encrypted shares and reconstructed image by Algorithm 1; (e), (f), and (g) two encrypted shares and reconstructed image by Algorithm 2; (h), (i), and (j) two encrypted shares and reconstructed image by Algorithm 3 195

7.2 Reconstructed results by Naor and Shamir’s approach for binary image B in Figure 7.1(a): (a) m = 2, (b) m = 4 196

7.3 Binary image B in Experiment 1 208

7.4 Implementation results of Algorithm 4 for VCRG-3 with respect to B: $(a) R_{1}^{4}, (b) R_{2}^{4}, (c) R_{3}^{4}; (d) R_{1}^{4} \otimes R_{2}^{4}, (e) R_{1}^{4} \otimes R_{3}^{4}, (f) R_{2}^{4} \otimes R_{3}^{4}; (g) R_{1}^{4} \otimes R_{2}^{4} \otimes R_{3}^{4}$ 209

7.5 Implementation results of Algorithm 5 for VCRG-3 with respect to $B : (a) R_{1}^{5}, (b) R_{2}^{5}, (c) R_{3}^{5}; (d) R_{1}^{5} \otimes R_{2}^{5}, (e) R_{1}^{5} \otimes R_{3}^{5}, (f) R_{2}^{5} \otimes R_{3}^{5}; (g) R_{1}^{5} \otimes R_{2}^{5} \otimes R_{3}^{5}$ 210

7.6 Implementation results of Algorithm 6 for VCRG-3 with respect to $B : (a) R_{1}^{6}, (b) R_{2}^{6}, (c) R_{3}^{6}; (d) R_{1}^{6} \otimes R_{2}^{6}, (e) R_{1}^{6} \otimes R_{3}^{6}, (f) R_{2}^{6} \otimes R_{3}^{6}; (g) R_{1}^{6} \otimes R_{2}^{6} \otimes R_{3}^{6}$ 211

7.7 Results of Algorithm 7 where Encryption_VCRG(H, 3) was implemented by Algorithm 4 with respect to gray-level image G in Experiment 2: (a) G; (b) halftone version H of G; $(c) R_{1}^{4}, (d) R_{2}^{4}, (e) R_{3}^{4}; (f) R_{1}^{4} \otimes R_{2}^{4}, (g) R_{1}^{4} \otimes R_{3}^{4}, (h) R_{2}^{4} \otimes R_{3}^{4}; (i) R_{1}^{4} \otimes R_{2}^{4} \otimes R_{3}^{4}$ 212

7.8 Reconstructed results of VCRG-3 with respect to $G : (a) R_{1}^{5} \otimes R_{2}^{5} \otimes R_{3}^{5}; (b) R_{1}^{6} \otimes R_{2}^{6} \otimes R_{3}^{6}$ 213

7.9 Results of Steps 1 and 2 of Algorithm 8 for VCRG-3 with respect to color image P in Experiment 3: (a) P; (b) P^c, (c) P^m, (d) P^y; (e) P^c, (f) P^m, (g) P^y 214

7.10 Results of Step 3 of Algorithm 8 with respect to P^m where Eycrypt_c VCRG(P^m, m, 3) was based upon Algorithm 4: $(a) R_{1}^{m}, (b) R_{2}^{m}, (c) R_{3}^{m}; (d) R_{1}^{m} \otimes R_{2}^{m}, (e) R_{1}^{m} \otimes R_{3}^{m}, (f) R_{2}^{m} \otimes R_{3}^{m}; (g) R_{1}^{m} \otimes R_{2}^{m} \otimes R_{3}^{m}$ 215

7.11 Results of Algorithm 8 for VCRG-3 with respect to P: (a) R₁, (b) R₂, (c) R₃; (d) R₁ ⊗ R₂, (e) R₁ ⊗ R₃, (f) R₂ ⊗ R₃; (g) R₁ ⊗ R₂ ⊗ R₃ (based upon Algorithm 4); (h) R′₁ ⊗ R′₂ ⊗ R′₃ (based upon Algorithm 5); (i) R″₁ ⊗ R″₂ ⊗ R″₃ (based upon Algorithm 6) 216

7.12 Results of Algorithms 4 for VCRG-4 with respect to binary image B: (a) B; (b) R₁, (c) R₂, (d) R₃, (e) R₄; (f) R₁ ⊗ R₂; (g) R₁ ⊗ R₂ ⊗ R₃; (h) R₁ ⊗ R₂; (g) R₁ ⊗ R₂ ⊗ R₃ ⊗ R₄ 217

7.13 Results of Algorithms 8 where Encrypt_c VCRG(P^x, x, 4) was based upon Algorithm 4 for VCRG-4 with respect to P (Figure 7.9(a)): (a) R₁, (b) R₂, (c) R₃, (d) R₄; (e) R₁ ⊗ R₂; (f) R₁ ⊗ R₂ ⊗ R₃; (g) R₁ ⊗ R₂ ⊗ R₃ ⊗ R₄ 218

8.1 Example of encoding a visual cryptography scheme 224

9.1 A construction for almost ideal contrast (Γ_Qual, Γ_Forb)-VCS with reversing 263

9.2 A construction for ideal contrast VCS with reversing using a BSS 267

9.3 Cimato, De Santis, Ferrara, and Masucci’s ideal contrast VCS with reversing 269

9.4 Hu and Tzeng’s ideal contrast VCS with reversing 272

9.5 Yang, Wang, and Chen’s ideal contrast VCS with reversing 274

9.6 Ideal contrast VCS with reversing starting from any VCS 277

10.1 Visual cryptography 283

10.2 The concept of 2-out-of-2 VC 284

10.3 A 2-out-of-3 visual secret sharing scheme 284

10.4 Cheating in visual cryptography 286

10.5 HCT1 288

10.6 Experiment of HCT1 288

10.7 HCT2 289

10.8 HT 290

10.9 Experiment of HT 291

10.10 TCH 292

10.11 PS1 293

10.12 PS2 293

11.1 The stacking results of the (2,2)-DVCS (a) when no share is shifted; (b) when one share is shifted by one subpixels; (c) when one share is shifted by two subpixel. A printed-text ”CRYPTO” is tested 302

11.2 Recovered secret images of a (2,2)-VCS for three misalignment deviations (a) (d_x, d_y) = (0, 0), (b) (d_x, d_y) = (0.5,0), and (c) (d_x, d_y) = (1, 2) 310

11.3 Stacked results of white pixels (a1: 1W1B+1W1B, a2: 1B1W+1B1W) and black pixels (b1: 1W1B+1B1W, b2: 1B1W+1W1B) for the same deviation (d_x, d_y) 311

11.4 The regions of deviation (d_x, d_y) that can recover the secret image 313

11.5 Recovered Lena images for (2,2)-VCS using the different sized subpixels: (a) the small-sized subpixel, (b) the medium-sized subpixel and (c) the large-sized subpixel. 316

11.6 Recovered secret image for a (2, 2)-VCS using two different-sized subpixels and (d_x, d_y) = (0.5, 0.5), (s₁/s₂) = 2: (a) the small subpixel and (b) the large subpixel; two secret image (a printed text “VSS” and a halftoned Lena image) are tested. 318

11.7 Regular and random masks for arranging the large and small subpixels: (a) regular mask and (b) random mask 320

11.8 Encrypt a 16 × 16-pixel secret image by using a (2, 2) misalignment VCS, where p_B = p_S = 50%, γ² = 4, and M_reg are used: (a) the small-scaled secret image I_S, (b) the large-scaled secret image I_B, and (c) two shares O⁽¹⁾ and O⁽²⁾ 322

11.9 Recovered secret images for a (2, 2) misalignment VCS using two-sized subpixels of γ² = 16: (a) p_B = 0%, (b) p_B = p_S = 50%, M_reg, (c) p_B = p_S = 50%, M_ran and (d) p_b = 100%, horizontal deviations: 0, 0. 5, 1, and 2 are tested (unit: small subpixel) 323

11.10 Recovered secret images for a (2, 2) misalignment tolerant VCS using p_B = p_S = 50%, M_reg and three size ratios: (a) γ² = 4, (b) γ² = 16 and (c) γ² = 64, horizontal deviations: 0, 0. 5, 1, 1 .5, 2, 2. 5, 3, and 3. 5 are tested (unit: small subpixel) 324

12.1 (a) The bank sends the information to be confirmed in an encrypted image to the user’s computer and (b) the user is able read this information using the transparency he got from the bank 330

12.2 A man-in-the-middle manipulation attack by a trojan on an online money transfer 331

12.3 The main method is also applicable to mobile banking 332

12.4 For confirmation, the user has to click the black balls placed between parts of the transaction data 334

12.5 Pixel-based (left) versus segment-based (right) visual cryptography 335

12.6 The main method using segment-based visual cryptography in (a) and (b) 336

12.7 Cardano cryptography: above a 1-factor confirmation (user types 3752), below a 2-factor confirmation (for example, in case his PIN is 1234, the user types in 4136) 337

12.8 (a) To log in, the server sends an encrypted image of a permutated keyboard, which the user can only read after placing the slide over it. (b) The user enters the PIN by clicking at the positions according to their order in the PIN 338

12.9 For confirmation, the user has to click his PIN using a permutation of digits on the right side in (a) and (b) 340

12.10 For confirmation, the user has to click his PIN using inverted numbers 341

12.11 Superimposing two encrypted images for the same key-slide shows the difference of the original picture 342

12.12 This example shows how the view from the observer (A) through prisms (B) is directed to areas 1,2,… or 5 on the encrypted image (C); the deviation depends on the slope of the prism 344

12.13 Some parts of the encrypted image (C) is magnified for the observer (A), while other parts are hidden. For example, d and j are in the focus while b, c, e, f, h, i, k, and l are hidden 345

12.14 Lenses are placed randomly on the slide (b). This can be done by spraying a transparent liquid that becomes hard on the side. The area in the focus of the lenses in the encrypted image (a) is colored in the color of the original image at this region. The rest of (a) is filled such that colors in (a) are equally distributed so that the original image can not be obtained from (a) alone but only together with the slide (b) 345

12.15 Each area of the slide (b) has fragments of lenses, which direct the view (c) in a magnifying manor to one of the symbols on the encrypted text (a) 346

12.16 The voter enters the vote, verifies the image, and separates the slides 347

12.17 Each trustee strips one layer of the doll (represented by the barcode) and uses it to modify the image. The order is randomly permutated 348

13.1 Error diffusion process 353

13.2 Original multitone ”Lena” (X) 354

13.3 Halftone image generated by error diffusion with the Steinberg kernel 355

13.4 Halftone image generated by error diffusion with the Jarvis kernel (Y₁) 355

13.5 Secret pattern ”UST” to be embedded in the halftone image (W) 358

13.6 DHSED-generated Y₂ (L = 5) of Lena with respect to X in Figure 13.2, W in Figure 13.5, and Y₁ in Figure 13.4 358

13.7 Image Y obtained by overlaying Y₁ in Figure 13.4 and Y₂ in Figure 13.6 359

13.8 The DHCED (Data Hiding by Conjugate Error Diffusion) process 360

13.9 DHCED-generated Y₂ (T = 10) of Lena with respect to X in Figure 13.2, W in Figure 13.5, and Y₁ in Figure 13.4 363

13.10 Image Y obtained by overlaying Y₁ in Figure 13.4 and Y₂ in Figure 13.9 364

13.11 Original multitone ”Pepper” (X₂) 364

13.12 DHCED-generated Y₂ (T = 10) of Pepper with respect to X₂ in Figure 13.11, W in Figure 13.5, and Y₁ in Figure 13.4 365

13.13 Image Y obtained by overlaying Y₁ in Figure 13.4 and Y₂ in Figure 13.12 365

13.14 Original multitone image ”Ramp” (X) 369

13.15 Secret pattern ”Column” to be embedded in the halftone image (W) 369

13.16 Halftone images generated by error diffusion with the Jarvis kernel (Y₁) 370

13.17 DHCED-generated Y₂ (T = 10) of Ramp with respect to X in Figure 13.14, W in Figure 13.15, and Y₁ in Figure 13.16. 370

13.18 Image Y obtained by overlaying Y₁ in Figure 13.16 and Y₂ in Figure 13.17. 371

13.19 Row-wise average intensity of W_b in Y in Figure 13.18 vs rowwise average intensity of X in Figure 13.14 (Ramp) 372

13.20 Row-wise Δintensity of Y in Figure 13.18 vs row-wise average intensity of X in Figure 13.14 (Ramp) 372

13.21 Contrast of Y in Figure 13.18 vs row-wise average intensity of X in Figure 13.14 (Ramp) 373

13.22 Row-wise average intensity of Y₁ in Figure 13.4 and Y₂ in Figure 13.9 vs row-wise average intensity of X in Figure 13.14 (Ramp) 373

13.23 DHSED-generated Y₂ (L = 5) of Ramp with respect to X in Figure 13.14, W in Figure 13.15 and Y₁ in Figure 13.16 375

13.24 Image Y obtained by overlaying Y₁ in Figure 13.16 and Y₂ in Figure 13.23. 375

13.25 Row-wise average intensity of W_b in Y in Figure 13.24 vs rowwise average intensity of X in Figure 13.14 (Ramp) 376

13.26 Row-wise Δintensity of Y in Figure 13.24 vs row-wise average intensity of X in Figure 13.14 (Ramp) 376

13.27 Contrast of Y in Figure 13.24 vs row-wise average intensity of X in Figure 13.14 (Ramp) 377

13.28 Row-wise average intensity Y₁ in Figure 13.4 and Y₂ in Figure 13.23 vs row-wise average intensity of X in Figure 13.14 (Ramp) 378

13.29 Theoretical average local intensity of W_b in Y for DHSED and DHCED vs row-wise average intensity of X in Figure 13.14 (Ramp) 378

13.30 Theoretical contrast of Y for DHSED and DHCED vs rowwise average intensity of X in Figure 13.14 (Ramp). 379

14.1 Principle of image sharing 383

14.2 Image sharing based on the Lagrange interpolation in (a) and (b) 390

14.3 Experimental results of image sharing based on the Lagrange interpolation in (a) and (b) 391

14.4 The image sharing by using a high degree polynomial interpolation in (a)-(c) 392

14.5 Intersection of two pencils of lines in (a) and (b) 394

14.6 Image sharing scheme based on moving lines 395

14.7 Improved algorithm of image sharing 397

14.8 The experimental results of image sharing by moving lines 397

14.9 The experimental results of image sharing by moving lines 398

14.10 The experimental results of image sharing by moving lines 398

14.11 Breaking the correlation of neighboring blocks in an image 399

15.1 The format of B_ij, where x_j, w_j, υ_i, and υ_i are represented as binary pattern 408

15.2 The format of stego-block ${\hat{B}}_{i j}$ with the size of 2 × 2 gray-level pixels 409

15.3 Stego-block ${\hat{B}}_{i j}$ used in Yang et al. which is revised from Figure 15.2, where hash is used in the pixel of ŵ_i = (w_j1, ⋯, w_i₅, h_i, y_i₃, y_i₄) 409

15.4 Demonstration of steps in RAHA 414

15.5 A secret sharing system with target secret embedding of high capacity and detection authentication: (a) Flowchart of target secret embedding procedures; (b) Recovery of target secret forms the stego-images in our secret sharing systems 417

15.6 (a) the target secret images; (b)–(e) the four cover-images; (b′)–(e′) the four stego-images 420

15.7 (a) and (b) the target secret images; (c)–(h) the four coverimages; (c′)–(h′) the four stego-images 420

15.8 (a) the target images; (b)–(e) the four cover images; (b′)–(e′) the four stego-images 421

15.9 Minor bit adjustments in the stego-image of ”airplane.” (a) Lin-Tsai scheme, (b) Yang et al. scheme, and (c) our scheme 421

15.10 Partial area adjustments in the stego-images of ”sailboat.” (a) Lin-Tsai scheme, (b) Yang et al.’s scheme, and (c) our scheme 422

15.11 Replacement of ”airplane” stego-image with ”pepper.” (a) original stego-image of ”Airplane”, (b) replaced by ”pepper” Lin-Tsai scheme, (c) replaced by ”pepper” in Yang et al.’s scheme, and (c) detected in our scheme 422

16.1 The ij-th block $B_{i j}^{k}$ of the k-th cover 429

16.2 The block of the k-th stego-image in Lin-Tsai’s scheme 430

16.3 The cover blocks used in Yang et al.’s scheme 431

16.4 The block of a stego-image in Yang et al.’s scheme 431

16.5 The block of a stego-image in Chang et al.’s scheme 433

16.6 The flowchart of Chang et al.’s scheme 434

16.7 Error diffusion architecture 435

16.8 The kernel weights of Floyd and Steinberg’s error filter 435

16.9 The positions of pixels located at the border in an image 436

16.10 The “excursion” skill 437

16.11 The neighboring pixels that accepted error diffusion for Case 1 438

16.12 The neighboring pixels that accepted error diffusion for Case 2 438

16.13 The neighboring pixels that accepted error diffusion for Case 3 439

16.14 Example of sampling an image: (a) Real signal R; (b) Sampled signal D of R; (c) Sampled signal D’ of D 439

16.15 The flowchart of Chung and Wu’s ELUT scheme 441

16.16 Procedure for generating final grayscale image in Step 4 443

16.17 The flowchart of the work by the sender 446

16.18 The flowchart of the work by the recipient 446

16.19 The z-th block of GI and the corresponding HI_z, P_z 447

16.20 The four pixels of each cover block CBi 448

16.21 Hiding the six data bits of F(Xi) 448

16.22 Hiding the check bits p₁, p₂ 449

16.23 The flowchart of Step 4 450

16.24 The four pixels of each stego block CB′j 451

16.25 The 2-bit check bits carried in CB′z when t =2 451

16.26 The bits of X_i and F(X_i) carried in the stego block 452

16.27 The test images 454

16.28 The experimental results for comparing the PSNR among the past work and ours 455

16.29 The visual quality of the reconstructed grayscale image 456

16.30 Three tampered stego-images 457

17.1 A (2, 2)-VCS of h = 1, l = 0, and m = 2: (a) the secret image (b) and (c) two shadows (d) the reconstructed image 467

17.2 A (2, 2)-GVCS of h = 1, l = 0, and m = 2: (a) and (b) two shadows (c) the reconstructed image 472

17.3 A (2, 2)-PISSS: (a) 512 × 512 gray-level Lena secret image (b) and (c) 512 × 256 gray-level noise-like shadows 475

17.4 The proposed (2, 2)-TiOISSS using base matrices with h = 1, l = 0, and m = 2: (a) 512 × 256 halftone image (b) and (c) two 512 × 512 gray-and-white shadows (d) the previewed image 476

17.5 The proposed (2, 2)-TiOISSS using base matrices with h = 1, l = 0, and m = 3: (a) and (b) two 512 × 512 gray-and-white shadows (c) the previewed image 477

Table of Contents for
Visual Cryptography and Secret Image Sharing

List of Figures

Table of Contents for Visual Cryptography and Secret Image Sharing

List of Figures

Table of Contents for
Visual Cryptography and Secret Image Sharing