XOR-Based Meaningful Visual Secret Sharing by Generalized Random Grids Xiaotian Wu, Lu Dai, Duanhao Ou, Wei Sun 報告者： 李宏恩

(2, 2) Visual Cryptography P (100 x 100) S 1 (100 x 200) S 2 (100 x 200) S 1  S 2 (100 x 200)

(2, 2)-threshold Visual Cryptography 3 P s1s1 s2s Pixel expansion = 2 s2  s2s2  s2

(2, 2) Random Grids Visual Secret Sharing S (100 x 100) R 1 (100 x 100) R 2 (100 x 100) R 1 = randomly choose 0 or 1.

PProbabilitys1s1 s2s2 s1 s2s1 s2 1/2 (2, 2) Random Grids Visual Secret Sharing

(2, 2) 隨機網格視覺密碼 Algorithm 1. Sharing a binary image into two RGs. Input: A M × N binary secret image S. Output: Two RGs R 1 and R 2. [R 1, R 2 ] = Encryption(S). Step 1: Generate a random grid R 1 that is full of random 0 (white) / 1 (black) pixels. Step 2: For each pixel S[i, j], if S[i, j] = 0, then R 2 [i, j] = R 1 [i, j], otherwise R 2 [i, j] = Step 3: Output the two shares R 1 and R 2. (2, 2) Random Grids Visual Secret Sharing

(2, 2) 隨機網格視覺密碼 Algorithm 1. Sharing a binary image into two RGs. Input: A M × N binary secret image S. Output: Two RGs R 1 and R 2. [R 1, R 2 ] = Encryption(S). Step 1: Construct a M × N matrix R 1 whose elements are randomly assigned the value 0 (white) or 1 (black). Step 2: For each pixel at position (i, j) of S, compute where R 1 (i, j) is the inverse of R 1 (i, j). Step 3: Output the two shares R 1 and R 2. (2, 2) Random Grids Visual Secret Sharing

(2, 2) Generalized RG-based VSS S (100 x 100) R 1 (100 x 100) R 2 (100 x 100) g(1) g(0)

(2, 2) Generalized RG-based VSS g(1) g(0) Secret image S1S1 S2S2 S1S2S1S2

(2, 2) Generalized RG-based VSS Algorithm 4. Generalized RG-based VSS for (2, 2) case. ( (2, 2)-GRG ) Input: a binary secret image S with M × N pixels, and three parameters u, v and d. Output: two shares R 1 and R 2. Step 1: For each position (i, j) in the secret image, Steps 2-3 are performed to generate two shared pixels R 1 (i, j) and R 2 (i, j). Step 2: Construct a shared pixel R 1 (i, j) by Step 3: Construct the other shared pixel R 2 (i, j) by Step 4: Output the two shares R 1 and R 2.

(n, n)-threshold Visual Secret Sharing 將欲分享給 n 位參與者的機密影像，機密 方法而得 n 張機密分享影像。 當任意 t 張且 1  t  n 的分享影像同時疊合 時，無法辨識出機密影像。 當所有 n 張分享影像同時疊合時才能辨識 出機密影像。

(n, n) Generalized RG-based VSS (n, n) generalized RG-based VSS is given, where the n shares are constructed by recursively applying the (2, 2) scheme for n−1 times.

(n, n) Generalized RG-based VSS

r3r3 r4r4 t2t2 n = 4

r3r3 r4r4 t2t2

(n, n) Generalized RG-based VSS Algorithm 5. Generalized RG-based VSS for (n, n) case. Input: a binary secret image S with M × N pixels, and three parameters u, v, d. Output: n shares R 1, , R n. Step 1: For each position (i, j) in the secret image, Steps 2 and 3 are performed to generate n shared pixels R 1 (i, j), ,R n (i, j). Step 2: By recursively applying the (2, 2) generalized RG based VSS for n − 1 times, n pixels r 1, r 2, , r n are constructed by Step 5: Output the n shares R 1, ,Rn.

XOR 的加密 OR XOR

S (100 x 100) R 1 (100 x 100) R 2 (100 x 100) R 1 = randomly choose 0 or 1. XOR

單一張分享影像可顯示出有意義的影像。 疊合分享影像時只會顯示機密，不會有 Cover Image 的影像。 Meaningful Visual Secret Sharing

Secret image Cover image S1S1 S2S2

(n, n) XOR-based meaningful VSS Algorithm 6. XOR-based meaningful VSS for (n, n) case. Input: a binary secret image S and a cover image, both with M × N pixels, and six parameters u 0, v 0, d 0 and u 1, v 1, d 1. Output: n meaningful shares R 1, , R n. Step 1: For each position (i, j) in the secret image, Step 2 or 3 is performed to generate n shared pixels R 1 (i, j), , R 2 (i, j). Step 2: if cover image pixel C(i, j) = 0, the n shared pixels are constructed by [R 1 (i, j), , R n (i, j)] = GRG[(n, n), S(i, j), u 0, v 0, d 0 ]. Step 3: if cover image pixel C(i, j) = 1, the n shared pixels are constructed by [R 1 (i, j), ,R n (i, j)] = GRG[(n, n), S(i, j), u 1, v 1, d 1 ]. Step 4: Output the n meaningful shares R 1, , R n.

Secret image Cover image S1S1 S2S2

Conclusion 優點：可擴展至 (n, n) XOR-based meaningful VSS 缺點：輸入變數過於多；只能單一張 Cover Image ， 無法用於兩張不同 Cover Image 。