An information steganography method based on neural implicit representation

Abstract

The application discloses an information steganography method based on neural implicit representation and belongs to the field of deep steganography, and comprises the following steps: based on neural implicit representation, the secret message of a plurality of types of data is implicitly represented to obtain a secret function; based on the secret function, a masking function is constructed; and based on the masking function and a shared key, a secret message is recovered. The application solves the problem of high cost of secure transmission and communication of a deep decoding network by disguising the secret message as a masking function. The application can empirically verify the proposed framework on diversified data sets with different data types, such as pictures, 3D data and weather data, and highly accurate recovery is obtained under the condition of guaranteeing embedding capacity.

Description

Technical Field

[0001] This invention belongs to the field of deep steganography technology, and particularly relates to an information steganography method based on neural implicit representation. Background Technology

[0002] Steganography is a technique for secret communication that embeds secret information into a masked medium and transmits it over a public channel. The medium can be digital text, audio, images, video, or 3D data. Traditional steganography schemes focus on designing handcrafted algorithms to subtly modify the masking medium for data embedding. However, this approach struggles to achieve a good balance between concealment and embedding capacity (or simply capacity).

[0003] Recently, several deep neural network-based steganography schemes have been proposed, achieving better performance compared to traditional hand-designed schemes. In deep steganography, the message sender uses an encoding network to embed secret information into a masking vector, and the message receiver needs to use a message decoder to recover the secret information from the masking vector, such as... Figure 1 The upper part is shown. However, there are two key problems in deploying deep steganography schemes in practical applications. (1) Such methods require sending a large amount of data to the message receiver, but it is not secure to make another transmission to pass the secret decoder. (2) A more covert and serious problem is that the presence of the decoder on the receiver will arouse the suspicion of the analyst regarding its steganographic behavior. One possible solution is to treat the secret decoder as ordinary data and hide it in a popular overlay medium (such as an image or video) using an existing steganography scheme. However, since the secret decoder is relatively large, traditional steganography schemes require a large amount of overlay medium data to meet the limited capacity, which will cause a large communication burden. Another solution is to embed the decoder network into another steganography network that performs other functions (such as image classification), but this masking network is even larger than the steganography network, which will also cause a communication burden. In addition to masking the message decoder, both of these schemes also require a masking carrier for transmitting secret messages, just like traditional steganography methods. Summary of the Invention

[0004] This invention proposes an information steganography method based on implicit neural representation, where implicit neural representation (INR) parameterizes a signal as a continuous function. In this invention, as... Figure 1As shown in the lower half, ① this embodiment first represents the secret message as a continuous secret function. ② Using the shared key, the secret function (network) is extended to construct a new network structure. ③ With fixed secret function parameters, the extended function is used to parameterize a masking carrier, thereby obtaining a masking function. The masking function is both the extractor and the masking carrier, and therefore can be securely transmitted over a public channel. The receiver only needs to use the shared key to recover the secret message from the masking function. Other users without the key can only obtain the masking carrier from the masking function. This invention solves the technical problems existing in the prior art.

[0005] To achieve the above objectives, the present invention provides an information steganography method based on neural implicit representation, comprising: Based on neural implicit representation, the secret message of several types of data is implicitly represented to obtain the secret function; Based on the secret function, a masking function is constructed; Based on the masking function and the shared key, the secret message is recovered.

[0006] Preferably, before implicitly representing the secret message of several types of data, the method further includes: Several types of data are converted into data coordinates and data features, wherein the several types of data include: image data and point data; the data coordinates and the data features correspond to the input pairs and output pairs of the secret function, respectively.

[0007] Preferably, the formula for the secret function is obtained as follows: in, Secret messages for image data Yes An initial function before parameterization. This refers to the parameterized function, i.e., the secret function. The parameterization process representing the implicit representation.

[0008] Preferably, when implicitly representing secret messages of several types of data, the method further includes: An MLP is used as the underlying network for implicit representation. Based on the underlying network, an implicit representation of the secret message is obtained, denoted as the network secret function.

[0009] Preferably, the formula for obtaining the implicit representation of the secret message is: in, It is an activation function. yesl Layer n A weighted summation of nodes, yes l Layer n The output of each node, the parameters of the MLP network are represented as a set of matrices and vectors. The network structure is represented as a vector consisting of the number of nodes in all layers. , Indicates the dimension of the input layer. For the output layer dimension, the MLP network is represented as The network secret function is represented as .

[0010] Preferably, the process of constructing the masking function includes: in, Let be the initial masking function. For the key, key Used for control function structure and Location For several types of data, For the final masking function, It is a masking function The parameter set.

[0011] Preferably, the function expansion strategies used when constructing the masking function include: horizontal expansion strategy, vertical expansion strategy, and hybrid expansion strategy.

[0012] Preferably, after constructing the masking function, the process further includes: Based on the mask, the parameters of the masking function are optimized and trained using the gradient descent method.

[0013] Preferably, the formula for recovering the secret message is: in, Representing the secret function The recovery process, Indicates to Sampling recovery, This is a secret message for image data.

[0014] Compared with the prior art, the present invention has the following advantages and technical effects: This invention provides an information steganography method based on neural implicit representation. By disguising the secret message as a masking function, it solves the problems of high network security transmission and communication costs in deep decoding. The masking function construction strategy based on the key utilizes the secret information shared by both parties to construct the structure of the masking function, and trains the parameters of the masking function through a partial optimization strategy based on the mask. This invention can empirically verify the proposed framework on diverse datasets with different data types, such as images, 3D data, and weather data, and achieve highly accurate recovery while ensuring embedding capacity. Attached Figure Description

[0015] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings: Figure 1 This is a schematic diagram illustrating an application scenario of the StegINR method according to an embodiment of the present invention; Figure 2 This is a schematic diagram of a steganography framework based on function hiding according to an embodiment of the present invention; Figure 3 This is a schematic diagram illustrating three strategies for constructing masking functions according to embodiments of the present invention; Figure 4 This is a schematic diagram illustrating how a function representing an image is hidden within a function representing a 3D model, according to an embodiment of the present invention. Figure 5 This invention utilizes a key k and a masking function in an embodiment of the invention. recover Schematic diagram; Figure 6 This is a schematic diagram of the test results of the method of the present invention; Figure 7 This is a schematic diagram illustrating the image performance under different scaling rates according to an embodiment of the present invention. Detailed Implementation

[0016] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0017] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.

[0018] Example 1 This embodiment provides an information steganography method based on neural implicit representation, including: Based on neural implicit representation, the secret message of several types of data is implicitly represented to obtain the secret function; Based on the secret function, a masking function is constructed; Based on the masking function and the shared key, the secret message is recovered.

[0019] The specific solution in this embodiment includes: First, represent the data as a function. This embodiment uses images as a clear guiding example to review implicit neural representations.

[0020] 1.1. Representing a single image as a function Assumption It is an image, in which Corresponding to pixel position The RGB value at that location. This embodiment aims to use a function... To represent this image, where Return pixel position The RGB values ​​at that location. To achieve this, this embodiment uses a weighted... Multilayer perceptron (MLP) to parameterize functions This is commonly referred to as a neural implicit representation. This embodiment can then learn this representation by minimizing the following loss function: (1) The summation is performed across all pixel positions. It's worth noting that this represents... It is independent of the number of pixels. Therefore, unlike most image representations, it represents... It is independent of image resolution.

[0021] 1.2. Use functions to represent general data.

[0022] The above example regarding images can be extended to more general data. Let... Represents coordinates, To represent a feature, assuming that this embodiment has already obtained a data point containing a set of coordinates and feature pairs. For example, for images, Corresponding to pixel position, Corresponding to RGB values, while This corresponds to the set of all pixel locations and RGB values. Given a set of coordinates and their corresponding features, this embodiment can learn a function representing this number by minimizing the following loss function. : (2) A key characteristic of these representations is that they scale with signal complexity, not signal size. In fact, for images, the memory required to store the data increases quadratically with resolution, and cubically for voxel grids. In contrast, for function representations, memory requirements are directly related to signal complexity: to represent a more complex signal, this embodiment requires increasing the memory required for the function. The capacity can be increased, for example, by increasing the number of layers in a neural network.

[0023] 1.3. Represents high-frequency functions.

[0024] Recent studies have shown that learning the function representation by minimizing equation (1) can lead to a bias towards low-frequency functions. While several methods have been proposed to mitigate this problem, this embodiment uses the randomized Fourier feature encoding (RFF) proposed by Tancik et al. because it is not biased towards axial variations [8] and does not require special initialization. Specifically, for a given coordinate Encoding function Defined as: (3) in It is a size of A (potentially learnable) random matrix whose elements typically come from... Sampling is performed during this process. Number of frequencies. sum matrix element variance These are hyperparameters. To learn high-frequency functions, this embodiment only needs to... Passed to MLP Encode it beforehand, that is Then minimize equation (1). The function representation of the image learned by the MLP using the ReLU activation function cannot capture high-frequency details, while the image can be accurately reproduced by using RFF encoding followed by a ReLU MLP.

[0025] II. Problem Description 2.1. Function Hiding For simplicity, this embodiment uses the implicit representation of an image as an example to describe the method of this embodiment, such as... Figure 2 As shown. Assume the secret message to be transmitted is... For the sender, the following three steps need to be completed in sequence to achieve steganography: (4) (5) (6) The first step, namely formula (4), involves processing the image... Perform parameterized representation. Yes An initial function before parameterization. This refers to the parameterized function, also known as the secret function. This represents the parameterization process of the implicit representation. The second step, as shown in formula (2), involves the sender... Hide in another function In, using a key ,exist Construct a masking function based on In this embodiment, the key Used for control function structure and The location. Thirdly, to achieve better concealment, this embodiment utilizes... To achieve the processing of images on a specific carrier The implicit representation yields the final masking function. ,in It is a masking function The parameter set.

[0026] For the message receiver, only the key is needed. and obtained from public channels The secret message can then be recovered. The receiver first uses formula (7) to recover the secret function. Finally, the secret message was recovered using the sampling process of INR. : (7) (8) in, Representing the secret function The recovery process, Indicates to Sampling to recover secret data .

[0027] 2.2. Data Representation As can be seen from the principle of implicit representation, in order to train and obtain the parameters of this function, the data must be transformed into a set of coordinates and features, that is... This set of coordinates and features corresponds to the input / output pairs of the function, enabling this embodiment to learn the function parameters. A single sample point corresponds to a set of coordinates and features (e.g., an image is a set of position coordinates and features). (pixel points). Using a set of coordinates and features is highly flexible, and this representation is unbiased by whether the data originates from a grid or the sampling resolution. Crucially, constructing the problem entirely based on sets also allows this embodiment to split individual data points into subsets and train on them. In particular, given a single data point... For example, a group Each pixel can be randomly sampled in this embodiment. Elements, such as those from the entire image Select from 1 pixel Training on these subsets eliminates the direct dependence on data resolution. This approach makes it easy to obtain an implicit representation network for low-resolution data when the transmitted data does not require higher resolution. Similarly, when training 3D shapes, this embodiment can train on a subset of the voxel grid instead of the entire grid, saving significant memory. This is impossible in standard convolutional models, which are directly correlated with grid resolution. Furthermore, the coordinate- and feature-set-based training method allows this embodiment to model more exotic data, such as function distributions on manifolds. In fact, this is possible simply by defining a coordinate system on the manifold (e.g., polar coordinates on a sphere). Based on this representation, the steganography method of this embodiment can be applied to all these forms of data, whether as secret messages or masking carriers.

[0028] Third, steganography schemes 3.1. Secret Function: An implicit representation of a secret message To simplify the method in this embodiment, an MLP is used as the underlying network for implicit representation. The first... Layers and The weights between layers can be written in matrix form, i.e., the weight matrix. The bias is written in vector form, i.e., the bias vector b. The dimension of the weight matrix is... , This represents the number of neurons on the right side of the two-layer neuron system. The number of neurons on the left side, the matrix OK The column represents the right-hand layer. The neuron and the left layer The weights between neurons. Then the above formula can be simplified to: (9) (10) in, It is an activation function. yes l Layern A weighted summation of nodes, yes l Layer n The output of each node, the parameters of the MLP network are represented as a set of matrices and vectors. The network structure is represented as a vector consisting of the number of nodes in all layers. , Indicates the dimension of the input layer. For the output layer dimension, the MLP network is represented as The network secret function is represented as .

[0029] For a given secret message In this embodiment, formula (1) is used to learn the network parameters, and the function obtained after training is expressed as follows: This is denoted as the secret function.

[0030] 3.2. Construction of the masking function There are many methods for constructing a masking function. In this embodiment, when the secret function is regarded as the secret message in traditional steganography, the masking function can be directly constructed using the strategy of carrier synthesis, that is, the masking function is constructed by synthesis based on the secret function. In this embodiment, the synthesis operation is limited to a special operation: function expansion. That is, while keeping the structure and parameters of the secret function unchanged, the masking function is constructed by adding neurons to it. Since implicit representation can adopt a relatively simple network structure, such as MLP, this embodiment can form a new masking network by inserting a large number of masking neurons without affecting performance. Another reason for adopting expansion instead of selection as in the prior art is that after implicit representation, the neural network has already fitted the data, and deleting any point may cause the secret function to fail to sample the original image data.

[0031] More importantly, it is desired that this extended masking function possesses certain functionalities to enhance its stealth during network transmission, i.e., to mask steganographic behavior with a specific action. Typically, there are two options: one is to utilize this masking function (network) to perform a standard machine learning task, such as image classification, as is done in existing technologies. In this embodiment, an alternative approach, consistent with the secret message, is adopted: masking steganographic behavior with implicit representation behavior.

[0032] When both the secret function and the masking function are used to represent the same type of data, taking an image as an example, this embodiment designs the following three strategies to implement function expansion, such as... Figure 3 As shown: 3.21. Horizontal Expansion Lateral scaling refers to inserting a new layer after the secret function to construct a new function, while keeping the preceding network parameters and structure unchanged. Figure 3 As shown in (a).

[0033] (11) (12) (13) (14) 3.22. Vertical Expansion Another method for expanding the function is to keep the number of network layers unchanged. Since both the masking function and the secret function are used to represent images, this embodiment only requires increasing the number of units in the hidden layers other than the input layer and the final output layer, such as... Figure 3 As shown in (b).

[0034] (15) (16) (17) (18) 3.23. Hybrid Extension Hybrid expansion is an operation that expands both vertically and horizontally, that is, increasing the number of layers while simultaneously increasing the number of neurons in the existing hidden layers. This is a general operation, such as... Figure 3 As shown in (c), under this operation, all content parameters and structure of the secret network are hidden inside a network.

[0035] (19) (20) (twenty one) (twenty two) In fact, both vertical and horizontal expansion can be seen as special examples of hybrid expansion operations. The aim of this embodiment is to achieve the masking objective using the simplest possible expansion method.

[0036] When the secret function and the masking function are used to represent different types of data, this embodiment can naturally adopt a hybrid extension method for construction. Figure 4 As shown. For example, the implicit representation of an image can be hidden within the implicit representation of a 3D model. Once the hiding function is determined... Given this structure, this embodiment can train it to represent a specific carrier data. It should be noted that these three extension methods share the common characteristic of using a secret function. The hidden function still exists as a whole, and the dependencies between the preceding and following layers are not broken. This will help in the design of the secret function recovery in this embodiment.

[0037] Since the structure of the masking function needs to be determined before expansion, this embodiment can view the function expansion operation as relying on secret information shared by the sender and receiver. As shown in formula (5). In the scheme of this embodiment, the key express exist The position in the middle, where each layer corresponds to one Bit-based binary stream ,in This indicates the number of neurons in the layer, with each bit corresponding to one neuron. 0 represents the location of a masking neuron, and 1 represents the location of a secret neuron. For example, Figure 3 The masking function shown in (c) corresponding The expression is {00,1010,1010101,1101,000}.

[0038] From the construction From the perspective of masking function In the key Under the influence of this key, by fixing the positions and parameters of some neurons and expanding using random numbers, this key-based method is obtained. The method for constructing the masked function is similar to that of the Carden lattice; the key k itself is a Carden lattice marking the location of the secret hiding unit. This embodiment utilizes the Carden lattice and an image generator to directly construct a complete masked image data from a partially damaged image. In this embodiment, the Carden lattice of the grid data is transferred to the function domain. Therefore, the method of this embodiment can also be called Carden lattice-based masking function generation. 。

[0039] 3.3. Training the masking function This embodiment achieves this using formula (1). An implicit representation of the carrier image c is used to obtain the parameterized masking function. . It contains two different types of parameters: secret function The original parameters and the parameters of the extended neurons To ensure that it can be obtained without damage from Extract During the training process, this embodiment fixes parameters Only adjust the parameters of the expanded neurons. Therefore, this embodiment uses a method from the prior art to introduce a mask. Come to Some optimizations were made. It is a with parameter set Binary mask vectors of the same size , (twenty three) in, yes The first in One parameter, The number of parameters can be determined by... or The calculated vector The value can be obtained from the key. Calculated.

[0040] set up The learning rate is represented by ⊙, which indicates element-wise multiplication. Gradient descent is used to update the algorithm. as follows: (twenty four) Through training, this embodiment will obtain the parameterized representation of the masking function on the carrier image c, that is... .

[0041] 3.4. Secret Function Recovery Masking function It can be transmitted over public channels, and ordinary users can only sample the masked data represented by the masking function. Since the secret function is not changed during the construction and training of the masking function, and the receiver of the secret message receives the function... Then, use the key. The secret function can then be recovered without loss. As shown in formula (7). Using the key This embodiment can not only identify hidden neurons, but also obtain the weight information between neurons. That is, from the key... Obtain the secret function parameters and structure .

[0042] like Figure 5 As shown, the receiver first... The value is overwritten by the masking function. neuron nodes Above, that is, if ,but =1. Next, this embodiment constructs a structure from the input layer. All nodes to the output layer Paths to all nodes ,in Indicates the first The first layer 1 node, Here, N represents the index of all paths, and N represents the total number of paths. This embodiment only needs to retain the weights on those paths that are accessible from the input layer to the output layer, i.e., when... , indicates that there is a path, which can be obtained No. The weight matrix of the layer is , the whole The parameters are: (25) Finally, through statistics The number of 1s in each layer, i.e., the number of secret neurons, gives the model structure: (26) 3.5. Extraction of Secret Messages From the secret function of recovery China resumes secret messages Essentially, it is a problem of sampling from implicit representation functions, that is: (27) This embodiment only requires... It is converted into the original format of the corresponding secret data. Taking an image as an example, this embodiment can be... Input a set of coordinates Thus, the corresponding RGB pixel values ​​are obtained. .

[0043] IV. Experiment The model of this embodiment is evaluated on images at various resolutions across three datasets: CelebAHQ[i], DIV2K, and COCO. This embodiment utilizes an N-layer MLP to represent the secret message and the masking carrier. The model of this embodiment is implemented using PyTorch[ii] and all training was performed on a single 2080Ti GPU with 11GB of memory.

[0044] The experimental setup is as follows: Taking CelebAHQ as an example, the secret message image size is 64*64. The network structure of the function representing the secret image, i.e., the secret function, is [2, 64, 64, 64, 3]. The input layer has a dimension of 2, representing pixel coordinates, and the output layer has a dimension of 3, representing RGB values. Each of the three hidden layers has 64 neurons. Since the input and output layers depend on the carrier type, only the hidden layer [64, 64, 64] is used to represent the entire network structure in the experiment. The network is trained for 2000 epochs to obtain the secret function (model). Stochastic gradient descent is used for training, with a learning rate of... The masking image is also 64*64 pixels, and the function used to represent the masking image is [1024, 512, 1024]. The network structure of the masking function is [1024, 512, 1024]. After training for 2000 epochs, the masking function (model) is obtained.

[0045] Each column represents the secret image, the image sampled from the secret function, the masking image, the masking image sampled from the masking function, and the secret image, respectively, with experimental results on a 64*64 image, as shown below. Figure 6 As shown. Column 1 is the secret message, column 2 is the secret message sampled from the secret function, column 3 is the masking image, column 4 is the masking image sampled from the masking function, and column 5 is the secret message extracted from the masking function.

[0046] The results above show that although the masking function causes some distortion in representing the masked image, possibly due to a slight loss in network fitting caused by fixing some parameters, it can still represent the overall information of the masked image quite well. Most importantly, with the key available, the secret function can be recovered from the masking function. The secret message sampled from the secret function has a high similarity to the original secret message, making them almost indistinguishable.

[0047] V. Performance Analysis To more comprehensively evaluate the performance of the proposed method, its performance was assessed in terms of the fidelity of the secret message representation, recoverability, masking function fidelity, and capacity.

[0048] 5.1 The Representation of Secret Messages For secret images m In this embodiment, MLP is used for representation, and the PSNR of the original image and the image obtained by sampling the secret function is used to represent the performance of the implicit representation. The representation of the secret message is shown in Table 1.

[0049] Table 1 As can be seen, with the increase in training iterations, a simple network can represent secret messages at multiple resolutions. In fact, although implicit representations cannot represent secret messages completely without distortion, they are acceptable in image-to-image steganography due to the large amount of redundant information contained in images.

[0050] 5.2, Recoverability This embodiment calculates the original secret function. From the masking function The secret function extracted from Table 4 shows the bit error rate (BER) of the secret model extracted from the masking function by the secret function with different structures. It can be seen that since the parameters of the secret model are fixed in the masking function, the secret function can be extracted losslessly, and the performance of the image represented by the secret function is completely unaffected. The accuracy of the function extraction is shown in Table 2.

[0051] Table 2 5.3, fidelity To evaluate the masking function To maintain fidelity, this embodiment trained a clean model. Its architecture and Same. Yes. Training and The training was performed on the same training set, and adjustments were made. All parameters were optimized to achieve the best performance. Furthermore, this embodiment uses the same test set to evaluate the performance of both models. Table 3 shows the performance of the clean function and masking function representing the vector. PSNR is... 23 PSNR represents the PSNR of the clean function sampled image and the mask function sampled image. 12 PSNR represents the original vector image and the clean function sampled image. 13 This represents the PSNR of the original carrier and the image sampled by the masking function. It can be seen that fixing some parameters does indeed lead to a decrease in the representational power of the masking function. As the number of parameters in the masking function model increases, the proportion of the secret function's parameters in the masking function decreases, and the representational power of the masking function is significantly improved. The performance of the clean function and the masking function... Table 3 Three different masking function strategies were evaluated to verify the effectiveness of different function expansion strategies, as shown in Table 4, where PSNR is the PSNR between the original carrier image and the masking function sampled image.

[0052] Table 4 The results above show that the hybrid expansion strategy produces the best results. This is partly because the expansion rate is relatively large, and the fixed parameters have a relatively small impact on the masking function.

[0053] 5.4, ​​Capacity From a function perspective, the method in this embodiment hides the parameters of one function within another. The capacity of the proposed method can be evaluated by the parameter expansion rate, which is defined as: (28) Where Nstego and Nsec refer to the number of parameters in the secret and steganographic DNN models, respectively. Therefore, this embodiment has .

[0054] This embodiment further evaluates how the performance of the proposed method changes when the expansion rate varies. Figure 7 This demonstrates the implicit representation capability of the masking function under different expansion rates.

[0055] As can be seen, the masking model's ability to represent the masked image gradually improves with the increase of the dilation rate. More interestingly, the method in this embodiment is also a multimedia steganography scheme. From the perspective of transforming the original message image into the masked image, this embodiment can represent a message of arbitrary resolution as a continuous function, thereby achieving a high-capacity steganography scheme.

[0056] Table 5 The message capacity is shown in Table 5. As can be seen from Table 5, when the resolution of the secret image gradually increases, the secret function structure remains unchanged and is independent of the resolution of the secret message. Therefore, the structure can still be hidden in the masking structure.

[0057] The steganography technique based on neural implicit representation proposed in this embodiment has the following advantages: (1) Security: In this embodiment, the masking function can be regarded as a message decoder. The masking function's ability to implicitly represent the masking carrier masks its message extraction function. This not only solves the security problem of message decoder transmission on public channels, but also ensures that the masking function still has masking properties at the receiving end, thus protecting the information receiver's steganography behavior.

[0058] (2) Capacity: Since implicit neural representation parameterizes the secret message as a continuous function, the memory required for parameterizing the signal is independent of the spatial resolution and only related to the complexity of the underlying signal. This allows this embodiment to achieve large-capacity steganography by means of continuous functions.

[0059] (3) Communication burden: In this embodiment, the hidden function itself is also the hidden carrier. In this embodiment, only the hidden function needs to be transmitted on the public channel to achieve covert communication. More importantly, the implicitly represented continuous function usually has a small size, which greatly reduces the communication burden compared with the prior art.

[0060] (4) Universality: Transforming secret message data into a unified data format, namely a function, this simple method in this embodiment provides a new implementation framework for data steganography, which can provide a consistent steganography framework for images, 3D models, and other data such as weather data.

[0061] (5) Efficiency: Compared with existing technologies, steganography based on implicit representation only requires training the implicit representation function on a specific set of data, without the need for large-scale training on other tasks. Moreover, during implicit representation training, it is usually necessary to transform the grid data into a coordinate- and feature-based form before operation. This representation also allows this embodiment to randomly sample a portion of the elements instead of all the data for representation, for example, from the entire image. Select from 1 pixel Training on these subsets not only eliminates the direct dependence on data resolution but also saves significant memory and improves the efficiency of model training.

[0062] This simple implicit representation steganography technique, as described in this embodiment, will have better application scenarios in the future. In particular, the recent development of neural implicit representation technology means that widely distributing visual data by sharing implicit representation model weights is becoming a trend. 3D representation driven by NeRF is a typical example of this. Based on this, this embodiment envisions a real-world scenario. People would share various multimedia data they capture online in function format, just as they currently share 2D images and videos online. In this context, this embodiment is also interested in the following research questions: "1: Injecting information into 2D images or 3D content for steganography or ownership identification is common, but can this embodiment achieve information hiding when people share information through implicit representation functions? 2: How to define steganalysis capacity when implementing embedding operations in implicit representation networks, and how does this key indicator differ from traditional steganography?" The StegaINR scheme proposed in this embodiment combines steganography with implicit representation technology for the first time, not only solving the problem of deep steganography model transmission but also systematically answering the above two questions.

[0063] The contributions of this embodiment can be summarized as follows: This embodiment addresses the novel problem of implicit representation steganography and makes the first attempt to embed customizable, imperceptible, and recoverable secret information into continuous functions.

[0064] This embodiment solves the problem of high network security transmission and communication costs in deep decoding by disguising the secret message as a masking function.

[0065] This embodiment proposes a key-based masking function construction strategy, which uses the secret information shared by both parties to construct the structure of the masking function, and trains the parameters of the masking function through a partial optimization strategy based on the mask.

[0066] This embodiment empirically validates the proposed framework on diverse datasets with different data types, such as images, 3D data, and weather data, achieving highly accurate recovery while ensuring embedding capacity.

[0067] The above description is merely a preferred embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. An information steganography method based on neural implicit representation, characterized in that, include: Based on neural implicit representation, the secret message of several types of data is implicitly represented to obtain the secret function; The formula for obtaining the secret function is: in, For confidential information, Yes An initial function before parameterization. This refers to the parameterized function, i.e., the network secret function. The parameterization process representing the implicit representation; Based on the secret function, a masking function is constructed; The process of constructing a masking function includes: in, Let be the initial masking function. For key, key Used for control function structure and Location For several types of data, For the final masking function, It is a masking function The parameter set; After constructing the masking function, the process also includes: optimizing and training the parameters of the masking function using gradient descent based on the mask; Based on the masking function and the shared key, the secret message is recovered.

2. The information steganography method based on neural implicit representation according to claim 1, characterized in that, Before implicitly representing secret messages of several types of data, the following steps are also included: Several types of data are converted into data coordinates and data features, wherein the several types of data include: image data and point data; the data coordinates and the data features correspond to the input pairs and output pairs of the secret function, respectively.

3. The information steganography method based on neural implicit representation according to claim 1, characterized in that, Implicit representation of secret messages for several types of data also includes: An MLP is used as the underlying network for implicit representation. Based on the underlying network, an implicit representation of the secret message is obtained, denoted as the network secret function.

4. The information steganography method based on neural implicit representation according to claim 3, characterized in that, The formula for obtaining the implicit representation of a secret message is: in, It is an activation function. yes l Layer n A weighted summation of nodes, yes l Layer n The output of each node, the parameters of the MLP network are represented as a set of matrices and vectors. The network structure is represented as a vector consisting of the number of nodes in all layers. , Indicates the dimension of the input layer. For the output layer dimension, the MLP network is represented as The network secret function is represented as .

5. The information steganography method based on neural implicit representation according to claim 1, characterized in that, The function expansion strategies used when constructing masking functions include: horizontal expansion strategy, vertical expansion strategy, and hybrid expansion strategy.

6. The information steganography method based on neural implicit representation according to claim 1, characterized in that, The formula for recovering the secret message is: in, Representing the secret function The recovery process, Indicates to Sampling recovery, This is a confidential message.

Images