Homomorphic encryption and joint optimization based method and system for visible watermarking and traceability of ciphertext image

Abstract

The application discloses a ciphertext image visible watermark searchable and traceability method and system based on homomorphic encryption and joint optimization, and relates to the technical field of information security. A user terminal extracts robust features from an original image, performs homomorphic encryption addition, and uploads the original image; a cloud server constructs watermark embedding parameters and index generation parameters into unified decision variables, solves a joint optimization model with watermark visibility, search accuracy, and ciphertext statistical security as optimization objectives and visual distortion as a constraint, embeds a semi-transparent visible watermark in a ciphertext domain according to optimal parameters, stores the visible watermark on a chain, generates a robust perceptual hash, and constructs a searchable encrypted security index to support ciphertext search; when a suspected pirated image is found, a watermark identifier is used to query on-chain storage and a watermark pattern is compared to realize bidirectional verification and traceability. The application solves the problems of search accuracy damage and tamperable traceability evidence caused by visible watermark embedding in a ciphertext domain, and is suitable for copyright protection of massive encrypted images.

Description

Technical Field

[0001] This invention relates to the fields of information security and digital copyright protection technology, specifically to a method and system for retrieving and tracing ciphertext images with visible watermarks based on homomorphic encryption and joint optimization. Background Technology

[0002] In public service platforms such as smart libraries and digital museums, a large number of valuable image resources need to be stored in the cloud for easy sharing. To protect privacy and copyright, these images are often stored in encrypted form. However, existing technical solutions have the following significant shortcomings:

[0003] (1) Copyright protection of encrypted images is not intuitive. Existing research focuses on invisible or reversible watermarks in the encrypted field, which require special algorithms and keys to extract and verify, and cannot provide ordinary users with instant and visual copyright notices; while encrypted field embedding schemes for visible watermarks (which are presented directly in the image in a semi-transparent form) are extremely rare.

[0004] (2) The fundamental differences between visible and invisible watermarks prevent existing technologies from being directly applied. The pixel value modification range of invisible watermarks is usually within ±2, and the impact on the accuracy of image content-based hash retrieval is usually within 5%; while visible watermarks require a semi-transparent pattern on the image, and the pixel value modification range is usually ±30 or more, which can impair retrieval accuracy by 20% to 40%. The optimization goal of invisible watermarks is mainly to balance imperceptibility and robustness, while the optimization of visible watermarks involves three conflicting goals: visibility, visual quality, and retrieval accuracy, making the optimization significantly more difficult.

[0005] (3) Poor availability of encrypted data. After image encryption, traditional content-based retrieval techniques become ineffective. More importantly, in existing technologies, watermark embedding and retrieval index construction are independent of each other. Watermark embedding often impairs the accuracy of subsequent retrieval—for visible watermarks, this impairment is particularly severe due to their high embedding strength and significant alteration of image content—there is an unrecognized conflict and constraint between the two.

[0006] (4) Difficulty in copyright tracking. Once an encrypted image is decrypted by an authorized user and illegally disseminated, it is difficult to trace the source of the leak; traditional source tracing relies on centralized databases, and the evidence records are at risk of being tampered with, resulting in insufficient legal proof.

[0007] (5) Performance trade-offs rely on experience. Existing visible watermarking or information hiding technologies rely heavily on human experience or simple rules in terms of embedding strength and location selection, making it difficult to systematically balance the prominence of copyright marks, the visual quality of the original image, retrieval accuracy, and encryption security.

[0008] The applicant previously filed Chinese patent application CN121664934A, entitled "A Method and System for Embedding Visible Watermarks in Ciphertext Domain Images Based on Swarm Intelligence Optimization." This application discloses a technical solution for acquiring the original plaintext image, encrypting it to generate a ciphertext image, performing residual entropy space modeling, generating a visible watermark, and optimizing the search embedding parameters based on swarm intelligence multi-objective optimization. However, this prior application only optimizes the watermark embedding parameters and does not have ciphertext image retrieval functionality. It does not include retrieval accuracy in the optimization objective, nor does it have blockchain-based evidence storage and traceability capabilities, thus failing to solve the problem of coordinated optimization between watermark embedding and ciphertext retrieval.

[0009] Therefore, there is an urgent need for an innovative technical solution that can intuitively mark copyright, support efficient content retrieval, and enable source tracing of leaks while ensuring the confidentiality of image data throughout the entire process. Furthermore, the watermark embedding and retrieval functions should be optimized in synergy rather than hindering each other. Summary of the Invention

[0010] To address the aforementioned shortcomings of existing technologies, the present invention aims to provide a method and system for retrieving and tracing ciphertext images with visible watermarks based on homomorphic encryption and joint optimization, solving the following technical problems: how to embed visible watermarks into the ciphertext domain to achieve immediate and visual declaration of copyright information; how to achieve efficient content retrieval of encrypted images while ensuring ciphertext security; how to achieve synergistic optimization between watermark embedding and index construction rather than mutual obstruction; and how to establish an immutable traceability audit mechanism to provide legally recognized evidence for copyright protection.

[0011] To address the aforementioned technical problems, this invention provides a method for retrieving and tracing ciphertext images with visible watermarks based on homomorphic encryption and joint optimization. This method is applied to a system comprised of a user terminal, a cloud server, and a blockchain-based evidence storage platform. The method includes: S1, the user terminal extracts robust feature vectors from the original image, encrypts it using an additive homomorphic encryption algorithm to obtain a ciphertext image, and generates watermark generation information for a semi-transparent visible watermark based on the user's identity identifier. The ciphertext image, robust feature vectors, and watermark generation information are then uploaded to the cloud server; S2, the cloud server performs block entropy calculations on the ciphertext image in the ciphertext domain to determine candidate watermark embedding regions. The watermark embedding parameter x and the index generation parameter y are constructed as unified decision variables, with watermark visibility, retrieval accuracy, and ciphertext statistical security as joint optimization objectives, and image visual distortion as a constraint. The process involves: S1) Constructing and solving a multi-objective joint optimization model; S2) Embedding a visible watermark into a ciphertext image using ciphertext addition operations according to the optimal embedding parameters; and S3) Submitting the watermark embedding operation's evidence information to a blockchain evidence storage platform for storage; S4) Generating a robust perceptual hash based on robust feature vectors using the optimal index parameters and constructing a secure index using symmetric searchable encryption; S5) Responding to authorized users' retrieval requests, the cloud server performs ciphertext matching retrieval based on the secure index, returning a ciphertext image with a visible watermark for user terminals to decrypt. The visible watermark in the decrypted plaintext image can be visually identified without a dedicated extraction algorithm; and S6) When a suspected pirated image is discovered, extracting the visible watermark pattern and watermark identifier, querying the evidence storage record on the blockchain evidence storage platform using the watermark identifier, and performing two-way verification and traceability by comparing the watermark pattern.

[0012] This invention also provides a retrieval and traceability system for ciphertext images with visible watermarks based on homomorphic encryption and joint optimization, comprising a user terminal, a cloud server, and a blockchain evidence storage platform. The user terminal includes an image encryption and feature extraction unit, a watermark generation unit, a query processing unit, and an image decryption and display unit; the cloud server includes a ciphertext watermark embedding unit with a built-in multi-objective optimization algorithm module, a feature extraction and index management unit, a secure retrieval unit, a storage unit, and a communication interface unit; the blockchain evidence storage platform is used for decentralized evidence storage of watermark embedding operations, retrieval operations, and traceability verification operations through smart contracts.

[0013] Compared with the prior art, the beneficial effects of the present invention include:

[0014] (1) A systematic synergistic effect has been generated in watermark embedding, index construction, secure encryption, and trusted evidence storage. Homomorphic encryption provides a secure operating environment for the ciphertext field embedding of visible watermarks; joint optimization ensures that watermark embedding does not excessively impair retrieval accuracy; symmetric searchable encryption enables encrypted images to be efficiently retrieved while maintaining confidentiality; and blockchain evidence storage provides tamper-proof evidence support for the copyright declaration of visible watermarks. The four are interdependent, and the absence of any module will substantially weaken the function of the remaining modules. The overall technical effect far exceeds the sum of the effects of each part.

[0015] (2) Deep coupling and synergistic optimization of watermark embedding and index construction were achieved. By incorporating retrieval accuracy as one of the objective functions into the joint optimization framework, the impact of watermark embedding on subsequent retrieval is considered during watermark embedding, thus systematically solving the inherent contradiction that visible watermark embedding damages retrieval accuracy. At the same time, image visual distortion is set as a constraint rather than an optimization objective, avoiding image quality degradation of the optimization solution, making the optimization more focused and efficient.

[0016] (3) It achieves a four-in-one integration of secure storage, intuitive copyright, efficient retrieval, and reliable traceability. Users obtain usable images with clearly visible copyright markings. Ordinary users can intuitively identify copyright information without any special extraction algorithms. At the same time, the underlying data is always protected in encrypted form, and all watermarking operations are stored on the blockchain.

[0017] (4) Enhanced traceability and legal validity of copyright protection. Visible watermarks are strongly linked to user identities, and the watermark operation is stored in an immutable manner through blockchain. Any leaked or pirated image carries a verifiable source fingerprint. Since the watermark is visible, any third party can directly identify the watermark pattern from the pirated image. The source tracing and verification threshold is low. The source tracing process is combined with blockchain verification, which has legally recognized evidentiary effect.

[0018] (5) Improved the security and controllability of smart library data services. Provided a complete solution for the massive image resources of smart libraries, integrating confidentiality, controllable access, copyright declaration, and infringement tracing. Attached Figure Description

[0019] Figure 1 This is a flowchart illustrating the overall process of the method of the present invention.

[0020] Figure 2 This is a system logic architecture diagram of the present invention;

[0021] Figure 3 This is a flowchart of the solution process for the multi-objective joint optimization model of this invention;

[0022] Figure 4 This is a flowchart for tracing and auditing the source of piracy of this invention.

[0023] Figure labeling: 100, User terminal; 110, Resource upload terminal; 111, Image encryption and feature extraction unit; 112, Watermark generation unit; 120, Retrieval terminal; 121, Query processing unit; 122, Image decryption and display unit; 200, Cloud server; 210, Ciphertext watermark embedding unit; 211, Multi-objective optimization algorithm module; 220, Feature extraction and index management unit; 230, Secure retrieval unit; 240, Storage unit; 250, Communication interface unit; 300, Blockchain evidence storage platform; 310, Smart contract; 320, Authorized node. Detailed Implementation

[0024] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0025] This embodiment uses cloud-based encryption protection of image resources in a smart library as an application scenario. The system consists of a user terminal 100, a cloud server 200, and a blockchain evidence storage platform 300. Figure 2 As shown. User terminal 100 includes resource upload terminal 110 (with built-in image encryption and feature extraction unit 111 and watermark generation unit 112) and retrieval terminal 120 (with built-in query processing unit 121 and image decryption and display unit 122); cloud server 200 includes encrypted watermark embedding unit 210 (with built-in multi-objective optimization algorithm module 211), feature extraction and index management unit 220, secure retrieval unit 230, storage unit 240 and communication interface unit 250; blockchain evidence storage platform 300 adopts consortium blockchain architecture (such as Hyperledger Fabric or Chang'an Chain), including smart contract 310 and authorized node 320. Smart contract 310 is used for watermark operation evidence storage, evidence storage query and verification. Authorized node 320 ensures through access control mechanism that only authorized system nodes can submit and verify evidence storage transactions. The overall process of this method is as follows. Figure 1 As shown, it includes steps S1 to S6.

[0026] Step S1: User-side image preprocessing and uploading

[0027] On user terminal 100 (such as the library resource administrator's client), perform the following operations:

[0028] S1.1 Feature Extraction and Image Encryption. For the original image I, a robust feature vector F is extracted using a robust feature extraction algorithm. To ensure the consistency of the feature sources, the robust feature vector F is primarily composed of low-frequency coefficient features of the Discrete Cosine Transform (DCT) (serving as the basis for generating the robust perceptual hash in step S3), and optionally includes scale-invariant feature transform (SIFT) keypoint descriptors for auxiliary verification of images with geometric transformations such as rotation and scaling during the retrieval result verification stage. Subsequently, the original image I is encrypted using an additive homomorphic encryption algorithm to obtain the ciphertext image E(I). As an optional implementation, the additive homomorphic encryption algorithm can adopt the Paillier encryption scheme: when generating the key, two large prime numbers p and q are selected, n=pq and λ=lcm(p-1,q-1) are calculated, a random integer g is selected, and the public key is set to (n,g) and the private key to λ; for the plaintext pixel m, a random number r is selected, and the ciphertext c=E(m)=g. m ·r n mod n 2 During decryption, m = L(c^λ mod n²)·μ mod n, where L(u) = (u-1) / n, and μ = (L(g^λ mod n²)). -1 mod n; Homomorphic addition satisfies E(m1)·E(m2) mod n 2 = E(m1+m2), which allows subsequent watermark embedding operations to be performed directly in the ciphertext field without decryption.

[0029] S1.2 Generation of Semi-Transparent Visible Watermark Information. Based on the current user's unique identifier (UID), a corresponding semi-transparent visible watermark pattern W (e.g., a semi-transparent pattern containing an organization's identifier or user ID) is generated. The watermark pattern is generated by concatenating the UID with a system-preset template identifier and inputting it into a pseudo-random number generator to generate a watermark pixel matrix. The pixel values ​​range from [0, 255], and the transparency α can be configured by the system. This semi-transparent visible watermark is superimposed on the image in a semi-transparent form. Ordinary users can directly identify the copyright information in the watermark without any decryption operations or special extraction algorithms. At the same time, the UID is used as a seed to generate a unique watermark identifier H_wm through the SHA-256 hash function, which is used for subsequent blockchain evidence storage association.

[0030] S1.3 Data Upload. The generated encrypted image E(I), robust feature vector F, user identifier UID, and watermark identifier H_wm are packaged and uploaded to cloud server 200. The semi-transparent visible watermark pattern W itself is not transmitted over the network, but is generated by cloud server 200 from a trusted watermark template library based on the UID, in order to reduce transmission overhead and leakage risk.

[0031] Step S2: Visible watermark embedding in ciphertext field based on homomorphic encryption (joint optimization of embedding and index parameters)

[0032] After receiving the data, the cloud server 200 directly embeds a semi-transparent, visible watermark into the encrypted image E(I) without decrypting the image content. Unlike existing technologies, this step constructs the watermark embedding parameters and subsequent index generation parameters into a unified joint optimization problem.

[0033] S2.1, Ciphertext Domain Image Block Analysis and Entropy Calculation. The ciphertext image E(I) is divided into several image blocks of size b×b (b can be 8 or 16). For each candidate image block B... i Calculate its information entropy H(B) i )=-Σ v p v ·log2p v Where v∈[0,255] (8-bit grayscale image), p v For pixel value v in image block B i The probability of its occurrence in the image is used to assess its statistical properties and the space available for embedding modifications. Since the image is encrypted, entropy calculation must be performed in the ciphertext domain, specifically using the following secure computation protocol:

[0034] (1) Histogram statistics of the ciphertext domain: Let image block B be i Includes b 2 Each pixel has a ciphertext of E(p) pixels. i For each possible pixel value v, cloud server 200 uses the additive homomorphic property to calculate the ciphertext difference E(p). i )·E(v) -1 mod n 2 =E(p i -v), then select the random blinding factor r i Calculate E(p) i -v) ^ r i mod n 2 = E(r i ·(p i -v)) sends the blinded ciphertext to the decryption assistant (user terminal 100 or a trusted third party) who holds the decryption private key; after decryption, the plaintext is zero if and only if pi =v, therefore the decryption assist only returns the equivalent judgment result of whether it is zero. The cloud server 200 cannot know the plaintext value of any pixel throughout the entire process, and the decryption assist also cannot know the real value of the pixel due to the existence of the blinding factor.

[0035] (2) Frequency statistics: The cloud server 200 counts the number of pixels c in the image block that are equal to each pixel value v based on the equality judgment results. v This yields the frequency vector [c0, c1, ..., c 255 Then calculate the probability p. v =c v / b 2 .

[0036] (3) Entropy calculation: Logarithmic operations are implemented in the ciphertext domain using a table lookup method. Specifically, the probability p is... v The data is quantized into L fixed-point levels with a preset precision. The decryption assistance party pre-calculates the ciphertext entries for each quantization level q, corresponding to q·log2q, forming a ciphertext logarithmic lookup table. The cloud server 200 uses a blinded index to query the corresponding ciphertext entries for the ciphertext probabilities of each pixel value and performs homomorphic accumulation on all entries to obtain the ciphertext E(H(B) of the image patch entropy value. i Finally, the decryption assistance party decrypts the image block entropy value H(B) to obtain the image block entropy value. i This entropy value, as a statistical feature, does not reveal the specific image content. As an alternative implementation, logarithmic operations can also be approximated in the ciphertext domain using Taylor series expansion.

[0037] The aforementioned secure computation protocol ensures that the cloud cannot obtain the plaintext value of any pixel during the computation process, and only obtains the final entropy value H(B). i This provides reliable input parameters for joint optimization and solves the problems of inability to measure image statistical features and blind selection of watermark embedding positions after homomorphic encryption.

[0038] S2.2 Construct and solve a multi-objective joint optimization model. A multi-objective joint optimization model is established with the objectives of maximizing watermark visibility, maximizing retrieval accuracy, and minimizing the impact on ciphertext statistical security.

[0039] Decision variable: x represents the watermark embedding parameter, x={(p k ,α k )}, where p k α represents the position index of the k-th image patch into which the watermark is embedded. k y represents the watermark embedding intensity coefficient of the image patch; y represents the index generation parameter, y=(y1,y2), where y1 represents the hash quantization parameter (controlling the step size of DCT coefficient quantization) and y2 represents the index label generation parameter (controlling the seed offset of pseudo-random mapping).

[0040] The objective function is defined as A(x,y)={V(x), A_r(x,y), S(x)}, where:

[0041] (1) V(x) is the watermark visibility function, defined as the contrast between the watermark area and the background area: μ_w and σ_w are the mean and standard deviation of the pixels in the watermark area, respectively, and μ_b and σ_b are the mean and standard deviation of the pixels in the background area, respectively.

[0042] (2) A_r(x,y) is the retrieval precision function, defined as the similarity preservation rate between the robust perceptual hash of the image after watermarking and the robust perceptual hash of the original image: A_r(x,y)=1-d(H(I),H(Î')) / L_h, where H(I) is the robust perceptual hash of the original image, H(Î') is the robust perceptual hash of the image after watermarking (its generation process is affected by the index parameter y), d(·,·) is the similarity metric function (such as Hamming distance), and L_h is the hash length.

[0043] It should be noted that since the cloud server 200 cannot obtain the plaintext of the image, the robust perceptual hash H(Î') of the watermarked image cannot be directly calculated in the ciphertext domain. Therefore, this embodiment uses a retrieval accuracy proxy model for evaluation: During system initialization, the user terminal 100 uses sample images to simulate the watermark superposition result Î'=I+αW under different combinations of watermark embedding parameters x and index generation parameters y in the plaintext domain, calculates the true similarity retention rate, and uses this to fit and generate a retrieval accuracy proxy model Ã_r(x,y) (e.g., using multinomial regression or radial basis function fitting). The proxy model parameters are then uploaded to the cloud server 200. In the optimization iteration, the cloud server 200 uses the proxy model evaluation value Ã_r(x,y) instead of the true retrieval accuracy in the solution. After watermark embedding is completed, the user terminal 100 performs consistency verification on the estimated true similarity retention rate of the watermarked image corresponding to the selected optimal embedding parameters. When the deviation between the true value and the proxy model evaluation value exceeds a preset deviation threshold (e.g., 2%), the recalibration of the retrieval accuracy proxy model is triggered. The above-mentioned "plaintext field identification - ciphertext field proxy - plaintext field verification" mechanism ensures the feasibility of the optimization process and the consistency of the optimization results.

[0044] (3) S(x) is the ciphertext statistical security function, defined as the change in the entropy value of the image block before and after embedding the watermark: S(x) = |H(B i )-H(B i ')|, where H(B) i ') is the entropy value of the image block after embedding the watermark (obtained based on the ciphertext domain entropy value calculation protocol of S2.1).

[0045] Constraint: The image visual distortion metric D(x) is used as a constraint rather than the objective function: D(x) = (1 / (M·N))·Σ i Σ j (I(i,j)-Î'(i,j)) 2 ≤D_max, where M and N are the height and width of the image, respectively, I(i,j) is the pixel value of the original image, Î'(i,j) is the estimated pixel value of the decrypted watermarked image, and D_max is the preset distortion tolerance threshold (generally D_max≤64, corresponding to a PSNR of about 30dB).

[0046] Analysis of the mechanism by which visible watermark embedding affects retrieval accuracy: Unlike invisible watermarks (which typically have low embedding strength and are imperceptible to the human visual system), semi-transparent visible watermarks are superimposed on the image in the form of a semi-transparent pattern, and their embedding strength is usually much greater than that of invisible watermarks. This characteristic determines that the changes that visible watermark embedding makes to the image content are explicit and significant: (a) the pixel values ​​of the watermark-covered area are systematically modified, changing the statistical distribution of that area; (b) robust perceptual hashing based on image content is sensitive to changes in pixel values, and changes in pixel values ​​in the watermark area will directly affect the generation of hash values; (c) when the watermark covers key feature areas (such as textured areas or edge areas), the impact on retrieval accuracy is particularly significant. Therefore, the conflict between visible watermark embedding and retrieval accuracy is more acute than that of invisible watermarking schemes, and this contradiction constitutes the practical necessity and technical motivation for the joint optimization of this invention.

[0047] The joint optimization mechanism of this invention generates synergistic effects at three levels: First, deep coupling at the parameter level, where decision variables x (watermark embedding position and strength) and y (index generation parameters) are solved collaboratively in the same objective function, and the watermark embedding position p... k and intensity α k Changes to the image pixel values ​​will affect the generation of the hash value H(Î'), thus impacting retrieval accuracy. Secondly, a unified trade-off at the target level places retrieval accuracy A_r, watermark visibility V, and statistical security S within the same optimization framework. This allows the system to consider copyright declaration effectiveness, data availability, and security simultaneously when deciding on a watermark embedding scheme, achieving a scientific trade-off rather than an empirical compromise. Thirdly, system-level functional enhancements include homomorphic encryption providing a secure operating environment for the ciphertext field embedding of visible watermarks, joint optimization ensuring that watermark embedding does not excessively impair retrieval accuracy, searchable encryption allowing encrypted images to still be efficiently retrieved, and blockchain evidence providing tamper-proof evidence for the copyright declaration of visible watermarks.

[0048] The solution process for the multi-objective joint optimization model is as follows: Figure 3As shown: The multi-objective optimization algorithm module 211 of the cloud server 200 uses a decomposition-based multi-objective evolutionary algorithm (MOEA / D) to solve the problem: (1) Initialization: Generate N uniformly distributed weight vectors, each weight vector corresponding to a subproblem, set the initial population (each individual contains the encoding of x and y), and calculate the ideal point of each subproblem; (2) Subproblem decomposition: Use the Chebyshev decomposition method to decompose the original multi-objective optimization problem into N single-objective subproblems; (3) Evolutionary operation: For each subproblem, find the nearest neighbor subproblem from its weight vector Euclidean distance. (3) Select parent individuals and perform simulated binary crossover and polynomial mutation operations to generate offspring individuals; (4) Update: Update the current solution and ideal point of the subproblem with the generated offspring individuals; (5) Termination criterion: When the proportion of non-dominated solutions in the population changes less than the convergence threshold ε (ε is 0.001) in G consecutive generations (G is 50~100), the algorithm converges and outputs the Pareto optimal solution set; (6) Solution selection: Adopt the compromise decision method based on fuzzy membership degree, calculate the fuzzy membership degree of each Pareto solution to each objective function, and select the solution with the highest comprehensive membership degree as the final solution.

[0049] S2.3, Perform watermark embedding. The cloud server 200 will jointly optimize and solve for the optimal embedding parameters x*={(p k *,α k The output is sent to the encrypted watermark embedding unit 210, which drives the encrypted watermark embedding unit 210 to perform a homomorphic addition operation on the encrypted image: for each pixel position (i,j) in the watermark area, calculate E(I'(i,j))=E(I(i,j))·E(α) k ·W(i,j)) mod n 2 The cloud server 200 generates a ciphertext image E(I') with a visible watermark. Simultaneously, the cloud server 200 outputs the optimal index parameters y* to the feature extraction and index management unit 220, driving the construction and updating of the secure index database. The entire embedding process is completed in the ciphertext domain; the cloud server 200 cannot know the plaintext content of the image or the plaintext visual form of the watermark. The above optimization results correspond one-to-one with the hardware execution actions: the optimized watermark embedding position index and strength coefficient directly drive the ciphertext addition operation of the ciphertext watermark embedding unit 210, and the optimized index parameters directly drive the updating of the secure index database; this is not a purely mathematical algorithm.

[0050] S2.4 Blockchain-based watermarking operation. The key information from this watermark embedding operation is packaged into a blockchain transaction, digitally signed by the cloud server 200, and submitted to the smart contract 310 of the blockchain evidence storage platform 300. The data structure of the evidence storage transaction includes: transaction type (WATERMARK_EMBED), user identification ID (UID), watermark identifier (H_wm), original image SHA-256 hash value, watermarked image SHA-256 hash value, embedding timestamp (Unix timestamp), SHA-256 digest of embedding parameter x*, and the cloud server's digital signature. This evidence record provides an immutable chain of evidence for subsequent copyright verification and traceability audits.

[0051] Step S3: Jointly optimize and generate a searchable encrypted image security index

[0052] To achieve efficient retrieval of massive amounts of watermarked encrypted images, the feature extraction and index management unit 220 of the cloud server 200 generates a secure index based on the optimal index parameters y* obtained by joint optimization in step S2.2.

[0053] S3.1 Generate a robust perceptual hash. Using the robust feature vector F received from the user terminal 100 (whose main component is the low-frequency coefficient feature of DCT, consistent with the feature extraction in S1.1), and combined with the hash quantization parameter y1* determined by joint optimization, a robust perceptual hash value H of fixed length for the image is generated. The specific hash generation algorithm is as follows: (1) Scale the image to a fixed size (e.g., 32×32) and convert it to grayscale; (2) Perform block DCT transformation on the scaled image, with a block size of 8×8; (3) Extract the first 8 low-frequency coefficients from each DCT block in Zigzag order; (4) Use the hash quantization parameter y1* to control the quantization step size and perform quantization judgment on the extracted DCT coefficients: if the coefficient is greater than the quantization threshold, set it to 1; otherwise, set it to 0; (5) Concatenate the quantization results of all blocks to form a binary hash string H of length L_h. The y2 in the index parameter y controls the offset of the quantization threshold and is used to generate different hash versions.

[0054] S3.2, Constructing a secure index. A secure index is constructed using Symmetric Searchable Encryption (SSE) technology: (1) Key set: The binary string of the robust-aware hash value H is split bitwise into several keys w. i Each key consists of a bit index j and a bit value, i.e., w. i =(j,H[j]); (2) Trapdoor generation: The index key K_idx is jointly derived from the user's public key and the system master key through the HKDF key derivation function, and a pseudo-random function (such as HMAC-SHA256) is used for each key w iGenerate trapdoor T(w) i = HMAC-SHA256(K_idx, w i (3) Inverted index construction: Construct an inverted index, and place the trapdoor T(w) into the inverted index. i (4) Index tag generation: The hash value H is encrypted as a whole to generate a secure index tag Token=HMAC-SHA256(K_idx⊕y2*, H), where y2* is the index tag generation parameter obtained by optimization in step S2.2; The generation of Token embeds the information embedded in the watermark. Any subsequent tampering with the watermark will cause H to change, thus causing Token verification to fail; (5) Index storage: Token and corresponding key-value pairs are stored in the secure index database in the cloud. The value of the key-value pair includes the encrypted image storage address, the blockchain evidence transaction identifier and the unique image identifier.

[0055] Step S4: Authorized users' encrypted image retrieval and use

[0056] When an authorized user (such as a library reader) needs to query an image:

[0057] S4.1 Generate a secure retrieval request. The user submits a query image Q on the retrieval terminal 120. The query processing unit 121 extracts the robust features of Q and generates a query hash H_q according to the method in step S3.1. Then, H_q is split bitwise into query keywords, and a set of query trapdoors {T(w)} for each query keyword is generated using the same index key K_idx. i ')} is sent to the cloud server 200 as a query token.

[0058] S4.2 Execute encrypted matching retrieval. The secure retrieval unit 230 of the cloud server 200 performs equivalent matching on each query trapdoor in the inverted index: For each image in the database, the number of trapdoors c that the image identifier hits under all L_h query trapdoors is counted; since the Hamming distance d(H_q,H)=L_h-c, when the number of hits c≥L_h-τ (τ is a preset matching threshold, generally taken as 10%~15% of the hash length), it is equivalent to the Hamming distance not being greater than τ, and the match is determined to be successful. The above-mentioned bit-by-bit trapdoor hit counting protocol allows the cloud server 200 to complete the similarity determination by performing only equivalent comparison of pseudo-random values, without needing to know the specific image content or hash value, thus protecting query privacy and the security of index data. After a successful match, the cloud server 200 verifies the copyright registration record of the image from the blockchain evidence storage platform 300 to ensure that the copyright ownership information of the returned image is credible.

[0059] S4.3 Return and decrypt the image. The cloud server 200 returns the successfully matched encrypted image E(I') with a visible watermark to the user. After the user uses their own homomorphic encryption private key to decrypt the image using the image decryption and display unit 122, they can obtain the plaintext image with a clearly visible watermark W, and intuitively understand the image copyright ownership.

[0060] Step S5: Blockchain-based Piracy Tracing and Audit Tracking

[0061] When a suspected pirated image I_p is discovered, the tracing process is as follows: Figure 4 As shown:

[0062] S5.1 Extracting visible watermarks. Since the watermark is visible, the watermark pattern W_p can be directly identified from the image I_p or extracted through simple image processing (such as threshold segmentation, template matching). At the same time, the watermark identifier H_wm' can be extracted from a specific area of ​​the watermark pattern (such as the QR code or coded block embedded in the lower right corner).

[0063] S5.2 Blockchain Evidence Query and Identity Matching. Using the extracted watermark identifier H_wm' as the keyword, the corresponding evidence transaction record is queried on the blockchain evidence platform 300 to obtain the user's identity identifier (UID), timestamp, and embedding parameter digest when the watermark was embedded. Then, the extracted watermark pattern W_p is compared and verified with the corresponding user's watermark pattern in the user watermark binding information database (Structural Similarity SSIM is calculated, with a threshold of 0.85). Only when the on-chain evidence record query matches and the SSIM comparison passes, the two-way verification is considered successful, locating the user who initially embedded the watermark, and a source tracing audit report is output; otherwise, the image is determined not to have been authorized for release from this platform, and the verification record is stored as evidence. Through the dual verification mechanism of "blockchain evidence storage + user watermark binding information database," the user who initially embedded the watermark can be quickly located, achieving accurate source tracing and audit tracking of piracy. The immutability of blockchain evidence storage ensures the legal validity of the source tracing results.

[0064] Step S6: Dynamic Index Update and Adaptive Adjustment of Watermark Parameters

[0065] When the smart library's image database undergoes incremental updates (adding or deleting images), the cloud server 200 performs dynamic index updates:

[0066] S6.1 New Image Processing. For new images, repeat steps S1 to S3 to generate a new watermarked ciphertext image and its security index, and store the watermarking operation on the blockchain for evidence.

[0067] S6.2 Watermark Update Processing. For existing images, if the watermark needs to be changed (e.g., due to a change in user permissions), there is no need to re-upload the original image. The cloud server 200 directly updates the watermark pattern in the encrypted domain: E(I'') = E(I')·E(α·(W_new-W_old)) mod n 2 This involves using the additive homomorphic property to perform the inverse operation to eliminate the old watermark and the additive embedding of the new watermark. Simultaneously, the index parameters y are recalculated and the security index is updated based on a multi-objective joint optimization model to ensure that retrieval accuracy is not affected after the watermark update.

[0068] S6.3 Adaptive Adjustment. The system periodically (e.g., monthly) adaptively adjusts the weight parameters in the multi-objective joint optimization model based on changes in the statistical characteristics of the image library (e.g., number of images, average entropy value, retrieval frequency, etc.) to keep the watermark embedding and index generation strategies in an optimal state.

[0069] Alternative implementation methods

[0070] The technical solution of the present invention has the following alternative implementation methods: (1) The addition homomorphic encryption scheme can be replaced by other homomorphic encryption schemes that support ciphertext addition operations, such as the addition variant of ElGamal or the BGV / BFV fully homomorphic encryption scheme; (2) The multi-objective evolutionary algorithm can be replaced by other multi-objective intelligent optimization algorithms such as NSGA-III and multi-objective particle swarm optimization; (3) The robust feature extraction algorithm can be replaced by ORB, SURF or features extracted based on deep convolutional neural networks; (4) The symmetric searchable encryption scheme can be replaced by public key searchable encryption (PEKS) or attribute-based searchable encryption according to different security models and efficiency requirements; (5) The blockchain evidence storage platform can be selected from different blockchain underlying technologies such as Ethereum, Hyperledger Fabric, and Chang'an Chain.

[0071] Security Analysis

[0072] This solution provides the following security guarantees under the semi-honest model (i.e., both the cloud server and the blockchain node are "honest but curious"): (1) Confidentiality of image content: The original image is uploaded after being encrypted by addition homomorphism on the user terminal. The cloud does not have the decryption private key during the entire watermark embedding and retrieval process and cannot know the plaintext content of the image; (2) Confidentiality of watermark pattern: The semi-transparent visible watermark pattern is not transmitted in the network. It is generated by the cloud from the trusted template library based on the UID, which reduces the risk of the watermark pattern being intercepted during transmission; (3) Privacy protection of query: During the retrieval process, the user only submits the query trapdoor. The cloud performs equal value matching on the ciphertext and cannot know the specific content or hash value of the query image; (4) Security of index data: The keywords in the index are all encrypted into trapdoors by pseudo-random functions. The cloud cannot deduce the original hash value from the trapdoor; (5) Immutability of evidence storage: The watermark operation record is stored on the blockchain. The consensus mechanism and hash chain structure of the blockchain ensure that the evidence storage record cannot be tampered with once it is written.

[0073] Example: Experimental Verification

[0074] (1) Experimental Deployment and Parameters. The user terminal is equipped with an Intel i7-12700H processor and 16GB of memory; the cloud server is equipped with a Xeon 8375C computing server; the blockchain evidence storage platform is deployed using the Chang'an Chain consortium chain node; the simulation compilation environment is Python 3.9 + PyTorch 1.13, the cryptographic algorithm calls the OpenSSL encryption library, the multi-objective optimization is reproduced based on the MOEA / D open source toolbox, and all operations are performed on physical hardware. The test dataset uses image resources from the public dataset OpenLibrary, and selects 1200 test images of books, ancient books, collections of paintings and calligraphy, and document scans. The resolution is uniformly 512×512, 8-bit grayscale; the image texture is divided into three categories: smooth background, dense texture, and complex edge. Global fixed hyperparameters: the distortion tolerance threshold corresponds to a baseline PSNR ≥ 28.3dB, the retrieval matching threshold is 12% of the hash length, the MOEA / D population size N=120, the maximum number of iterations G=80; the Paillier encryption key length is 2048 bits. The control groups were set as follows: Control 1 was the applicant's prior patent CN121664934A scheme (only watermark embedding parameters were optimized, without encrypted text retrieval and blockchain evidence storage); Control 2 was the traditional separate optimized encrypted visible watermark scheme (watermark embedding and retrieval index parameters were optimized respectively); Control 3 was the encrypted invisible watermark + searchable baseline scheme.

[0075] (2) Experimental results. The quantitative comparison results of each group of schemes are shown in Table 1.

[0076] Table 1. Comparison of Overall Performance of Different Technical Solutions Prior patent CN121664934A 1.41 61.2 28.1 2.1 Traditional separation optimization scheme 1.38 72.5 27.6 3.8 Invisible watermark baseline scheme 0.19 89.1 29.0 1.5 Invention Solution 1.36 87.8 28.5 2.3

[0077] Experimental results show that existing visible watermarking schemes generally suffer from the contradiction that "if the visibility meets the standard, the retrieval accuracy will decrease significantly, and if the retrieval is guaranteed, the watermark will be blurry." Although the invisible watermark baseline scheme has high retrieval accuracy (89.1%), the watermark visibility is only 0.19, making it impossible to identify the copyright with the naked eye. This invention, through joint coupling optimization of embedding parameters and indexing parameters, achieves a retrieval accuracy of 87.8% while retaining a highly recognizable visible watermark (V=1.36), which is 26.6 percentage points higher than the prior patent. At the same time, it meets the baseline image quality of the collection (PSNR=28.5dB), proving that joint optimization effectively solves the problem of visible watermark embedding damaging retrieval accuracy. Furthermore, by setting visual distortion as a constraint, the problem of image quality degradation in the optimized solution is avoided, and the optimization convergence efficiency is improved by 19.4%.

[0078] Encrypted domain security performance verification: The entire process involves capturing cloud server operation logs, with a cloud pixel plaintext acquisition rate of 0%, ciphertext entropy calculation error ≤1.7%, and ciphertext statistical feature deviation rate below 2.3%. Compared to the plaintext entropy statistical scheme, the risk of information leakage is reduced by 99.2%. Watermark dynamic update adaptation performance verification: Simulating scenarios of permission changes and copyright iterations, a second watermark replacement is performed in the encrypted domain. Traditional solutions require the terminal to re-upload the original image, index reconstruction takes an average of 2.17 seconds, and retrieval accuracy decreases by 11.3%. This invention relies on homomorphic inverse operations, eliminating the need for original image re-uploading, watermark updates take 0.42 seconds, and retrieval accuracy decreases by ≤1.1% after adaptive index updates. Source tracing and evidence validity verification: Constructing three piracy scenarios—watermark tampering, image cropping, and illegal forwarding—and conducting a total of 500 source tracing tests, the centralized evidence storage source tracing verification success rate was 71.4% with a 12.8% risk of log tampering. The success rate of the blockchain two-way verification source tracing of this invention was 99.6%, and the success rate of on-chain evidence storage tampering attacks was 0. The actual measured evidence storage transaction solidification latency was ≤1.2s.

[0079] Module Collaborative Ablation Experiment: Ablation tests were conducted by sequentially removing four modules: joint optimization, homomorphic encryption, blockchain, and searchable index. The results are shown in Table 2.

[0080] Table 2 Comparison of Performance Attenuation in Module Ablation Experiments Remove joint optimization module 25.7 No new risk of leakage efficient Remove homomorphic encryption modules 3.2 100% risk of plaintext leakage efficient Remove blockchain evidence storage module 1.0 No new risk of leakage Complete failure Remove searchable index modules 91.0 No new risk of leakage efficient

[0081] Ablation experiments show that: the absence of the joint optimization module significantly reduces retrieval accuracy by 25.7%; the absence of the homomorphic encryption module results in a 100% risk of plaintext leakage; the absence of the blockchain evidence storage module renders traceability evidence completely ineffective; and the absence of the searchable index module reduces resource retrieval efficiency by 91%. These four modules are not simply a stack of known technologies; they exhibit strong coupling and synergistic effects, resulting in an overall performance gain of 37.2%.

[0082] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for retrieving and tracing visible watermarks in ciphertext images based on homomorphic encryption and joint optimization, characterized in that, The method, applied to a system consisting of a user terminal, a cloud server, and a blockchain-based evidence storage platform, includes: S1. The user terminal extracts robust feature vectors from the original image, encrypts the original image using an additive homomorphic encryption algorithm to obtain a ciphertext image, and generates watermark generation information for a semi-transparent visible watermark based on the user's identity identifier. The ciphertext image, the robust feature vectors, and the watermark generation information are then uploaded to the cloud server. The watermark pattern itself is not transmitted over the network; it is generated by the cloud server from a trusted watermark template library based on the watermark generation information. S2. The cloud server calculates the block entropy value of the ciphertext image in the ciphertext domain to determine the candidate watermark embedding region; the watermark embedding parameter x and the index generation parameter y are constructed as a unified decision variable, with watermark visibility, retrieval accuracy and ciphertext statistical security as joint optimization objectives, and image visual distortion as a constraint condition, to construct and solve a multi-objective joint optimization model to obtain the optimal embedding parameter and the optimal index parameter; according to the optimal embedding parameter, the visible watermark is embedded into the ciphertext image using the ciphertext addition operation of the additive homomorphic encryption algorithm to obtain a ciphertext image with a visible watermark, and the evidence information of the watermark embedding operation is submitted to the blockchain evidence storage platform for evidence storage; wherein, the watermark embedding parameter x includes the watermark embedding position index and the embedding strength coefficient, and the index generation parameter y includes the hash quantization parameter and the index label generation parameter; S3. The cloud server generates a robust-aware hash of the original image based on the robust feature vector according to the optimal index parameters, and constructs a secure index on the robust-aware hash using symmetric searchable encryption. S4. In response to the retrieval request of the authorized user, the cloud server performs a ciphertext matching retrieval based on the security index, and returns the successfully matched ciphertext image with a visible watermark to the user terminal. The user terminal decrypts the image to obtain a plaintext image with a visible watermark. The visible watermark is presented in the plaintext image in the form of a semi-transparent pattern and can be identified by the naked eye without the need for a special extraction algorithm. S5. When a suspected pirated image is discovered, a visible watermark pattern and watermark identifier are extracted from the suspected pirated image. The corresponding evidence record is queried on the blockchain evidence storage platform using the watermark identifier. The extracted visible watermark pattern is compared with the pre-stored user watermark binding information database. The leaked user is located through two-way verification by comparing the on-chain evidence storage record with the watermark pattern.

2. The method for retrievable and traceable ciphertext image visible watermarks based on homomorphic encryption and joint optimization according to claim 1, characterized in that, S2 involves calculating the block entropy value of the ciphertext image in the ciphertext domain, including: The encrypted image is divided into several b×b image blocks. For each image block, for each pixel value v in the pixel value domain, the cloud server uses the homomorphic property of the additive homomorphic encryption algorithm to calculate the ciphertext difference between each pixel ciphertext and the pixel value v. After blinding the ciphertext difference with a random blinding factor, the ciphertext difference is sent to the decryption assistance party holding the decryption private key. The decryption assistance party decrypts the ciphertext difference and only returns the equivalence judgment result of whether the plaintext corresponding to the ciphertext difference is zero. The cloud server counts the frequency of each pixel value based on the equivalence judgment result. The decryption assistance party is the user terminal or a trusted third party. The pixel value probability is calculated based on the frequency of each pixel value. After the pixel value probability is quantized into a fixed number, the ciphertext table entry corresponding to the probability and logarithm product of each quantization level is obtained through a pre-calculated ciphertext logarithmic lookup table. The ciphertext table entry is homomorphically accumulated to obtain the ciphertext of the image block entropy value, which is then decrypted by the decryption assistance party to obtain the image block entropy value. The cloud server cannot know the plaintext value of any pixel during the calculation process.

3. The method for retrievable and traceable ciphertext image visible watermarking based on homomorphic encryption and joint optimization according to claim 1, characterized in that, The joint optimization objectives of the multi-objective joint optimization model include: The watermark visibility function is defined as the ratio of the difference between the mean pixel value of the visible watermark region and the mean pixel value of the background region to the joint measure of the standard deviation of the pixels in the two regions. The retrieval accuracy function is defined as the similarity retention rate between the robust perceptual hash of the watermarked image and the robust perceptual hash of the original image. The robust perceptual hash of the watermarked image is evaluated based on the retrieval accuracy proxy model. The retrieval accuracy proxy model is generated by the user terminal during the initialization phase by simulating the watermark superposition results under different combinations of watermark embedding parameters and index generation parameters in the plaintext domain using sample images, calculating the true similarity retention rate, fitting it accordingly, and then uploading it to the cloud server. The encrypted statistical security function is defined as the change in the entropy value of an image block before and after embedding the watermark. The constraint condition is that the image visual distortion metric defined by mean square error does not exceed a preset distortion tolerance threshold. After the watermark is embedded, the user terminal calculates the true similarity retention rate of the estimated watermarked image corresponding to the selected optimal embedding parameters. When the deviation between the true similarity retention rate and the evaluation value of the retrieval accuracy proxy model exceeds a preset deviation threshold, the recalibration of the retrieval accuracy proxy model is triggered.

4. The method for retrievable and traceable ciphertext image visible watermarking based on homomorphic encryption and joint optimization according to claim 1, characterized in that, The construction and solution of the multi-objective joint optimization model includes: A decomposition-based multi-objective evolutionary algorithm is used to generate N uniformly distributed weight vectors. The Chebyshev decomposition method is used to decompose the multi-objective joint optimization model into N single-objective subproblems. For each subproblem, parent individuals are selected from the nearest neighboring subproblems in terms of Euclidean distance of their weight vectors. Simulated binary crossover and polynomial mutation are performed to generate offspring individuals, and the current solution and ideal point of each subproblem are updated. The iteration stops when the proportion of non-dominated solutions in the population changes less than the convergence threshold for G consecutive generations, and the Pareto optimal solution set is output. A compromise decision-making method based on fuzzy membership degree is adopted to select the solution with the highest comprehensive membership degree from the Pareto optimal solution set as the optimal embedding parameter and the optimal index parameter; The cloud server outputs the optimal embedding parameters to the ciphertext watermark embedding module, drives the ciphertext watermark embedding module to perform ciphertext addition operation on the ciphertext image, and outputs the optimal index parameters to the index building module to update the secure index database.

5. The method for retrievable and traceable ciphertext image visible watermarking based on homomorphic encryption and joint optimization according to claim 1, characterized in that, The robust feature vector includes low-frequency coefficient features of discrete cosine transform; the generation of robust perceptual hash in S3 includes: scaling the image to a fixed size and converting it to a grayscale image, performing block-based discrete cosine transform, extracting the first few low-frequency coefficients of each discrete cosine transform block in Zigzag order, using the hash quantization parameter to control the quantization step size to quantize the low-frequency coefficients to obtain binary bits, and concatenating the quantization results of each block to form a fixed-length binary hash string; The robust feature vector also includes a scale-invariant feature transformation keypoint descriptor, which is used to assist in the verification of images with geometric transformations during the retrieval result verification stage.

6. The method for retrievable and traceable ciphertext image visible watermarking based on homomorphic encryption and joint optimization according to claim 1, characterized in that, The S3 section employs symmetric searchable encryption to construct a secure index for the robust-aware hash, including: The binary string of the robust-aware hash is split bitwise into several keys, each key consisting of a bit sequence number and a bit value; An index key is jointly derived from the user's public key and the system master key using a key derivation function. A trapdoor is then generated for each keyword based on the index key using a pseudo-random function. Construct an inverted index that maps each trapdoor to the corresponding set of image identifiers; The robust-aware hash is encrypted using the index tag generation parameters to generate an index tag. The index tag embeds watermark embedding information. When the visible watermark is tampered with, causing the robust-aware hash to change, the index tag verification fails. The index tag is associated with the storage address of the corresponding encrypted image with a visible watermark and the blockchain evidence transaction identifier and stored as a key-value pair.

7. The method for retrievable and traceable ciphertext image visible watermarking based on homomorphic encryption and joint optimization according to claim 6, characterized in that, The encrypted matching retrieval performed in step S4 based on the secure index includes: The user terminal generates a query hash for the query image, splits the query hash into query keywords bit by bit, generates query trapdoors for each query keyword using the same index key, and sends each query trapdoor to the cloud server. The cloud server performs equal-value matching on each query trapdoor in the inverted index, counts the number of trapdoors that the same image identifier hits, and determines that the corresponding image is successfully matched when the number of hits is not less than the difference between the hash length and the preset matching threshold. After a successful match, the cloud server verifies the copyright registration record of the matched image from the blockchain evidence storage platform, and then returns the corresponding encrypted image with a visible watermark.

8. The method for retrievable and traceable ciphertext image visible watermarks based on homomorphic encryption and joint optimization according to claim 1, characterized in that, The evidence storage information includes transaction type, user identity identifier, watermark identifier, original image hash value, watermarked image hash value, embedded timestamp, embedded parameter digest, and digital signature of the cloud server; the watermark identifier is generated by the user identity identifier using a hash function; In step S5, the extracted visible watermark pattern is compared with the pre-stored user watermark binding information database, including: calculating the structural similarity between the extracted visible watermark pattern and the corresponding watermark pattern in the user watermark binding information database; when the structural similarity is not less than 0.85, the comparison is deemed to be successful; the two-way verification is deemed to be successful only when the evidence record query is successful and the comparison is successful.

9. The method for retrievable and traceable ciphertext image visible watermarking based on homomorphic encryption and joint optimization according to claim 1, characterized in that, The method further includes: When it is necessary to replace the embedded visible watermark, the cloud server uses the homomorphic property of the additive homomorphic encryption algorithm to perform the inverse operation to eliminate the old watermark and the additive embedding of the new watermark on the ciphertext image with the visible watermark in the ciphertext domain, without requiring the user terminal to re-upload the original image. The index generation parameters are recalculated and the security index is updated based on the multi-objective joint optimization model. The weight parameters of the multi-objective joint optimization model are adaptively adjusted according to changes in the statistical features of the image library at a preset period.

10. A ciphertext image visible watermark searchable and traceable system based on homomorphic encryption and joint optimization, characterized in that, This includes user terminals, cloud servers, and blockchain-based evidence storage platforms; The user terminal includes an image encryption and feature extraction unit, a watermark generation unit, a query processing unit, and an image decryption and display unit. The image encryption and feature extraction unit extracts robust feature vectors from the original image and encrypts the original image using an additive homomorphic encryption algorithm to obtain a ciphertext image. The watermark generation unit generates watermark generation information with a semi-transparent visible watermark based on the user's identifier. The query processing unit generates a secure retrieval request. The image decryption and display unit decrypts and displays the plaintext image containing the visible watermark. The cloud server includes a ciphertext watermark embedding unit, a feature extraction and index management unit, a secure retrieval unit, a storage unit, and a communication interface unit. The ciphertext watermark embedding unit incorporates a multi-objective optimization algorithm module, which constructs watermark embedding parameters and index generation parameters as unified decision variables. It solves a multi-objective joint optimization model with watermark visibility, retrieval accuracy, and ciphertext statistical security as joint optimization objectives and image visual distortion as a constraint. The model then embeds a visible watermark in the ciphertext domain according to the optimal embedding parameters obtained from the solution. The feature extraction and index management unit generates robust perceptual hashes based on the optimal index parameters and constructs, updates, and maintains a secure index using symmetric searchable encryption. The secure retrieval unit performs ciphertext matching retrieval based on the secure index. The storage unit stores ciphertext images with visible watermarks, a secure index database, and a user watermark binding information database. The communication interface unit communicates with the user terminal via network data. The blockchain-based evidence storage platform is used to perform decentralized evidence storage for watermark embedding, retrieval, and traceability verification operations through smart contracts, and to respond to evidence storage query and verification requests.

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