A data hiding method based on information sharing via PNG images for applications of color image authentication and metadata embedding

A data hiding method based on information sharing via PNG

images for applications of color image authentication and

metadata embedding

$

Che-Wei Lee

, Wen-Hsiang Tsai

Department of Computer Science and Information Engineering, National Chiao Tung University, Hsinchu 30010, Taiwan b

Department of Information Communication, Asia University, Taichung 41354, Taiwan

a r t i c l e

i n f o

Article history:

Received 14 February 2012 Received in revised form 9 November 2012 Accepted 10 January 2013 Available online 4 February 2013 Keywords:

Data hiding Secret sharing

Color image authentication PNG image

Alpha channel

a b s t r a c t

A new data hiding method via PNG images based on Shamir’s (k, n)-threshold secret sharing scheme is proposed. The coefficients of the polynomial used by the Shamir’s method are taken as carriers to carry given data. The data to be hidden then are transformed into partial shares and embedded into the alpha-channel plane of a cover PNG image. Undesired white noise created in the resulting stego-image is removed by skillfully mapping the computed share values into suitable ranges in the embedding process. An important application of the proposed method to color image authentication is also proposed, with detailed authentication algorithms for PNG images presented. Compared with existing methods, the proposed image authentication method possesses the merits of losslessness during image authentication, high sensitivity to image alterations, good tampering localization capability, and very low false acceptance and rejection ratios. Experimental results proving the effectiveness of the proposed methods are also included.

&_{2013 Elsevier B.V. All rights reserved.}

1. Introduction

Data hiding is a process of embedding information into a certain digital file that acts as a host. Through data hiding techniques, information such as authentication signals can be embedded into a digital file for the purpose of verifying the integrity or fidelity of the file[1–4]. In the application of copyright protection, an owner of a digital file can use data hiding techniques to embed a visible or invisible digital watermark into the file content to claim

the ownership of the content[5–8]. Another application of data hiding is covert communication[9–10] in which people hide a secret message into a cover file, resulting in a stego-file; and a receiver of the latter can extract the hidden message from the stego-file to complete the communication.

In addition, information sharing was proposed to pro-tect the security of concerned data by transforming a secret message into several shares which are then dis-tributed to a number of participants to keep. Such a secret sharing scheme is useful for reducing the risk of incidental data loss and advantageous for keeping a balance among the participants: only when all the shares or a sufficient number of them are collected from the participants can the secret message be recovered correctly. This concept of secret sharing was proposed first by Shamir [11]. Con-ventionally, data hiding and information sharing are two irrelevant issues in the domain of information security. Contents lists available atSciVerse ScienceDirect

journal homepage:www.elsevier.com/locate/sigpro

Signal Processing

0165-1684/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.sigpro.2013.01.009

$

This work was supported partially by the NSC project No. 99-2631 -H-009-001.

n

Corresponding author at: National Chiao Tung University, Department of Computer Science and Information Engineering, Hsinchu 30010, Taiwan. Tel.: þ 886 3 5728368; fax: þ886 3 5734935.

E-mail addresses: paradiserlee@gmail.com (C.-W. Lee), whtsai@cis.nctu.edu.tw (W.-H. Tsai).

In this study, a new data hiding method based on the technique of information sharing is proposed for hiding data into PNG (portable network graphics) images.

In the literature, many data hiding methods exploring the spatial domain and frequency domain of images

[12–16] have been proposed. Bender et al.[12]proposed the technique of least-significant-bit (LSB) replacement, in which a secret message is embedded in the least significant bits of image pixel values. Mielikainen [13]

proposed a modified LSB replacement method which embeds as many bits as the conventional method, but changes less pixel values. Yang et al. [14] proposed an adaptive k-LSB substitution method in which larger values of k are adopted in the edge areas of the cover image and smaller ones are used for the smooth areas. Wang et al.[15]

transformed image block contents into coefficients in the frequency domain by the discrete cosine transform (DCT) and embedded secret bits by modifying the magnitude relations between the AC values of image blocks. Besides data embedding techniques using the DCT, the discrete wavelet transform (DWT) [17] and the discrete Fourier transform (DFT)[18,19] have also been used.

From another viewpoint, different types of images and files can be used as cover media for developing data hiding

[20,21]. In[21], Lee and Wu proposed a lossless data hiding method for palette-based images, which adjusts palette colors and image data to embed secret data and side information for reconstruction of the original image con-tent. Lee and Tsai[9]hid data into PDF files’ characters by using special ASCII codes. Liu[10]made use of the change tracking function in Microsoft Word to hide data by a document degeneration technique.

In this paper, in addition to the aforementioned spatial domain, frequency domain and palettes of images for use in data hiding, we try to explore a new embeddable space for data hiding, aiming at providing more data hiding capacity, better quality of the resulting stego-image and stronger applicability. As a result, the PNG image with the alpha channel plane is found to be capable of meeting these requirements mentioned previously. Specifically, in the information-sharing-based data hiding method pro-posed in this study, a PNG image is used as the cover image in which the alpha-channel value of each pixel is set to be 255 initially. That is, the cover image is a totally transparent color one at the beginning of the proposed data hiding process. A data string to be hidden is trans-formed into shares by the Shamir’s secret sharing method, which is then embedded into the alpha-channel plane of the cover PNG image. Coefficient parameters involved in the Shamir method are used as carriers of the data to be hidden in the proposed method. A prime number used in the method, which is found to dominate the resulting visual quality and data hiding capacity of the stego-image, is properly selected. Also, a mapping function is designed for adjusting the alpha-channel values to create uniform transparency in the alpha-channel plane, resulting in an imperceptible effect in the stego-image. The original R, G, and B channels are untouched so that the original image appearance revealed by the color information of these three channels is kept.Fig. 1illustrates these core ideas of the proposed method.

In practical uses, the proposed data hiding method is suitable for applications of image authentication and metadata hiding. In particular, the application of the proposed method to image authentication is investigated in detail in this study and relevant algorithms are pro-posed in this paper.

Some other merits of the proposed method are described in the following.

(1) Causing no destruction to the original cover image — The proposed method manipulates the alpha-channel plane but leaves the RGB color channels untouched in the entire data hiding and extraction process, result-ing in a stego-image with a destruction-free color content, which is beneficial for certain applications like metadata hiding for digital archiving.

(2) Having the discardability of the alpha channel — Since data are embedded into the alpha channel in the proposed method, the alpha channel can be discarded for the purpose of obtaining the original image con-tent. In the application of image authentication, an intact protected image can be regained after the process of authentication. The proposed method does not leave permanent distortion to an input image as that done by conventional image authentication methods.

(3) Fully using channels in images for data hiding — Different from commonly seen color images with three color channels, namely, R, G, and B, the PNG image format has a fourth channel, namely, alpha. By the proposed method, the alpha channel of a PNG image can be used to offer an additional data hiding channel for various applications.

The remainder of this paper is organized as follows. In Section 2, the Shamir method on which the proposed data hiding method is based is reviewed first. InSection 3, the details of the proposed method, including the data embedding and extraction processes, are described. In

Section 4, algorithms for image authentication as an appli-cation of the proposed data hiding method are described. A discussion on security consideration of the proposed method is given in Section 5. Some experimental results are shown in Section 6. Finally, conclusions are made in

Section 7.

channel Alpha

RGB channels Stego image

Message shares

2. Review of the Shamir method for secret sharing The proposed method for data hiding is based on the so-called (k, n)-threshold secret sharing method proposed by Shamir[11], where n is the number of participants in the secret sharing activity and k is a threshold specifying the minimum number of shares which should be collected to recover the secret. The detail of the method is reviewed as an algorithm in the following.

Algorithm 1. (k, n)-threshold secret sharing.

Input: a secret d in the form of an integer, the number n of participants, and a threshold k not larger than n. Output: n shares in the form of integers for the n participants to keep, respectively.

Step 1. Choose a prime number p randomly.

Step 2. Select k  1 integer values c1, c2, y, ck  1within

the range of 0 through p  1.

Step 3. Select n distinct real values x1, x2, y, xn.

Step 4. Use the following (k 1)-degree polynomial to generate n equations to compute n function values F(xi), called partial shares, as follows:

FðxiÞ ¼ ðd þ c1xiþc2xi2þ    þck1xik1Þmodp, ð1Þ where i¼1, 2, y, n.

Step 5. Deliver the 2-tuple (xi, F(xi)) as a share to the i th

participant, respectively, where i¼1, 2, y, n.

Since there are k coefficients, including d and c1

through ck  1, in Eq.(1), it is necessary to collect at least

k shares from the n participants to form k equations of the form of (1) to solve these k coefficients. This explains the term, threshold, for k as well as the name, (k, n)-threshold, for the Shamir method[11]. Below is a description of such a way of equation solving for secret recovery.

Algorithm 2. Secret recovery.

Input: k shares collected from the n participants with k being the threshold mentioned inAlgorithm 1.

Output: the secret d hidden in the shares; and the prime number p and the coefficients ci used in the equations

described by (1) inAlgorithm 1, where i¼1, 2, y, k 1. Steps.

Step 1. Use the k shares (x1, F(x1)), (x2, F(x2)), y,

(xk, F(xk)) to set up the following equations:

FðxjÞ ¼ ðd þc1xjþc2xj2þ    þck1xk1j Þmodp, ð2Þ where j ¼1, 2,y, k.

Step 2. Solve the k equations above by Lagrange’s inter-polation to obtain the desired secret value d[22]as follows: d ¼ ð1Þk1 _Fðx 1Þ x2x3  xk ðx1x2Þðx1x3Þ    ðx1xkÞ  þFðx2Þ x1x2  xk ðx2x1Þðx2x3Þ    ðx2xkÞ þ    þFðxkÞ x1x2  xk1 ðxkx1Þðxkx2Þ    ðxkxk1Þ  mod p :

Step 3. Compute the values c1through ck  1by expanding

the following equality and comparing the result with (2) in Step 1 while regarding the variable x in the equality below to be xjin (2): FðxÞ ¼ Fðx1Þ ðxx2Þðxx3Þ    ðxxkÞ ðx1x2Þðx1x3Þ    ðx1xkÞ  þFðx2Þ ðxx1Þðxx3Þ    ðxxkÞ ðx2x1Þðx2x3Þ    ðx2xkÞ þ    þFðxkÞ ðxx1Þðxx2Þ    ðxxk1Þ ðxkx1Þðxkx2Þ    ðxkxk1Þ  mod p :

Step 3 in the above algorithm is included additionally for the purpose of computing the values of the parameters ciin the proposed method. In other applications, if only

the secret value d need be recovered, this step may be eliminated.

3. Proposed method for data hiding via PNG images Based on the Shamir method [11] described pre-viously, the basic idea of the proposed method for hiding a given data string M in a cover PNG image I to yield a stego-image I0_{is described as four major steps as} follows.

1. Transform M into a sequence M0_{of integers.}

2. Take sequentially a number of integers from M0 _{as the} values of d and ciin Eq.(1)to compute partial shares F(xi).

3. Embed F(xi) into I by replacing some alpha-channel

values of I with F(xi).

4. Repeat (2) and (3) until no integer is left in M0_{, resulting} in a stego-image I0_.

A block diagram describing the processes in the proposed method is shown inFig. 2, and the details of the ways we embed and extract the shares are presented as algorithms in the following.

Algorithm 3. Data embedding by secret sharing using a PNG image.

Input: a cover PNG image I and a secret message M in the form of a binary data string.

Output: a stego-image I0 _{in the PNG format.} Steps.

Step 1. (Initialization) Divide M into t-bit segments with t ¼3, and transform each segment into an

inte-ger, resulting in an integer sequence

M0_¼d

1d2d3ywhere 0rd_ir7.

Step 2. (Beginning of looping) Take the first four ele-ments from M0 _{as m}

1, m2, m3, and m4, starting

from the beginning of M0_.

Step 3. (Partial share creation) Set p, ci, and xiin Eq.(1)of

Algorithm 1to be the following values:

(a) p ¼11 (the smallest prime number larger than 7);

(b) d ¼m1, c1¼m2, c2¼m3, and c3¼m4;

resulting in the following equations: q1¼Fðx1Þ ¼ ðm1þm2x1þm3x21þm4x31Þmodp,

q2¼Fðx2Þ ¼ ðm1þm2x2þm3x22þm4x32Þmodp, q3¼Fðx3Þ ¼ ðm1þm2x3þm3x23þm4x33Þmodp,

q4¼Fðx4Þ ¼ ðm1þm2x4þm3x24þm4x34Þmodp; ð4Þ and compute the partial shares of q1 through q4

accordingly.

Step 4. (Mapping of partial share values) Add 245 to each of q1 through q4 to form q10, q20, q30, and q40,

respectively.

Step 5. (Data embedding) Embed q10through q40into the

alpha-channel plane of I in the following way. 5.1. Take in a raster-scan order four unprocessed

pixels of I and set their alpha-channel values to be q10_{through q4}0_{, respectively.} 5.2. Remove mithrough miþ3 from M0.

Step 6. (End of looping) If M0 _{is not empty, then go to} Step 2 to process the next four integers in M0_; otherwise, take the final I as the desired stego-image I0_.

The above algorithm can be regarded as a (4, 4)-threshold secret sharing method. The possible values of q1through q4

yielded by Eq. (4) in Step 3 of the above algorithm and inserted in the alpha channels of I are between 0 and 10 because the value of p used in Eq.(4)is 11. After performing Step 4 of the algorithm, the values of q10 through q40form a

small range of integer values from 245 to 255 which are then embedded into the alpha channels of the cover image I. The distribution of the alpha-channel values within such a small range of values means that very similar values appear everywhere in the alpha channels, resulting in a nearly uniformly transparent PNG image, as desired.

Also, it can be seen from the algorithm that every four 3-bit segments of the secret data string are embedded into the alpha-channel values of four pixels of the cover image I to yield the stego-image I0_{. This means that if the} size of the cover image is S, then the data hiding capacity is R ¼(4  3)  (S/4)¼3S bits. This is for the case of t ¼3

where t is as mentioned in Step 1. More generally, if every four t-bit segments are transformed and embedded simi-larly, then it is easy to figure out that R¼(4  t)  (S/4)¼tS bits, which means that the data hiding capacity is propor-tional to the chosen value of t. Since S is the dimension of the cover image, this capacity of tS is large in general.

However, it should be noted that the larger the value of t is chosen to be, the lower the visual quality of the stego-image will become. The reason is that a larger value of t, according to Step 2 ofAlgorithm 1, implies that a larger value of p is chosen, and so the possible values of q1through qk,

according to Step 3 ofAlgorithm 3, will be spread in a larger range of values from 0 through p 1 due to the use of the mod-p operation. This will cause a wider range of alpha-channel values even after the value mapping of Step 4 of

Algorithm 3 is conducted. This wider alpha-channel value range in turn leads to a more obvious non-uniform transpar-ency effect appearing on the stego-image. This also explains the reason why we segment, in Step 1 ofAlgorithm 3, the message M into segments of t¼3 bits for use in Eq.(4), which is a compromise between the resulting data hiding capacity and stego-image quality according to our experimental experience. Of course, if a higher image quality of the stego-image is required, we may use a smaller t like t¼2 at the sacrifice of the data hiding capacity.

In addition, it is noted thatAlgorithm 3takes every four integer numbers of the string M0_{each time and embeds them} into the alpha channels of four pixels of the cover image. It is not difficult to figure out that the algorithm can be general-ized to take n integers each time and embeds them into n pixels. For this, just modify part of Step 3 to be as follows:

. . .

ðbÞ d ¼ m1,c1¼m2,c2¼m3,. . .,cn¼mn; ðcÞ x1¼1,x2¼2,x3¼3,. . .,xn¼n, resulting in the following equations:

q1¼Fðx1Þ ¼ ðm1þm2x1þm3x21þ    þmnxn1Þmodp, q2¼Fðx2Þ ¼ ðm1þm2x2þm3x22þ    þmnxn2Þmod p, q3¼Fðx3Þ ¼ ðm1þm2x3þm3x32þ    þmnxn3Þmod p,

^

qn¼FðxnÞ ¼ ðm1þm2xnþm3x2nþ    þmnxnnÞmod p: ð40Þ The resulting generalized algorithm yields, as can be figured out again, a data hiding capacity of R¼(n  t)  (S/n)¼tS bits which is identical to the original algorithm. Now, the process of hidden data extraction is described in the following. A block diagram describing the proposed data extraction processes is shown inFig. 3. Cover image

in PNG format with an alpha channel

message Secret sharing

scheme Mapping Partial shares Mapped partial shares Alpha RGB Stego-image in PNG format Embedding

Fig. 2. Block diagram of proposed data hiding processes.

Stego-image in PNG format

Extracting partial shares from alpha channel

Secret sharing scheme Partial shares Backward mapping of partial share Message

Algorithm 4. Data extraction from a stego-image. Input: a stego-image I0_{created byAlgorithm 3in the PNG} format.

Output: the binary data string M hidden in I0_. Steps.

Step 1. (Initialization) Create an empty string M. Step 2. (Beginning of looping) Take in a raster-scan order

four alpha-channel values q10, q20, q30, and q40

from I0_.

Step 3. (Backward mapping of partial share values) Sub-tract 245 from each of q10 through q40to obtain

q1through q4, respectively.

Step 4. (Data extraction) Perform the secret recovery process described byAlgorithm 2to extract four integers m1through m4hidden in q1through q4,

transform m1 through m4into binary numbers,

and append them in a sequential order to the end of M.

Step 5. (End of looping) If all shares embedded in I0 _are processed, then take the final M as output; otherwise, go to Step 2.

Similarly to generalization of Algorithm 3 as men-tioned previously,Algorithm 4above may also be general-ized to take care of data extraction from images yielded by the generalized version ofAlgorithm 3. The details are simple and so omitted.

4. Application of proposed method to image authentication

A possible application of data hiding is image authentica-tion. To implement image authentication by the proposed data hiding method, an input image with RGB channels (like a BMP image) to be protected is transformed first into a PNG image with the alpha-channel values all set initially to be 0. The PNG image is processed next to generate color-dependent authentication signals, which are then embedded into the alpha channel by using the previously proposed data hiding method to yield the resulting stego-image. Then, in

the later authentication signal verification process, the embedded authentication signals are extracted from the alpha channel plane of a stego-image and verified against those computed from the color values of the pixels of the image. A pixel with mismatched signals is regarded as being tampered with.Fig. 4illustrates the processes of authentica-tion signals generaauthentica-tion and embedding in the proposed color image authentication method, andFig. 5illustrates the image verification processes of the proposed method. More details are described as two algorithms (Algorithms 5 and 6) in the following.

Algorithm 5. Authentication signal generation and embedding.

Input: a PNG image I and a key K.

Output: a protected image I0_{with authentication signals} embedded.

Steps.

Step 1. (Initialization and beginning of looping) Take in a raster-scan order three pixels p1, p2, and p3from I,

and use K as the seed for a random number generator to get a number sequence S ¼s1, s2, y.

Step 2. (Creation of authentication signals) For each of p1,

p2 and p3, denoted as pi, perform the following

steps.

2.1 Take the R, G, and B values of pi, denoted as

VR, VG, and VB, respectively.

2.2 Take in order three elements from S, denoted as sj, sj þ 1, and sj þ 2, to perform the following

operations to obtain three bits r, g, and b, respectively:

ðVRþsjÞmod2¼r; ðVGþsj þ 1Þmod2¼g; ðVBþsj þ 2Þmod2¼b:

2.3 Concatenate r, g, and b as a 3-bit string rgb, and transform it into a decimal integer as the authentication signal Difor pi.

Step 3. (Authentication signal embedding into three pixels) Perform the previously-described generalized

Cover image in PNG format with an alpha channel Secret sharing scheme Mapping Partial shares Mapped partial shares RGB Alpha RGB Stego-image in PNG format Image transformation Embedding Cover image Creation of authenticaiton signals Data of RGB channels

version ofAlgorithm 3to embed the three authen-tication signals D1, D2, and D3into three pixels of I,

except that in the step of mapping of partial share values (Step 4) inAlgorithm 3, 244 instead of 245 is added to each partial share value.

Step 4. (End of looping) If there exists any unprocessed pixel in I, then go to Step 2; otherwise, take the final I as the desired stego-image I0_.

Algorithm 6. Authentication signal verification.

Input: a protected stego-image I0_{created byAlgorithm 5,} and a key K used there.

Output: image I0_{with altered pixels being marked if} found.

Steps.

Step 1. (Initialization and beginning of looping) Take in a raster-scan order three pixels p1, p2 and p3

from I0_{; let their alpha-channel values be} denoted as q10, q20, and q30, respectively; and

use K as the seed for a random number gen-erator to generate a random number sequence S¼s1, s2, y.

Step 2. (Extraction of authentication signals embedded in

alpha channels) Perform the

previously-described generalized version of Algorithm 4

with q10, q20, and q30 as input to extract the

authentication signals D10, D20, and D30cept that

in the step of backward mapping of partial share values (Step 3) inAlgorithm 4, 244 instead of 245 is subtracted from each of q10 through q30.

Step 3. (Computation of authentication signals from pixels’ color values) For each of p1, p2and p3, denoted as

pi, perform the following steps.

2.1. Take the R, G, and B values of pi, denoted as

VR, VG, and VB, respectively.

2.2. Take in order three elements from S,

denoted as sj, sj þ 1, and sj þ 2, to perform the

following operations to obtain three bits r, g, and b, respectively:

ðVRþsjÞmod2¼r; ðVGþsj þ 1Þmod2¼g; ðVBþsj þ 2Þmod2¼b:

2.3. Concatenate r, g, and b as a 3-bit string rgb, and transform it into a decimal integer as the authentication signal Difor pi.

Step 4. (Matching of extracted and computed authentica-tion signals) Match D1, D2, and D3with D10, D20,

and D30, respectively, and if there exists any

mismatched pair, then mark the corresponding pixel as being tampered with in the input image I0_.

Step 5. (End of looping) If there exists any unprocessed pixel in I0_{, then go to Step 2; otherwise, take the} final I0_{, possibly marked, as output.}

Totally six algorithms so far having been introduced in this study,Table 1is therefore given for a rapid reviewing of the previously-described algorithms’ content.

5. Security consideration

The secret key K used in Step 2.2 ofAlgorithm 5provides a measure to protect the authentication signals to be counterfeited. More specifically, since three bits consist of an authentication signal for each pixel, the probability of correctly guessing an authentication signal for each pixel is 1/8. To enhance further the security of the proposed method, an additional measure is adopted but not included in the above algorithms for clarity of algorithm descriptions. It is randomization of the constant values of x1through xnused in

Step 3 of the generalized version ofAlgorithm 3within the allowed integer range of 0rxiop [11] with the help of

another secret key. Then, the probability of correctly guessing values of x1through x3used in a set of three pixels can be

RGB

Computation of Data of RGB

Extracting partial shares

Backward mapping Secret sharing

scheme Extracted authentication signals Computed authentication signals No image Alpha Yes Authentic Match? Mark corresponding pixel authenticaiton signals channels Stego-of partial share

figured out to be

1=½p  ðp 1Þ      ðpn þ1Þ ¼ 1=½11  ð111Þ  ð113 þ 1ÞÞ ¼ 1=990  0:1%:

As a result, the possibility of correctly guessing all these values used in a stego-image of size S is 1=½p  ðp1Þ      ðpn þ 1ÞS=n _{which is small enough} in general cases. Through the use of above security measures, it is almost impossible for an attacked color stego-image with counterfeit authentication signals to pass the proposed image authentication processes.

Furthermore, the authentication data may possibly be erased by discarding or modifying the content of the alpha channel without producing any alteration to the content of the color channels. For this, it is noted that the aim of the image authentication is to make a stego-image be trusted by an authentication side after the authentication process. Accordingly, avoiding a coun-terfeit image to pass the authentication process is a major concern, which is different from the major con-cern of robustness in the copyright protection — a surviving and recognizable watermark such as a logo has to be extracted from the stego-image even after attacks. Therefore, at an authentication side, if a stego-image ready to be authenticated has no the alpha channel, it means the integrity of the stego-image is seriously lost because an undamaged stego-image must have the alpha channel. In short, if an attacker erases the authentication data by just discarding or modifying the alpha channel of the stego-image and producing no alteration to the image color channels, such a kind of attack will evidently be found by the proposed method and the malicious aim to deceive the authentication processes will fail.

6. Experimental results

In this section, experimental results of the proposed data hiding method and the comparison with existing methods in data hiding are described first. Subsequently, experimental results of the proposed color image authen-tication method, which is based on the aforementioned proposed data hiding method, and the comparison with existing methods in color image authentication are given. 6.1. Experimental results of data hiding using color images

A lot of experiments have been conducted to test the proposed algorithms on totally above 100 color images. Some results using test images, named Lena, jet, Tiffany,

Baboon, boat and mountain as given inFig. 6(a), (c), (e), (g), (i) and (k), respectively, are shown here. The results of applying the proposed method using Algorithm 3 to embed a long sequence of binary message data into the three images are shown inFig. 6(b), (d), (f), (h), (j) and (l), respectively. As can be seen from the figures, the stego-images are visually almost identical to the cover stego-images, respectively, although the alpha-channel contents of the stego-images include embedded message data. Note that inAlgorithm 3, the value of t, which is the number of bits taken as a segment and transformed into an integer for use in the secret sharing process performed byAlgorithm 3, was taken to be 3.

Next, we show the effect of choosing different values of t in Step 1 ofAlgorithm 3. Recall that the data hiding capacity has been computed to be R¼tS where S is the size of the cover image. Although accordingly t may be chosen to be the maximum of 7 to increase the data hiding capacity, the yielded stego-image quality degrades very much, as illustrated by the results shown inFig. 7, where Fig. 7(a) is the stego-image of Lena yielded by

Algorithm 3with t taken to be 7 which includes, as can be seen, a lot of white noise. For comparison, a better result of using t ¼3 shown inFig. 6(b) is repeated inFig. 7(b) in which the white noise created by the algorithm is almost imperceptible, as mentioned previously.

Furthermore, we show in more detail the data hiding capacities and the corresponding stego-image qualities for all possible values of t¼ 1, 2, y, 7 for the aforementioned six images Lena, Jet, Tiffany, Baboon, Pepper and Mountain used as cover images. Specifically, inTables 2 and 3 we show, in addition to the data hiding capacities, the qualities of the alpha-channel planes of the six corresponding stego-images in terms of the MAE (Mean Average Error) measure. The MAE introduced in [23] is an objective metric to measure the visual quality, and the larger value of MAE means the image is with poorer quality. According to the statistics of conducted experiments shown inTables 2 and 3, the alpha channel provides satisfactory transparency effect when the value of MAE not larger than around 4.25. Furthermore, in Fig. 8, we show the stego-images corresponding to t¼1, 2, y, 7. As can be seen, when t¼4, the value of MAE is 4.25 and the corresponding stego-image quality shown in Fig. 8(c) is still visually good. According to the statistics of other conducted experiments shown in Tables 2 and 3, the alpha channel provides sufficient transparency effect when the value of MAE not larger than around 4.25. In addition, the corresponding data hiding capacity is R¼tS¼3  512  512¼75 K¼786 432 bits, which is good enough for applications.

Table 1

Six algorithms described in this study and the corresponding descriptions.

Algorithms Descriptions

Algorithm 1 Encoding phase of (k, n)-threshold secret sharing method

Algorithm 2 Decoding phase of (k, n)-threshold secret sharing method

Algorithm 3 Proposed data embedding method based on Algorithm 1

Algorithm 4 Proposed data extraction processes based onAlgorithm 2 Algorithm 5 Proposed color image authentication method based onAlgorithm 3 Algorithm 6 Proposed color image verification processes based onAlgorithm 4

In fact, it can be seen fromFig. 8(d) that even when t is taken to be 4, the stego-image quality is still acceptable with the data hiding capacity increased to 100 K bits. On the contrary, if image quality is the most serious concern, then t may be reduced to 2 or even 1 at the sacrifice of the data hiding capacity. Note that the data hiding capacity is related to the t value only; it is independent of the cover image content. It is also noted that, different from other methods, the channels of R, G, and B of the cover image are not processed by the proposed method, yielding a lossless result in the color channels.

To further demonstrate the feasibility of the proposed method for metadata embedding, an art image of Gleaner shown inFig. 9(a) and the history data related to this art image shown inFig. 9(b) are respectively taken to be the input cover image and the metadata. Since the size of the metadata is 1.85 KB ( ¼15 156 bits), it is adequate to set the value of t used inAlgorithm 3to be 1 for embedding the metadata into Fig. 9(a). The resulting stego-image with the MAE value of 0.11 is shown inFig. 9(c) and, as can be seen, the stego-image is visually identical to the cover image ofFig. 9(a). Finally, the result of applying the

proposedAlgorithm 4to extract the embedded metadata fromFig. 9(c) is shown inFig. 9(d).

6.2. Comparison with existing data hiding method

To measure the performance of the proposed method, we compare the proposed method with Kim’s method

[26]which produces high data hiding capacity with the good visual quality of a stego-image in the field of lossless data hiding. Importantly, both the proposed method and Kim’s method have a parameter t that can be adjusted to control the data hiding capacity. With the increasing of the value of t, the data hiding capacity increases while the quality of the stego-image decreases for both methods. In more detail, in Kim’s method [26], the parameter t denotes the number of hiding levels; in the proposed method, the t denotes the number of bits of a message segment as mentioned in Step 1 ofAlgorithm 3. As can be observed from Table 4, the proposed method gets a significant improvement in hiding capacity, while causes no destruction to the original content of RGB channels. Fig. 6. Results of applyingAlgorithm 3to embed a long sequence of binary message data into test images: (a) Cover image Lena; (b) Stego-image of Lena; (c) Cover image jet; (d) Stego-image of jet; (e) Cover image Tiffany; (f) Stego-image of Tiffany; (g) Cover image baboon; (h) Stego-image of baboon; (i) Cover image pepper; (j) Stego-image of pepper; (k) Cover image mountain; (l) Stego-image of mountain.

To further reveal the performance of the proposed method, we also compare the proposed method with Luo’s method[27]. The method of[27]uses interpolation technique to fulfill the reversible watermarking and outperforms many existing methods such as[28–29]. As

can be seen from Table 5, the proposed method

yields more data hiding capacity than that of the method of[27].

6.3. Experimental results of color image authentication In this section, we show some experimental results of applying the proposed image authentication algorithms (Algorithms 5 and 6) to authenticate stego-images attacked by two common image editing operations, i.e., superimposing and painting. It was found that if the superimposing operation is used in the attack, the alpha channel values will be replaced with the new value 255 at the attacked part. Since the largest alpha channel value generated by the proposed method is 254 (see Step 3 in

Algorithm 5), attacked pixels can be easily detected and marked by checking the existence of the specific value 255 in the alpha channel. As an example,Fig. 10(a) shows a cover image ‘‘Tiffany’’ andFig. 10(b) is the stego-image of Tiffany. InFig. 10(c), the stego-image was attacked by superimposing a fake mouth on the face.Fig. 10(d) shows the authentication result in which all altered pixels were detected and marked in black. Table 6 includes the statistics of the performance of the proposed method shown by the above experimental results in terms of the three parameters: detection ratio, false acceptance ratio, and false rejection ratio, which are defined in the following:

(1) detection ratio¼ (the number of detected pixels)/(the number of tampered pixels);

(2) false acceptance ratio¼(the number of tampered pixels marked as untampered)/(the total number of tampered pixels);

(3) false rejection ratio¼(the number of untampered pixels marked as tampered)/(the total number of untampered pixels).

As can be observed from Table 6, both the false acceptance ratio and false rejection ratio are 0% for the reason that, as mentioned previously, alpha channel values 255 only occur at attacked pixels.

Another example of a tampered image attacked by superimposing a rose to the hair part of Tiffany is shown in Fig. 11(b). The authentication result is shown in

Fig. 11(c) in which all pixels consisting of the added rose were successfully detected and marked in black. The corresponding statistics is also given inTable 6.

Some experimental results of using painting operations to attack stego-images are shown in Fig. 12. Specifically,

Fig. 12(a) and (b) are respectively an input cover image ‘‘jet’’ and a generated stego-image. InFig. 12(c), a logo and words printed on the body of the plane were smeared by painting color similar to the plane body. The authentication result generated fromAlgorithm 6is shown inFig. 12(d) in which tampered regions were successfully detected and marked in black. However, as can be seen, some tampered pixels were not detected and appeared as noise in the marked region. This phenomenon results from the case that the authentica-tion signals extracted from the alpha channel incidentally match the authentication signals computed from the tam-pered pixels. This is also the reason why the false acceptance ratio exists. It is noted that the alpha channel content keeps intact after the painting operation and so the extracted authentication signals are always true, yielding the false rejection ratio is 0%. Related statistics of the experiment is given inTable 7.

Since the authentication signal of each pixel is com-posed of three bits, there is a probability of 1/8 for an erroneous authentication, leading to a false acceptance ratio of around 12.5%. As an example,Fig. 13(b) shows that the stego-image of jet was tampered with by smear-ing the entire plane out of the image content. The authentication result is shown in Fig. 13(c) in which Fig. 7. An example of experimental results showing compromise between data hiding capacity and stego-image quality: (a) Stego-image of Lena yielded by choosing t ¼ 7 with more data hidden but showing more white noise coming from the alpha channel; (b) Stego-image of Lena yielded by choosing t ¼3 with less data hidden but with almost no noise due to nearly total transparency in the alpha channel.

Fig. 8. Stego-images yielded byAlgorithm 3for t ¼1–7: (a)–(g) correspond to t¼ 1, 2, y, 7, respectively.

Table 2

Data hiding capacities and stego-image qualities for t ¼1–7 using test images Lena, jet and Tiffany (DHC¼ data hiding capacity; MAE ¼mean average error; PSNR¼ peak of signal to noise ratio).

t value Lena Jet Tiffany

DHC (bits) MAE of alpha channel (dB) PSNR of RGB channels (dB) DHC (bits) MAE of alpha channel (dB) PSNR of RGB channels (dB) DHC (bits) MAE of alpha channel (dB) PSNR of RGB channels (dB) t ¼ 1 262 144 0.720 N 262 144 0.721 N 262 144 0.721 N t ¼ 2 524 288 1.210 N 524 288 1.203 N 524 288 1.211 N t ¼ 3 786 432 2.732 N 786 432 2.737 N 786 432 2.733 N t ¼ 4 1 048 576 4.250 N 1 048 576 4.233 N 1 048 576 4.251 N t ¼ 5 1 310 720 9.246 N 1 310 720 9.238 N 1 310 720 9.246 N t ¼ 6 1 572 864 16.236 N 1 572 864 16.242 N 1 572 864 16.238 N t ¼ 7 1 835 008 32.837 N 1 835 008 32.835 N 1 835 008 32.833 N

85.02% of tampered pixels were detected and marked in black. In other words, 14.98% of tampered pixels incidentally passed the authentication process, which meets the prob-abilistic expectation of around 12.5% authentication misses. The corresponding statistics is also given inTable 7.

In addition, it is noted that though we use the previously mentioned alpha value 255 as a distinguishing one to detect tampering caused by superimposing for the reason of efficiency, we may actually just useAlgorithm 6

proposed in this study to deal with such cases normally. The reason is that the proposed method detects attacks by

matching authentication signals computed from the color channels and those extracted from the alpha channel. If there exists any mismatched pair, then the correspond-ing pixel will be marked as becorrespond-ing tampered with.

6.4. Comparison with existing color image authentication methods

Several existing authentication methods related to color images are taken to compare with the proposed Table 3

Data hiding capacities and stego-image qualities for t¼ 1–7 using test images Baboon, Boat and Mountain (DHC ¼data hiding capacity; MAE¼mean average error; PSNR¼ peak of signal to noise ratio).

t value Baboon Boat Mountain

DHC (bits) MAE of alpha channel (dB) PSNR of RGB channels (dB) DHC (bits) MAE of alpha channel (dB) PSNR of RGB channels (dB) DHC (bits) MAE of alpha channel (dB) PSNR of RGB channels (dB) t¼ 1 262144 0.723 N 262144 0.719 N 262144 0.722 N t¼ 2 524288 1.215 N 524288 1.213 N 524288 1.220 N t¼ 3 786432 2.732 N 786432 2.727 N 786432 2.722 N t¼ 4 1048 576 4.246 N 1048 576 4.220 N 1048 576 4.233 N t¼ 5 1310 720 9.264 N 1310 720 9.262 N 1310 720 9.259 N t¼ 6 1572 864 16.219 N 1572 864 16.231 N 1572 864 16.222 N t¼ 7 1835 008 32.839 N 1835 008 32.823 N 1835 008 32.840 N

Fig. 9. Experimental results of metadata embedding and extraction by applying proposedAlgorithms 3 and 4: (a)Cover image Gleaner; (b) History data used as metadata; (c) Stego-image of Gleaner; (d) Metadata extracted from (c).

method for the purpose of presenting contributions made in this study. A comparison table in terms of important capabilities is given inTable 8. As can be observed, since the proposed method makes use of the alpha channel instead of conventional illumination[1]or RGB [24–25] channels for embedding authentication signals, the pro-posed method is the only one which has the characteristic of losslessness of the image content.

Furthermore, it is a challenge to create the authentica-tion signal for each color pixel and to find embeddable space that is large enough to accommodate these authen-tication signals. Therefore, though some image authentica-tion methods developed for color images, to the best of our knowledge, only the proposed method and the method of

[25] belong to the category of pixel-level authentication methods. This means that other color image authentication methods localize tampered area in the unit of block composed of many pixels, while the proposed method and the method of[25]localize the tampered area in the unit of pixel, yielding a finer localization result. For a fair comparison, we compare the proposed method with the method[25]also developed at the pixel-level authentica-tion precision in terms of the false rejecauthentica-tion ratio and false acceptance ratio. As can be seen from Table 9, since the authentication signal of each pixel is composed of three bits in the proposed method, a probability for an erroneous authentication is 1/8, leading to a false acceptance ratio of around 12.5%. However, the authentication signal of each pixel is one bit in the method of[25], so a probability for an

erroneous authentication is 1/2, leading to a false accep-tance ratio of around 50%. It is noted that, in the method of

[25], the authentication signals will not be damaged as long as a protected image without being tampered with, leading to a false rejection ratio of 0%. In addition, as can be seen fromTable 8, the localization capability only works when the alteration occurs in the blue channel in[25]. This fact results from that the method of[25] uses the blue channel for embedding authentication signals generated from channels of red and green. As a result, when the image content in the red and green channels altered, the method of[25]is able to detect the existence of the attack but unable to localize alterations precisely.

Moreover, it is worth to note that the method of[1]

embeds watermarks in the illumination channel and leaves chrominance channel untouched. Therefore, mod-ifications involved in illumination can be detected effi-ciently but those made in the chrominance channel will be neglected. In contrast, the proposed method, which generates authentication signals from data of the RGB channels, provides high sensitivity to alterations occur-ring in each channel.

At last, the method in [1] allows reasonable image processing such as JPEG compression without raising false positive alarms and is practical for some applications. In this aspect, the proposed method yields a stego-image in the PNG format which in normal cases will not be compressed further, reducing the possibility of erroneous authentication caused by incidental image compression. Table 5

Comparison of performance of proposed method with the method of [27].

Methods Lena Baboon Airplane Boat

Capacity PSNR of color content Capacity PSNR of color content Capacity PSNR of color content Capacity PSNR of color content

Luo et al.[27] 71674 48.82 22696 48.36 84050 48.94 38734 48.50

Proposed (t ¼1)

262144 1 262144 1 262144 1 262144 1

Table 4

Comparison of performance of proposed method with the method of [26].

(# of levels of[26]) 1 2 3 4 5 6 7

(t value of our method) Lena (bits) (dB) Kim[26] 31 865 (48.98) 81 511 (44.40) 114 536 (42.00) 137 326 (40.47) 153 558 (39.37) 165 641 (38.53) 174 964 (37.86) Proposed method 262 144 (N) 524 288 (N) 786 432 (N) 1 048 576 (N) 1 310 720 (N) 1 572 864 (N) 1 835 008 (N) Airplane (bits) (dB) Kim[26] 48 774 (49.17) 104 898 (45.06) 135 903 (42.84) 154 882 (41.34) 167 828 (40.22) 176 870 (39.32) 183 720 (38.57) Proposed method 262 144 (N) 524 288 (N) 786 432 (N) 1 048 576 (N) 1 310 720 (N) 1 572 864 (N) 1 835 008 (N) Baboon (bits) (dB) Kim[26] 7249 (48.72) 21 141 (43.02) 34 592 (39.80) 47 424 (37.59) 59 459 (35.95) 70 783 (34.66) 81 216 (33.62) Proposed method 262 144 (N) 524 288 (N) 786 432 (N) 1 048 576 (N) 1 310 720 (N) 1 572 864 (N) 1 835 008 (N) Boat (bits) (dB) Kim[26] 21 442 (48.87) 60 903 (43.89) 93 559 (41.32) 117 827 (39.67) 135 222 (38.46) 147 692 (37.49) 156 937 (36.66) Proposed method 262 144 (N) 524 288 (N) 786 432 (N) 1 048 576 (N) 1 310 720 (N) 1 572 864 (N) 1 835 008 (N)

7. Conclusions

A new type of data hiding via PNG images based on information sharing has been proposed. The Shamir’s secret sharing method is used first in a novel way to generate partial shares from a given data string. The alpha-channel plane of a cover PNG image is utilized next to embed the partial shares, yielding a stego-image with

undesirable white noise. The white noise is then elimi-nated skillfully by choosing a small prime number, divid-ing the input data strdivid-ing into 3-bit segments, and mapping computed share values into a range of large alpha-channel values which create high transparency. Generalization of the method to allow compromise between the resulting data hiding capacity and stego-image quality has also been proposed.

Fig. 11. Authentication result of an attacked image of Tiffany with an added rose: (a) Stego-image with authentication signals; (b) Modified stego-image; (c) Result with altered pixels detected and marked in black.

Fig. 10. Authentication result of an attacked stego-image of Tiffany with a pasted fake mouth: (a) Cover image; (b) Stego-image with authentication signals; (c) Modified stego-image; (d) Result with altered pixels detected and marked in black.

Moreover, detailed algorithms for applying the pro-posed method to color image authentication have been proposed. Shown by the results is the applicability of the proposed authentication algorithms to detect attacks

implemented by common image-content alternation operations. Good experimental results prove the effec-tiveness of the proposed methods in the aspects of tampering detection ratio, characteristic of losslessness,

Fig. 12. Authentication result of an attacked stego-image of jet with the smeared logo and words: (a) Stego-image with authentication signals; (b) Modified stego-image; (c) Result with altered pixels detected and marked in black.

Table 7

Statistics of experimental results. Experimental result (image size ¼512  512)

No. of tampered pixels

No. of detected pixels (detection ratio)

False acceptance ratio (%)

False rejection ratio (%)

Exp. 3 shown inFig. 11 5886 5379 (91.39%) 8.61 0

Exp. 4 shown inFig. 12 57 037 48 491 (85.02%) 14.98 0

Table 6

Statistics of experimental results. Experimental result

(image size ¼512  512)

No. of tampered pixels

No. of detected pixels (detection ratio)

False acceptance ratio (%)

False rejection ratio (%)

Exp. 1 shown inFig. 9 5886 5886 (100%) 0 0

and false acceptance and rejection ratios. Future studies may be directed to applications of the proposed method to copyright protection, digital rights management, recov-ery of altered image contents, etc.

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Peng & Liu[24]

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Byun et al.[25]

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channel

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Yes Yes Pixel-level Yes Alpha channel Free from

the misgiving

Table 9

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Proposed method

E12.5 0

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