Visual Cryptography for Gray-Level Images by Dithering Techniques Author：Chang-Chou Lin, Wen-Hsiang Tsai Source：Pattern Recognition Letters 24 （2003） 349-358 Speaker：Shu-Fen Chiou（邱淑芬）

Outline Introduction Space-filling Curve Ordered Dithering (SFCOD) (k, n)-threshold visual encryption of gray-level images Experimental results Conclusions Comments

Introduction (1/2) Input a gray-level image Share image1 Transform by SFCOD decode encode Apply (2, 2) visual cryptography The decoded image An approximate binary image Share image2

Introduction (2/2) Binary images are usually restricted to represent text-like messages. Verheul and van Tilborg (1997) first tried to extend visual cryptography into gray-level images, but their method has the disadvantage of size increase in the decoded image.

Space-filling Curve Ordered Dithering (SFCOD) Yuefeng Zhang Comput. & Graphics, Vol. 22 No.4, pp. 559-563, 1998

Hilbert curve Rule Iteration = 0 Iteration = 1 Iteration = 2

Subdividing a 88 image into 4 4 regions by using a Hilbert curve 7 7 7 10 1 2 3 4 7 6 5 8 9 11 12 15 13 14 48 51 52 53 49 50 55 54 62 61 56 57 63 60 59 58 42 41 38 37 43 40 39 36 44 45 34 35 47 46 33 32 26 25 22 21 27 24 23 20 28 29 18 19 31 30 17 16 5 6 9 10 5 6 9 10 6 6 6 4 7 8 11 4 7 8 11 5 5 5 3 2 13 12 3 2 13 12 4 4 4 1 14 15 1 14 15 3 3 3 15 12 11 10 5 4 3 2 2 2 14 13 8 9 6 7 2 1 1 1 1 1 2 7 6 9 8 13 14 3 4 5 10 11 12 15 1 2 3 4 5 6 7 1 2 3 4 5 6 7 1 2 3 4 5 6 7

Dithering Technique (1/3) PROCEDURE SFCOD (M, B, t ,I ,H) BEGIN FOR i = 0 TO m – 1 DO FOR j = 0 TO m – 1 DO IF I (i, j) /256 ≥ (B (M (i, j) MOD t )+0.5)/ t THEN H (i, j) = 1(白色) ELSE H (i, j) = 0 ;(黑色) END 定義 I：大小為m*m的灰階影像 M(i, j)：traversal-order number B：space-filling curve dither array t：array length H(i, j)：轉 binary image 後的 pixel value

Dithering Technique (2/3) Step1: Gray-level image I with mm. Step2: Divide I into many pixels of a block. Step3: Transform each gray block into binary block M(0,0) I(0,0) 1 2 3 4 5 6 7 10 8 9 11 12 15 13 14 48 51 52 53 49 50 55 54 62 61 56 57 63 60 59 58 42 41 38 37 43 40 39 36 44 45 34 35 47 46 33 32 26 25 22 21 27 24 23 20 28 29 18 19 31 30 17 16 Original Image I Hilbert curve order t=4, t<=M

Dithering Technique (3/3) Space-filling curve dither array B, size(B)=t 作用在於打亂, B 對於每一個block 可以Fixed or not fixed t=4 B(0)=1, B(1)=0, B(2)=2, B(3)=3

Example of Dithering Technique Step1: y=I(0,0)/256=100/256=0.390625 Step2: x=M(i, j) mod t = M(0, 0) mod 4= 21 mod 4=1 Step3: B(x)=B(1)=0 B(0)=1, B(1)=0, B(2)=2, B(3)=3 Step4: q= (B(x)+0.5) / t =(0+0.5)/4=0.125 Step5: Test (y >= q) ? If yes, white color else black color.

(k, n)-threshold visual encryption of gray-level images Verheul and van Tilborg, 1997 We describe an example for the case of a (3, 3)-threshold scheme. If there are 3 gray levels original image.

An example (1/4) Gray-level 0 Gray-level 1 Gray-level 2 original image

An example (2/4) share1 share2 share3 0 0 0 1 1 1 2 2 2 0 0 0 1 1 1 2 2 2 0 1 2 0 1 2 0 1 2 0 1 2 1 2 0 2 0 1 share1 A0 = share2 share3 0 0 0 1 1 1 2 2 2 0 1 2 0 1 2 0 1 2 2 0 1 0 1 2 1 2 0 A1 = 0 0 0 1 1 1 2 2 2 0 1 2 0 1 2 0 1 2 1 2 0 2 0 1 0 1 2 A2 =

An example (3/4) C0 = { all the matrices obtained by permuting the columns of A0 } C1 = { all the matrices obtained by permuting the columns of A1 } C2 = { all the matrices obtained by permuting the columns of A2 } EX： 0 0 0 1 1 1 2 2 2 0 1 2 0 1 2 0 1 2 0 1 2 1 2 0 2 0 1 A0 = 0 0 0 1 1 1 2 2 2 0 1 2 0 1 2 0 1 2 2 0 1 0 1 2 1 2 0 A1 = 0 0 0 1 1 1 2 2 2 0 1 2 0 1 2 0 1 2 1 2 0 2 0 1 0 1 2 original image share1 share2 share3 result A2 =

An example (4/4) (k, n)-threshold visual cryptography k = 3, n = 3 share1 share2 share3 (k, n)-threshold visual cryptography k = 3, n = 3 size increase ck-1 at least when c ≥ n Decoding image

Experimental results (1/2) The original image with 16 gray levels The image after using SFCOD

Experimental results (2/2) share1 + The decoded image share2

A person authentication application Public key Secret key authentication Encrypting a portrait of the user

Conclusions This scheme possesses the advantages of inheriting any developed cryptographic technique for binary images and having less increase of image size in ordinary situations. EX： If there are 3 gray levels original image before this scheme 33-1 = 9 times 4 times

Comments 可以直接用灰階影像或是彩色影像來做視覺密碼學。 還原的影像可以和原始影像的尺寸大小一樣。