Controllable Transparency Image Sharing Scheme for ... - IEEE Xplore
Controllable Transparency Image Sharing Scheme for Grayscale and Color Images with Unexpanded Size Yi-Chong Zeng*, and Chi-Hung Tsai† *
Advanced Research Institute, Institute for Information Industry, Taipei, Taiwan, R.O.C. E-mail: [email protected] Tel:+886-2-66072958 † Advanced Research Institute, Institute for Information Industry, Taipei, Taiwan, R.O.C. E-mail: [email protected] Tel:+886-2-66072922
Abstract—Aimed at transparency controlling to secret image, we propose an image sharing scheme to encrypt secret image among two or more sharing images. The overall effects of the proposed method are the achievements of controllable transparency of secret image and unexpanded size of sharing images. The controllable transparency image sharing scheme is realized based on the principle of penetrability. While light passes through a medium, medium declines illumination of light. We treat pixel as medium and adjust pixels’ value of multiple sharing images, so that transparency of decrypted-secret image is controllable. The experiment results will demonstrate that our scheme can be applied to grayscale and color images for visual cryptography. Furthermore, similarity between sharing image and secret image is low by using the proposed scheme.
I.
INTRODUCTION
Visual cryptography techniques encrypted secret information among two or more shares. For n-out-of-n visual cryptography method [1, 2], secret is decrypted incorrect while number of sharing images is not equal to n. In the past studies, researchers presented numerous visual cryptography techniques for black-and- white images, and crypto-array the base of sharing image was mentioned in literatures. Furthermore, researchers intended to use k-out-of-n visual cryptography methods performed on grayscale and color images, such as [3-9]. Blude et al. analyze and defined visual cryptography schemes for gray-level images in [3]. They emphasized on how to employ k-out-of-n visual cryptography applied to grayscale shares. In [4], Lin and Tsai used dithering technique to convert a grayscale image to an approximate binary image, and then k-out-of-n visual cryptography was implemented to the approximate binary image. In [5], Chang and Yu introduced a sharing method hided gray-level secret image into color sharing images. Furthermore, Chang et al. adopted voting strategies to modify the previous method in [6]. The major contribution of this method is to improve quality of reconstructed grayscale image. In [7], Katta proposed a visual image sharing method applied to grayscale image, which is a probabilistic 2-out-of-3 sharing method. Kandar and Maiti introduced a k-out-of-n secret sharing method for color image [8], which utilized random number generator to yield sharing images. During decryption process, the bitwise OR operator was performed to pixels of sharing images in order to reconstruct secret image. The integration of color halftoning and k-out-of-n visual cryptography was presented in [9]. Rao et al.’s method generated meaningful sharing images which hide color secret image.
In this work, two issues are considered in the development of grayscale and color image sharing schemes: physical realization and size of sharing image. Naor and Shamir’s method [1, 2] can print sharing images on transparencies, then the transparencies are superposed together to reveal secret. Therefore, the conventional k-out-of-n visual cryptography can be realized on physical medium. Review to [3-9], these methods were performed by arithmetic operation, but cannot be realized on physical medium. The issue of image size expanding is unavoidable due to visual cryptography method employed crypto-array to generate sharing images. The size of sharing image is depended on that of crypto-array. In this paper, we propose an image sharing scheme, which is capable of performing on grayscale and color images. The overall effects of the proposed method are the achievements of controllable transparency of secret image and unexpanded size of sharing images. The controllable transparency image sharing scheme is realized based on the principle of penetrability. While light passes through a medium, medium declines illumination of light. We treat pixel as medium and adjust pixels’ value of multiple sharing images, so that transparency of decrypted-secret image is controllable. Furthermore, the proposed method can be realized on physical medium. Table I lists the comparisons of the six existing methods and the proposed scheme. The single-bit means sharing image consists of 1-bit pixels; the multi-bit means pixels of sharing image are larger than or equal to 2 bits. The rest of this paper is organized as follows: the controllable transparency image sharing scheme for grayscale image and color image will be introduced in Sections II and III, respectively. Experiment results will be shown in Section IV, and the concluding remarks will be drawn in Section V.
II.
CONTROLLABLE TRANSPARENCY IMAGE SHARING
The controllable transparency image sharing (CTIS) scheme is realized based on the principle of penetrability. While light penetrates through a medium, it declines illumination of light. A medium carried low rate of penetration is more serious than one carried high rate of penetration in illumination declining. In this work, we treat pixel as medium. White pixel consists of none of ink/powder in printing system, therefore, it carries high rate of penetration. In contrast, black pixel carries low one. Fig.1 depicts illumination declining of light penetrated through two media with different rates of penetration. Let M1 and M2 be the first medium and the second medium carried the rates of penetration r1 and r2, respectively. Assume that the denotation I represents
TABLE I COMPARISONS OF THE SIX EXISTING METHODS AND THE H PROPOSED SCHEME
Grayscale
[4]
[5]
[6]
[7]
√
√
√
√
[8]
√
Multi-bit (bit) Size Expanding Physical Medium
√ (2)
Operation
OR
√
√
Ours √
Color Single-bit
[99]
√
√
√
√
√
√
√ (8) √
Fig.1. Illumination declining of o light penetrated through two media with different rates of pennetration
√
√
√ XOR XOR
OR
OR
XO OR
Multiplication
the initial light illumination. After light penettrates through two media, the light illumination is declined as, (1) I ' = I × r1 × r2 ,
1st Sharing Image
p1 p , and r2 = 2 , 255 255
(2)
1st Sharing Image
=
p1 × p2 255
,
(3)
where Iinit denotes the initial light illumination,, and Iinit is set 255 in all of our experiments. The variable α is a factor to control transparency of secret image, where 0 α and max(Iinit) denotes the maximum pixel value of Iinit. We can adjust α to achieve transparency controlling. In the beginning of the CTIS scheme, we have a grayscale secret image of sized w×h. Analyze (3), ps is a given pixel value, but p1 and p2 are two unknown pixel values.. We will find the proper p1 and p2, so that the estimated pixel vallue of secret image (p's, where p's= p1×p2/255) approximates to α× ×ps. The limitation of p1 and p2 is that those pixel values must be laarger than or equal to α×ps. If one of two sharing pixel values is sm maller than α×ps, it results in the other pixel value is larger than 255, which contradicts to (2). The procedure of the CTIS scheme is described as below, Step 1. Set the transparency factor α, where 0 < α ≤ 1. Step 2. Input a pixel value of secret image ps. Step 3. Yield a random integer p1 which rangges from α×ps and 255. Hence, the pixel of the secondd sharing image is given by, α × ps × 255 , (4) p2 = round( ) p1
2nd Sharring Image
Decrypted Secret Image
( (b)
where p1, p2∈{0, 1, ..., 255}. The pixel value of o secret image (ps) is defined as the following equation,
α × ps = I init × r1 × r2
Decrypted Secret Image
( (a)
where I' denotes the declined illumination of light, and 0 ≤ r1, r2 ≤ 1. In our study, light penetrates two or more sharing pixels for revealing hidden secret image. Accordingg to the above hypothesis, we define p1 and p2 as the pixel values of the first and the second sharing images, respectiveely. The rate of penetration is depended on pixel value, which is i given by, r1 =
2nd Sharring Image
Fig.2. Experiments of image sharing (a) without using pixel swapping, and (b) by using pixel swapping.
where the function rounnd(x) rounds the variable x to the nearest integer. Step 4. Yield a random numbeer R and 0≤R≤1. If the number R is smaller than 0.5, we w swap p1 and p2 to each other. Otherwise, p1 and p2 arre unaltered. Step 5. Repeat the steps 2 to 4 until all pixels of sharing image are estimated completeely. The CTIS scheme can be furtheer performed on sharing image to generate another two new sharinng images. Therefore, the number of sharing images is flexible. Inn the step 4, the objective of pixel swapping is for improving security of sharing images. For example, Fig.2(a) shows the seecret image and the two sharing images. It is obvious that the seecond sharing image is similar to the secret image. After impplementing pixel swapping, the problem has been solved. Swapping pixel randomly, it b a pixel and its neighbor disintegrates similar structure between ones. During decryption proceess, secret image is decrypted by manipulating all sharing imagess using (3).
III.
CONTROLLABLE TRANSPA ARENCY COLOR IMAGE SHARING
The CTIS scheme is only applied to grayscale image (or called luminance componentt). In order to increase the applicability of the CTIS sccheme, we further propose the controllable transparency color image sharing (CTCIS) scheme. b on not only the principle of The CTCIS scheme is realized based
penetrability but also principle of color mixing. We transform a color image from RGB colorspace to HSL colorspace. Subsequently, the CTIS scheme is applieed to luminance component, and the color mixing is performed to hue component. Saturation component is unaltered. Consequenntly, the encrypted hue, the encrypted luminance and the saturattion are combined together and transformed to RGB colorspace. Fig.3 is a hue disk and depicts arrangementt to all colors. We assume that a hue is the mixture of two neigghboring hues. For example, red is the mixture of magenta and yellow. The denotation hs and hi are, respectively, the hues of the secret pixel and the i-th sharing pixel, where i∈{1, 2}. Inn addition, the hue difference between the secret pixel and thee sharing pixel is defined as θ. hs can be generated by mixinng h1 and h2. The procedures of color mixing are described as folllows: Step 1. Input a pixel ps of secret image, whiich is transformed from RGB colorspace to HSL colorspacce. Let hs, ss, and ls be the hue, the saturation, and the luminnance of ps, where 0°≤hs
Advanced Research Institute, Institute for Information Industry, Taipei, Taiwan, R.O.C. E-mail: [email protected] Tel:+886-2-66072958 † Advanced Research Institute, Institute for Information Industry, Taipei, Taiwan, R.O.C. E-mail: [email protected] Tel:+886-2-66072922
Abstract—Aimed at transparency controlling to secret image, we propose an image sharing scheme to encrypt secret image among two or more sharing images. The overall effects of the proposed method are the achievements of controllable transparency of secret image and unexpanded size of sharing images. The controllable transparency image sharing scheme is realized based on the principle of penetrability. While light passes through a medium, medium declines illumination of light. We treat pixel as medium and adjust pixels’ value of multiple sharing images, so that transparency of decrypted-secret image is controllable. The experiment results will demonstrate that our scheme can be applied to grayscale and color images for visual cryptography. Furthermore, similarity between sharing image and secret image is low by using the proposed scheme.
I.
INTRODUCTION
Visual cryptography techniques encrypted secret information among two or more shares. For n-out-of-n visual cryptography method [1, 2], secret is decrypted incorrect while number of sharing images is not equal to n. In the past studies, researchers presented numerous visual cryptography techniques for black-and- white images, and crypto-array the base of sharing image was mentioned in literatures. Furthermore, researchers intended to use k-out-of-n visual cryptography methods performed on grayscale and color images, such as [3-9]. Blude et al. analyze and defined visual cryptography schemes for gray-level images in [3]. They emphasized on how to employ k-out-of-n visual cryptography applied to grayscale shares. In [4], Lin and Tsai used dithering technique to convert a grayscale image to an approximate binary image, and then k-out-of-n visual cryptography was implemented to the approximate binary image. In [5], Chang and Yu introduced a sharing method hided gray-level secret image into color sharing images. Furthermore, Chang et al. adopted voting strategies to modify the previous method in [6]. The major contribution of this method is to improve quality of reconstructed grayscale image. In [7], Katta proposed a visual image sharing method applied to grayscale image, which is a probabilistic 2-out-of-3 sharing method. Kandar and Maiti introduced a k-out-of-n secret sharing method for color image [8], which utilized random number generator to yield sharing images. During decryption process, the bitwise OR operator was performed to pixels of sharing images in order to reconstruct secret image. The integration of color halftoning and k-out-of-n visual cryptography was presented in [9]. Rao et al.’s method generated meaningful sharing images which hide color secret image.
In this work, two issues are considered in the development of grayscale and color image sharing schemes: physical realization and size of sharing image. Naor and Shamir’s method [1, 2] can print sharing images on transparencies, then the transparencies are superposed together to reveal secret. Therefore, the conventional k-out-of-n visual cryptography can be realized on physical medium. Review to [3-9], these methods were performed by arithmetic operation, but cannot be realized on physical medium. The issue of image size expanding is unavoidable due to visual cryptography method employed crypto-array to generate sharing images. The size of sharing image is depended on that of crypto-array. In this paper, we propose an image sharing scheme, which is capable of performing on grayscale and color images. The overall effects of the proposed method are the achievements of controllable transparency of secret image and unexpanded size of sharing images. The controllable transparency image sharing scheme is realized based on the principle of penetrability. While light passes through a medium, medium declines illumination of light. We treat pixel as medium and adjust pixels’ value of multiple sharing images, so that transparency of decrypted-secret image is controllable. Furthermore, the proposed method can be realized on physical medium. Table I lists the comparisons of the six existing methods and the proposed scheme. The single-bit means sharing image consists of 1-bit pixels; the multi-bit means pixels of sharing image are larger than or equal to 2 bits. The rest of this paper is organized as follows: the controllable transparency image sharing scheme for grayscale image and color image will be introduced in Sections II and III, respectively. Experiment results will be shown in Section IV, and the concluding remarks will be drawn in Section V.
II.
CONTROLLABLE TRANSPARENCY IMAGE SHARING
The controllable transparency image sharing (CTIS) scheme is realized based on the principle of penetrability. While light penetrates through a medium, it declines illumination of light. A medium carried low rate of penetration is more serious than one carried high rate of penetration in illumination declining. In this work, we treat pixel as medium. White pixel consists of none of ink/powder in printing system, therefore, it carries high rate of penetration. In contrast, black pixel carries low one. Fig.1 depicts illumination declining of light penetrated through two media with different rates of penetration. Let M1 and M2 be the first medium and the second medium carried the rates of penetration r1 and r2, respectively. Assume that the denotation I represents
TABLE I COMPARISONS OF THE SIX EXISTING METHODS AND THE H PROPOSED SCHEME
Grayscale
[4]
[5]
[6]
[7]
√
√
√
√
[8]
√
Multi-bit (bit) Size Expanding Physical Medium
√ (2)
Operation
OR
√
√
Ours √
Color Single-bit
[99]
√
√
√
√
√
√
√ (8) √
Fig.1. Illumination declining of o light penetrated through two media with different rates of pennetration
√
√
√ XOR XOR
OR
OR
XO OR
Multiplication
the initial light illumination. After light penettrates through two media, the light illumination is declined as, (1) I ' = I × r1 × r2 ,
1st Sharing Image
p1 p , and r2 = 2 , 255 255
(2)
1st Sharing Image
=
p1 × p2 255
,
(3)
where Iinit denotes the initial light illumination,, and Iinit is set 255 in all of our experiments. The variable α is a factor to control transparency of secret image, where 0 α and max(Iinit) denotes the maximum pixel value of Iinit. We can adjust α to achieve transparency controlling. In the beginning of the CTIS scheme, we have a grayscale secret image of sized w×h. Analyze (3), ps is a given pixel value, but p1 and p2 are two unknown pixel values.. We will find the proper p1 and p2, so that the estimated pixel vallue of secret image (p's, where p's= p1×p2/255) approximates to α× ×ps. The limitation of p1 and p2 is that those pixel values must be laarger than or equal to α×ps. If one of two sharing pixel values is sm maller than α×ps, it results in the other pixel value is larger than 255, which contradicts to (2). The procedure of the CTIS scheme is described as below, Step 1. Set the transparency factor α, where 0 < α ≤ 1. Step 2. Input a pixel value of secret image ps. Step 3. Yield a random integer p1 which rangges from α×ps and 255. Hence, the pixel of the secondd sharing image is given by, α × ps × 255 , (4) p2 = round( ) p1
2nd Sharring Image
Decrypted Secret Image
( (b)
where p1, p2∈{0, 1, ..., 255}. The pixel value of o secret image (ps) is defined as the following equation,
α × ps = I init × r1 × r2
Decrypted Secret Image
( (a)
where I' denotes the declined illumination of light, and 0 ≤ r1, r2 ≤ 1. In our study, light penetrates two or more sharing pixels for revealing hidden secret image. Accordingg to the above hypothesis, we define p1 and p2 as the pixel values of the first and the second sharing images, respectiveely. The rate of penetration is depended on pixel value, which is i given by, r1 =
2nd Sharring Image
Fig.2. Experiments of image sharing (a) without using pixel swapping, and (b) by using pixel swapping.
where the function rounnd(x) rounds the variable x to the nearest integer. Step 4. Yield a random numbeer R and 0≤R≤1. If the number R is smaller than 0.5, we w swap p1 and p2 to each other. Otherwise, p1 and p2 arre unaltered. Step 5. Repeat the steps 2 to 4 until all pixels of sharing image are estimated completeely. The CTIS scheme can be furtheer performed on sharing image to generate another two new sharinng images. Therefore, the number of sharing images is flexible. Inn the step 4, the objective of pixel swapping is for improving security of sharing images. For example, Fig.2(a) shows the seecret image and the two sharing images. It is obvious that the seecond sharing image is similar to the secret image. After impplementing pixel swapping, the problem has been solved. Swapping pixel randomly, it b a pixel and its neighbor disintegrates similar structure between ones. During decryption proceess, secret image is decrypted by manipulating all sharing imagess using (3).
III.
CONTROLLABLE TRANSPA ARENCY COLOR IMAGE SHARING
The CTIS scheme is only applied to grayscale image (or called luminance componentt). In order to increase the applicability of the CTIS sccheme, we further propose the controllable transparency color image sharing (CTCIS) scheme. b on not only the principle of The CTCIS scheme is realized based
penetrability but also principle of color mixing. We transform a color image from RGB colorspace to HSL colorspace. Subsequently, the CTIS scheme is applieed to luminance component, and the color mixing is performed to hue component. Saturation component is unaltered. Consequenntly, the encrypted hue, the encrypted luminance and the saturattion are combined together and transformed to RGB colorspace. Fig.3 is a hue disk and depicts arrangementt to all colors. We assume that a hue is the mixture of two neigghboring hues. For example, red is the mixture of magenta and yellow. The denotation hs and hi are, respectively, the hues of the secret pixel and the i-th sharing pixel, where i∈{1, 2}. Inn addition, the hue difference between the secret pixel and thee sharing pixel is defined as θ. hs can be generated by mixinng h1 and h2. The procedures of color mixing are described as folllows: Step 1. Input a pixel ps of secret image, whiich is transformed from RGB colorspace to HSL colorspacce. Let hs, ss, and ls be the hue, the saturation, and the luminnance of ps, where 0°≤hs
