1. Introduction
Recently, as engineering technology has rapidly developed, the performance of computers has become increasingly stronger in terms of computing ability, storage capacity, etc. At the same time, the higher transmission capacity offered by wired/wireless networks allows users to share data anywhere, anytime. Obviously, digital images can be conveniently and transparently transmitted via the Internet; however, the Internet cannot always promise reliable and secure transmission, since it is openly accessible. In other words, it is easy for an intruder to intercept data transmitted over the Internet and then corrupt them, intentionally or non-intentionally. For example, attackers can insert vulgar words into a digital image in an imperceptible manner. Such malicious behavior presents a huge challenge to the security, usability, and integrity of personal information. Therefore, it is urgent to protect the integrity and verifiability of the digital image. Under this scenario, it is expected that a technique is provided to solve this problem.
Researchers have conducted a series of scientific studies on image authentication. Roughly, authentication methods can be classified into two categories: Digital signature-based methods [
1,
2,
3,
4] and digital watermark-based methods [
5,
6,
7,
8,
9,
10,
11,
12,
13,
14,
15,
16,
17,
18,
19,
20,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30,
31]. Generally, the digital signature-based method performs the encryption of the hashed results of the features of the image using a private key to form a unique signature, which will be used later for authentication. The process of authentication can be implemented by comparing the hashing result of the image under question and the original hashed version, which can be decrypted from the signature using an associated public key. By this way, the digital signature-based method performs well on image authentication because it is extremely sensitive to any kind of modification to the image, even if only one bit has been modified. Sometimes, the digital image may be allowed a little distortion in some applications, as long as the tamper regions can be localized precisely. Unfortunately, the digital signature-based method is not workable under this scenario.
The digital watermark-based method imperceptibly embeds relevant or irrelevant information called the authentication code (AC) into a digital image. The digital watermark-based method includes three categories: Fragile, semi-fragile, and robust watermarking. Of these, fragile watermarking embeds the authentication code into the cover image and makes it very sensitive to the modification of the image so that it can be used to verify its authenticity. In the authentication phase, receiver(s) can judge whether the image has been tampered with by comparing the extracted and recalculated authentication code. If they are the same, the received image has not been tampered with, and vice versa.
In recent decades, several forms of fragile watermarking-based image authentication have been proposed. An early fragile watermarking-based method was proposed by [
5], where the authentication code is generated from the parity check of the pixel value and embedded into the least significant bit (LSB) of the original image. A possibility of false judgement exists since the tampered 1 LSB could be the same as the computed parity check value of the tampered 7 most significant bits (MSBs). Other fragile watermarking methods based on cryptographic theory were presented by [
6,
7,
8]. Here, authentication codes are derived from a hashing function with various inputs, such as the image content, image index, block index, and pseudo-random number. These methods offer acceptable tampering detection performance. However, some of them could not withstand a vector quantization attack [
9] or the tampering coincidence problem [
10]. To overcome those problems, other fragile watermarking strategy-based block mappings were proposed by [
11,
12,
13,
14,
15,
16]. In these schemes, the original image is divided into non-overlapping blocks and the authentication code is generated by employing different kinds of technologies for each block, including the discrete cosine transform (DCT)-based method [
11,
12], the singular value decomposition (SVD)-based method [
13,
14], and the coding-based method [
15,
16]. Then, the authentication code of block is scrambled, mapped to the other block, and then inserted into it. The block mapping is one-to-one. Verification is conducted by comparing the extracted and recalculated authentication code. These schemes [
11,
12,
13,
14,
15] also adopt a multi-hierarchical tampering detection strategy to improve the tampering detection rate; for example, a first hierarchical tampering detection strategy is used to initially identify the tampered area and a second hierarchical tampering detection strategy serves as a remediation measure. As a consequence, these approaches have high precision in tampering detection. Hence, their schemes make it more probable that the tampering region can be restored with respect to satisfactory recovered image quality.
Image authentication technology is also widely used in the compression domain. The aim of image compression algorithms, such as joint photographic experts group (JPEG) [
17,
18], vector quantization (VQ) encoding [
19,
32], and absolute moment block truncation coding (AMBTC) [
33], is to reduce the size of an image to alleviate the burden of data communication. Of these, AMBTC is a variation of block truncation coding (BTC) [
34]. Considering the BTC family is simple and less computationally complex while AMBTC offers better image quality than BTC, many scholars have proposed image authentication schemes for either BTC- or AMBTC-compressed images in the last decade. In 2004, Tu and Hsu [
20] proposed a copyright protection scheme for digital images based on BTC. The authentication code, called the ownership share, is constructed by combining the determined authentication code with the binary image generated from the permuted host image using BTC. It is stored by a trusted third party for future authentication. On average, this scheme can extract the authentication code at around 92.13%. In 2009, Jiang et al. [
21] proposed a fragile watermarking method that inserts the authentication code into the host image according to the parity of the reconstruction levels of the BTC quantizer. In 2011, Yang and Lu [
22] proposed an image authentication method using BTC. Their authentication code is embedded into the block according to the odevity of the number of ‘1’s in the bitmap. If the authentication code bit is ‘1’, the number of ‘1’s in the bitmap is made odd by changing, at most, the three-pixel value of the block. If the authentication code bit is ‘0’, the number of ‘0’s in the bitmap is modified following a similar rule. In the tampering detection phase, the authentication code can be extracted according to the odevity of the number of ‘1’s in each block. In 2013, Hu et al. [
23] proposed a fragile watermarking method based on AMBTC. In their approach, the authentication code is derived using a pseudo-random generator. For each block, the corresponding bitmap is further divided into
k sub-bitmaps with the same size. Then, based on the idea of bit-flipping in [
35], each sub-bitmap is used to carry a one-bit authentication code by adjusting the parity of the number of ‘1’s to make it equal to that of the one-bit authentication code. Moreover, to achieve the better image quality, the most suitable flipping bit was determined using the least distortion criterion [
24]. Besides, two quantization levels are recomputed to further improve the quality of the compressed image block. The renewed AMBTC compression codes are further compressed using the linear prediction technique and the Huffman coding technique to cut down the storage cost of the AMBTC compression codes. Among these methods [
22,
23], weaknesses have been noted, in that changing the bitmap may further distort reconstructed image quality.
To solve this problem, Hu et al. [
25] in 2013 proposed another image authentication scheme for BTC-compressed images. For each image block, the AC was thus embedded into quantization levels by adjusting the
k-bit parity value of their difference to be the same as the
k-bit AC. In 2014, Nguyen et al. [
26] discovered the mean square error provided by scheme [
25] was increased because of adjustment of the quantization levels. Thus, a reference table was designed to carry the AC to achieve a better image quality. The
PSNR provided by their scheme is around 32.43 dB. In the same year, Lin et al. [
27] adopted the odevity of the bitmap of AMBTC compression codes to derive the authentication code and then inserted the authentication code into the quantization levels. To enhance the security of the authentication code, the embedding position of the authentication code would be selected with the aid of a pseudo-random sequence. For tampering detection, a two-hierarchy tampering detection strategy is employed to increase performance. In the end, 15 of 16 tampered blocks can be successfully detected when each block carries a four-bit authentication code. Compared to Hu et al. [
23], the method proposed by Lin et al. [
27] has better visual quality and good detection accuracy. In 2016, Li et al. [
28] proposed a novel image authentication scheme to verify the integrity of the AMBTC-compressed image. For each block, the authentication code is inserted into the quantization levels according to the determined reference matrix. The length of the to-be-inserted authentication code can be flexibly decided as the user requires. In this way, their true detection ratio is close to 93.75%, while the authentication code is designed as four bits. For these schemes [
25,
26,
27,
28], there is room for improvement in detecting the compression codes’ attack and collage attack.
To achieve this goal, in 2017, Lin et al. [
29] proposed a hybrid image authentication method to protect the integrity of the AMBTC-compressed image. To begin with, they considered the bitmap of the smooth area rather than the complex area as more suitable for parity-check coding [
36]. Hence, their scheme first classified the image’s blocks into two groups: Smooth and complex. For the smooth group, they forced the parity of the sub-bitmap to match that of the to-be-embedded authentication bit using the bit-flipping technique. For the complex block, on the other hand, the authentication code is embedded into the quantization levels according to a reference table. The different traversal sequence, decided by the number of ‘1’s in a bitmap, is chosen as the hiding sequence to carry the authentication code. In the tampering detection phase, a hybrid strategy is used to ensure superior localization accuracy along with better visual image quality. Experimental results confirm Lin et al.’s scheme outperforms previous schemes on the image quality of watermarked images and tamper detection. However, it is a little regrettable that the scheme [
29] did not completely solve the compression codes’ attack. Hence, in 2018, Hong et al. [
30] proposed an efficient image authentication method for AMBTC-compressed images using adaptive pixel pair matching. In their scheme, image blocks are classified into edge and non-edge blocks using a predetermined threshold. For each block, the bitmap and location information are inputted into a hashing function to generate the authentication code. The length of the authentication code ranges from one to four bits and can be flexibly determined, according to the type of image block. Then, the authentication code is embedded into the quantization levels using an adaptive reference table. Their scheme significantly reduces image distortion caused by embedding the authentication code and provides a lower false detection rate, averaging at 0.17%. However, their embedding strategy could break the natural relationship between high and low quantization levels; thus, it can only confirm the authenticity of AMBTC compression codes rather than being effective for AMBTC-compressed images. Additionally, their embedding strategy does not always guarantee the minimum distortion for an embedded edge block because a predetermined distance between two quantization levels must be maintained after authentication code embedding.
The same year, Hong et al. [
31] proposed two image authentication schemes, i.e., LSBP and MSBP, for tampering detection for AMBTC compression codes. For each block, their schemes can embed an (
a +
b)-bit authentication code generated from the bitmap and quantization levels’ MSBs. LSBP is a strategy that embeds the
a-bit authentication code into a high quantization level and the
b-bit authentication code into a low quantization level using LSBs replacement. Due to the rough embedding strategy, MSBP is suggested to minimize distortion using an MSBs perturbation technique. Their schemes have the ability to achieve a tampering detection rate of more than 93.75%. However, in a few cases, their scheme fails to authenticate the watermarked image due to having broken the natural correlation between quantization levels.
Table 1 gives summaries of those authentication schemes [
23,
25,
26,
27,
28,
29,
30,
31]. In short, some of them [
26,
28,
29,
30] need to store a reference matrix during the AC embedding and authentication phase, and some schemes [
23,
25,
26,
27,
28,
29] have a limitation against the compression codes’ attack or collage attack. Also, most existing methods [
23,
26,
27,
28,
29,
30] have the weakness that the upper bound of their first hierarchical tampering detection accuracy is around 93.75%. Hence, most of them employ a second hierarchical tampering detection strategy, such as neighborhood elimination, to improve the tampering detection rate. To overcome those problems, this paper proposes a novel image authentication scheme that protects the integrity of both AMBTC compression codes and AMBTC-compressed images. The proposed scheme does not need a reference matrix during AC embedding and extraction and can resist both the compression codes’ attack and collage attack. Our approach achieves a higher tampering detection rate in the first hierarchical tampering detection round without a remediation mechanism and sustains acceptable visual quality.
The rest of this paper is organized as follows: We briefly review related works in
Section 2, including AMBTC compression technology and matrix encoding; in
Section 3, we describe the proposed scheme in detail; in
Section 4, we perform a series of experiments to show the performance of our approach; finally, we provide conclusions in
Section 5.