Quantitative index modulation steganography method based on chaos assistance

Abstract

The invention discloses a quantization index modulation steganography method based on chaos assistance, and aims to improve the security and concealment of information hiding. According to the method, a high-complexity pseudo-random sequence is generated by combining a delay coupling Lorentz chaotic system, the pseudo-random sequence is converted into a uniformly-distributed sequence through modular lattice operation, the uniformly-distributed sequence serves as external jitter to be introduced into a lattice quantization process, and therefore safe embedding of messages is achieved. According to the method, high-density embedding can be realized while carrier signal statistical characteristics are kept to effectively resist statistical steganalysis, and the method has relatively good image quality and robustness and is suitable for various types of digital carriers such as images, audios and the like.

Description

Technical Field

[0001] The present invention belongs to the technical field of information hiding, and in particular relates to a chaos-assisted quantization index modulation steganography method. Background Art

[0002] In information hiding techniques, quantization index modulation (QIM) stands out for its robustness and efficiency, achieving a relatively perfect balance between capacity, robustness, and fidelity. Its core concept is to encode secret messages as small perturbations of the carrier signal by designing the indexing rules of the quantizer. For example, in image steganography, QIM maps pixel values ​​or frequency-domain coefficients onto a pre-set quantization grid, using the parity of the grid spacing to distinguish embedded bits. This allows information to be recovered during extraction with a simple threshold decision. This mechanism is not only computationally efficient but also resistant to certain noise interference and compression attacks.

[0003] However, existing quantitative index modulation methods are limited in that they are susceptible to statistical steganographic attacks while minimizing distortion, while maintaining security at the expense of significant distortion. Ensuring the security of the stego signal requires that the statistical properties of the stego signal remain consistent with those of the original signal to resist statistical steganalysis attacks, while minimizing distortion requires maintaining high stego signal quality. Therefore, achieving secure and minimally distorted covert communication has become a critical challenge that needs to be addressed. Summary of the Invention

[0004] The main purpose of the present invention is to overcome the shortcomings and deficiencies of the prior art and provide a chaos-assisted quantized index modulation steganography method.

[0005] In order to achieve the above object, the present invention adopts the following technical solutions: A chaos-assisted quantization index modulation steganography method, the quantization index modulation steganography method comprising the following steps: S1. Get the embedded message and carrier signal , and the default grid basis , amplification factor ; S2, according to Geji and amplification factor , generate the corresponding coset representative; S3. Carrier signal Processing to obtain preprocessed carrier signal ; S4. Obtain chaotic sequence based on the Lorentz system with delayed coupling ; S5. Chaotic Sequence Perform modular operations to obtain uniformly distributed sequences ; S6, according to Geji , amplification factor , coset representatives, and uniformly distributed sequences , using quantized index modulation technology to convert the message Embedded into pre-processed carrier signal , and obtain the stego signal.

[0006] Furthermore, the process of step S2 is as follows: S21, through the input amplification factor , construct the dimension basis set , where v is an element in the dimension basis set, represents a set of integers; S22, based on lattice dimension , for the dimension basis set Perform Cartesian product operation to generate candidate sets , where the candidate set Include candidate elements; S23. Map the Cartesian product candidate elements to normalized dimensional integer lattice vector, Candidate elements correspond to unique vectors ,in , get all normalized vectors Forming the grid The coset representative of .

[0007] During step S2, according to the amplification factor Constructing a dimensional basis set , based on the lattice basis Dimensional basis set Perform Cartesian product operation to generate candidate sets , and maps each candidate element to a normalized -dimensional integer vector Finally, all normalized vectors are output to form a coset representative. The constructed coset representative is prepared for the embedding of subsequent messages.

[0008] Furthermore, the process of step S3 is as follows: S31, carrier signal Perform block processing to obtain 8×8 non-overlapping carrier signal blocks; S32, applying discrete cosine transform to each carrier signal block to obtain discrete cosine transform coefficients; S33, selecting mid-high frequency discrete cosine transform coefficients as embedding areas; S34, combining each embedding region in order to obtain a pre-processed carrier signal .

[0009] In step S3, the carrier signal is processed by block and discrete cosine transform, and combined in order to obtain a pre-processed carrier signal The discrete cosine transform concentrates the energy of the carrier signal in a small number of coefficients, improving the embedding efficiency of the quantization index modulation. The block processing destroys the spatial continuity of the carrier signal, and the statistical characteristics of the discrete cosine transform coefficients are disturbed, reducing the recognizability of the steganographic traces.

[0010] Further, the step S4 is as follows: S41, obtaining a preset initial coordinate and a delay time; S42, calculating a three-dimensional chaotic sequence by using a Lorenz system combined with delay coupling according to the initial coordinate and the delay time; The three-dimensional chaotic sequence is calculated by the Lorenz system combined with delay coupling according to the following formula,

[0011]

[0012]

[0013]

[0014]

[0015]

[0016] wherein, , , respectively represent the updated horizontal coordinate, vertical coordinate and vertical coordinate components of the three-dimensional chaotic sequence at time , represents the current time, represents the delay time, , , respectively represent the horizontal coordinate, vertical coordinate and vertical coordinate of the Lorenz system at time , , , respectively represent the horizontal coordinate, vertical coordinate and vertical coordinate of the Lorenz system at the last delay time, represents the function value modulo 1 operation, i.e. the control result is between , Indicates the initial coordinates of the horizontal coordinate, vertical coordinate, and vertical coordinate; S43. Randomly select one-dimensional output from the three-dimensional chaotic sequence as a chaotic sequence .

[0017] In step S4, the original Lorenz system has few initial parameters, and the chaotic sequence it outputs is relatively simple, making it easy for an attacker to decipher. By introducing delayed coupling and modulo operations, the original Lorenz system is improved, reducing the correlation between chaotic sequences in adjacent time periods. This results in a more complex chaotic sequence, increasing the system's complexity and randomness, making it more difficult for an attacker to decipher.

[0018] Furthermore, the process of step S5 is as follows: S51, Chaotic Sequence The sequence points Perform modular operation to obtain uniform sequence points , where the calculation formula for the modular operation is as follows;

[0019] in, Indicates the grid base, represents a point in the lattice basis; S52, all uniform sequence points Combine in order to get a uniformly distributed sequence ; S53, for uniformly distributed sequences Randomly select a starting point and pre-process the carrier signal The length is cut and updated to obtain a uniformly distributed sequence .

[0020] During step S5, the chaotic sequence Perform modular operations to obtain uniformly distributed sequences , this sequence can be used to quantize the external jitter of index modulation to increase the randomness and security of index modulation. Randomly select a starting point. Even if the attacker knows the specific structure and initial conditions of the chaotic system, he cannot obtain the uniform sequence used for quantitative index modulation. ,This operation not only ensures the stability and randomness of the data, but also prevents attackers from using ,previous data for prediction, thereby increasing the difficulty of cracking the system.

[0021] Furthermore, the process of step S6 is as follows: S61, multiplying the lattice basis and the amplification coefficient to obtain an amplified lattice basis; S62, will expand the lattice basis, coset representative and uniform distribution sequence Substitute the quantization index modulation formula and use the quantization index modulation formula to preprocess the carrier signal Each carrier signal in Perform calculations to obtain the steganographic signal; Among them, the message is analyzed according to the following formula and carrier signal The calculation formula is as follows:

[0022] in, represents the amplified lattice basis, Represents the preprocessed carrier signal The carrier signal, Indicates the A steganographic signal, represents the coset representative, Represents a uniformly distributed sequence No. values, express distance.

[0023] In step S6, the pre-processed carrier signal is modulated by the quantization index modulation formula according to the embedded message. The quantization of is used to represent the corresponding message embedded to obtain the stego signal.

[0024] Compared with the prior art, the present invention has the following advantages and beneficial effects: (1) The present invention proposes a chaos-assisted quantization index modulation steganography method based on chaos theory. This method innovatively generates a pseudo-random sequence by combining a delayed coupled chaotic system, which is converted into a uniformly distributed sequence after a modular operation and used as an external jitter in the quantization process, thereby achieving secure and hidden message embedding.

[0025] (2) This invention fully utilizes the unpredictability and uniformity of chaotic sequences, making the steganographic signal after embedding the message highly consistent with the carrier signal in terms of statistical distribution, in line with the principle of statistical indistinguishability. Both theoretical analysis and experiments have shown that this method can effectively resist statistical steganalysis techniques such as histogram analysis and chi-square analysis.

[0026] (3) During the message embedding process, the chaos-assisted quantized index modulation technology adopted in the present invention can effectively control the disturbance range caused by message embedding, and has little impact on the carrier signal during the embedding process. The generated stegosig signal has low distortion and high subjective quality.

[0027] (4) Compared with traditional steganographic algorithms, the present invention achieves high-density embedding by effectively planning the quantized index space and using high-dimensional grid points, thus achieving a higher embedding rate while ensuring the quality of the steganographic signal.

[0028] (5) The present invention introduces a uniformly distributed chaotic sequence as dither during the steganographic process. Coupled with the lattice-based quantization process, the embedded message can still be accurately extracted in the face of disturbances such as additive Gaussian noise, salt and pepper noise, and speckle noise, showing strong robustness. In common attack scenarios, the bit error rate remains low, demonstrating a certain degree of anti-attack capability. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.

[0030] Figure 1 This is a flowchart of the application implementation of a chaos-assisted quantized index modulation steganography method disclosed in an embodiment of the present invention; Figure 2 This is a flowchart of an application implementation of generating a coset representative in a chaos-assisted quantized index modulation steganography method disclosed in an embodiment of the present invention; Figure 3 This is a flowchart of an application implementation of generating a pre-processed carrier signal in a chaos-assisted quantization index modulation steganography method disclosed in an embodiment of the present invention; Figure 4 Schematic diagram of zigzag scanning in a chaos-assisted quantized index modulation steganography method disclosed in an embodiment of the present invention; Figure 5 This is a flowchart of the application implementation of generating a chaotic sequence in a chaos-assisted quantized index modulation steganography method disclosed in an embodiment of the present invention; Figure 6 This is a flowchart of an application implementation of generating an initial jitter sequence in a chaos-assisted quantization index modulation steganography method disclosed in an embodiment of the present invention; Figure 7 This is a flowchart of an application implementation of generating a final jitter sequence in a chaos-assisted quantization index modulation steganography method disclosed in an embodiment of the present invention; Figure 8 This is a flowchart of an application implementation of generating a steganographic signal in a chaos-assisted quantization index modulation steganographic method disclosed in an embodiment of the present invention; Figure 9It is the original grayscale image used in Example 1 of the chaos-assisted quantization index modulation steganography method disclosed in the embodiments of the present invention; Figure 10 A grayscale image after embedding a message in Example 1 of a chaos-assisted quantization index modulation steganography method disclosed in an embodiment of the invention. DETAILED DESCRIPTION

[0031] In order to enable those skilled in the art to better understand the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments in the present invention, all other embodiments obtained by those skilled in the art without creative work are within the scope of protection of the present invention.

[0032] References to "embodiments" in this application mean that a particular feature, structure, or characteristic described in connection with the embodiment may be included in at least one embodiment of the application. The appearance of this phrase in various places in the specification does not necessarily refer to the same embodiment, nor does it constitute an independent or alternative embodiment that is mutually exclusive of other embodiments. It is understood, both explicitly and implicitly, by those skilled in the art that the embodiments described in this application may be combined with other embodiments.

[0033] Example 1 With the continuous development of multimedia technology and network communications, more and more image data is frequently transmitted over the internet, and the demand for secure and covert image information transmission is growing. In real life, while traditional image embedding strategies based on quantized index modulation (QIM) offer high embedding efficiency, they often destroy the local statistical properties of the image during the embedding process, making the stegoimage susceptible to detection and identification using methods such as histograms and chi-square analysis, resulting in insufficient concealment. Furthermore, while some chaos-based image steganography methods leverage the unpredictability of chaotic sequences to improve security, they often result in significant image distortion and complex system parameter control, making them unsuitable for practical deployment.

[0034] To address the above issues, this embodiment mainly studies chaos-assisted quantization index modulation and proposes a chaos-assisted quantization index modulation secure steganography method, which achieves high-fidelity, high embedding rate and high security image information hiding.

[0035] The following combination Figure 1 The specific process of a chaos-assisted quantization index modulation secure steganography method disclosed in this embodiment is described in detail.

[0036] This embodiment discloses a chaos-assisted quantization index modulation secure steganography method, comprising the following steps: S1. Get the embedded message and carrier signal , and the default grid basis , amplification factor ; Select a grayscale image with a pixel size of 256×256 and a grid basis of , amplification factor =4. Embedded message In the range [0, ], where =2.

[0037] S2, according to Geji and amplification factor , generate the corresponding coset representative; The following will be combined Figure 2 Description based on Geki and amplification factor The implementation process of generating the corresponding coset representative: S21, through the input amplification factor , construct the dimension basis set , where v is an element in the dimension basis set, represents a set of integers; S22, based on lattice dimension , for the dimension basis set Perform Cartesian product operation to generate candidate sets , where the candidate set Include candidate elements; S23. Map the Cartesian product candidate elements to normalized dimensional integer lattice vector, Candidate elements correspond to unique vectors ,in , get all normalized vectors Forming the grid The coset representative of .

[0038] Figure 2 Constructing a Set , for the set Perform a double Cartesian product to obtain a candidate set , a total of 16 elements. Map the candidate set into a two-dimensional vector and output the coset representative for quantizing index modulation to embed different messages .

[0039] S3. Carrier signal Processing to obtain preprocessed carrier signal ; The following will be combined Figure 3 、 Figure 4 Describe the carrier signal Processing to obtain preprocessed carrier signal Implementation process: S31, carrier signal Perform block processing to obtain 8×8 non-overlapping carrier signal blocks; S32, applying discrete cosine transform to each carrier signal block to obtain discrete cosine transform coefficients; S33, selecting mid-high frequency discrete cosine transform coefficients as embedding areas; S34, combine each embedded area in sequence to obtain a preprocessed carrier signal .

[0040] Figure 3 Select a 256×256 grayscale image as the carrier signal , the image is divided into 8×8 non-overlapping image blocks, resulting in a total of 1024 blocks. Subsequently, a two-dimensional discrete cosine transform is performed on each image block, converting it from the spatial domain to the frequency domain to obtain the corresponding discrete cosine transform coefficient matrix. The purpose of converting the grayscale image from the spatial domain to the frequency domain is to disperse the influence of the embedded signal to multiple pixels, rather than concentrating it in several pixels of the embedded message, which is easy to be analyzed by statistical steganalysis and will cause large distortion. In each discrete cosine transform coefficient matrix, several coefficients in the mid- and high-frequency parts are selected as the embedding area to improve the concealment of the steganography and reduce the impact on the visual quality of the image. Finally, the mid- and high-frequency coefficients selected from each image block are extracted in a fixed order using the zigzag scanning method, and the coefficients extracted from all blocks are spliced ​​in sequence according to the block order to form a preprocessed carrier signal in the form of a one-dimensional vector. , for subsequent embedding operations.

[0041] Figure 4 This is a zigzag scan method. It scans in a zigzag pattern from the upper left corner to the lower right corner. Taking a 4×4 image block as an example, the left image shows the zigzag scan, and the right image shows the order after scanning.

[0042] S4. Obtain chaotic sequence based on the Lorentz system with delayed coupling ; The following combination Figure 5 Describe the chaotic sequence obtained from the Lorentz system with delayed coupling Implementation process: S41, obtaining a preset initial coordinate and delay time; S42, according to the initial coordinates and delay time, a Lorentz system combined with delayed coupling is used for calculation to obtain a three-dimensional chaotic sequence; Among them, the three-dimensional chaotic sequence is calculated by the following formula in combination with the delayed coupled Lorentz system:

[0043]

[0044]

[0045]

[0046]

[0047]

[0048] in, , , They represent the three-dimensional chaotic sequence at time The updated horizontal, vertical and vertical coordinate components, Indicates the current time, Indicates the delay time, 、 、 They represent the Lorentz system at time The horizontal coordinate, vertical coordinate, and vertical coordinate of 、 、 They represent the horizontal, vertical and vertical coordinates of the Lorentz system at the last delay time, Indicates that the function value modulo 1 operation is controlled by the result between, Indicates the initial coordinates of the horizontal coordinate, vertical coordinate, and vertical coordinate; S43. Randomly select one-dimensional output from the three-dimensional chaotic sequence as a chaotic sequence .

[0049] Figure 5 Set the initial coordinates of the system , total iteration time and time step As the initial input of the chaotic system, according to the Lorentz difference formula combined with delayed coupling, the three-dimensional chaotic sequence is obtained by iterative solution in the time domain. , where each component exhibits typical chaotic characteristics. Finally, select Components are used as chaotic sequences for subsequent embedding The sequence has good randomness and ergodicity, providing security for disturbance sources in the quantization index modulation process.

[0050] S5. Chaotic Sequence Perform modular operations to obtain uniformly distributed sequences ; The following combination Figure 6 、 Figure 7 Describing chaotic sequences Perform modular operations to obtain uniformly distributed sequences Implementation process: S51, Chaotic Sequence The sequence points Perform modular operation to obtain uniform sequence points , where the calculation formula for the modular operation is as follows;

[0051] in, Represents the grid base, represents a point in the lattice basis; S52, all uniform sequence points Combine in order to get a uniformly distributed sequence ; S53, for uniformly distributed sequences Randomly select a starting point and pre-process the carrier signal The length of the cut is updated to obtain a uniformly distributed sequence .

[0052] Figure 6 Based on Geki Chaotic Sequence Performing point-by-point grid projection, we obtain the uniformly distributed sequence Y, which is the initial jitter sequence. This sequence is an approximation of the uniform distribution and has periodicity and statistical flatness.

[0053] Figure 7 Implemented dithering sequence and pre-processed carrier signal The length is aligned and a random starting position is introduced to increase the embedding security and prevent attackers from using a fixed perturbation window for reverse analysis.

[0054] S6, according to Geji , amplification factor , coset representatives, and uniformly distributed sequences , using quantized index modulation technology to convert the message Embedded into pre-processed carrier signal , and obtain the stego signal.

[0055] The following combination Figure 8 Description based on Geki , amplification factor , coset representatives, and uniformly distributed sequences , using the quantized index modulation method to convert the message Embedded into pre-processed carrier signal In the implementation process of the steganographic signal, we can get: S61, multiplying the lattice basis and the amplification coefficient to obtain an amplified lattice basis; S62, will expand the lattice basis, coset representative and uniform distribution sequence Substitute the quantization index modulation formula and use the quantization index modulation formula to preprocess the carrier signal Each carrier signal in Perform calculations to obtain the steganographic signal; Among them, the message is analyzed according to the following formula and carrier signal The calculation formula is as follows:

[0056] in, represents the amplified lattice basis, Represents the preprocessed carrier signal The carrier signal, Indicates the A steganographic signal, represents the coset representative, Represents a uniformly distributed sequence No. values, express distance.

[0057] Figure 8 Computational amplification lattice , for each preprocessed carrier signal For all, there are corresponding uniformly distributed sequences The value of is used as the external jitter in the quantization process. Depending on the embedded message, the pre-processed carrier signal with the external jitter added is Quantize to the nearest grid point to generate the stego signal.

[0058] This embodiment uses a chaos-based quantization index modulation method on the grayscale image to embed random messages into the grayscale image. Figure 9 and Figure 10 The original grayscale image and the grayscale image with the embedded message are shown. Compared with the original grayscale image, the grayscale image with the embedded message in this embodiment has a mean square error of 0.5037 and a peak signal-to-noise ratio of 51.1094. The resulting changes are not perceptible to humans, proving the effectiveness of the present invention.

[0059] Example 2 This embodiment applies the present invention to color images, and achieves higher embedding capacity and security by embedding messages in the three color channels of RGB respectively.

[0060] In Example 2, except for steps S3, S5 and S6, the same steps as in Example 1 are referred to.

[0061] Step S1 and step S2 refer to steps S1 and S2 in embodiment 1, and select a color image with a pixel size of 256×256 and a grid basis of , amplification factor , embedded messages In the range [0, ], where .

[0062] S3. Carrier signal The three RGB channels are processed separately to obtain the preprocessed carrier signal 、 and ; The process is as follows: S31, performing block processing on the three RGB channels respectively to obtain 8×8 non-overlapping carrier signal blocks; S32. Perform a two-dimensional discrete cosine transform on each carrier signal block to obtain discrete cosine transform coefficients; S33, selecting mid-high frequency discrete cosine transform coefficients as embedding areas; S34, combine each embedded area in sequence to obtain a preprocessed carrier signal 、 and .

[0063] Step S3 pre-processes the color image, filters it according to the RGB channels and performs discrete cosine transform to obtain the pre-processed carrier signal 、 and .

[0064] Step S4 refers to step S4 in embodiment 1.

[0065] S5. Chaotic Sequence Perform modular operations to obtain uniformly distributed sequences ; The process is as follows: Step S51 and step S52 refer to step S51 and step S52 in embodiment 1; S53, for uniformly distributed sequences Randomly select a starting point and pre-process the carrier signal 、 and The length of the cut is updated to obtain a uniformly distributed sequence , and crop to generate three channels 、 and .

[0066] Step S5: chaotic sequence Perform modular operations to obtain uniformly distributed sequences , according to the length of the preprocessed carrier signal of the three channels, the updated uniform distribution sequence Perform cropping to generate sequences corresponding to three channels as external dithering in the quantization process.

[0067] S6, according to Geji , amplification factor , coset representatives, and uniformly distributed sequences , using quantized index modulation technology to convert the message Embedded into pre-processed carrier signal 、 and In the process, the stego signal is obtained, and the stego signals of the three channels are combined to output the stego image.

[0068] Step S6 uses the quantization index modulation method to embed the message into the pre-processed carrier signal 、 and In [1], the steganographic signals of the three channels are subjected to inverse discrete cosine transform and the channels are merged to generate the steganographic image.

[0069] This example uses a chaos-based quantized index modulation method to embed a random message into a color image. Compared to the original image, the embedded color image achieves a mean square error of 2.3641 and a peak signal-to-noise ratio of 41.2148. The resulting changes are imperceptible to humans, demonstrating the effectiveness of this invention.

[0070] In summary, the present invention constructs a chaos-assisted quantization index modulation method to resist statistical steganalysis and noise attacks. This method innovatively introduces a delay-coupled Lorentz system to generate a highly complex pseudo-random sequence. This sequence is converted into a uniformly distributed perturbation through modular lattice operations, which is then used as external dither during the quantization process, thereby enabling message embedding without compromising the statistical properties of the carrier. Through effective partitioning of the quantization space and high-dimensional coset design, this method significantly improves embedding capacity while ensuring low distortion and high subjective quality. Experimental and theoretical analysis demonstrate that this method resists statistical steganalysis attacks such as histogram analysis and the chi-square test, and exhibits good robustness and stability under common attack conditions such as additive Gaussian noise and salt-and-pepper noise, with a low bit error rate and strong concealment. Compared to traditional steganographic methods, this method exhibits excellent adaptability to multimodal carriers such as images and audio, combining statistical indistinguishability with engineering value, making it suitable for application in multiple scenarios such as digital copyright protection and secure communications.

[0071] The technical features of the above embodiments can be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0072] The above embodiments are preferred implementation modes of the present invention, but the implementation modes of the present invention are not limited to the above embodiments. Any other changes, modifications, substitutions, combinations, and simplifications that do not deviate from the spirit and principles of the present invention should be considered as equivalent replacement methods and are included in the scope of protection of the present invention.

Claims

1. A chaos-assisted quantized index modulation steganography method, characterized in that: The quantization index modulation steganography method comprises the following steps: S1. Get the embedded message and carrier signal , and the default grid basis , amplification factor ; S2, according to Geji and amplification factor , generate the corresponding coset representative; S3. Carrier signal Processing to obtain preprocessed carrier signal ; S4. Obtain chaotic sequence based on the Lorentz system with delayed coupling ; S5. Chaotic Sequence Perform modular operations to obtain uniformly distributed sequences ; S6, according to Geji , amplification factor , coset representatives, and uniformly distributed sequences , using quantized index modulation technology to convert the message Embedded into pre-processed carrier signal , and obtain the stego signal.

2. The chaos-assisted quantization index modulation steganography method according to claim 1, characterized in that: The process of step S2 is as follows: S21, through the input amplification factor , construct the dimension basis set , where v is an element in the dimension basis set, represents a set of integers; S22, based on lattice dimension , for the dimension basis set Perform Cartesian product operation to generate candidate sets , where the candidate set Include candidate elements; S23. Map the Cartesian product candidate elements to normalized dimensional integer lattice vector, Candidate elements correspond to unique vectors ,in , get all normalized vectors Forming the grid The coset representative of .

3. The chaos-assisted quantization index modulation steganography method according to claim 1, characterized in that: The process of step S3 is as follows: S31, carrier signal Perform block processing to obtain 8×8 non-overlapping carrier signal blocks; S32, applying discrete cosine transform to each carrier signal block to obtain discrete cosine transform coefficients; S33, selecting mid-high frequency discrete cosine transform coefficients as embedding areas; S34, combine each embedded area in sequence to obtain a preprocessed carrier signal .

4. The chaos-assisted quantization index modulation steganography method according to claim 1, characterized in that: The process of step S4 is as follows: S41, obtaining a preset initial coordinate and delay time; S42, according to the initial coordinates and delay time, a Lorentz system combined with delayed coupling is used for calculation to obtain a three-dimensional chaotic sequence; Among them, the three-dimensional chaotic sequence is calculated by the following formula for the Lorentz system combined with delayed coupling: , in, , , They represent the three-dimensional chaotic sequence at time The updated horizontal, vertical and vertical coordinate components, Indicates the current time, Indicates the delay time, 、 、 They represent the Lorentz system at time The horizontal coordinate, vertical coordinate, and vertical coordinate of 、 、 They represent the horizontal, vertical and vertical coordinates of the Lorentz system at the last delay time, Indicates that the function value modulo 1 operation is controlled by the result between, Indicates the initial coordinates of the horizontal coordinate, vertical coordinate, and vertical coordinate; S43. Randomly select one-dimensional output from the three-dimensional chaotic sequence as a chaotic sequence .

5. The chaos-assisted quantization index modulation steganography method according to claim 1, characterized in that: The process of step S5 is as follows: S51, Chaotic Sequence The sequence points Perform modular operation to obtain uniform sequence points , where the calculation formula for the modular operation is as follows; in, Represents the grid base, represents a point in the lattice basis; S52, all uniform sequence points Combine in order to get a uniformly distributed sequence ; S53, for uniformly distributed sequences Randomly select a starting point and pre-process the carrier signal The length of the cut is updated to obtain a uniformly distributed sequence .

6. The chaos-assisted quantization index modulation steganography method according to claim 1, characterized in that: The process of step S6 is as follows: S61, multiplying the lattice basis and the amplification coefficient to obtain an amplified lattice basis; S62, will expand the lattice basis, coset representative and uniform distribution sequence Substitute the quantization index modulation formula and use the quantization index modulation formula to preprocess the carrier signal Each carrier signal in Perform calculations to obtain the steganographic signal; Among them, the message is analyzed according to the following formula and carrier signal The calculation formula is as follows: in, represents the amplified lattice basis, Represents the preprocessing carrier signal The carrier signal, Indicates the A steganographic signal, represents the coset representative, Represents a uniformly distributed sequence No. values, express distance.

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