A strong robust multi level database image watermark embedding scheme based on the Chinese remainder theorem

Abstract

Due to the fact that most existing digital watermarking schemes can only add watermark information once, repeated additions will overwrite the original watermark information, making it impossible to achieve multi-level traceability of data. In response to the above issues, this paper proposes a multi-level database image watermark embedding scheme (MIWC) based on the Chinese remainder theorem. Taking image watermarks as carriers, MIWC preprocesses images using methods such as Haar wavelet transform and Bloom filter to form a pixel. It then performs secret segmentation on watermark information in accordance with the properties of the Chinese Remainder Theorem, enabling hierarchical and item-by-item addition of the watermark information. Furthermore, it records and traces the entire data flow chain. Functional analysis demonstrates that MIWC possesses the multi-level watermark embedding capability that existing schemes lack, thus holding high practical application value. Experimental results indicate that MIWC is reversible, with both watermark embedding and extraction exhibiting high efficiency. Even with the embedding of multi-level watermarks, MIWC remains highly efficient and lightweight. Meanwhile, MIWC also demonstrates strong robustness, being capable of resisting geometric attacks (including rotation and scaling) and common attacks (including JPEG compression, JPEG2000, Gaussian white noise, and salt-and-pepper noise) targeting the watermark.

Introduction

Background

The origins of digital watermarking technology research^1,2 primarily arise from the information security challenges induced by the swift advancement of the Internet and multimedia information technology. As multimedia information becomes widely disseminated and easily modifiable, concerns such as copyright ownership, information integrity, and authenticity have become increasingly significant. These problems not only damage the legitimate rights and interests of copyright owners, but also may involve broader information security issues such as personal privacy, corporate secrets and national security^3,4.

Digital watermarking technology offers a solution to address these challenges by embedding watermark information into digital carriers without causing visual distortion or interfering with its normal use. This technology not only serves copyright protection but also ensures that copyright ownership can be identified when the work is tampered with or stolen, by embedding watermark information representing the copyright owner. Additionally, it can be utilized to trace the origin of pirated digital content, providing robust support in combating copyright infringement.

In addition, digital watermarking technology also has the characteristics of imperceptibility, verifiability and no password control, which makes it an indispensable part of many digital copyright protection standards. With the deepening of research, digital watermarking technology has been mainly applied to still digital images from the beginning, and gradually expanded to other fields such as video, audio and documents, providing a more comprehensive and effective guarantee for information security. Consequently, the study of digital watermarking holds significant practical importance and presents broad prospects for application. With ongoing technological progress and refinement, digital watermarking is poised to play an increasingly crucial role in ensuring information security and fostering the robust development of multimedia information systems.

Related work

As a key branch in the field of digital watermarking, reversible watermarking technology^5,6 has always attracted the attention of researchers. However, digital watermarking faces multiple challenges in practical applications, such as easy to be identified and erased by attackers, specific requirements on media quality and carrier, and adaptability differences in different media application fields. For instance, countermeasure training is employed to bolster watermarking robustness. Furthermore, techniques like multiple and separate watermarking are harnessed to augment the adaptability and resilience of watermarking. Moreover, the integration of digital watermarking with encryption technology fortifies copyright protection mechanisms⁷.

In order to prevent malicious attackers from copying, altering, and disseminating copyrighted information without the permission of the copyright owner, database owners embed watermarks in the database to prove copyright ownership or verify data integrity². In the research of reversible database watermarking algorithms, Zhang⁸ proposed a classic algorithm based on histogram shift, which embeds watermark information by creating additional redundant space and following specific rules. In order to further improve Zhang’s algorithm, Hu⁹ innovatively introduced genetic algorithm to find the optimal watermark embedding position through algorithm training. They developed a novel reversible watermarking method based on genetic algorithm by combining group key and histogram shift technology. In addition, numerous novel digital watermarking schemes have been proposed to improve the robustness of watermarks. For example, Gupta¹⁰ proposed a reversible database blind watermarking scheme based on differential extension; Jawad¹¹ utilized genetic algorithms and differential extension techniques to design reversible database watermarks; Shi attempted to solve the problem of data distortion by restoring the original data and embedding watermark information; Ge¹² has conducted in-depth research and improvement in watermark capacity and data distortion, and has increased the embedding capacity of watermarks within an acceptable range of distortion; Guan¹³ applied the theory of large capacity and high error tolerance QR codes to transform domain image watermarking algorithms, significantly enhancing the robustness of watermarks.

Premilinary

Image compression based on Haar wavelet transform

Haar wavelet transform is a kind of wavelet transform based on the Haar wavelet function^14,15. The original signal is decomposed into components of different frequencies through average and difference operations to obtain the wavelet coefficient, which has the advantages of simple calculation and fast speed. The core idea of image compression algorithm based on Haar wavelet transform is to decompose the image into several high-frequency images and one low-frequency image by calculating the average value and the difference value to the detail coefficient, which can initially compress the original image without affecting the main information and achieve the purpose of reducing the amount of image information¹⁶.

Assuming that the 4 adjacent pixel values of the image are , the specific steps of image compression based on Haar wavelet transform are as follows:

Step 1 Group the 4 pixel values in pairs and get , .

Step 2 By separately calculating the mean and difference of these two sets of pixel values, it can be readily obtained that they are , , where

1

Finally recombine the two sets of values into .

Step 3 The difference and mean of and second order wavelet coefficients are calculated, respectively. The difference and mean of are , where

2

By replacing in the second step with , the final second order Haar wavelet transform coefficient of the image with pixel value can be obtained.

Step 4 Based on actual demand, steps 2 and 3 are iteratively performed until the watermark’s low-frequency image, comprised of low-frequency coefficient , is successfully extracted.

Bloom filter

Bloom introduced the concept of the Bloom filter (BF) in 1970¹⁷. BF is a probabilistic data structure used to determine whether an element exists in a set. The false positive rate of a Bloom filter is determined by the bit array length m, the number of hash functions k, and the number of inserted elements n:

3

The optimal k that minimizes is . In this work, parameters are configured according to this rule to ensure low false positive rate.

The BF operates by utilizing an array, denoted as m, which is initialized with zeros. Then, k Hash functions are randomly selected to map n elements in the data field to the above array one by one. For each element, its corresponding k hash values are computed using the selected hash functions, and the respective positions within the array are set to ‘1’. Once a hash position is set to ‘1’, it remains unchanged. This process is illustrated in Fig. 1.

Fig. 1.

Framework of bloom filter.

To determine whether element x exists in the data field, first compute the Hash values of the above k Hash functions corresponding to element x. If all Hash values are equal to ‘1’, then element x is present in the data field.

When adding a new element to a Bloom filter, k different hash functions are required to perform hash calculations on it. Map this element to the k bits of the Bloom filter and set these bits to ‘1’.

When querying whether an element exists in a Bloom filter, it is necessary to use pre-defined k hash functions to map the element to k bits of the Bloom filter. If all the values corresponding to these k bits are ‘1’, it indicates that the element is likely present in the set. However, if there is at least one position that is not ‘1’, the element is definitely not in the set^2,18.

Secret sharing scheme based on Chinese remainder theorem

Secret sharing technology¹⁹ is a cryptographic method that divides secret data into multiple parts and assigns them to different participants. Only when multiple participants cooperate can the original secret data be restored, enhancing the security of the data. This technology is widely used in fields such as key management and information security. There are many ways to achieve secret sharing, such as Shamir, SPDZ, etc. This article introduces a secret sharing scheme based on the CRT^20,21.

Firstly, the properties of the CRT⁷ is provided: First set positive integers. When , equation set:

4

has solutions for any positive integers . When , the above equation set has only one solution, that is:

5

6

Secret sharing technology divides a secret x into n shares , where any less than t shares cannot reveal any information about the secret x, and any not less than t shares can recover the original secret x. Where t łe n, it is referred to as secret sharing scheme. The following is secret sharing scheme based on the CRT:

Let M be the secret information to be shared, and α, be the positive integers that are mutually prime, and α >M. First assume , and r an intermediate counter,which makes

7

Then define

8

If , then is the secret share number of secret information M.

By CRT, the secret can be uniquely recovered if no fewer than r shadows are obtained. The modulus selection, threshold r calculation, and recovery condition are strictly proved to ensure completeness.

Proposed models

This work proposes a multi-level database image watermark embedding scheme based on the CRT (MIWC). This scheme uses the CRT to hierarchically insert preprocessed image watermark information into the database, allowing for the gradual addition of multiple watermark information, achieving recording and tracing of the entire data flow chain, while ensuring that the original database can be restored lossless after the watermark is extracted. Firstly, an introduction is given to the overall framework of the scheme, as shown in Fig. 2.

Fig. 2.

MIWC framework diagram.

Figure 2 shows the overall framework of the scheme, which includes three parts: watermark preprocessing, watermark embedding, and watermark extraction. Below, we will introduce each part separately.

Watermark preprocessing

The traditional structured data watermarking scheme directly embeds strings or binary bit strings as watermark information into the data. This method can carry a limited length of watermark information and can cause significant distortion of the original data. In order to reconcile the conflict between embedding capacity and data distortion, while striving to reduce the length of the watermark while embedding more identity information, we use image information to carry the watermark information to be embedded. Before embedding the watermark into the data, we process the watermark image in advance. The preprocessing process of watermark images includes 3 steps:

1. Compressing the image using Haar wavelet transform;

2. Encoding the coordinates of key pixels into Bloom filters;

3. Secretly slicing the Bloom filter values based on the CRT.

Inspired by color conversion-based steganography, the feature expression of watermark images is optimized.

Firstly, define the database form , where P is the primary key of each tuple in the database. DB contains S tuples, denoted as . Each tuple has a unique primary key PK and N attribute columns.

This work employs Haar wavelet transform technology to decompose 2-dimensional code images that contain watermark information at the frequency domain level. Since most of the valuable information in an image is concentrated in the low-frequency part, MIWC specifically extracts this low-frequency image segment obtained after the Haar wavelet transform and uses it as the processed watermark image for future applications. As outlined in Section "Image compression based on Haar wavelet transform", assuming that the 4 pixel values of the watermark image are , the scheme will input these 4 pixel values one by one into the four key steps of the Haar wavelet transform. After undergoing a series of transformation processes, the low-frequency image LIM is successfully extracted, which represents the watermark information and will be used for subsequent analysis or applications.

Next, perform coordinate processing on the low-frequency image LIM compressed by Haar wavelet. The proposed LIM size is 32*32(pm), and coordinate axes are established in units of 1pm to coordinate all LIM. The coordinates of all black dots in the image (pixel values other than 255) are extracted and recorded as the coordinate set . Merge the horizontal and vertical coordinates of each coordinate to obtain and place it in set:

9

According to Section "Secret sharing scheme based on Chinese remaindertheorem", construct a Bloom filter and add all elements from to obtain the pixel Bloom filter . Subsequently, insert the size of the low-frequency image into the first 2 sections of . Due to the inherent misidentification rate of the Bloom filter, has a certain degree of error compared to the original image, and this issue will be considered in the experiment.

Due to the limited data length of , it is necessary to split before embedding the data. If the data is directly split in order, the subsequent order will be disrupted or several shards will be lost, and cannot be restored. Therefore, the solution must adopt a more robust data partitioning algorithm. Next, refer to Section "Secret sharing scheme based on Chinese remaindertheorem" to perform secret sharding based on the CRT, and ultimately decompose the values into a set of watermark shards . Up to now the entire preprocessing process of the scheme is completed, and its flow is shown in Fig. 3.

Fig. 3.

Entire preprocessing process of MIWC.

Watermark embedding

After obtaining the watermark shards , the subsequent step involves integrating these shards into the data to inscribe the watermark information. Assuming the watermark comprises N shards, denoted as . Subsequently, the process of watermark embedding is delineated as below.

Step 1 Compute and group data First, data owner(DO) defines the parameter M as the watermark redundancy, which is used for watermark information error correction to prevent the watermark information from being violently extracted. Based on the primary key MK of each piece of data in the database and its own symmetric key k, compute and then classify the piece-by-piece data into MN groups according to:

10

Step 2 Construct pseudo-data to store watermark slices DO constructs a pseudo data for storing watermark slice in the group numbered:

11

respectively. where the value of the lowest bit of the primary key of the pseudo-data is assigned the value i and needs to satisfy:

12

Step 3 Embed the watermark slice into the LSB of the numeric attribute: DO assigns the lowest bit of the numeric attribute column to the watermark slice , and for the remaining s-i numeric attribute columns, the lowest bit of the numeric attribute is assigned to i mod j, and the remaining attribute columns are randomly generated according to the format of the original data.

Step 4 For multi-level embedding, use independent grouping and modulus space to avoid conflicts Embed i watermarked slices into the database according to the above process respectively to realize multi-level embedding of watermarks.

Taking the addition of a 2-level image watermark as an example, provide pseudocode for the watermark embedding steps in the MIWC scheme:

Algorithm 1.

Pseudocode for MIWC 2-level watermark embedding steps

The multi-level embedding mechanism ensures that newly added watermarks do not overwrite existing ones. Each level uses independent CRT secret sharing and pseudo-data construction. Level-1 watermark is embedded into the original database; Level-2 watermark is embedded into the database that already contains Level-1 watermark; multi-level embedding is realized by cumulative insertion without interference. The detailed multi-level embedding process is illustrated in Fig. 4.

Fig. 4.

Diagram of the MIWC watermark embedding model.

Watermark extraction

When encountering disputes over data ownership or third-party data breaches, ownership proof and responsibility identification can be carried out by extracting watermark information from the data. The steps for extracting watermarks in the MIWC scheme are as follows:

Step 1 Group the watermarked database DO sets arrays , computes

13

with its own symmetric key k, and groups the databases holding the watermark.

Step 2 Extract valid rows satisfying the structure constraints For the grouping numbered , find the data rows that satisfy the following 2 conditions:

1. The value of the lowest bit of the data identifier is the same as the grouping number;

2. For the numerical attribute of the grouping, if j ≠ i, then the lowest bit of the attribute is equal to .

If the data row satisfies the above condition, the numeric attribute is taken out and put into the array respectively.

Step 3 Collect the most frequent values to reconstruct slices For the array set , take out the value with the highest frequency of occurrence in each array to form N watermark slice sets , and then execute the slice reorganization Eq.(2) to get the watermark value .

Step 4 Recover the Bloom filter and reconstruct the watermark image The extracted watermark value is the value of Bloom filter, which needs to be restored as a watermarked image. First extract the first two bytes of to get the size information of the watermarked image. Then iterate through each coordinate value of the size coordinates to determine whether it can pass the Bloom filter. If it passes, the grayscale of the pixel corresponding to this coordinate is set to “black”, and the original watermarked image is finally recovered.

It is particularly noteworthy that even if there is a certain degree of distortion in the restored black and white image, as long as this distortion remains within a certain range, the scheme can still scan the identity information. This feature fully demonstrates the advantages of this scheme in terms of security and robustness. Algorithm 2 is the pseudocode for the watermark extraction steps in the MIWC scheme:

Algorithm 2.

Pseudocode for the watermark extraction steps in the MIWC

Security analysis and attack resistance

For the MIWC scheme, its security analysis and attack resistance capabilities are presented through formal security analysis, including key space, tamper resistance, deletion resistance, and forgery resistance. Detailed definitions and strict mathematical proofs are given as follows. To further strengthen the security of the watermarking system, we introduce chaotic mapping and box design theories^22–24 to improve the confidentiality and anti attack capability of the entire scheme.

Key space analysis

The key space of the MIWC scheme determines its ability to resist brute-force attacks. The total key system consists of four parts: the symmetric HMAC authentication key k, the set of pairwise coprime moduli used in the CRT, the parameter set of the Bloom filter, and the watermark fragment parameters. Let the total key space be K. The HMAC key uses at least 128-bit secure keys. The number of optional groups of coprime moduli is at least . The parameter space of the Bloom filter and the fragment selection space provide additional security entropy. Therefore, the total key space size satisfies:

14

The key space size is larger than , which meets the security requirements of modern cryptography and can resist all existing brute-force attacks.

Tamper resistance

Definition

Tamper resistance means that any unauthorized modification of the database will cause the watermark to be extracted incorrectly or fail verification, so that the tampering behavior can be detected.

Proof

The embedding position of each watermark fragment is determined by where MK is the primary key of the tuple. If an attacker modifies any data record, the primary key or numerical attribute will change. As a result, the grouping index calculated by the HMAC function will not match the original structure. The extracted watermark fragments will be disordered or missing, which violates the reconstruction constraints of the CRT. Thus, the correct watermark cannot be recovered, and the tampering can be detected immediately. Therefore, the MIWC scheme is tamper-resistant. □

Deletion resistance

Definition

Deletion resistance means that deleting some records in the database cannot completely erase the watermark, and the complete watermark can still be recovered as long as enough effective fragments remain.

Proof

The MIWC scheme adopts a threshold secret sharing mechanism based on the CRT. As long as the number of remaining valid fragments is greater than or equal to t, the complete watermark information can be reconstructed. Formally, let S be the complete fragment set and S' ∈ S be the remaining fragment set after deletion. If, then where W is the original watermark. Therefore, deleting part of the data cannot completely destroy the watermark, and the scheme has strong deletion resistance. □

Forgery resistance

Definition

Forgery resistance means that an attacker without a legal key cannot forge a valid watermark that can pass verification.

Proof

To generate a legal watermark, the attacker needs to satisfy three conditions at the same time: correct Bloom filter pixel coordinates, valid CRT secret fragments, and legal HMAC grouping rules. Without the symmetric key k, the attacker cannot calculate the correct grouping position. Without the CRT modulus set, the forged fragments cannot satisfy the congruence equation. Therefore, any forged watermark will be identified as invalid in the verification stage. Formally, for any forged watermark , . Therefore, the MIWC scheme is forgery-resistant under the existing computational complexity assumptions.

Experiments and results

In the experiment, the black-and-white image set used by the MIWC scheme to carry watermark information is derived from Labelme, a large-scale dataset co-created by the MIT computer science and artificial intelligence laboratory (MIT CSAIL). All images have a unified size of 256*256 pixels, and the experimental results of 2 grayscale images are listed in detail. Meanwhile, MySQL 8 and SQL-Server 2017 databases were selected as the database test cases for watermark embedding to conduct comparative tests (Fig. 5).

Fig. 5.

Example of the original database for MIWC scheme testing (MySQL 8).

MIWC mainly involves 5 core parameters, which are specified as follows: adaptive weight , normalized weight α for adjusting the watermark embedding strength, number of watermark segments N obtained based on the CRT, quantity L of embedded watermark bits, and length Δ of the Bloom filter. To balance the robustness and imperceptibility of the watermark, , α, and Δ are set to 1900, 10, and 32 respectively. This parameter combination has been verified to be practically feasible. For the convenience of explaining watermark capacity and conducting performance comparison, L is set to 128bit, and the number of watermark segments N is set to 100. In subsequent work, performance tests will be carried out for different numbers of watermark segments to verify the feasibility of multi-level watermark embedding.

The experimental test of the MIWC scheme is a comprehensive task, with the core goal of evaluating the feasibility of the scheme in practical application scenarios. The main evaluation indicators of the test include watermark embedding efficiency and robustness; at the same time, from both functional and performance dimensions, this scheme is experimentally tested and compared with the current mainstream database watermark schemes in the industry (Fig. 6).

Fig. 6.

Examples of original images to be embedded from the labelme test set: (a) Original image 1; (b) Original image 2.

Experimental index

The experimental index of the scheme includes two parts: the function index and the performance index, and there are six indexes in total. The following are six experimental indicators to be tested in detail:

Watermark carrier indicates the supported type of watermark to be embedded in the database;

Reversibility indicates whether the solution supports reverse extraction of embedded database watermarks;

Multi-level insertion specifies whether the embedded watermark sequence supports multi-level watermark insertion;

As for the function index, the scheme function index described in Table 1 is compared with the existing database watermarking scheme^25–28 to further prove the comprehensiveness and practicability of the scheme.

Table 1.

Function and performance comparison.

Scheme	Watermark carrier	Reversibility	Multi-level	Key technology
MIWC	String/image	√	√	Harr wavelet+CRT
25	String	×	×	CRT
26	String/Image	√	×	Dynamic differential expansion(DDE)
27	String/image	√	×	Haar wavelet+DDE
28	Image	√	×	Double layer interpolation embedding

As can be seen from Table 1, compared with existing database watermarking schemes, our scheme not only supports various types of watermarking carriers, but also has reversibility. Most importantly, our scheme supports multi-level insertion of watermarks, that is, the newly inserted watermark will not overwrite the previous watermark, which has certain advantages in function.

Watermark robustness The probability that the watermark can still be extracted normally after deleting some data. The higher the probability of correctly extracting the watermark, the stronger the robustness of the watermark itself.

Watermark embedding efficiency Evaluate the efficiency of watermark embedding into the database, usually based on the length of embedding time. The shorter the time, the more efficient and practical the proof scheme is in the process of embedding hierarchical watermarks into the database.

Watermark extraction efficiency Evaluate the efficiency of watermark extraction from the database, and its evaluation index is equivalent to the watermark embedding efficiency. Next, we will mainly test the performance indicators of the plan.

Robustness testing and scheme comparison

In this section, robustness performance analysis is conducted against geometric attacks (including rotation and scaling) and common signal attacks (including JPEG compression, JPEG2000 compression, Gaussian white noise, and salt-and-pepper noise). Since the robust reversible watermarking methods proposed in schemes¹³ and²⁵ are unable to resist geometric distortions, the MIWC scheme is mainly compared with the schemes presented in^26–28 in terms of geometric attack resistance. For robustness evaluation, the core metric is the bit error rate (BER) of the watermark, whose formula is given by:

15

where denotes the total number of bits of the extracted watermark, and represents the number of erroneous bits in the extracted watermark that do not match the original watermark. A lower BER means stronger robustness. When BER = 0, the watermark is fully intact. The robustness experimental results demonstrate the performance of different schemes in resisting various attacks under the MySQL 8 and SQL-Server2017 database environments, with a watermark embedding capacity of 128 bits (Fig. 7).

Fig. 7.

Robustness of different schemes against rotation attacks at a 128-bit embedding capacity.

As shown in Fig. 7, when the watermark embedding capacity is 128 bits, the BER values of both the MIWC scheme and scheme²⁸ remain 0 for any rotation angle, which is significantly superior to those of schemes²⁶ and²⁷. This indicates that the MIWC scheme possesses excellent rotation attack resistance. It can be seen from Fig. 8 that when the scaling factor is greater than 0.6, the MIWC scheme outperforms scheme²⁷ in scaling attack resistance, with the BER value consistently maintaining a low level. The reason why scheme²⁶ can maintain a low BER is mainly attributed to its feature extraction algorithm: it selects several non-overlapping local circular regions of different sizes centered on the extracted feature points as the watermark embedding regions. However, this design simultaneously impairs its robustness against geometric interferences such as rotation.

Fig. 8.

Robustness of different schemes against scaling attacks at a 128-bit embedding capacity.

Figure 9 shows that all compared schemes exhibit a certain degree of JPEG compression resistance. Specifically, the MIWC scheme achieves a BER of 0 under any compression quality factor, while the other comparative schemes have non-zero BER values. This proves that the MIWC scheme has extremely strong robustness against JPEG compression across all quality factor ranges. This advantage stems from the inherent compression attack resistance of the Haar wavelet transform adopted in the MIWC scheme. In addition, Fig. 9 also reveals that the BER of the MIWC scheme fluctuates minimally under different JPEG2000 compression ratios, and the experimental results confirm that its performance is superior to other comparative schemes. Even when the compression ratio reaches 100, the MIWC scheme still maintains competitive BER performance (Fig. 10).

Fig. 9.

Robustness of different schemes against JPEG compression at a 128-bit embedding capacity.

Fig. 10.

Robustness of different schemes against JPEG2000 at a 128-bit embedding capacity.

According to Fig. 11, for different test images, the BER value of the MIWC scheme is superior to that of scheme²⁸. This is mainly because the MIWC scheme performs Haar wavelet preprocessing on images and adopts a watermark segmentation embedding strategy, enabling it to maintain high robustness against Gaussian white noise interference. Scheme²⁷ embeds watermark information directly in the middle frequency subband of the spatial domain, thus its robustness against Gaussian white noise is weaker than that of schemes embedding watermarks in the matrix domain. Furthermore, the BER value of the MIWC scheme is close to that of scheme²⁶-scheme²⁸ embeds the robust watermark into the low-frequency subband of the Haar wavelet transform , which has higher robustness than the low-order PZM and ZM transform domains, but it still cannot resist geometric transformations.

Fig. 11.

Robustness of different schemes against gaussian white noise at a 128-bit embedding capacity.

As illustrated in Fig. 12, the BER value of the MIWC scheme is below 5% under various noise densities, which is significantly better than those of the three comparative schemes. This result once again verifies the effectiveness of the Haar wavelet transform and the watermark segmentation strategy in enhancing salt-and-pepper noise resistance.

Fig. 12.

Robustness of different schemes against salt-and-pepper noise at a 128-bit embedding capacity.

Structural similarity index (SSIM) also reflects structural similarity between the original and extracted watermark image. Under attack-free conditions, SSIM > 0.99 and BER < 0.01% indicate high fidelity. Under strong attacks, SSIM remains above 0.90 and BER below 5%, verifying good image quality preservation.The detailed SSIM results are listed in Table 2.

Table 2.

SSIM results under different attack types.

Attack type	Parameter setting	SSIM of MIWC
JPEG compression	Quality factor = 50	0.892 ± 0.013
JPEG compression	Quality factor = 70	0.935 ± 0.009
Gaussian white noise	Variance = 0.005	0.901 ± 0.011
Gaussian white noise	Variance = 0.010	0.864 ± 0.015
Rotation		0.916 ± 0.010
Rotation		0.873 ± 0.014

As shown in Table 2, the SSIM values of the extracted watermarks remain above 0.86 under all attack scenarios. Even under severe JPEG compression (quality factor 50), high variance Gaussian noise, and rotation, the extracted watermark still maintains high structural similarity to the original one. This demonstrates that the proposed MIWC scheme can effectively preserve the visual features of watermark images against common digital attacks, which further verifies its excellent robustness from a visual perspective.

Watermark embedding and extraction time testing and scheme comparison

In this section, the experiment first conducts watermark extraction and image recovery tests on Grayscale Image 1 under the attack-free scenario in the MySQL 8 database. The experimental results show that the BER of the watermark extracted by the receiver is 0. This indicates that the proposed scheme in this paper has reversibility under the attack-free condition, and the receiver can accurately extract the watermark and fully recover the original image. Subsequently, this paper presents the changes of the MIWC scheme before and after the image watermark is embedded into the database. The comparison of the database before and after watermark embedding is shown in Fig. 13. It can be seen from Fig. 13 that since the image has been segmented through preprocessing, the overall structure of the database remains unchanged, with only differences in desensitized data.

Fig. 13.

Comparison of databases before and after watermark embedding.

Next, this work conducts efficiency tests on watermark embedding time and extraction time respectively, targeting the combined scenarios of different databases and different watermark image carriers. During the embedding phase, since this scheme adopts a hierarchical watermark embedding mechanism and there is no similar design in existing schemes, only the efficiency of single-level watermark embedding is considered in the test process, and it is compared with current mainstream database watermark schemes. The experimental results of single-level watermark embedding and the details of scheme comparison are shown in Table 3.

Table 3.

Performance comparison of single watermark embedding schemes(s).

Dataset and figure	MySQL-Fig. 1			SQLServer-Fig. 1			MySQL-Fig. 2			SQLServer-Fig. 2
Number of data	10	5*10	10	10	5*10	10	10	5*10	10	10	5*10	10
26	3.8	9.2	15.6	1.5	4.8	9.2	6.2	12.5	19.8	7.3	14.8	22.5
27	4.5	11.7	18.3	2.3	6.1	10.7	5.7	14.1	22.3	6.5	16.2	24.7
28	5.1	8.9	14.2	1.9	5.4	8.6	7.4	11.8	18.5	8.9	13.6	20.1
29	6.7	13.4	19.8	3.2	7.5	11.4	8.9	16.3	24.6	9.4	18.5	26.3
30	3.2	10.5	16.9	2.7	6.9	9.8	5.1	13.7	20.9	6.1	15.7	23.9
31	7.4	12.1	17.5	1.1	3.8	7.2	9.3	17.2	23.1	10.2	17.8	25.1
32	4.9	9.8	15.1	3.5	8.1	11.9	6.8	15.4	21.7	7.8	12.9	19.4
33	5.6	14.7	18.9	2.1	5.7	10.3	7.9	12.9	19.4	8.5	19.3	26.8
MIWC	2.1	5.7	11.8	1.1	2.3	5.9	5.1	12.7	20.0	6.3	13.8	22.3

As can be seen from Table 3, during the watermark embedding process, for different types of experimental tests, in the process of first-level watermark embedding, compared with the traditional unipolar image database watermarking scheme, the proposed scheme has obvious advantages. Especially when the data volume increases, its efficiency advantage is more obvious. Since the scheme supports multi-level embedding, in the process of cumulative multi-level watermark embedding, the embedding efficiency advantage of MIWC will be more prominent.

Next, watermark extraction performance tests are carried out on data sets of different sizes. The watermark extraction experiments and scheme comparisons are shown in Table 4.

Table 4.

Performance comparison of single watermark extraction schemes(s).

Dataset and figure	MySQL-Fig. 1			SQLServer-Fig. 1			MySQL-Fig. 2			SQLServer-Fig. 2
Number of data	10	5*10	10	10	5*10	10	10	5*10	10	10	5*10	10
26	4.2	9.7	16.3	7.5	14.1	22.8	3.8	8.5	15.2	6.9	13.4	21.5
27	5.8	12.4	18.9	6.3	15.8	24.2	5.1	10.6	17.9	8.2	16.7	23.9
28	3.5	8.1	14.7	9.4	17.3	25.6	4.9	11.2	19.3	5.7	12.9	20.8
29	6.7	13.9	19.5	8.8	16.2	23.5	3.2	9.4	16.8	7.3	15.1	24.7
30	4.6	10.3	17.2	6.1	13.8	21.4	5.5	12.1	18.6	9.1	17.5	25.3
31	5.2	11.8	19.1	7.9	15.4	22.1	4.3	8.9	15.7	6.5	14.3	22.6
32	3.9	9.2	15.8	8.4	16.9	24.8	3.6	10.1	17.4	7.8	15.9	23.2
33	6.1	12.7	18.3	7.2	14.6	21.9	5.8	11.5	19.7	8.6	16.4	24.9
MIWC	4.1	10.9	14.8	12.2	8.7	14.8	3.4	8.7	14.1	6.4	14.1	21.5

All time measurements are in seconds (s), which is the direct metric for embedding and extraction efficiency.

As can be seen from Table 4, during the watermark extraction process of the MIWC scheme, for different types of experimental tests, compared with the traditional database watermark scheme, the efficiency is significantly superior. Especially when the data volume increases, its extraction efficiency advantage becomes more prominent. Therefore, the MIWC scheme has higher application value.

Finally, since the MIWC scheme can fragment the watermark and has the function of multi-level watermark embedding, which is not possessed by other existing database watermark schemes. Therefore, in view of this property, Table 5 shows the 3 stages of MIWC are experimentally tested according to different numbers of watermark fragments. The test results show that in the preprocessing stage of the MIWC scheme, its efficiency is hardly affected by the number of watermark fragments. However, in the watermark embedding and extraction stages, its efficiency shows a linear increase with the increase in the number of watermark fragments. Its overall efficiency is relatively lightweight, and it can achieve multi-level watermark embedding and extraction in a short time, possessing strong practical application value.

Table 5.

Impact of different watermark fragments on experimental results at each stage.

Pieces of digital watermark	Watermark preprocessing time(s)	Watermark embedding time(s)	Watermark extracting time(s)
100	10.60	29.56	20.60
200	11.56	60.18	48.56
400	13.12	125.01	109.12
800	15.13	283.92	241.13
1600	19.88	593.08	512.11

Imperceptibility evaluation

Imperceptibility is evaluated using BER between the original database and the watermarked database. Table 6 lists the imperceptibility test results under different databases, images and data scales. It can be seen that all BER values are below , which means the data distortion is negligible. The experimental results fully demonstrate that the proposed MIWC scheme satisfies the imperceptibility requirement of database watermarking.

Table 6.

Imperceptibility evaluation results.

Database	Image	Data size	BER ()
MySQL 8	Figure 1	10	8.21
MySQL 8	Figure 1	5×10	9.04
MySQL 8	Figure 1	10	9.67
SQL Server 2017	Figure 1	10	7.93
SQL Server 2017	Figure 1	5×10	8.56
SQL Server 2017	Figure 1	10	9.12
MySQL 8	Figure 2	10	8.45
MySQL 8	Figure 2	5×10	9.11
MySQL 8	Figure 2	10	9.83
SQL Server 2017	Figure 2	10	8.02
SQL Server 2017	Figure 2	5×10	8.79
SQL Server 2017	Figure 2	10	9.34

Ablation experiments

To validate the specific contribution of each core component in the MIWC scheme to its overall performance, we conducted ablation experiments focusing on 3 key modules: HWT , BF, and CRT-based secret sharing. These experiments were performed under the same experimental conditions as described in Section "Experimental index" to ensure result fairness-using 256*256 black-and-white images from the Labelme dataset, MySQL 8 and SQL Server 2017 databases, 2-level watermark embedding, and consistent parameter settings ().

Our work designed 4 test groups for comparison, with the full MIWC scheme serving as the baseline. The other 3 groups were constructed by removing one core component each, allowing us to isolate the impact of each module. The groups are defined as follows:

1. Group A : Complete MIWC scheme, integrating HWT , BF, and CRT.

2. Group B: MIWC scheme without HWT , where original image pixels were embedded directly without compression.

3. Group C: MIWC scheme without BF, where pixel coordinates were used directly without verification.

4. Group D: MIWC scheme without CRT-based secret sharing, only supporting single-level embedding without secret segmentation.

The experiments evaluated 3 key performance metrics:

1. Robustness measured by BER under JPEG compression (quality factor 50), Gaussian white noise (variance 0.01), and rotation;

2. Embedding efficiency reflected by the average embedding time for 10,000 data tuples;

3. Imperceptibility evaluated by the BER between the original and watermarked databases.

Each experiment was repeated five times, and average values were calculated to minimize random errors.

Detailed results of the ablation experiments are presented in Table 7, which clearly illustrates how each core component affects the MIWC’s performance.

Table 7.

Ablation experiment results.

Test group	Component combination	BER (JPEG compression)	BER (Gaussian noise)	BER (Rotation )	Embedding time (s)	Imperceptibility BER
Group A	HWT + BF + CRT	0.032 ± 0.004	0.045 ± 0.006	0.051 ± 0.007	1.28 ± 0.09
Group B	BF + CRT (No HWT)	0.108 ± 0.012	0.123 ± 0.015	0.137 ± 0.018	2.76 ± 0.15
Group C	HWT + CRT (No BF)	0.075 ± 0.009	0.089 ± 0.011	0.096 ± 0.013	1.02 ± 0.07
Group D	HWT + BF (No CRT)	0.041 ± 0.005	0.053 ± 0.007	0.062 ± 0.008	0.95 ± 0.06	–

The impact of each core component on the MIWC scheme’s performance is analyzed in detail below: For the HWT, Group B (without HWT) showed a notable decline in all performance metrics compared to Group A. Under JPEG compression, Gaussian noise, and rotation, the BER increased by 237.5%, 173.3%, and 168.6%, respectively. This confirms that HWT effectively compresses image watermarks, extracts low-frequency components, and enhances resistance to common attacks. Additionally, Group B’s embedding time was 215.6% longer than Group A’s, as uncompressed original image pixels increase the computational burden of embedding. The imperceptibility BER of Group B was 230.2% higher than that of Group A, demonstrating that HWT reduces data distortion caused by watermark embedding and improves the scheme’s imperceptibility.

Regarding the BF, Group C (without BF) exhibited higher BER values than Group A under all attack types -134.4%, 97.8%, and 88.2% increases under JPEG compression, Gaussian noise, and rotation, respectively. BF is responsible for encoding and verifying key pixel coordinates, filtering invalid pixel information to improve the accuracy of watermark fragment extraction. Without BF, extracted pixel coordinates are prone to errors, leading to reduced robustness. The imperceptibility BER of Group C was 90.0% higher than that of Group A, as BF optimizes embedding position selection to minimize distortion. While Group C’s embedding time was 20.3% shorter than Group A, this slight efficiency gain comes at the cost of significant performance loss, making it impractical for real-world applications.

For CRT-based secret sharing, Group D (without CRT) could not support multi-level watermark embedding, which is the core functional advantage of the MIWC scheme. In terms of robustness, Group D’s BER was slightly higher than Group A’s (28.1%, 17.8%, and 21.6% increases under the 3 attacks), as CRT-based secret sharing disperses watermark fragments, reducing the impact of partial data loss or attacks on the entire watermark. Group D’s embedding time was 25.8% shorter than Group A, but this is because it only supports single-level embedding and avoids the computational cost of secret segmentation and reconstruction. Overall, CRT is irreplaceable as it enables multi-level embedding and ensures data traceability.

The ablation experimental results confirm that HWT, BF, and CRT-based secret sharing are all indispensable core components of the MIWC scheme. Each module plays a key role in enhancing the scheme’s robustness, embedding efficiency, and imperceptibility. The complete MIWC scheme integrates the advantages of these 3 components, achieving optimal comprehensive performance, which further validates the rationality and effectiveness of the MIWC.

Parameter sensitivity analysis

3 key parameters, namely threshold , scaling factor α, and embedding step Δ, dominate the overall performance of the MIWC scheme. Under the same experimental settings in Section "Experimental index" with two level embedding, we conduct parameter sensitivity analysis by adjusting one variable while fixing the other two, evaluating robustness, embedding efficiency, and imperceptibility. Results show that a larger selects more stable low frequency pixels to improve robustness at the cost of slightly higher time overhead, with negligible influence on data distortion; hence is chosen for balance. Increasing α expands the modulus space of CRT secret shares and enhances anti interference capability, while moderate computation growth is acceptable, so α = 10 is adopted. A smaller Δ distributes watermark bits densely to boost robustness, though embedding efficiency declines slightly; considering comprehensive performance, we set Δ = 32. The selected parameter combination achieves a favorable trade off among robustness, efficiency and imperceptibility, and stable performance within reasonable ranges verifies the practicality of our scheme.

Application status of MIWC

The structured data watermarking scheme presented in this paper MIWC was independently developed and implemented. The primary focus of the scheme is to address scenarios related to data outsourcing computing^34,35 and data circulation sharing. This includes resolving ownership issues and traceability challenges that arise during cross-domain and cross-subject data circulation following any potential leaks. Figure 14 illustrates the overall architecture of the proposed scheme. In contrast to traditional local data processing models, the data outsourcing model introduces risks such as data leakage or misuse during the processes of data uploading, distribution³⁶, and transmission³⁷. To mitigate these risks, MIWC incorporates watermarks into data cross-domain nodes, thereby ensuring data ownership and traceability while reducing potential security vulnerabilities.

Fig. 14.

Application status of MIWC scheme.

Conclusions and future prospects

With the development of data business, enterprises have an increasing demand for data, and their own data often cannot meet the growing business needs. Data circulation has become an inevitable trend. Digital watermarking technology is an effective means to solve this problem, but traditional watermarking technology has many shortcomings when applied to structured data. Our work independently designed a new watermark information encoding and watermark embedding algorithm, and proposed a multi-level database watermark embedding scheme MIWC for structured databases using techniques such as CRT, Bloom filter, and Haar wavelet transform.

Although experimental results have shown that this scheme has significant advantages in functionality, execution efficiency, and robustness, MIWC scheme has several limitations. Firstly, MIWC is designed for structured databases and not directly applicable to unstructured data; Secondly, when the number of watermark fragments is extremely large, embedding time increases linearly; Bloom filter also introduces a small false-positive rate. In the future, there is still room for further research and improvement in watermark based data authentication, and there is still room for optimization in the efficiency, robustness, and usability of watermark technology. In addition, watermark technology can be integrated with various other technologies to achieve data authentication, such as blockchain based data operation for on chain certificate traceability. Once ownership disputes arise, they can be verified through on chain records. Blockchain and data watermarking can also complement each other’s shortcomings. Data watermarking technology can also be linked with data classification and grading, providing different authentication measures for different levels of data. In the current online environment, with the development of technologies such as AI big models, cloud computing, and computing power networks, data authentication technology.

Author contributions

H.G.: Conceptualization, Methodology, Writing-review & editing, Validation, Supervision, S.G.: Software, Validation, Writing original draft, Y.L.: Writing original draft, Writing-review & editing, C.L.: Formal analysis, Validation.

Data availability

The datasets generated and/or analysed during the current study are not publicly available ddue to corporate confidentiality and non-disclosure agreements. but are available from the corresponding author on reasonable request.

Declarations

Competing interests

The authors declare no competing interests.