Blockchain-based image copyright registration method supporting multi-dimensional data query

Traditional image copyright registration

Traditional research on image copyright registration covers methods based on cryptography, digital watermarking, image content retrieval, and artificial intelligence technology (Chalom, Asa & Biton, 2013). Methods based on cryptography mainly establish copyright by protecting the secure distribution of image content, such as copyright protection schemes based on proxy re-encryption (PRE), public key infrastructure (PKI) (Akram & Anaissi, 2024), identity encryption (Deng et al., 2020), attribute encryption (Walid, Joshi & Choi, 2024). However, once the content is decrypted, the image becomes ordinary content, devoid of copyright information, and this kind of method cannot track its subsequent reproduction or dissemination. Copyright registration methods based on digital watermarking technology can be used to protect the author identity, control the integrity of data, and verify the source of data, including robust watermarking (Hemdan, 2021) and fragile watermarking. The former is often used for image copyright authentication, while the latter is used to protect the integrity of the content.

The methods based on image content retrieval and big data technology are mostly used to monitor and analyze suspected infringing content, which is conducive to infringement warnings and rights protection. Among them, image content retrieval includes unencrypted image retrieval and encrypted image retrieval. Traditional methods cannot prevent infringement at the source of copyright registration and instead rely on the arbitration of a third party authority.

Copyright registration based on blockchain

The integration of blockchain into copyright protection has evolved significantly. Early approaches focused on storing cryptographic hashes (e.g., SHA256) on-chain to ensure data immutability, as seen in the work of Jing, Liu & Sugumaran (2021) on code copyright. However, this method is unsuitable for images, where perceptual similarity is key, as any minor modification results in a completely different hash.

This limitation led to a crucial evolution: the adoption of perceptual hashes and local features to capture visual similarity. For instance, Mehta et al. (2019) utilized perceptual hashing for originality detection, but their approach did not store the resulting fingerprints on the blockchain, thus sacrificing the benefits of decentralized traceability. Addressing this, works by Agyekum et al. (2019) and Shi et al. (2020) integrated perceptual hashing and local features (like Scale-Invariant Feature Transform (SIFT)) with blockchain storage. While these systems represented an important step towards content-based verification, their on-chain query mechanisms remained rudimentary, often relying on inefficient, single-mode searches. This early focus on feature-based similarity highlighted a foundational challenge that would be addressed by subsequent, more specialized research: how to efficiently query multi-dimensional data on-chain.

As the field has matured, recent state-of-the-art research has diverged into several distinct research thrusts.

1. On-chain indexing

Some research explored building on-chain indexes to improve query efficiency. For instance, the hybrid index by Zheng et al. (2020) and the Adaptive Balanced Merkle (ABM) scheme (based on SE-chain) by Jia et al. (2021) and utilize tree-based structures to accelerate the retrieval of one-dimensional data. These works are significant as benchmarks for on-chain indexing. However, their fundamental limitation is that the index structure is designed for single-dimensional data and is unsuitable for the multi-dimensional similarity search required for image content analysis, where its performance degrades significantly.

2. Transactional security and fair trading

A significant research thrust aims to secure the copyright transfer and trading process against malicious activities. A prime example is the “Proactive Defense” scheme by Chen et al. (2023), which uses advanced cryptographic tools like double-authentication-preventing (DAP) signatures to prevent the fraudulent double-selling of a copyright before a transaction is finalized. Similarly, Yu et al. (2023) proposed a fair image trading scheme that uses searchable symmetric encryption and smart contracts to ensure fairness and privacy during the transaction process. While these works provide robust security for the transaction phase, their query mechanisms are designed to trace the history of a specific, exact copyright hash or to facilitate private retrieval between specific users. This highlights that even the most secure transaction frameworks still fundamentally rely on an efficient underlying mechanism to first determine a work’s originality, a problem they do not solve.

3. Data integrity and lifecycle management

Another direction concentrates on ensuring the integrity of the original media and managing its entire lifecycle. The work by Wang et al. (2022) combines a zero-watermarking algorithm with blockchain and InterPlanetary File System (IPFS), allowing copyright information to be associated with an image without modifying the image data itself. The framework by Liu et al. (2021) utilizes Hyperledger Fabric and smart contracts to manage the full life cycle of digital rights, including registration, transfer, and query. While these schemes provide robust frameworks for verification and management, their query mechanisms are based on specific identifiers (like a copyright number or user ID) or exact hash values. They are designed for one-to-one verification of known items, indicating that robust lifecycle management requires an efficient, one-to-many originality search as a foundational component, which remains an unaddressed challenge in these approaches.

4. Comprehensive systems with similarity search

A third approach involves building complete, end-to-end Digital Rights Management (DRM) systems that incorporate similarity-based originality checks. The DRPChain proposed by Yun et al. (2024) exemplifies this. They developed a robust anti-cropping perceptual hash for similarity detection and designed a novel consensus algorithm, K-Raft, tailored for copyright management. A similar approach is taken by Zhou et al. (2024), who use the SIFT algorithm for feature extraction and similarity computation within a Hyperledger Fabric framework. Both systems address originality by comparing a new image’s features against existing records. However, their search mechanism relies on a linear scan of all stored fingerprints. As the number of registered images grows, this exhaustive search will inevitably become a significant performance bottleneck, hindering the system’s scalability.

As illustrated in Table 1, state-of-the-art research addresses different but important facets of the copyright protection problem. Schemes that focus on transactional security, such as those by Chen et al. (2023) and Yu et al. (2023), excel at preventing fraudulent transfers but are not designed for content-based originality checks. Approaches centered on data integrity and lifecycle management, like those of Wang et al. (2022) and Liu et al. (2021), are effective for verifying specific images but lack a large-scale search capability. Comprehensive systems that do incorporate similarity checks, represented by Yun et al. (2024) and Zhou et al. (2024), often rely on a linear scan, making their efficiency a significant concern for large-scale applications. Similarly, early on-chain indexing efforts, such as those by Jia et al. (2021) and Zheng et al. (2020), provide efficient one-dimensional indexes but are not applicable to the multi-dimensional search required for image content. Our scheme addresses this specific scalability bottleneck by providing an indexed search mechanism (the MKD-Tree), which is designed for efficient, multi-dimensional similarity queries directly on-chain.

Blockchain image copyright registration model

The proposed blockchain-based image copyright registration model involves three main participants: copyright registration authorities, copyright registration users and blockchain registration system. Since each node does not store complete block data, the model relies on on-chain queries to complete image copyright registration. Before copyright confirmation, originality detection based on multi-dimensional data queries must be completed.

(1) Registered copyright users

The copyright registration user is the applicant for image copyright. The user first applies to the copyright registration agency and then submits the user’s basic information and the image to be registered. The image query summary generated through image originality detection is stored on the blockchain and in the copyright database to complete the image copyright confirmation. Users who have completed the copyright registration can query the confirmed image copyright information based on their user ID.

(2) Copyright registration agency

After registration, the copyright agency can join the blockchain network and accept the applications from copyright registration users. It interacts with copyright registration users, assists users in completing the originality detection, queries, records copyright information on the chain to confirm the right, maintains their own off-chain image copyright database, and stores the image query information off-chain.

(3) Blockchain registration system

Multiple copyright registration agencies joined the blockchain network, overcoming the issue of image copyright information silos. The blockchain registration system interacts with the agencies, uses the image multi-dimensional feature data for originality detection and querying, and completes the copyright data confirmation work.

The blockchain-based image copyright registration model is shown in Fig. 1. All copyright registration agencies join the blockchain copyright registration system and store copyright data in a collaborative manner. Copyright registration users obtain copyright by applying to copyright registration agencies. After the copyright registration agency carries out the originality detection and query, the image copyright information is stored on the chain for copyright confirmation.

Blockchain image copyright registration method

This section proposes a blockchain image copyright registration method that supports multi-dimensional data queries, named the MDQ scheme, which includes block storage structure construction based on MKD trees, image originality detection and querying, and user copyright information querying. Finally, a detailed copyright registration process for blockchain images supporting multi-dimensional data queries is designed. In the process of image copyright registration, the image fingerprint is stored on the chain to support the approximate querying of multi-dimensional data. At the same time, users can query copyright information by unique identifier. The blockchain image copyright registration method we designed can choose the image fingerprint generation method as needed. This section takes image content feature data as an example.

The method mainly includes three parts: image copyright registration application and right confirmation, image originality detection and querying, and user copyright information querying. The copyright registry stores the image copyright information it accepts on the chain and synchronizes the data according to its own storage capacity. Therefore, before copyright registration, originality detection querying is divided into on-chain querying and local querying. At the same time, the MKD tree structure improves the query efficiency within each block and supports the querying of user copyright information.

For ease of exposition, the abbreviations in our method are defined in Table 2.

Implementing an efficient multi-dimensional query system on a blockchain presents a significant technical challenge centered on the inherent trade-off between query efficiency and the blockchain’s fundamental requirement for data verifiability.

Traditional databases utilize dynamic index structures like R-trees, which are optimized for fast spatial queries but are mutable and not natively verifiable in a decentralized context. Conversely, blockchains guarantee data integrity through immutable, hash-linked structures like Merkle trees. While excellent for verification, Merkle trees are extremely inefficient for search operations, as they offer no indexing capability and typically require a full scan of the data.

Therefore, designing a practical solution requires a novel hybrid data structure that can synergistically combine the search capabilities of a spatial index with the verifiable integrity of a Merkle-based structure, all while remaining lightweight enough to be viable on-chain. Our proposed MKD-tree is specifically engineered to address these challenges.

Block storage structure based on MKD tree

The traditional hash fingerprint method has strict requirements on the uniqueness of the image. In fact, images need to be represented in terms of content (such as global or local features), and for some photographs, positional features can also be used. In order to achieve approximate queries, images need to be represented by features that can represent the similarity of images rather than the traditional hashing method. Therefore, the image fingerprint used in this article has the characteristics of representing similarity. The originality on-chain query of this method is to retrieve approximate images through multi-dimensional data. In the original Merkle tree storage mode of the blockchain, originality detection queries need to traverse the data of each block for similarity judgment, which is inefficient and does not support multi-dimensional data queries.

To support the originality detection function of our method, this article designs a block storage structure based on the Merkle-KD tree (MKD Tree). The MKD tree is a binary tree structure that integrates a Merkle tree with a KD tree. The Merkle structure ensures data integrity and tamper-resistance, while the KD tree enables efficient indexing and retrieval in multi-dimensional feature space (Zheng et al., 2022).

Specifically, this structure is designed to support multi-dimensional data queries (MDQ), where each image is represented as a multi-dimensional feature vector (e.g., color histograms, textures, spatial information). These feature vectors are organized using the KD tree structure to allow for range-based or nearest-neighbor queries. The Merkle tree component provides verifiability of the retrieved results, ensuring that the query process is auditable and secure.

In our MDQ scheme, given a query image, its feature vector is extracted and used to traverse the MKD tree to find similar images. This integration of KD-based indexing and Merkle-based verification enables the system to perform fast, accurate, and secure similarity queries required for blockchain-based copyright registration. Taking the image content feature data as an example to describe the image, suppose that the selected image multi-dimensional feature data is $<P,L>$, then an image can be expressed as $tuple=<P,L>$, which is the image fingerprint used in image originality detection. For example, $P$ can represent content-based features, while $L$ can represent positional features. Then, the MKD tree is constructed by using the multi-dimensional feature data of the image. Assume that each block contains $n$ multi-dimensional features of image data set $v=\left\{<P_1,L_1>,<P_2,L_2>,<P_3,L_3>,\dots ,<P_n,L_n>\right\}$, where the multi-dimensional feature data of the $i$-th image $v_i=<P_i,L_i>$. Firstly, the KD-tree index is constructed according to the set $v$. In order to make it preserve the verifiable query feature of the blockchain, the MKD-tree root is generated by merging the Merkle hash values of the nodes. Taking the user address as the unique user identification, we define the node data structure of the MKD tree, including leaf nodes, internal nodes, and root nodes, as shown in Fig. 2.

Let the MKD-tree have a total of 10 leaf nodes, which are denoted by $p_i$, and $p_i=\left\{O_i,v_i\right\}$. Let $u_i$ be the internal node of the MKD tree, and $u_i$ contains $h_{u_i}$. Let the left child node of $u_i$ be $q$, the right child node be $w$, and $l_i$ be the split line, then $h_{u_i}=Hash\left(h_q,h_w,l_i\right)$. $u_1$ represents the root node of the MKD tree, $u_1$ contains $h_{u_1}$. The leaf nodes contain the maximum value $Max$ and the minimum value $Min$ of the user addresses. The MKD tree structure is shown in Fig. 3.

The efficiency of the registration process is enhanced by our block storage structure, which utilizes the MKD tree. This architecture serves as the foundation for performing both image originality detection and user copyright information queries. A diagram of this on-chain storage structure is provided in Fig. 4.

Blockchain copyright registration based on MKD tree

The blockchain-based image copyright registration algorithm first accepts the user’s registration application through the copyright registration authority. After verifying the identity of the user, the copyright registration authority makes an originality query of the registered image. When the image passes the originality detection, the copyright agency stores the image’s on-chain query summary and the user identity information (such as user address) in the blockchain as copyright data in the structure of the MKD tree, ensuring the immutability of the on-chain query summary and improving the efficiency of on-chain queries. At the same time, it supports users who have registered copyrights to query based on identity.

This section first introduces the summary of on-chain queries, then designs a blockchain-based image copyright registration process, and explains the originality query process and user copyright information query process in detail.

On-chain query summary

The MKD tree-based block storage architecture supports two types of on-chain queries, including the user copyright information query and the originality detection query. The user copyright information query can use the user identity (such as the user address) as the on-chain query summary. Originality detection query is based on the multi-dimensional feature data of the image, and the image fingerprint $v_r$ is the query summary on the chain. By searching and querying the authenticated image feature data $v_r$ on the blockchain, the approximate query is used to determine the results of the originality audit. When the $v_u$ of an image uploaded by a user is similar to the corresponding on-chain query summary, the image is considered to be similar.

Image copyright registration process

• (1)

  Before submitting a copyright registration application, the image uploader $IU$ must first encrypt the image to be registered $I_u$ and submit it to the blockchain together with relevant metadata. Subsequently, the $IU$ submits a registration application to the nearest $RA$ in its area, which includes the $I{U}^{\mathrm{\prime }}s$ identity information and the image to be registered $I_u$.

• (2)

  After receiving the copyright registration application, $RA$ verifies the identity of $IU$, obtains the image $I_u$ to be registered, and carries out the originality detection based on on-chain query summary. If a registration is rejected due to image duplication, $IU$ may choose to disclose the confidential image content to prove its ownership of the image and challenge the rejection.

• (3)

  $RA$ performs on-chain data query, starting from the MKD tree root of the current block, until the corresponding leaf node is found, and $k{v}_r$ that are similar to $v_u$ are found;

• (4)

  Determine whether the images represented by $v_r$ and $v_u$ meet the approximation under a certain threshold. If so, $RA$ returns a notification that the $IU$ originality test has not passed and the registration has failed, and the query ends; if not, query the next block;

• (5)

  If all blocks are queried and there is no similar on-chain query summary, the result of $RA$ originality detection passing is returned

• (6)

  $RA$ uploads the user identifier of the copyright registration (such as user address) and the image on-chain query summary $v_u$ to the blockchain and stores them in the MKD tree structure to complete the ownership confirmation.

Originality detection query

This section introduces the query process of image originality detection. First, after submitting an image for registration, the user sends the copyright image to be registered to the copyright registration agency, which verifies the user’s identity and runs the originality detection and query algorithm. $RA$ uses the query summary to query in the local block and will refuse to register if similar results are returned. Otherwise, other nodes are requested to query the on-chain query summary $v_r$ of the image copyright registry blockchain using $v_u$ to retrieve approximate data. If similar results are returned, the result of denied registration is still returned. When similar images are not queried, the copyright registration blockchain system confirms the copyright of the user’s image, stores the image copyright data in the blockchain, and completes the registration. Taking the number of approximate items as 1 as an example, the query process of originality detection on the blockchain is shown in Algorithm 1.

The core of the process is an efficient nearest neighbor search performed within each block. For each block, the system takes the query image’s fingerprint, $v_u$, and uses the block’s MKD-tree to find the single most similar fingerprint, $v$, that has been previously registered. This search operation is highly optimized by the MKD-tree’s structure, which avoids an inefficient linear scan of all data within the block. The search algorithm operates as follows:

(1) The search starts at the root of the MKD-tree and traverses down to a leaf node. This path is determined by comparing the query fingerprint $v_u$ against the splitting criteria at each internal node, leading to an initial candidate for the nearest neighbor.

(2) The algorithm then backtracks up the tree from the leaf. During this process, it continuously updates the “current best” nearest neighbor if a closer one is found. Crucially, it prunes entire branches of the tree that cannot possibly contain a fingerprint closer than the one already identified, which is the source of the KD-tree’s efficiency.

After the search within a block is complete, the algorithm proceeds to the decision step. As shown in Algorithm 1, the distance between the query fingerprint $v_u$ and the found nearest neighbor $v$ is calculated. If this distance is less than or equal to a predefined similarity threshold $d$, the image is deemed non-original, and the registration process is immediately rejected. If the entire blockchain is traversed without finding such a match, the image is confirmed as original and can be registered.

Experimental setup

This section elaborates on the experimental environment established to validate our proposed scheme. We utilized the SimBlock blockchain simulation platform for our experiments. SimBlock is an open-source, Java-based simulation tool capable of effectively modeling node behaviors, block propagation, transaction processing, and consensus mechanisms within a blockchain network. This allows for the performance evaluation various protocols and optimization schemes in a highly controllable environment.

Our experimental environment was set up on a server equipped with an Intel(R) Core(TM) i5-12600KF CPU and 32.00 GB of RAM, running CentOS 7.8 as the operating system. This setup provides sufficient computational resources to support simulations involving a large number of nodes and transactions. SimBlock itself is developed in Java. To run and modify the SimBlock source code, we installed Java Development Kit (JDK) 11 and Gradle 6.9 for project management and building. Furthermore, Git was used for version control and source code management. Within the SimBlock simulation platform, we made necessary modifications and extensions to its core modules to accommodate our scheme.

Efficiency analysis

Baseline comparison and causal link analysis

To establish the causal relationship between the theoretical innovation and the observed efficiency improvement and to illustrate the effectiveness of our scheme, we conducted a baseline comparison experiment. In this experiment, we compared the MDQ scheme with a linear scan method (labeled as “baseline”). The baseline scheme performs originality detection by exhaustively comparing the query fingerprint with all $n$ fingerprints in the block without utilizing any index structure.

The results are presented in Fig. 5. As shown, the query time of the baseline scheme grows linearly with the number of transactions per block (denoted as $n$), which is consistent with its theoretical $O\left(n\right)$ time complexity. In stark contrast, the query time for our MDQ scheme remains consistently low and exhibits almost flat, sub-linear growth across the same range of data volumes.

This result provides direct evidence that the dramatic efficiency gain is causally linked to the spatial pruning capability of the MKD-tree. By avoiding a full scan of the data, the MKD-tree’s underlying $O\left(logn\right)$ average query complexity is empirically validated. This comparison confirms that the MKD-tree’s ability to perform multi-dimensional spatial pruning is the primary driver of the significant efficiency improvement observed in the MDQ scheme. The experiment thus empirically validates the causal link between our proposed data structure and its high query efficiency.

Performance comparison with ABM scheme

To evaluate the performance of our MDQ scheme against a relevant state-of-the-art method, we selected the ABM scheme (Jia et al., 2021) as the primary baseline for this comparison. Unlike systems that focus primarily on off-chain storage or simple duplication checks (e.g., Agyekum et al., 2019), the ABM scheme represents an advanced, on-chain indexing structure designed for efficient data retrieval, making it a suitable and challenging benchmark. It integrates the fast search capability of a balanced binary tree with the verification efficiency of a Merkle tree and dynamically adjusts its structure based on query demand.

Our simulation experiments were designed to compare the two schemes across two key metrics: (1) block storage structure construction time and (2) originality detection query time. These metrics were evaluated under various conditions, including different numbers of approximate items ( $k$) and transactions per block ( $n$). The specific experimental parameters are detailed in Table 3.

Table 3:

Experimental parameters.

Parameter	Number	Parameter	Number
$k$	10	$Nu{m}_{tx}$	128
	20		256
	30		512
	40		1,024
	50		2,048
	60		4,096
	70		8,192

DOI: 10.7717/peerj-cs.3284/table-3

For the query of the ABM scheme and MDQ query of the proposed scheme, the construction time of the block storage structure is shown in Fig. 6 under different numbers of transactions per block. It can be seen from the experimental results that when the number of transactions in a single block is 128, 256, or 512, the construction time of the storage structure of our scheme is similar to that of the ABM scheme, both of which are in the millisecond range. As the number of transactions increases, the construction time of the block storage structure of the MDQ scheme is lower than that of the ABM scheme. The results in Fig. 6 show that the construction time of the block storage structure of the MDQ scheme is similar to other schemes when the number of transactions per block is small, and the time consumption is lower when the number of transactions per block increases to a large value, which demonstrates certain advantages. This efficiency stems from the $O\left(nlogn\right)$ average-case complexity of building the KD-tree structure, which scales effectively with a large number of transactions ( $n$). The MDQ scheme’s ability to support multi-dimensional data storage with low construction time gives it a distinct advantage over the ABM scheme.

As shown in Fig. 7, we plot the relationship between the number of searches $k$ and the query time consumption of originality detection when the number of transactions per block is 512, 1,024, and 2,048, respectively. With the increase in the number of approximate items searched, the query time of the ABM scheme and the MDQ scheme increases. The experiments compare the query time of the schemes under three different numbers of transactions: 512, 1,024, and 2,048. The originality detection query time of the MDQ scheme is lower than that of the ABM scheme. The experimental results show that the MDQ scheme has higher query efficiency in originality detection queries compared to the ABM scheme.

Figure 8 shows the originality detection query time of the proposed scheme and ABM scheme for the same $k$ value. The experimental results show that the number of searches $k$ is closely related to the originality detection query efficiency. Let the similarity threshold be $d$ and the similarity function be $SIM$. We discuss this in two cases:

• (1)

  $k=1$. In the originality detection, the search number $k$ is set to 1, that is, the image that is most similar to the image to be registered in each block is searched. Its on-chain query summary is $v_r$, and the similarity $SIM\left(v_u,v_r\right)=MIN\left(B\right)$. Since the current $v_r$ is the fingerprint data with the highest similarity to $v_u$ in this block, the similarity distance between $v_r$ and $v_u$ is the minimum value in this block. Therefore, the originality detection result of the current block is shown in Eq. (1): (1) $$\begin{array}{c}\{\begin{array}{c}MIN\left(B\right)\le d,Existenceofsimilarimages\\ MIN\left(B\right)>d,Therearenosimilarimages\end{array}\end{array}.$$

• If $MIN\left(B\right)\le d$, it means that the fingerprint most similar to the image fingerprint to be registered in this block satisfies the similarity threshold condition, so the originality detection query fails and the registration is rejected. If $MIN\left(B\right)>d$, it means that the similarity distance between the most similar image fingerprint in this block and the image fingerprint $v_u$ to be registered has exceeded the threshold, so there is no similar image in this block, and the next block is directly queried.

• (2)

  $k>1$. For originality detection, the number of searches $k>1$, that is, the top $k$ image fingerprints in each block that are similar to the image fingerprint to be registered are queried. In this case, it is necessary to calculate the similarity distance $SIM\left(v_u,v_r\right)$ between $k$ $v_r$ and $v_u$ one by one. If $SIM\left(v_u,v_r\right)<d$ exists, the originality detection query fails and the registration is rejected. If there is no $SIM\left(v_u,v_r\right)<d$, then there is no approximate image in this block, and the query continues to the next block.

When $k>1$, it can query several approximate images, which is more accurate than $k=1$. However, the method of range query on the MKD tree (that is, giving the similarity threshold and query target, retrieving the nodes that meet the threshold condition) needs to traverse all nodes, and the query efficiency is low. Considering several cases, $k>1$ is a compromise scheme, that takes into account both accuracy and query efficiency, and can be flexibly selected in specific applications.

The performance disparities observed between our MDQ scheme and the ABM scheme are not indicative of a flaw in the ABM approach, but rather highlight a fundamental mismatch between its design principles and the specific requirements of the originality detection task.

The ABM scheme is an efficient one-dimensional index, optimized for key-value retrieval. However, when tasked with a multi-dimensional similarity query, its underlying B+-Tree variant structure cannot leverage multiple feature dimensions to prune the search space. To satisfy such a query, the search process is compelled to traverse a substantial portion of its nodes to compute the multi-dimensional distance for each data point. This effectively neutralizes its indexing advantage for this specific task, causing its performance to scale in a manner that approaches the linear complexity of a full scan, which is consistent with the $O\left(n\right)$-like growth observed in our experiments.

In contrast, our MDQ scheme’s MKD-tree is a native multi-dimensional index. Its KD-tree foundation is specifically designed to partition the high-dimensional feature space. During a k-NN search, the algorithm can aggressively prune entire hyper-rectangles of the search space that are guaranteed not to contain any points closer than the current k-th nearest neighbor. This spatial pruning is the core mechanism that allows our scheme to maintain its theoretical $O\left(klogn\right)$ average-case complexity. This deeper analysis underscores that for complex tasks like image copyright protection, a data structure that is natively aligned with the multi-dimensional nature of the data is paramount for achieving on-chain scalability.