A new blind image authentication method with a data repair capability for binary-like grayscale document images based on secret sharing has been proposed.
Both the generated authentication signal and the content of a block are transformed into partial shares by the Shamir method, which are then distributed in a well-designed manner into an alpha channel plane to create a stego-image in the PNG format. The undesired opaque effect visible in the stego-image coming from embedding the partial shares is eliminated by mapping the share values into a small range of alpha channel values near their maximum transparency value of 255.
In the process of image block authentication, a block in the stego-image is regarded as having been tampered with if the computed authentication signal does not match that extracted from corresponding partial shares in the alpha channel plane. For self-repairing of the content of a tampered block, the reverse Shamir scheme is used to compute the original content of the block from any two untampered shares.
Measures for enhancing the security of the data embedded in the alpha channel plane were also proposed. Experimental results have been shown to prove the effectiveness of the proposed method. Future studies may be directed to choices of other block sizes and related parameters (prime number, coefficients for secret sharing, number of authentication signal bits, etc.) to improve data repair effects. Applications of the proposed method to authentication and repairing of attacked color images may also be tried.
Chapter 4
A New Approach to Binary Image
Authentication via Uses of PNG Images and Secret Sharing Technique with an Image Recovery Capability
4.1 Introduction
This study explores the issue of authenticating binary images which are popular for preserving text-type or line-art documents. It is hoped that if a critical image part is authenticated to have been altered illicitly, its original content can be recovered.
Such binary image content verification and self-recovery capabilities are useful for authentication of many kinds of document data. However, the simple bi-level nature of binary images leads to shortage of data-embeddable space as well as creation of easily-perceptible changes after authentication signals are embedded into the image pixels. Therefore, a good solution to binary image authentication should take into account not only the possibility of creating sufficient space for data embedding but also the necessity of keeping the visual quality of the resulting image.
4.2 Merits of Proposed Method
Some other merits of the proposed method are described in the following.
(1) Causing no destruction to the cover binary image Existing binary image authentication methods usually embed authentication data into the cover image at the price of causing image destruction. Different from such methods, the proposed method utilizes the pixels’ values of the alpha channel for the purpose of image authentication and data recovery, leaving the intensity channel of the PNG image untouched and so causing no destruction to it.
(2) Having the reversibility to the original binary image The proposed method simply removes the alpha channel and rescales the sample depth of the stego-image to obtain the original binary image, thus achieving the reversibility to
the input image content. This is beneficial for certain applications like art image archiving.
(3) Creating good concealments by secret sharing The proposed method embeds data in the form of shares into the alpha channel of the binary PNG image. The effect may be regarded as double-fold concealments, one fold contributed by the shares as a disguise of the original image data and the authentication signals, and the other fold contributed by the use of the alpha channel which is created by the proposed method to be nearly transparent with imperceptible noise.
(4) Fully using channels in images for data embedding Different from the commonly-seen binary image with only one channel the intensity channel, the PNG image has an additional channel the alpha channel, which is fully utilized by the proposed method to embed the share data.
Being blind in the process of image authentication Some authentication methods for binary images need auxiliary data such as a lookup table to decode embedded signals. In contrast, the proposed method requires no auxiliary information other than the stego-image in the process of authentication.
4.3 Proposed Method for generation of a stego-image
In the proposed method, a binary cover image transformed into the PNG format is first divided into nonoverlapping blocks of size 2×3, and an authentication signal is generated from each of them. Next, the generated data for use in later processes of authentication and self-recovery of block contents are gathered to form a secret message. The message then is transformed into n shares by the Shamir’s (k, n)-threshold secret sharing scheme described in Chapter 3.2. Finally, the shares are embedded into the alpha-channel of the cover image to form a stego-image. Later, if some, but no more than k, of the shares for an image block are attacked and destroyed, then k of the remaining untouched shares are retrieved to recover the original image block content. In this way, as mentioned previously, the chance of data survival against attacks is raised. These main concepts of the proposed method are described in detail in this section. The values of (k, n) are taken to be (2, 6), respectively.
A. Algorithm for generation of a stego-image
A detailed algorithm for describing the generation of a stego-image in the PNG
format of the proposed method is presented in the following, with the used symbols listed in Table 4.1.
Algorithm 1: generation and embedding of authentication signals and shares.
Input: a binary image I with pixel values 0 and 1 in the intensity channel, and a key K.
Output: a stego-image I′ composed of the intensity channel and an additional alpha channel in the PNG format with embedded data for authentication and self-recovery.
Steps.
1. (Transforming the cover image into the PNG format and scaling the image sample depth) Transform I into a PNG image with the original intensity channel, denoted as M, and an additional alpha channel, denoted as L, by the following steps.
(1) Scale the sample depth (sd) of the intensity values of M from sdin = 1 up to sdout = 8 by the following linear equation to create a new value v for each pixel’s intensity value v in M:
v = v × (msout/msin) + 0.5 (3)
where
(a) msin = the maximum sample (pixel) intensity value in the input image I
= 2 sdin 1 = 21 1 = 1;
(b) msout = the maximum sample (pixel) intensity value in the output image I'
= 2 sdout 1 = 28 1 = 255;
(c) is the integer floor function.
(2) Create an 8-bit alpha channel L for I.
2. (Beginning of looping) In the raster-scan order, take a 2×3 block B with pixel values p1 through p6 from the intensity channel M.
Table 4.1 List of symbols used in Algorithms 3 and 4.
3. (Creation of authentication data) If pi = 0, set pi = 0; otherwise, set pi = 1, where i = 1, 2, …, 6.
4. (Creation of secret and coefficient values for secret sharing using Algorithm 1) Create two binary values m1 = p1p2p3; m2 = p4p5p6 and transform them into decimal numbers m1 and m2, respectively.
5. (Partial share generation) Set p, ci, and xi in Eq. (1) of Algorithm 1 described in Chapter 3.2 to be the following values:
(a) p = 11 (the smallest prime number larger than 7);
(b) d = m1, c1 = m2;
(c) x1 = 1, x2 = 2, …, x6 = 6;
and perform Algorithm 1 of Chapter 3.2 as a (2, 6)-threshold secret sharing scheme to generate six partial shares q1 through q6 using the following equations:
qi = F(xi) = (d + c1xi)mod p, (4) where i = 1, 2, …, 6.
6. (Mapping of partial share values) Add 244 to each of q1 through q6, resulting in the new values of q1 through q6, respectively, which fall in the nearly total transparency range of 244 through 254.
7. (Embedding of two partial shares at the current block) Take the block B in the alpha channel L which in position corresponds to B in the intensity channel M, select in the raster-scan order the values p1 and p2 of the first two pixels in B, and change them to be q1 and q2, respectively.
8. (Embedding the remaining partial shares at random positions) Perform the following steps to embed the remaining partial shares.
(1) Use the input key K to select randomly four pixels in L which are outside B′, unselected yet in this step, and not the first two pixels of any block, and let their values be p3 through p6.
(2) Set the values p3 through p6 respectively to be the four mapped partial shares q3 through q6 of B generated in Step 6 above.
9. (End of looping) If there exists any unprocessed block in the intensity channel M, then go to Step 2; otherwise, denote the resulting alpha channel L to be L and the resulting intensity channel M to be M'; and take M' and L′ together as the desired stego-image I.
After Step 1, the black and white pixels in the binary cover image are represented by values 0 and 255, respectively, in the resulting image. The sample depth scaling is achieved by using the linear equation (3) defined by the PNG standard [57] in which a binary image is regarded as an extreme case of a grayscale image with sample depth 1.
The possible values q1 through q6 yielded by the formulas in (4) above and inserted in the alpha channel L of image I are between 0 and 10 because the value of p used in (4) is 11. And after performing Step 6 of the above algorithm, the values q1
through q6 become q1 through q6, respectively, which fall in a small range of integers from 244 to 254. The embedding of these values within such a small range means that very similar values will appear everywhere in the alpha channels after Steps 7 and 8 are completed, resulting in a nearly uniformly transparent binary PNG image with an imperceptible effect, as mentioned previously. In addition, we use Fig. 4.1 to illustrate Steps 7 and 8 of Algorithm 1 where a core idea of the proposed method is presented:
two shares of the generated six are embedded within the current block and the other four embedded at four randomly-selected pixels outside the block, with each selected pixel not being either of the first two in any block.
Fig. 4.1 Illustration of embedding six shares created for a block two shares embedded within the current block and the other four in four randomly-selected pixels outside the block, with each selected pixel not being either of the first two in any block.