Encryption domain reversible data hiding method based on multi-prediction and parameterized binary tree marking

Abstract

The invention discloses an encryption domain reversible data hiding method based on multi-prediction and parameterized binary tree marking, and the specific process is as follows: a content owner uses an MED + GAP multi-predictor to calculate the prediction error of each pixel, carries out the pixel-level encryption of an image, carries out the classification marking of the pixels through employing an efficient parameterized binary tree marking method and the errors, and carries out the hiding of the pixels. Generating an encrypted image containing mark information; the data concealer embeds the encrypted secret into the pixels of the embeddable category of the received image according to the encrypted pixel marking category; a legal receiver with a corresponding secret key can extract secret information in a lossless mode and reversibly recover original image content. Under a reversible data hiding mechanism of current user identity identification information embedding, an encryption domain reversible data hiding mechanism based on multi-prediction and efficient parameterization binary tree marking is provided, and the problems that in the data embedding process, the embedding amount of user identity identification information is low, and prediction precision is not high are solved.

Description

Technical Field

[0001] The present invention belongs to the technical field of reversible data hiding in the encrypted domain in the field of cloud storage security, and specifically relates to a reversible data hiding method in the encrypted domain based on multi-prediction and parametric binary tree marking. Background Art

[0002] In today's digital information age, with the increasing demand of users for data transmission, storage and sharing, cloud technology and cloud storage have become a very prominent technology [1]. Along with the rapid popularization of cloud computing and cloud storage, more and more multimedia data are uploaded to cloud servers [2]. However, cloud servers are third-party storage platforms, and the user privacy data stored may face potential security risks, and the confidentiality, integrity and authentication of data are constantly threatened [3]. For example, when storing sensitive data on cloud platforms such as Baidu Cloud and Alibaba Cloud, it is necessary to ensure that the sensitive data of users is not stolen by unauthorized persons. Cloud platform managers need to use specific technologies such as data hiding technology to effectively manage and classify user data on the premise of ensuring the invisibility of user data [4]. Data hiding is a technology that embeds secret data into a cover medium so that the intended user can extract the embedded data from the marked medium [5]. In some special cases, it is necessary to accurately restore the original carrier medium, so the reversible data hiding (RDH) technology [6-10] came into being. This technology embeds secret data into the carrier by slightly modifying the pixel values of the carrier image under the condition of perceptual invisibility.

[0003] With the development of digital products, the demand of users for privacy protection has increased rapidly, which has exacerbated the dependence on third-party platforms such as cloud storage platforms. The reversible data hiding in encrypted images (RDHEI) technology was proposed precisely to meet this application demand. While effectively protecting the privacy content of content owners, RDHEI embeds secret data into the protected content

[12] to achieve purposes such as tamper detection, copyright protection, and traitor tracing. According to the order of image encryption operations, existing RDHEI methods are mainly divided into two categories: vacating room after encryption (VRAE) [12, 14-24] and reserving room before encryption (RRBE) [25-29].

[0004] Zhang

[12] divides the encrypted image into non - overlapping pixel blocks, and only 1 bit of information is embedded in each block. Specifically, this scheme encrypts the original image using a pseudo - random stream key, and embeds the secret data by flipping the 3 least significant bits (LSB) of all pixels in the encrypted block. However, the embedding space generated by this embedding method is limited, and when the size of the image block is too small, there will be a certain bit error rate in the non - smooth area of the restored image, resulting in the inability to accurately restore the low - order bit data of the image. Liu and Pun

[17] proposed a redundant space transfer (RST) - based RDHEI scheme, which transfers the redundant space from the original image to the encrypted image, thus increasing the embedding capacity. Subsequently, Qin et al.

[18] proposed an RDHEI scheme based on RST and sparse block coding, which improved for different types of encrypted binary blocks and used sparse matrix coding to achieve the embedding of secret data. Yi and Zhou

[19] proposed a parametric binary tree labeling method and applied it to the VRAE scheme, with average embedding rates of 1.9656 bpp and 1.8808 bpp on the BOSSbase and BOW - 2 datasets respectively. Fu et al.

[20] proposed a Huffman coding method to compress the most significant bit (MSB) of the high - order plane of the embeddable block, and embed the auxiliary information, Huffman - coded codewords and secret data into the vacated space, thus achieving a higher embedding capacity.

[0005] The RRBE-based method can reserve space for information hiders or provide necessary information to information hiders by performing some preprocessing operations at the content owner's end before image encryption. In 2013, Ma

[25] reserved space using the least significant bits of the original pixels. Subsequently, Puteaux et al.

[26] predicted the MSB based on the correlation of local pixels, improving the image quality and embedding capacity. Wang

[28] calculated the prediction error between adjacent pixels and further compressed the coding length using the correlation between adjacent image pixels. Different from the VRAE method, the RRBE method utilizes the spatial correlation of the original image to reserve the embedding space before image encryption. Most embedding methods are difficult to losslessly restore the original image while efficiently embedding a large amount of information. Therefore, to improve the embedding capacity and ensure lossless restoration, the RRBE method is usually adopted. In 2019, Wu et al.

[11] proposed an improved parametric binary tree labeling RDHEI scheme based on Yi et al.

[19] . Different from Yi et al., this scheme defines the first row and the first column of the carrier image as the reference set, greatly increasing the number of embeddable pixels, and thus improving the resulting data payload. In 2023, Feng et al.

[30] proposed an RDHEI scheme based on an extended parametric binary tree labeling. This scheme divides the image into multiple blocks and uses parametric binary trees to label the divided blocks to achieve data hiding and extraction. Specifically, when hiding data, the data is embedded by adjusting the label value, and when extracting data, the hidden data is recovered by checking the label value. This method can achieve reversible data hiding and extraction without damaging the image quality.

[0006] However, the problem with Feng et al.

[30] is that this scheme does not improve the algorithm in terms of image prediction accuracy. It only uses a single predictor, the Median Edge Detection (MED), for prediction and does not fully consider the influence of other neighboring pixels, resulting in a large prediction error. A large error will lead to a reduction in the number of embedding bits carried by the pixel labels. Therefore, replacing the single predictor with a predictor with more accurate prediction accuracy can further improve the embedding performance. The methods of Yi et al.

[19] and Wu et al.

[11] only simply classify the prediction error into two categories, namely non-embeddable categories and embeddable categories, and do not further refine the processing of non-embeddable pixels, resulting in a relatively small improvement in the embedding capacity compared to past methods. Therefore, if we attempt to improve the image pixel classification and labeling strategy in traditional algorithms and further refine the processing of non-embeddable pixels, the embedding capacity performance can be improved.

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[0040]

[33] R. Kumar, D. Sharma, A. Dua, K. - H. Jung, A review of different prediction methods for reversible data hiding, Journal of Information Security and Applications 78(2023)103572. Summary of the Invention

[0041] In order to improve the problems in traditional algorithms, such as the overly simple processing of non - embeddable - type pixels, the excessive length of auxiliary information, and the low prediction accuracy caused by single prediction, the present invention proposes a reversible data hiding method in the encrypted domain based on multi - prediction and parametric binary tree labeling. In the technical solution, the content owner uses the MED + GAP multi - predictor to calculate the prediction error of each pixel, then performs pixel - level encryption on the image, and uses an efficient parametric binary tree labeling method and the error to classify and label the pixels, generating an encrypted image with labeling information; the data hider embeds the encrypted secret into the embeddable - type pixels of the received image according to the encrypted pixel labeling category; the legitimate receiver with the corresponding key can losslessly extract the secret information and reversibly restore the original image content.

[0042] The present invention adopts the following technical solutions to solve the above technical problems. It is an encryption domain reversible data hiding method based on multi-prediction and parametric binary tree marking. The multi-prediction process is as follows: The original image is divided into a reference pixel part and a non-reference pixel part. For the reference pixel part with fewer pixels, median edge detector (MED) prediction is adopted, and for the non-reference pixel part with more pixels, gradient adjustment predictor (GAP) is used for prediction. Through the combination of MED+GAP multi-prediction, the pixel features of the original image can be better utilized, thus achieving a more accurate prediction effect than single prediction. After completing the multi-prediction, an encrypted image is generated using image encryption technology. The parametric binary tree marking process is as follows: Based on the prediction error generated in the multi-prediction process, the prediction error is marked as embeddable category, self-recording category, and non-embeddable category using the parametric binary tree marking method. After marking, the marked error is used as a template to perform the same type of marking on the encrypted image, and the pixels marked as self-recording category do not generate additional auxiliary information, reducing the generation of auxiliary information, thereby increasing the embedding amount of the secret information. After receiving the encrypted image with marked information, the data hider can reversibly embed the encrypted secret into the pixels of the embeddable category according to the marked category.

[0043] Further defined, the specific process of multi-prediction is as follows:

[0044] Step S1: Divide the plaintext image of size M×N into a reference pixel part and a non-reference pixel part;

[0045] Step S2: Perform median edge prediction (MED) on each pixel in the reference pixel part:

[0046]

[0047] Among them, pixel x and P(x) represent the currently predicted pixel and the prediction result respectively, and pixels B, A, and C represent 3 pixels adjacent to pixel x;

[0048] Step S3: Perform gradient adjustment prediction (GAP) on each pixel in the non-reference pixel part:

[0049]

[0050] Among them, Y1, Y2, and Y3 represent 3 thresholds, g h and g v represent the horizontal gradient and the vertical gradient respectively, and pixels L, LL, LT, T, RT, TT, and RTT represent 7 pixels adjacent to pixel x respectively;

[0051] Step S4: After generating the prediction image of the plaintext image, generate the prediction error image e:

[0052] e = x - p x (4)

[0053] Further defined, the specific process of image encryption is as follows:

[0054] Step S1: After obtaining all the prediction error results of the original image, use Equation (5) to convert each pixel in the original image into an 8-bit binary sequence:

[0055]

[0056] where k is the bit corresponding to the corresponding binary sequence;

[0057] Step S2: Determine the key K e , and then generate a pseudo-random matrix R of the same size as the original image through the key K e . Next, convert the current pixel x(i, j) and its corresponding pseudo-random number r(i, j) into 8-bit binary sequences according to Equation (5), and perform a bitwise exclusive OR (XOR) encryption operation according to Equation (6) to obtain the encrypted 8-bit binary sequence:

[0058]

[0059] where is the encrypted 8-bit binary sequence, is the bitwise exclusive OR operation;

[0060] Step S3: Calculate the encrypted pixel x e (i, j) through Equation (7), thereby generating the encrypted image I e :

[0061]

[0062] Further defined, the specific process of parametric binary tree marking is as follows:

[0063] Pixel marking divides the encrypted image pixels into two parts according to the prediction error of the image pixels, namely the reference pixel part and the non-reference pixel part. Select a pixel at a fixed position from the reference pixels as a special pixel to record the values of the marking parameters α and γ. The parameter α is used to mark the pixels in the non-reference pixels that are embeddable categories, and its value serves as the marking bit; the parameter γ is used to record the pixels in the non-reference pixels that are non-embeddable categories, and uses continuous γ-bit all 0s for recording. Record the original value of the selected special pixel into the auxiliary information, convert the parameters α and γ into two 4-bit binary sequences respectively to replace the value of the special pixel. For the non-reference pixel part, according to the prediction error value of the pixel and the values of the marking parameters α and γ, mark the non-reference pixels as embeddable category pixels P e , self-recording category pixels P r and non-embeddable category pixels Pne ;

[0064] Suppose n e represents the total number of embeddable categories, and n r represents the total number of self-recording pixel categories. According to the marking parameters α and γ, equations (8) and (9) respectively define the calculation processes of n e and n r as follows:

[0065]

[0066] Scan each pixel of the encrypted image in order from top to bottom and from left to right, and classify the encrypted pixels according to the prediction error value of the pixels. The classification rule is defined as equation (10):

[0067]

[0068] Compared with the prior art, the present invention has the following advantages and beneficial effects: Under the reversible data hiding mechanism for embedding current user identity information, the present invention proposes a reversible data hiding mechanism in the encryption domain based on multi-prediction and efficient parameterized binary tree marking, which solves the problems of low embedding amount of user identity information and low prediction accuracy in the data embedding process. Description of the Drawings

[0069] Figure 1 is the technical solution diagram.

[0070] Figure 2 is the parameterized binary tree marking distribution diagram.

[0071] Figure 3 is the parameterized binary tree pixel marking result based on the marking parameters sum.

[0072] Figure 4 is the schematic diagram of pixel marking and encryption. Figure 4 In (a) is the original image. Figure 4 In (b) is the predicted image. Figure 4 In (c) is the prediction error image. Figure 4 In (d) is the encrypted image. Figure 4 In (e) is the marked prediction error image. Figure 4 In (f) is the encrypted image with marks.

[0073] Figure 5 is an example of the generation process of the encrypted image with marks. Figure 5 In (a) is the predicted image with marks. Figure 5 In (b) is the encrypted image. Figure 5 In (c) is the encrypted image of the category identifier. Figure 5 In (d) is the encrypted image with marks.

[0074] Figure 6 It is an example of the process of embedding secret information. Figure 6 In (a), it is the encrypted image with marks. Figure 6 In (b), it is the encrypted image with secret information.

[0075] Figure 7 It is the result of a simulation experiment with Lena as an example. Figure 7 In (a), it is the original Lena image. Figure 7 In (b), it is the encrypted Lena image. Figure 7 In (c), it is the encrypted Lena image with marks. Figure 7 In (d), it is the encrypted Lena image with secret information. Figure 7 In (e), it is the restored Lena image.

[0076] Figure 8 It is the histogram distribution result with Lena as an example. Figure 8 In (a), it is the histogram of the original Lena image. Figure 8 In (b), it is the histogram of the encrypted Lena image. Figure 8 In (c), it is the histogram of the encrypted Lena image with marks. Figure 8 In (d), it is the histogram of the encrypted Lena image with secret information. Figure 8 In (e), it is the histogram of the restored Lena image.

[0077] Figure 9 It is the embedding rate result of different prediction methods when the marking parameter is [parameter value].

[0078] Figure 10 It is the embedding rate result of introducing the self - recording category and not introducing the self - recording category.

[0079] Figure 11 It is the embedding rate result of using different predictors MED, GED, and GAP.

[0080] Figure 12 It is the embedding rate result of the single predictor GAP and the multi - predictor MED + GAP.

[0081] Figure 13 It is the embedding rate result on the public datasets BOSSbase, BOWS - 2, and UCID. Detailed implementation manners

[0082] The above content of the present invention will be further described in detail through the following embodiments. However, it should not be understood that the scope of the above - mentioned subject matter of the present invention is limited to the following embodiments. Any technology implemented based on the above content of the present invention belongs to the scope of the present invention.

[0083] Embodiment

[0084] Aiming at the problems of overly simple processing of pixels of non-embeddable categories and too long auxiliary information in traditional algorithms, as well as the problem of low prediction accuracy caused by single prediction, the present invention proposes a reversible data hiding method in the encrypted domain based on multi-prediction and efficient parameterized binary tree marking. The specific technical solution diagram of the present invention is as shown in Figure 1 . In the technical solution, the content owner uses the MED+GAP multi-predictor to calculate the prediction error of each pixel, then encrypts the image, and classifies the error and encrypted pixels using an efficient parameterized binary tree marking method to generate an encrypted image containing marking information. The data hider embeds the encrypted secret into the pixels of the embeddable category of the received image according to the marking category of the encrypted pixels. When the legitimate receiver has the corresponding key, the secret information can be losslessly extracted and the original image content can be reversibly restored. Compared with existing mechanisms: (1) The present invention uses a multi-predictor to predict the original pixels, fully utilizes the pixel correlation between adjacent pixels to improve the accuracy of prediction, can obtain more embeddable bits of non-reference pixels, thus freeing up more embeddable space; (2) The present invention introduces the concept of self-recording pixels, enabling pixels of non-embeddable categories to directly record the replaced bit positions in a self-recording manner, improving the problem of overly simple processing of pixels of non-embeddable categories and too long auxiliary information in traditional algorithms. The introduction of self-recording category pixels reduces the length of auxiliary information and increases the embedding capacity.

[0085] Value:

[0086] With the increasing demand of users for data transmission, storage and sharing, cloud technology and cloud storage have become a very valuable technology. Along with the rapid popularization of cloud computing and cloud storage, more and more multimedia data are uploaded to the cloud server side. However, the cloud server belongs to a third-party storage platform, and the user privacy data stored may face potential security risks, and the confidentiality, integrity and authentication of the data are continuously affected. For example, when storing sensitive data on cloud platforms such as Baidu Cloud and Alibaba Cloud, it is necessary to ensure that the sensitive data of users is not stolen by unauthorized persons. Cloud platform managers need to use specific technologies such as data hiding to effectively manage and classify user data on the premise of ensuring the invisibility of user data. Because the value of the present invention lies in solving the security of privacy data stored in third-party platforms such as cloud storage, reducing the storage and management overhead of cloud managers, and improving the security of user data.

[0087] Significance:

[0088] The encrypted domain data hiding technology is a key technology for managing and protecting users' private data in cloud storage platforms. How to embed more identity information to facilitate the efficient management of massive user data by cloud managers is a key issue that urgently needs to be solved. The significance of this invention lies in that by introducing the multi-predictor technology, the prediction accuracy of image pixels is greatly improved, which helps cloud managers embed more user identity information. On this basis, by using the efficient parametric binary tree labeling technology, while ensuring the embedding of more identity information, the reversibility of information embedding and extraction is ensured. After decrypting the image content after information extraction, this invention can losslessly restore the original image information, meeting the users' repeated use of their stored private data.

[0089] Innovation points:

[0090] Under the current reversible data hiding mechanism for embedding user identity information, a reversible data hiding mechanism in the encrypted domain based on multi-prediction and efficient parametric binary tree labeling is proposed, which solves the problems such as low embedding amount of user identity information and low prediction accuracy in the data embedding process.

[0091] (1) A multi-predictor method is proposed to generate prediction error values, further improving the information embedding capacity. The combination of different predictors to predict the original pixels can make full use of the correlation between adjacent pixels to improve the prediction accuracy, obtain more embeddable bits for non-reference pixels, and thus free up more embeddable space.

[0092] (2) The concept of self-recording pixels is introduced, enabling pixels of non-embeddable categories to directly record the replaced bit positions in a self-recording manner, thus improving the problems in traditional algorithms such as overly simple processing of non-embeddable category pixels and too long auxiliary information. The introduction of self-recording category pixels reduces the length of the auxiliary information, thereby increasing the embedding capacity.

[0093] (3) This invention conducts comprehensive experiments including single prediction / multi-prediction and the introduction of self-recording category pixels / non-self-recording category pixels to analyze and prove the effectiveness and practicality of this invention.

[0094] 1. Efficient parametric binary tree labeling

[0095] Yi and Zhou

[19] proposed a pioneering parametric binary tree labeling (PBTL) method. The PBTL method classifies pixels into three categories: reference pixels, non-embeddable part G NE and embeddable part G E . After classification, according to the PBTL rules for G NE and G EMake a mark. Scheme

[19] uses marking parameters α and β to record G NE and G E 's encoding rules. Figure 2 Shows a full binary tree based on PBTL and its binary encoding distribution. In Figure 2 , the blue part represents an example of the non-embeddable group G NE , and the parameter β represents the bit length.

[0096] Different from Scheme

[19] , the present invention proposes a new and efficient parameterized binary tree marking scheme. Compared with the pixel marking method of Yi and Zhou

[19] , the present invention uses marking parameters α and γ to divide pixels into three different categories of pixels, including the non-embeddable category G NE , the self-recording category G R and the embeddable category G E . To better explain the pixel classification method of the present invention, Figure 3 Shows the pixel marking results with parameters α = 1 to 7 and γ = 2. In Figure 3 , the blue dotted line part represents the non-embeddable category G NE , the green dotted line part represents the self-recording category G R , and the yellow dotted line part represents the embeddable category G E . By introducing the self-recording category, all pixels in the self-recording category do not generate auxiliary information, and these pixels can self-record the marking bits, thereby reducing the generation of auxiliary information and increasing the embedding amount of identity identification information.

[0097] 2. MED + GAP multi-prediction

[0098] This part will explain why the present invention is committed to researching MED + GAP multi-prediction as a predictor. In the MED predictor, only 3 adjacent pixels are used to predict the target pixel, and the correlation between adjacent pixels is not fully utilized. The GAP predictor is based on 7 adjacent pixels and 3 thresholds for prediction, and has been proven to have better prediction performance than the MED predictor. However, when using the GAP predictor, only sufficient non-reference pixels can be predicted. If the number of pixels in the reference pixel part is increased, the number of pixels in the non-reference pixel part will decrease, and thus the embedding capacity will decrease. In view of this, the present invention continues to only use the original reference pixel part, uses the MED predictor to predict the target pixel lacking sufficient adjacent pixels, and uses the GAP predictor to predict the remaining target pixels. The MED + GAP predictor can make full use of the features between pixels and improve the prediction accuracy.

[0099] The MED + GAP multi-predictor is further defined as:

[0100] Step S1: Divide the plaintext image of size M×N into a reference pixel part and a non-reference pixel part;

[0101] Step S2: Perform Median Edge Detection (MED) on each pixel in the reference pixel part:

[0102]

[0103] where pixel x and P(x) represent the currently predicted pixel and the prediction result respectively, and pixels B, A, and C represent three pixels adjacent to pixel x;

[0104] Step S3: Perform Gradient Adjustment Prediction (GAP) on each pixel in the non-reference pixel part:

[0105]

[0106] where Y1, Y2, and Y3 represent three thresholds, g h and g v represent the horizontal gradient and the vertical gradient respectively, and pixels L, LL, LT, T, RT, TT, and RTT represent seven pixels adjacent to pixel x;

[0107] Step S4: After generating the predicted image of the plaintext image, generate the prediction error image e:

[0108] e = x - p x (4)

[0109] 3. Image Encryption

[0110] The image encryption process is as follows:

[0111] Step S1: After obtaining all the prediction errors of the original image, convert each pixel in the original image into an 8-bit binary sequence using Equation (5):

[0112]

[0113] where k is the bit corresponding to the binary sequence.

[0114] Step S2: Determine the key K e , and then generate a pseudo-random matrix R of the same size as the original image through the key K e . Next, convert the current pixel x(i,j) and its corresponding r(i,j) into 8-bit binary sequences according to Equation (5). Then perform an exclusive OR (XOR) encryption operation according to Equation (6) to obtain the encrypted 8-bit binary sequence.

[0115]

[0116] where, is the 8-bit binary sequence after encryption, is the bitwise exclusive OR operation.

[0117] Step S3: The encrypted pixel x e (i,j) can be calculated through Equation (7), so as to obtain the encrypted image I e .

[0118]

[0119] 4. Image Pixel Marking

[0120] The image pixel marking divides the encrypted image pixels into two parts according to the prediction error of the image pixels, namely the reference pixel part and the non-reference pixel part. From the reference pixels, a pixel at a fixed position is selected as a special pixel to record the values of the marking parameters α and γ. The parameter α is used to mark the number of bits used for the pixels of the embeddable category in the non-reference pixels, and the parameter γ is the number of consecutive 0s used for the pixels of the non-embeddable category in the non-reference pixels. The original value of the selected special pixel is recorded in the auxiliary information, and the parameters α and γ are respectively converted into 4-bit binary numbers to replace the value of the special pixel. For the non-reference pixel part, according to the prediction error value of the pixel and the values of the marking parameters α and γ, the non-reference pixels are marked as pixels P e of the embeddable category, pixels P r of the self-recording category, and pixels P ne of the non-embeddable category.

[0121] Suppose n e represents the embeddable pixel category, and n r represents the self-recording pixel category. According to the marking parameters α and γ, Equations (8) and (9) are defined to calculate n e and n r as follows:

[0122]

[0123] Scan each pixel of the encrypted image in sequence from top to bottom and from left to right, and classify the encrypted pixels according to the prediction error value of the pixel. The classification result is shown in Equation (9):

[0124]

[0125] To more clearly show the execution process of the present invention, Figure 4 a schematic diagram of pixel marking and encryption is given. In Figure 4 , the yellow, green, and blue text colors respectively represent the embeddable, self-recording, and non-embeddable categories, and the gray background represents the reference pixels. Figure 4 (a) shows the input image of size 5×5,Figure 4 Figure (b) shows the prediction results generated using the MED+GAP predictor. Calculate Figure 4 the difference between the original content in Figure (a) and its prediction results Figure 4 in Figure (b) to generate Figure 4 the prediction error image shown in Figure (c), where the reference pixels remain unchanged during this process. According to the classification division defined in Equation (10), Figure 4 the prediction error image shown in Figure (c) is divided into three categories: embeddable, self-recording, and non-embeddable. Use the specified key to Figure 4 encrypt the original content in Figure (a) to obtain Figure 4 the encrypted version shown in Figure (d). Depending on the marked category of the prediction error image, further mark the encrypted version to finally obtain Figure 4 the marked encrypted image shown in Figure (f).

[0126] In addition,[[]] Figure 5 a detailed example is provided to illustrate how to generate a marked encrypted image using the marking parameters α = 4 and γ = 3. As Figure 5 known, the initial value of the special pixel in the encrypted image is 18. Embed the binary representation of α ('0100', corresponding to decimal 4) and the binary representation of γ ('0011', corresponding to decimal 3) into the special pixel 18 to obtain a modified value of 67. For the pixel 123 in the non-embeddable category, invert its binary form from '01111011' to '11011110'. Set the first γ bits to '000' and keep the remaining bits unchanged to get '00011110'. Then, invert the bits again to '01111000' to obtain a new decimal value of 120. For the pixel 181 in the self-recording category, first invert its binary from '10110101' to '10101101', then mark the first γ bits as '001', and the remaining bits are replaced with 1 sign bit ('1') and 4 self-recording bits ('0101'). The sign bit represents the sign of the calculated difference ('1' for positive and '0' for negative). This process results in the marked bit '0011001', which is inverted again to '10101100' through a bitwise inversion operation to obtain the marked encrypted pixel with a decimal value of 17. Similarly, for the pixel 63 in the embeddable category, convert its binary form from '00111111' to '1111100'. Mark the first α bits (4 bits) as '1100' and keep the remaining bits as bits to be embedded to get the tagged binary bit '11001100', which is converted to '0011001' through a bitwise inversion operation to obtain the marked encrypted pixel with a decimal value of 51.

[0127] 5. Secret Information Embedding

[0128] In the secret information embedding stage, the data hider first encrypts the data to be hidden using the held data hiding key to obtain the encrypted hidden data. Then, the obtained data is embedded into the space reserved by the embeddable category of pixels in the received image. Specifically, the data hider first checks the received pixels in sequence, converts the decimal value of the pixel to binary bits, and performs a bitwise negation operation on the generated binary bits. According to the marked category, the target pixel may be an embeddable, self-recording, or non-embeddable pixel. If the target pixel type is an embeddable category, the (8-α) bits of the encrypted hidden data are embedded into the reserved space, and the remaining bits remain unchanged. For the other two categories of pixels, they remain unchanged in this stage. After all embeddable pixels have been checked, the data hider will determine whether the hidden data has been fully embedded.

[0129] Figure 9 Shows a detailed example of the data embedding process using the marking parameters α = 4 and γ = 3. The yellow dashed box highlights the embedding process of the embeddable category of pixels with an initial value of 195. From Figure 9 it can be found that the example image only contains one special pixel and one non-embeddable category of pixels. The original binary bits '0010010' of the special pixel and the replacement bits '110' together form the auxiliary information '0001001110' with a length of 11 bits. These bits together with the secret data form the hidden data. The data hider encrypts the hidden data to obtain the encrypted hidden data. Subsequently, the obtained data is embedded into the embeddable category of pixels. For example, for the embeddable category of pixels with an initial value of 195, first convert the decimal value to binary representation, i.e., '11000011'. Then, reverse this binary sequence (although it remains unchanged in this case) and embed the bits '1011' into the remaining (8-α) bits.

[0130] 6 Data extraction and image restoration

[0131] In the data extraction and image restoration stages, the legitimate receiver retrieves the embedded data and restores the original image based on the key it holds. These operations are carried out in a separable and error - free manner. Before that, two marker parameters are read from special pixels, and these two parameters provide the extraction and restoration rules. Specifically, before processing each pixel, we invert the binary bits of the current pixel through a bitwise negation operation. If the first γ bits of the binary of a pixel are all zero, the pixel is recorded as a non - embeddable category, calculate the replacement bits and skip it. If the first α bits of a pixel are marker bits, the pixel is recorded as an embeddable category, obtain its last (8 - α) bits as the extracted data, and save its prediction error according to the first α markers. Then, the extracted data is the encrypted hidden data. Next, the hidden data is obtained by decrypting the extracted data.

[0132] To reconstruct the original image, the receiver first restores the special pixels to the encrypted state according to the auxiliary information, and restores the non - embeddable pixels to their corresponding encrypted states. Then, a bit - by - bit exclusive - OR operation is performed on the received image, where the reference pixels, special pixels, and non - embeddable pixels can be decrypted losslessly to generate a partially decrypted image. Based on the decrypted reference pixels, the receiver uses the MED+GAP predictor to calculate the predicted image and uses the generated prediction errors to restore the remaining pixels. Specifically, for embeddable pixels, the prediction error can be determined by checking their marker bits, while for self - recorded pixels, the prediction can be obtained by analyzing the recorded bits.

[0133] 7. Experimental Results and Analysis

[0134] 7.1 Effectiveness Analysis

[0135] To verify the effectiveness of the present invention, taking Lena as an example, a simulation test experiment is carried out on the MATLAB platform to obtain Figure 7 the simulation results at different stages as shown. Figure 7 In (a) is the original Lena image. After performing the image encryption operation, the encrypted image shown in Figure 7 (b) is obtained. According to the coding rules, the encrypted image is marked with different types of pixels. Figure 7 (c) shows the result of the marked Lena encrypted image. During the marking process, the auxiliary information is generated from the initial bits and replacement bits of the selected pixels. After embedding these bits together with the processed secret information into Figure 7 the encrypted content shown in (c), the Lena encrypted image with secret information as shown in Figure 7 (d) is generated. After the image restoration operation, the restored image content shown in Figure 7 (e) is generated, which is the same as Figure 7is exactly the same as the original image shown in (a), indicating that there is no loss in restoring the image content in the present invention.

[0136] 7.2 Histogram Analysis

[0137] The statistical characteristics of the histogram are an important indicator reflecting the anti - attack ability of the algorithm. In this subsection, the test image Lena is used to measure the performance results of the histogram analysis of the present invention. Figure 8 respectively show the histogram distribution results of the original image Lena, its encrypted image, the encrypted image with marks, and the encrypted image with secret information. As can be seen from Figure 8 (a), the pixel distribution of the original image Lena is relatively concentrated, so it is easy to distinguish its features from other images. After the encryption operation, Figure 8 the pixel distribution of the encrypted image shown in (b) becomes uniform, and no statistical feature information related to the original image can be observed by the naked eye from Figure 8 (b). In addition, after embedding the marked data, Figure 8 there is no obvious difference in the pixel distribution between the encrypted content with marks shown in (c) and the encrypted content with secret information. Therefore, without the corresponding key, it is impossible for the naked eye to detect whether there is additional secret in the encrypted image with marks or the encrypted image with secret information. Based on the above discussion, the present invention has a certain robustness against statistical attacks.

[0138] 7.3 Prediction Performance

[0139] The present invention first discusses the prediction performance, which is an important factor affecting the embedding performance of the present invention. Generally speaking, there are mainly two ways to expand the net embedding capacity, that is, increasing the total capacity or reducing the generation length of auxiliary bits. The predictor used in the present invention affects the embedding capacity in two aspects. On the one hand, a suitable predictor can make the prediction result closer to the true value, thus significantly increasing the total capacity. On the other hand, more accurate prediction can generate fewer marked bits, thus reducing the number of auxiliary bits and further expanding the net embedding capacity. For the above reasons, the present invention attempts the following solutions to expand the total capacity. One is to select a suitable prediction method to make full use of the features of the original image, and the other is to introduce self - recording pixels to minimize the generation of auxiliary information. Traditional methods use the MED predictor to predict the reference pixels, while the present invention attempts to use different predictor methods and experimentally compares and analyzes the performance of various predictor methods. Figure 9 shows the embedding rates of different prediction methods.

[0140] 7.4 Embedding Capacity

[0141] The embedding capacity refers to the total number of bits that can be embedded into the image pixels and can also be evaluated using the embedding rate. The embedding rate usually represents the number of bits that can be embedded in each pixel and is measured in bits per pixel (bpp). In this subsection, we set different parameters α and γ to analyze the embedding rate performance. Tables 1 to 3 list the maximum embedding rate results of four different test images under the parameters γ = 3 to 5 and α = 1 to 7. In the tables, the symbol ' / ' indicates that the secret information cannot be embedded. In such cases, it means that the length of the auxiliary information exceeds the reserved embedding space and the secret information cannot be embedded any further. As can be seen from the tables, when the parameter α is set to a smaller value, such as α = 1 or α = 2, the present invention cannot embed a large amount of secret data. In addition, we can also find that the texture complexity of the input image has an important impact on the embedding performance. The pixels in relatively smooth images have a higher correlation with each other, resulting in more embeddable pixel categories and thus a higher embedding rate. For example, when the parameters are set to α = 4 and γ = 3, the maximum embedding rate of the image Jetplane reaches 3.3195 bpp. Therefore, it is crucial to select reasonable parameters for images with different characteristics to achieve better embedding effects.

[0142] Table 1 Embedding rate results (bpp) with parameters set to γ = 3 and α = 1 to 7

[0143]

[0144] Table 2 Embedding rate results (bpp) with parameters set to γ = 4 and α = 1 to 7

[0145]

[0146] Table 3 Embedding rate results (bpp) with parameters set to γ = 5 and α = 1 to 7

[0147]

[0148] 7.4 Comparative Analysis

[0149] In the present invention, different experiments are simulated with and without introducing the self - recording category to test the embedding rate comparison results of different predictors. Through comparative analysis, we gradually explain the necessity of selecting the MED + GAP multi - predictor for prediction and introducing the self - recording category. First, Figure 10 shows the embedding rate results of predicting with a single predictor MED. In the figure, the blue and red bars respectively show the embedding rate results with and without introducing the self - recording category. According to Figure 10It can be found that in the case of introducing the self - recording category, the simulation experiment obtained higher embedding rate performance. Therefore, self - recording pixels can reduce the auxiliary bits generated during the marking process, thereby improving the overall embedding capacity.

[0150] Based on the above discussion, in the following experiment, the embedding rate performance under different conditions was simulated by introducing the self - recording category. In this subsection, the present invention simulated and tested the performance of different single predictors. Figure 11 The embedding performance results obtained by using the MED, GED, and GAP predictors for prediction respectively are shown. In Figure 11 , the blue, red, and yellow bar charts represent the embedding rate results obtained by using the single predictors MED, GED, and GAP respectively. It can be Figure 11 found that when using different predictors, the embedding rates are slightly different, and the embedding rate obtained by the GAP predictor is the highest. The reason is that the GAP predictor utilizes more adjacent pixels to predict the target pixel. Using the GAP predictor can capture more local features around the target pixel, making the prediction result more accurate. According to the Figure 11 results in, it can be concluded that using the GAP predictor can obtain a higher embedding rate.

[0151] To analyze the prediction performance more deeply, the present invention tested the better GAP predictor and the MED + GAP multi - predictor in the single predictors, and calculated the embedding rates of different images under the two types of predictors. The experimental results are as Figure 12 shown. In Figure 12 , the blue and red bar charts represent the embedding rate results of the GAP predictor and the MED + GAP multi - predictor respectively. It can be seen from the figure that the performance of the MED + GAP multi - predictor is significantly better than that of the single GAP predictor, which indicates that the MED predictor is used to predict the boundary non - reference, and on this basis, the GAP predictor is used to predict the remaining non - reference pixels. The combination of the two can ensure more accurate prediction. The performance improvement of the MED + GAP multi - predictor can be attributed to the fact that this predictor can more effectively capture the features of the boundary and internal pixels. By combining the advantages of the two types of predictors, a higher embedding rate is achieved.

[0152] Without loss of generality, the present invention conducted general tests on the conventional datasets BOSSbase, BOWS - 2, and UCID, and compared them with other recently advanced methods. Figure 13 The comparison of the average embedding rates between the present invention and four related advanced methods (PBTL, IPBTL, Extend - PBTL, and EPBTL) is shown. In Figure 13 , the blue, red, and green bar charts represent the average embedding rates of the BOSSBase, BOWS - 2, and UCID datasets respectively. From Figure 13As can be seen, the average embedding rate of the present invention on BOSSbase is 3.177 bpp, on BOWS-2 is 3.08 bpp, and on UCID is 2.722 bpp. These results exceed those of the PBTL, IPBTL, Extend-PBTL, and BTL methods. These experimental results indicate that the proposed method exhibits better embedding performance under various image datasets.

[0153] The above embodiments describe the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited by the above embodiments. What is described in the above embodiments and the specification only illustrates the principles of the present invention. Without departing from the scope of the principles of the present invention, the present invention will have various changes and improvements, and these changes and improvements all fall within the scope of protection of the present invention.

Claims

1. Reversible data hiding method in the encrypted domain based on multi-prediction and parametric binary tree labeling, characterized in that The multi-prediction process is as follows: The original image is divided into a reference pixel part and a non-reference pixel part. For the reference pixel part with fewer pixels, median edge detector (MED) prediction is adopted, and for the non-reference pixel part with more pixels, gradient adjustment predictor (GAP) is used for prediction. Through the combination of MED + GAP multi-prediction, the pixel features of the original image can be better utilized, thus achieving a more accurate prediction effect than single prediction. After multi-prediction, an encrypted image is generated using image encryption technology. The parametric binary tree marking process is as follows: Based on the prediction error generated in the multi-prediction process, the parametric binary tree marking method is used to mark the prediction error as embeddable category, self-recording category, and non-embeddable category. After marking, the marked error is used as a template to perform the same type of marking on the encrypted image, and the pixels marked as self-recording category do not generate additional auxiliary information, reducing the generation of auxiliary information and thus increasing the embedding amount of the secret information. After receiving the encrypted image containing the marked information, the data hider can reversibly embed the encrypted secret into the pixels of the embeddable category according to the marked category.

2. The reversible data hiding method in the encrypted domain based on multi-prediction and parametric binary tree labeling according to claim 1, wherein The specific multi-prediction process is as follows: Step S1: Divide the plaintext image of size M×N into a reference pixel part and a non-reference pixel part. Step S2: Perform median edge prediction (MED) on each pixel in the reference pixel part: Among them, pixel x and P(x) represent the currently predicted pixel and the prediction result respectively, and pixels B, A, and C represent the 3 pixels adjacent to pixel x. Step S3: Perform gradient adjustment prediction (GAP) on each pixel in the non-reference pixel part. where Y1, Y2, and Y3 represent three thresholds, and g h and g v represent the horizontal gradient and the vertical gradient respectively, and pixels L, LL, LT, T, RT, TT, and RTT represent seven adjacent pixels of pixel x respectively; Step S4: After generating the prediction image of the plaintext image, generate the prediction error image e. e = x - p x (4).

3. The reversible data hiding method in the encrypted domain based on multi-prediction and parametric binary tree labeling according to claim 1, characterized in that The specific image encryption process is as follows: Step S1: After obtaining all the prediction error results of the original image, use Equation (5) to convert each pixel in the original image into an 8-bit binary sequence: Among them, k is the bit corresponding to the corresponding binary sequence. Step S2: Determine the key K e , and then generate a pseudo-random matrix R of the same size as the original image through the key K e . Next, convert the current pixel x(i, j) and its corresponding pseudo-random number r(i, j) into an 8-bit binary sequence according to Equation (5), and perform a bitwise exclusive OR (XOR) encryption operation according to Equation (6) to obtain the encrypted 8-bit binary sequence: Among them is an 8-bit binary sequence after encryption, is a bitwise exclusive OR operation; Step S3: Calculate the encrypted pixel x e (i,j) through Equation (7), thereby generating the encrypted image Ie:

4. The reversible data hiding method in the encrypted domain based on multi-prediction and parametric binary tree labeling according to claim 1, characterized in that The specific parametric binary tree marking process is as follows: The pixel marking divides the encrypted image pixels into two parts according to the prediction error of the image pixels, namely the reference pixel part and the non-reference pixel part. A pixel at a fixed position is selected from the reference pixels as a special pixel to record the values of the marking parameters α and γ. The parameter α is used to mark the pixels in the non-reference pixels that are of the embeddable category, and its value serves as a marking bit. The parameter γ is used to record the pixels in the non-reference pixels that are of the non-embeddable category, and is recorded as a continuous γ-bit all-0. The original value of the selected special pixel is recorded in the auxiliary information. The parameters α and γ are respectively converted into two 4-bit binary sequences to replace the value of the special pixel. For the non-reference pixel part, according to the prediction error value of the pixel and the values of the marking parameters α and γ, the non-reference pixels are marked as embeddable category pixels P e , self-recording category pixels P r and non-embeddable category pixels P ne ; Assume n e represents the total number of embeddable categories, and n r represents the total number of self-recording pixel categories. According to the marking parameters α and γ, equations (8) and (9) respectively define the calculation processes of n e and n r as follows: Scan each pixel of the encrypted image in sequence from top to bottom and from left to right, classify the encrypted pixels according to the prediction error value of the pixel, and the classification rule is defined as Equation (10):

Images