CN115131253B - A Secret Image Sharing Method and System Against JPEG Heavy Compression - Google Patents

Abstract

The invention proposes a secret image sharing method and system for resisting JPEG heavy compression, belonging to the technical field of image processing. The secret image to be shared is a JPEG image, and the secret information contained in the JPEG image is a quantized DCT coefficient. The JPEG re-compression refers to the compression processing performed after the JPEG image is shared. against the compression process while maintaining the JPEG image.

Description

A secret image sharing method and system for counteracting JPEG heavy compression

Technical Field

The present invention belongs to the technical field of image processing, and in particular to a secret image sharing method and system for resisting JPEG heavy compression.

Background Art

Secret sharing technology encrypts secret information into multiple shadow images (shadow, shadowimage or share) and distributes them to multiple participants. Only a subset of authorized participants can decrypt together, while unauthorized subsets cannot decrypt. A secret sharing algorithm generally includes two stages: secret sharing (share or generate) and recovery (recover), sometimes also called encryption (encrypt) and decryption (decrypt) or encoding (encode) and decoding (decode). In the (k,n) threshold secret sharing scheme, where k≤n, the secret information is encrypted into n shadow images. Only when equal to or greater than k shadow images are obtained can the original secret be decrypted; when there are less than k shadow images, no secret can be obtained.

Digital images are one of the most important media types. Researchers have extensively studied the application of secret sharing technology to digital image objects, and secret image sharing (SIS) technology has flourished. Compared with data, the special features of digital images in the field of secret image sharing are: (1) The special file storage structure of digital images. Taking grayscale BMP format digital images as an example, the pixel value space is [0, 255]. Therefore, in the secret image sharing scheme, the value range of secret values, sharing values and related parameters should be fully considered to avoid information loss during the sharing or recovery process, resulting in the inability to recover the secret image. (2) Digital images are composed of a large number of pixels. Secret sharing only performs sharing operations on one or several pixel values at a time. Therefore, the efficiency of sharing and recovery algorithms should be emphasized during the scheme design process. (3) There is correlation between adjacent pixel values. There is coherence and correlation between adjacent pixel points in the image, which may cause the leakage of image secret information. Therefore, the secret image sharing scheme should consider both single-time sharing security and visual security. (4) Image transmission ultimately relies on human visual system recognition. Due to the low-pass filtering characteristics of the human eye, lossless image restoration is not required. (5) Images are special data, and the secret image sharing scheme can be applied to general data secret sharing scenarios with simple changes. The performance evaluation indicators of the secret image sharing scheme include: secret image restoration quality, pixel expansion, (k,n) threshold, secret image restoration complexity, shadow image understandability, gradualness, secret image type, etc.

The mainstream principles of secret sharing include: (k,n) threshold secret sharing scheme based on polynomials, secret sharing scheme based on the Chinese remainder theorem, and visual encryption scheme. This technical scheme is a secret sharing scheme based on polynomials. The following introduces a (k,n) threshold secret sharing scheme based on polynomials.

The polynomial secret sharing scheme in the prior art embeds the secret into a random k-1 degree polynomial. During decryption, the polynomial can be reconstructed by Lagrange interpolation to obtain the secret information embedded in the polynomial. Given the secret information s, share it as n shadow shares sc ₁ ,sc ₂ ,…,sc _n . The specific scheme is as follows:

(1) In the initialization phase, determine the value of the threshold (k,n), where k≤n. Select a large prime number p such that p＞n and p＞s, and let GF(p) be a finite field, all elements of which are elements of GF(p), and all operations are performed in the finite field GF(p).

(2) In the sharing phase, in order to encrypt s into the shadow value sc _i , a k-1 degree polynomial is randomly generated in the finite field GF(p):

f(x)＝a ₀ +a ₁ x+…+a _k-1 x ^k-1

The secret s is embedded into the first coefficient of the polynomial, that is, a ₀ = s, and the remaining coefficients a ₁ ,…, a _k-1 are randomly selected from the finite field GF(p). Then calculate

sc ₁ =f(1),…,sc _k =f(k),…,sc _n =f(n)

Take (i, sc _i ) as a shadow pair, where i is an information tag or sequence number tag, and sc _i is a shadow pixel value. Distribute n shadow shares to n participants to complete secret sharing.

其中，

可以构建如下的线性方程组：(3) In the recovery phase, obtain any k secret pairs held by n participants.

in,

The following linear equations can be constructed:

Because i _l (1≤l≤k) are all different, the following polynomial can be constructed using the Lagrange interpolation formula:

Thus, the secret s = f(0) can be obtained. If k-1 participants want to obtain the secret, they can construct k-1 equations and form a linear system of equations, where the k coefficients of the shared polynomial are unknowns. Since the labels i _l are different, each shadow share corresponds to a unique polynomial that satisfies the linear system of equations. Therefore, it is known that k-1 shadows cannot solve the linear system of equations containing k unknowns, and thus cannot obtain any information about the secret. Therefore, this solution is perfect.

With the increasing influence of social networks, Facebook, Twitter, Instagram, WeChat and Sina Weibo have penetrated deeply into people's daily lives, and photo sharing has become a popular activity for users to communicate with friends. As of February 2022, 35 billion photos have been uploaded to Facebook. Using images on social networks to transmit or store information can achieve the covert transmission and storage of secret information, meet the needs of the country and society for convenient and secure communication, and have important value in ensuring information security. At present, Secret Image Sharing (SIS) can solve the problem of covert communication and covert storage using images as the medium. Secret image sharing technology uses the idea of secret sharing to split the storage of secrets to prevent secrets from being too concentrated, and achieves the purpose of dispersing risks and tolerating intrusion (loss). This technology encrypts secret information into multiple shadow images (shadow, shadow image or share) and distributes them to multiple participants. Only a subset of authorized participants can decrypt together, while unauthorized subsets cannot be decrypted. Generally, covert communication based on secret image sharing is multi-channel, which can solve the problems faced by single image steganography, such as the inability to achieve multi-channel covert communication, authority control, and loss tolerance.

However, in a large-scale social network environment, due to the limitations of social network performance and backend servers, images passing through lossy channels of social networks will be subjected to lossy operations such as recompression, resulting in reduced shadow image quality and information loss. Traditional secret image sharing technology is designed for lossless channels, which makes traditional technology no longer applicable in social network environments. When the existing secret image sharing technology is applied to social networks on the public Internet, the distributor shares the secret image as several shadow images and hands them over to several participants; the participants upload the shadow images they hold to their social network accounts such as Facebook, Twitter, WeChat and other social platforms, and the shadow images will be transmitted through the channels of the public Internet; the uploaded shadow images will be subjected to lossy operations such as recompression, resulting in reduced shadow image quality and information loss; if the restorer wants to successfully restore the lossy shadow images after receiving them, it is necessary to design a robust secret image sharing scheme to generate shadow images that are robust to JPEG recompression.

A robust secret sharing scheme against JPEG heavy compression is the only way and foundation for applying secret image sharing to social networks. In addition, better secret image sharing properties should be pursued, such as understandable shadow images and high image quality of recovered secret images.

Traditional secret image sharing technology is designed for lossless channels. When uploading images to social networks, the images will be subjected to lossy recompression operations, resulting in traditional secret image sharing technology no longer being applicable in social network environments. Currently, there is no robust secret image sharing solution that is effective against JPEG recompression. A robust secret sharing solution that resists JPEG recompression is the only way and basis for applying secret image sharing to social networks. In order to combat the loss of shadow images caused by JPEG recompression, this patent finds the stable amount before and after JPEG recompression, and uses the screening mechanism and stable block conditions of the polynomial-based secret image sharing solution to construct a robust shadow image that can resist JPEG recompression.

Summary of the invention

In view of the above technical problems, the present invention proposes a secret image sharing solution for resisting JPEG heavy compression.

The first aspect of the present invention discloses a secret image sharing method for resisting JPEG recompression. The secret image to be shared is a JPEG image, the secret information contained in the JPEG image is a quantized DCT (Discrete Cosine Transform) coefficient, the JPEG recompression refers to the compression process performed on the JPEG image after the sharing process, and the method resists the compression process while sharing the JPEG image; the method comprises:

Step S1, extracting and preprocessing the acquired n+1 images to extract a complete DCT coefficient list of each image in the n+1 images, wherein the n+1 images include one secret image to be shared and n carrier images;

Step S2, based on the n+1 complete DCT coefficient lists, determining the DCT coefficient list to be shared of the secret image to be shared and the n DCT coefficient lists to be used corresponding to the n carrier images, and determining the prime number p according to the maximum DCT coefficient value in the DCT coefficient list to be shared and the n DCT coefficient lists to be used;

Step S3, using the DCT coefficient list to be shared, the n DCT coefficient lists to be used, the prime number p and the threshold value k, obtaining by calculation n sharing value lists corresponding to the n DCT coefficient lists to be used and containing the secret information of the secret image to be shared;

Step S4, for each of the n sharing value lists, executing: forming B×B shadow DCT blocks according to each sharing value thereof, and decompressing the B×B shadow DCT blocks to obtain B×B shadow image spatial domain blocks;

Step S5, determining whether the element value in each image spatial domain block of a total of n×B×B shadow image spatial domain blocks obtained based on the n sharing value lists is within a specified range, and if so, using the B×B shadow image spatial domain blocks corresponding to each sharing value list as B×B shadow DCT blocks to resist the JPEG recompression;

Step S6: for each of the B×B shadow DCT blocks corresponding to the shared value list that resist the JPEG recompression, determine one shadow image that resists the JPEG recompression, and obtain a total of n shadow images that resist the JPEG recompression. The sender sends the n shadow images that resist the JPEG recompression to the receiver to share the secret image while resisting the JPEG recompression.

Wherein, n, p, k, and B are all positive integers, k≤n, and the threshold value k represents the minimum number of shadow images required to restore the secret image.

According to the method of the first aspect of the present invention, in step S1, the preprocessing specifically includes performing the following steps on each of the n+1 images:

Extracting a quantized DCT coefficient matrix of the current image by entropy decoding, the DCT coefficient matrix comprising M×M DCT coefficients, performing block processing on the DCT coefficient matrix into B×B DCT blocks, each of which comprises A×A DCT coefficients, wherein M=B×A;

For each DCT block containing A×A DCT coefficients, extract the first C DCT coefficients in a zigzag order to obtain a DCT coefficient list of each DCT block, thereby constructing a complete DCT coefficient list of the current image, the length of the DCT coefficient list of each DCT block is C, and the length of the complete DCT coefficient list of the current image is C×B×B;

Among them, M, A, and C are all positive integers.

According to the method of the first aspect of the present invention, step S2 specifically comprises:

Determine whether the minimum DCT coefficient in the n+1 complete DCT coefficient lists is greater than 0;

If yes, one of the n+1 complete DCT coefficient lists of the secret image to be shared is used as the DCT coefficient list to be shared, and n of the n+1 complete DCT coefficient lists of the carrier image are used as the n DCT coefficient lists to be used;

If not, perform value shift on all DCT coefficients in the n+1 complete DCT coefficient lists, the shift amount of the value shift is the absolute value of the minimum DCT coefficient, and use the complete DCT coefficient list of the secret image to be shared after the value shift as the DCT coefficient list to be shared, and use the complete DCT coefficient lists of the n carrier images after the value shift as the n DCT coefficient lists to be used;

The maximum DCT coefficient value in the DCT coefficient list to be shared and the n DCT coefficient lists to be used is obtained, and the minimum prime number greater than the maximum DCT coefficient is taken as the prime number p.

According to the method of the first aspect of the present invention, the length of the DCT coefficient list to be shared, the length of each of the n DCT coefficient lists to be used, and the length of each of the n shared value lists are all C×B×B; the step S3 specifically includes:

For each position in each of the n shared value lists, calculate its DCT shadow value using the formula f(x)=s+a ₁ x+a ₂ x ² +…+ak _-1 x ^k-1 (mod p);

Wherein, f(x) is the DCT shadow value at the current position in the current list in the n shared value lists, s is the DCT coefficient at the position in the DCT coefficient list to be shared corresponding to the current position in the current list, a ₁ , a ₂ , ..., a _k-1 are arbitrarily selected random numbers, x is a selected value, and (mod p) represents a modulo p operation;

Determine whether the high δ bits of f(x) are equal to the high δ bits of the DCT coefficient at the position corresponding to the current position in the current list in the n DCT coefficient lists to be used, wherein

If so, the DCT shadow value f(x) is used as the shared value at the current position in the current list of the n shared value lists at the current position;

If not, adjust _a1 , _a2 , ..., _ak-1 and recalculate f(x) until its high δ bits are equal to the high δ bits of the DCT coefficient at the position corresponding to the current position in the current list in the n DCT coefficient lists to be used, and obtain the sharing value at the current position.

According to the method of the first aspect of the present invention, in step S3, for each position in the current list, when calculating its DCT shadow value, x remains unchanged, and the selected values x of the n shared value lists are different, and the value ranges of f(x), x, and _a1 , _a2 , ..., _ak-1 are integers on [0, p-1].

According to the method of the first aspect of the present invention, step S4 specifically comprises:

For each of the n shared value lists: extract C shared values each time, and concatenate them with the C+1th to A×Ath DCT coefficients in the corresponding DCT block of the corresponding carrier image in the n carrier images to form a complete shadow DCT list; repeat the above operation to obtain n complete shadow DCT lists;

For each of the n shadow DCT lists: obtain B×B shadow DCT blocks of size A×A by inverse zigzag arrangement, decompress the B×B shadow DCT blocks respectively, wherein the decompression process includes inverse DCT transformation and rounding process, thereby obtaining B×B shadow image spatial domain blocks; repeat the above operation to obtain a total of n×B×B shadow image spatial domain blocks;

Before executing the inverse zigzag arrangement, it is determined whether all DCT coefficients in the n+1 complete DCT coefficient lists have been value shifted in step S2. If so, all shared values and all DCT values in the n shadow DCT lists are inversely value shifted, and the shift amount of the inverse value shift is the absolute value of the minimum DCT coefficient.

According to the method of the first aspect of the present invention, in step S5:

The specified range is [-128, 127);

If the element value in each image spatial domain block of the n×B×B shadow image spatial domain blocks obtained based on the n sharing value lists is not within the specified range, a ₁ , a ₂ , ..., a _k-1 are adjusted and steps S3 to S5 are re-executed until the element value in each image spatial domain block is within the specified range.

In step S6:

For the B×B shadow DCT blocks corresponding to each of the sharing value lists that resist the JPEG recompression, the shadow DCT matrix is formed by splicing, and the shadow DCT matrix is entropy encoded to obtain a shadow image that resists the JPEG recompression; repeat the above operation to obtain a total of n shadow images that resist the JPEG recompression;

Selected values x ₁ , x ₂ , ..., x _n of n shared value lists are obtained. The sender sends the selected values x ₁ , x ₂ , ..., x _n together with the n shadow images to the receiver. The receiver restores the secret image based on the received l shadow images and the selected values x ₁ , x ₂ , ..., x _n , where k≤l≤n.

The second aspect of the present invention discloses a secret image sharing system for resisting JPEG recompression. The secret image to be shared is a JPEG image, the secret information contained in the JPEG image is a quantized DCT (Discrete Cosine Transform) coefficient, the JPEG recompression refers to the compression process performed on the JPEG image after the sharing process, and the system resists the compression process while sharing the JPEG image; the system comprises:

A first processing unit is configured to: extract the acquired n+1 images for preprocessing to extract a complete DCT coefficient list of each image in the n+1 images, wherein the n+1 images include one secret image to be shared and n carrier images;

The second processing unit is configured to: determine the DCT coefficient list to be shared of the secret image to be shared and the n DCT coefficient lists to be used corresponding to the n carrier images based on the n+1 complete DCT coefficient lists, and determine the prime number p according to the maximum DCT coefficient value in the DCT coefficient list to be shared and the n DCT coefficient lists to be used;

The third processing unit is configured to: use the DCT coefficient list to be shared, the n DCT coefficient lists to be used, the prime number p and the threshold value k to obtain, by calculation, n sharing value lists corresponding to the n DCT coefficient lists to be used and containing the secret information of the secret image to be shared;

The fourth processing unit is configured to: for each of the n sharing value lists, perform: forming B×B shadow DCT blocks according to each sharing value thereof, and decompressing the B×B shadow DCT blocks to obtain B×B shadow image spatial domain blocks;

A fifth processing unit is configured to: determine whether an element value in each image spatial domain block of a total of n×B×B shadow image spatial domain blocks obtained based on the n sharing value lists is within a specified range, and if so, use the B×B shadow image spatial domain blocks corresponding to each sharing value list as B×B shadow DCT blocks to resist the JPEG recompression;

The sixth processing unit is configured to: determine, for each of the B×B shadow DCT blocks corresponding to the sharing value list and resistant to the JPEG recompression, one shadow image resistant to the JPEG recompression, and obtain a total of n shadow images resistant to the JPEG recompression;

The sender shares the secret image while resisting the JPEG recompression by sending n shadow images resisting the JPEG recompression to the receiver;

Wherein, n, p, k, and B are all positive integers, k≤n, and the threshold value k represents the minimum number of shadow images required to restore the secret image.

According to the system of the second aspect of the present invention, the preprocessing specifically includes performing the following steps on each of the n+1 images:

Extracting a quantized DCT coefficient matrix of the current image by entropy decoding, the DCT coefficient matrix comprising M×M DCT coefficients, performing block processing on the DCT coefficient matrix into B×B DCT blocks, each of which comprises A×A DCT coefficients, wherein M=B×A;

For each DCT block containing A×A DCT coefficients, extract the first C DCT coefficients in a zigzag order to obtain a DCT coefficient list of each DCT block, thereby constructing a complete DCT coefficient list of the current image, the length of the DCT coefficient list of each DCT block is C, and the length of the complete DCT coefficient list of the current image is C×B×B;

Among them, M, A, and C are all positive integers.

According to the system of the second aspect of the present invention, the second processing unit is specifically configured as follows:

Determine whether the minimum DCT coefficient in the n+1 complete DCT coefficient lists is greater than 0;

If yes, one of the n+1 complete DCT coefficient lists of the secret image to be shared is used as the DCT coefficient list to be shared, and n of the n+1 complete DCT coefficient lists of the carrier image are used as the n DCT coefficient lists to be used;

If not, perform value shift on all DCT coefficients in the n+1 complete DCT coefficient lists, the shift amount of the value shift is the absolute value of the minimum DCT coefficient, and use the complete DCT coefficient list of the secret image to be shared after the value shift as the DCT coefficient list to be shared, and use the complete DCT coefficient lists of the n carrier images after the value shift as the n DCT coefficient lists to be used;

The maximum DCT coefficient value in the DCT coefficient list to be shared and the n DCT coefficient lists to be used is obtained, and the minimum prime number greater than the maximum DCT coefficient is taken as the prime number p.

According to the system of the second aspect of the present invention, the length of the DCT coefficient list to be shared, the length of each of the n DCT coefficient lists to be used, and the length of each of the n shared value lists are all C×B×B; the second processing unit is specifically configured as follows:

For each position in each of the n shared value lists, calculate its DCT shadow value using the formula f(x)=s+a ₁ x+a ₂ x ² +…+ak _-1 x ^k-1 (mod p);

Wherein, f(x) is the DCT shadow value at the current position in the current list in the n shared value lists, s is the DCT coefficient at the position in the DCT coefficient list to be shared corresponding to the current position in the current list, a ₁ , a ₂ , ..., a _k-1 are arbitrarily selected random numbers, x is a selected value, and (mod p) represents a modulo p operation;

Determine whether the high δ bits of f(x) are equal to the high δ bits of the DCT coefficient at the position corresponding to the current position in the current list in the n DCT coefficient lists to be used, wherein

If so, the DCT shadow value f(x) is used as the shared value at the current position in the current list of the n shared value lists at the current position;

If not, adjust _a1 , _a2 , ..., _ak-1 and recalculate f(x) until its high δ bits are equal to the high δ bits of the DCT coefficient at the position corresponding to the current position in the current list in the n DCT coefficient lists to be used, and obtain the sharing value at the current position.

According to the system of the second aspect of the present invention, for each position in the current list, when calculating its DCT shadow value, x remains unchanged, and the selected values x of the n shared value lists are different, and the value ranges of f(x), x, and _a1 , _a2 , ..., _ak-1 are integers on [0, p-1].

According to the system of the second aspect of the present invention, the fourth processing unit is specifically configured as follows:

For each of the n shared value lists: extract C shared values each time, and concatenate them with the C+1th to A×Ath DCT coefficients in the corresponding DCT block of the corresponding carrier image in the n carrier images to form a complete shadow DCT list; repeat the above operation to obtain n complete shadow DCT lists;

For each of the n shadow DCT lists: obtain B×B shadow DCT blocks of size A×A by inverse zigzag arrangement, decompress the B×B shadow DCT blocks respectively, wherein the decompression process includes inverse DCT transformation and rounding process, thereby obtaining B×B shadow image spatial domain blocks; repeat the above operation to obtain a total of n×B×B shadow image spatial domain blocks;

Before executing the inverse zigzag arrangement, it is determined whether all DCT coefficients in the n+1 complete DCT coefficient lists have been value shifted in step S2. If so, all shared values and all DCT values in the n shadow DCT lists are inversely value shifted, and the shift amount of the inverse value shift is the absolute value of the minimum DCT coefficient.

According to the system of the second aspect of the present invention, the specified range is [-128, 127); the fifth processing unit is specifically configured to: if the element value in each image spatial domain block of a total of n×B×B shadow image spatial domain blocks obtained based on n sharing value lists is not within the specified range, adjust a ₁ , a ₂ , ..., a _k-1 and re-execute steps S3-S5 until the element value in each image spatial domain block is within the specified range.

According to the system of the second aspect of the present invention, the sixth processing unit is specifically configured as follows:

For the B×B shadow DCT blocks corresponding to each of the sharing value lists that resist the JPEG recompression, the shadow DCT matrix is formed by splicing, and the shadow DCT matrix is entropy encoded to obtain a shadow image that resists the JPEG recompression; repeat the above operation to obtain a total of n shadow images that resist the JPEG recompression;

Obtaining selected values x ₁ , x ₂ , ..., x _n of n shared value lists, the sender sending the selected values x ₁ , x ₂ , ..., x _n together with the n shadow images to the receiver;

The receiver recovers the secret image based on the received l shadow images and the selected values x ₁ , x ₂ , . . . , x _n , where k≤l≤n.

The third aspect of the present invention discloses an electronic device. The electronic device includes a memory and a processor, the memory stores a computer program, and when the processor executes the computer program, the steps of any one of the secret image sharing methods for resisting JPEG recompression described in the first aspect of the present disclosure are implemented.

The fourth aspect of the present invention discloses a computer-readable storage medium having a computer program stored thereon, and when the computer program is executed by a processor, the steps of any one of the secret image sharing methods for resisting JPEG recompression described in the first aspect of the present disclosure are implemented.

In summary, the technical solution provided by the present invention applies secret image sharing technology to social networks to achieve covert transmission and storage of secret information, meet the needs of the state and society for convenient and secure communication, and have important value in ensuring information security. The solution proposed by the present invention implements a white-box robust solution for JPEG recompression, and realizes (k,n) threshold and understandable shadow images. The solution can be applied to the field of covert communication for social networks.

BRIEF DESCRIPTION OF THE DRAWINGS

In order to more clearly illustrate the specific implementation methods of the present invention or the technical solutions in the prior art, the drawings required for use in the specific implementation methods or the description of the prior art will be briefly introduced below. Obviously, the drawings in the following description are some implementation methods of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

FIG1 is a schematic flow chart of a secret image sharing method for resisting JPEG recompression according to an embodiment of the present invention;

FIG2 (a-k) is a schematic diagram of the results of (3,3) threshold, δ=4, num (i.e., C)=9, id=[11,13,19], and QF=75 according to an embodiment of the present invention;

FIG3 (a-h) is a schematic diagram of the results of (2,2) threshold, δ=3, num (i.e., C)=9, id=[11,13], and QF=75 according to an embodiment of the present invention;

FIG. 4 is a structural diagram of an electronic device according to an embodiment of the present invention.

DETAILED DESCRIPTION

In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution 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 of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

Secret Sharing: Secret Sharing (SS) technology encrypts secret information into multiple shadow images (shadow, shadow image or share) and distributes them to multiple participants. Only a subset of authorized participants can decrypt together, while unauthorized subsets cannot decrypt.

Secret Image Sharing: Secret Image Sharing (SIS) encrypts a secret image into multiple shadow images (shadow, shadow image or share) and distributes them to multiple parties. Only a subset of authorized parties can decrypt them together, while unauthorized subsets cannot decrypt them.

Shadow images are understandable: Shadow images are understandable, rather than meaningless images, which can reduce suspicion of encryption and increase the efficiency of shadow image management. The quantitative indicator of shadow image understandability is evaluated by visual quality (PSNR is used in this application).

Peak signal-to-noise ratio (PSNR): This application uses the PSNR indicator to evaluate the image quality of the shadow image and the restored secret image.

(k, n) threshold: Among n shadow images, k or more shadow images are required to recover the secret. When the threshold is k, it has a certain fault tolerance and can allow up to n-k shadows to be lost.

Mean filtering: It is the most commonly used method in image processing. From the frequency domain point of view, mean filtering is a low-pass filter. High-frequency signals will be removed, so it can help eliminate sharp noise in the image and achieve image smoothing, blurring and other functions. The ideal mean filter replaces each pixel in the image with the average value calculated from each pixel and its surrounding pixels. The sampling kernel data is usually a 3×3 matrix, but it can be of any shape.

JPEG image: JPEG (Joint Photographic Experts Group) is a standard for continuous-tone static image compression. The file extension is .jpg or .jpeg, and it is the most commonly used image file format.

The compression quality factor (QF) is obtained by calculation (the calculation method is shown in the following formula). Table 1 shows a quantization table for compression quality factor QF=75. The elements in the quantization table control the compression ratio, and a larger value produces a greater compression.

Where Q0(u, v) represents the quantization step size at the position (u, v) in the standard quantization table.

8 6 5 8 12 20 26 31 6 6 7 10 13 29 30 28 7 7 8 12 20 29 35 28 7 9 11 15 26 44 40 31 9 11 19 28 34 55 52 39 12 18 28 32 41 52 57 46 25 32 39 44 52 61 60 51 36 46 48 49 56 50 52 50

Table 1 Quantization table for QF=75

White-box robustness: In this application, white-box robustness refers to the known compression quality factor QF of the recompression channel or the use of the recompression channel at one's own will. The robustness to JPEG recompression under the condition of known compression quality factor QF of the recompression channel is a kind of white-box robustness.

The first aspect of the present invention discloses a secret image sharing method for resisting JPEG recompression. The secret image to be shared is a JPEG image, the secret information contained in the JPEG image is a quantized DCT (Discrete Cosine Transform) coefficient, the JPEG recompression refers to the compression process performed on the JPEG image after the sharing process, and the method resists the compression process while sharing the JPEG image.

Specifically, the present application has discovered a stable quantity that remains unchanged before and after recompression, that is, when QM1=QM2 (QM1 represents the quantization table matrix of the secret jpeg image, and QM2 represents the quantization table matrix used in recompression), and the recompression channel QF≤92, as long as: -128≤[IDCT(D)]＜127 is satisfied, the DCT coefficients before and after recompression will not change. The present application refers to this condition as a stable block condition, that is, if the spatial domain pixel value obtained after IDCT transformation of each 8×8 of the DCT coefficient matrix after entropy decoding of the original image (hereinafter referred to as the original DCT coefficient matrix) is in [-128,127), then this block is called a stable block. The present application provides a method for constructing a robust shadow image based on the stable block condition, so that the DCT number of the constructed shadow image does not change when passing through the recompression channel, that is, the constructed shadow image is robust to the recompression channel.

The method comprises:

Step S1, extracting and preprocessing the acquired n+1 images to extract a complete DCT coefficient list of each image in the n+1 images, wherein the n+1 images include one secret image to be shared and n carrier images;

Step S2, based on the n+1 complete DCT coefficient lists, determining the DCT coefficient list to be shared of the secret image to be shared and the n DCT coefficient lists to be used corresponding to the n carrier images, and determining the prime number p according to the maximum DCT coefficient value in the DCT coefficient list to be shared and the n DCT coefficient lists to be used;

Step S3, using the DCT coefficient list to be shared, the n DCT coefficient lists to be used, the prime number p and the threshold value k, obtaining by calculation n sharing value lists corresponding to the n DCT coefficient lists to be used and containing the secret information of the secret image to be shared;

Step S4, for each of the n sharing value lists, executing: forming B×B shadow DCT blocks according to each sharing value thereof, and decompressing the B×B shadow DCT blocks to obtain B×B shadow image spatial domain blocks;

Step S5, determining whether the element value in each image spatial domain block of a total of n×B×B shadow image spatial domain blocks obtained based on the n sharing value lists is within a specified range, and if so, using the B×B shadow image spatial domain blocks corresponding to each sharing value list as B×B shadow DCT blocks to resist the JPEG recompression;

Step S6: for each of the B×B shadow DCT blocks corresponding to the shared value list that resist the JPEG recompression, determine one shadow image that resists the JPEG recompression, and obtain a total of n shadow images that resist the JPEG recompression. The sender sends the n shadow images that resist the JPEG recompression to the receiver to share the secret image while resisting the JPEG recompression.

Wherein, n, p, k, and B are all positive integers, k≤n, and the threshold value k represents the minimum number of shadow images required to restore the secret image.

In some embodiments, in step S1, the preprocessing specifically includes performing the following steps on each of the n+1 images:

Extracting a quantized DCT coefficient matrix of the current image by entropy decoding, the DCT coefficient matrix comprising M×M DCT coefficients, performing block processing on the DCT coefficient matrix into B×B DCT blocks, each of which comprises A×A DCT coefficients, wherein M=B×A;

For each DCT block containing A×A DCT coefficients, extract the first C DCT coefficients in a zigzag order to obtain a DCT coefficient list of each DCT block, thereby constructing a complete DCT coefficient list of the current image, the length of the DCT coefficient list of each DCT block is C, and the length of the complete DCT coefficient list of the current image is C×B×B;

Among them, M, A, and C are all positive integers.

In some embodiments, step S2 specifically includes:

Determine whether the minimum DCT coefficient in the n+1 complete DCT coefficient lists is greater than 0;

If yes, one of the n+1 complete DCT coefficient lists of the secret image to be shared is used as the DCT coefficient list to be shared, and n of the n+1 complete DCT coefficient lists of the carrier image are used as the n DCT coefficient lists to be used;

If not, perform value shift on all DCT coefficients in the n+1 complete DCT coefficient lists, the shift amount of the value shift is the absolute value of the minimum DCT coefficient, and use the complete DCT coefficient list of the secret image to be shared after the value shift as the DCT coefficient list to be shared, and use the complete DCT coefficient lists of the n carrier images after the value shift as the n DCT coefficient lists to be used;

The maximum DCT coefficient value in the DCT coefficient list to be shared and the n DCT coefficient lists to be used is obtained, and the minimum prime number greater than the maximum DCT coefficient is taken as the prime number p.

In some embodiments, the length of the DCT coefficient list to be shared, the length of each of the n DCT coefficient lists to be used, and the length of each of the n shared value lists are all C×B×B; the step S3 specifically includes:

For each position in each of the n shared value lists, calculate its DCT shadow value using the formula f(x)=s+a ₁ x+a ₂ x ² +…+ak _-1 x ^k-1 (mod p);

Wherein, f(x) is the DCT shadow value at the current position in the current list in the n shared value lists, s is the DCT coefficient at the position in the DCT coefficient list to be shared corresponding to the current position in the current list, a ₁ , a ₂ , ..., a _k-1 are arbitrarily selected random numbers, x is a selected value, and (mod p) represents a modulo p operation;

Determine whether the high δ bits of f(x) are equal to the high δ bits of the DCT coefficient at the position corresponding to the current position in the current list in the n DCT coefficient lists to be used, wherein

If so, the DCT shadow value f(x) is used as the shared value at the current position in the current list of the n shared value lists at the current position;

If not, adjust _a1 , _a2 , ..., _ak-1 and recalculate f(x) until its high δ bits are equal to the high δ bits of the DCT coefficient at the position corresponding to the current position in the current list in the n DCT coefficient lists to be used, and obtain the sharing value at the current position.

In some embodiments, in step S3, for each position in the current list, when calculating its DCT shadow value, x remains unchanged, and the selected values x of the n shared value lists are different, and the value ranges of f(x), x, and _a1 , _a2 , ..., _ak-1 are integers on [0, p-1].

In some embodiments, step S4 specifically includes:

For each of the n shared value lists: extract C shared values each time, and concatenate them with the C+1th to A×Ath DCT coefficients in the corresponding DCT block of the corresponding carrier image in the n carrier images to form a complete shadow DCT list; repeat the above operation to obtain n complete shadow DCT lists;

For each of the n shadow DCT lists: obtain B×B shadow DCT blocks of size A×A by inverse zigzag arrangement, decompress the B×B shadow DCT blocks respectively, wherein the decompression process includes inverse DCT transformation and rounding process, thereby obtaining B×B shadow image spatial domain blocks; repeat the above operation to obtain a total of n×B×B shadow image spatial domain blocks;

Before executing the inverse zigzag arrangement, it is determined whether all DCT coefficients in the n+1 complete DCT coefficient lists have been value shifted in step S2. If so, all shared values and all DCT values in the n shadow DCT lists are inversely shifted, and the shift amount of the inverse value shift is the absolute value of the minimum DCT coefficient.

In some embodiments, in step S5:

The specified range is [-128, 127);

If the element value in each image spatial domain block of the n×B×B shadow image spatial domain blocks obtained based on the n sharing value lists is not within the specified range, a ₁ , a ₂ , ..., a _k-1 are adjusted and steps S3 to S5 are re-executed until the element value in each image spatial domain block is within the specified range.

In some embodiments, in step S6:

For the B×B shadow DCT blocks corresponding to each of the sharing value lists that resist the JPEG recompression, the shadow DCT matrix is formed by splicing, and the shadow DCT matrix is entropy encoded to obtain a shadow image that resists the JPEG recompression; repeat the above operation to obtain a total of n shadow images that resist the JPEG recompression;

Selected values x ₁ , x ₂ , ..., x _n of n shared value lists are obtained. The sender sends the selected values x ₁ , x ₂ , ..., x _n together with the n shadow images to the receiver. The receiver restores the secret image based on the received l shadow images and the selected values x ₁ , x ₂ , ..., x _n , where k≤l≤n.

The algorithm of the specific implementation is as follows (combined with Figure 1):

For the i-th original DCT coefficient matrix block S_DCTblock _i ,cover ₁ _DCTblock _i ,…,cover_DCTblock _i of the secret jpeg image S and n carrier jpeg images, first extract the first num bits of these blocks in zigzag order and input them into the polynomial-based shadow-comprehensible secret sharing algorithm to obtain n shadow DCT lists, which are concatenated with the last 64-num bits of the corresponding shadow image and inversely zigzag-ordered to obtain n shadow DCT blocks SC ₁ _DCTblock' _i ,SC ₂ _DCTblock' _i ,…,SC _n _DCTblock' _i .

Then, a decompression operation is performed on it, and the decompression operation specifically includes IDC transformation and rounding, and decompression is performed into the shadow image spatial domain blocks SC ₁ _Spatialblock _i , SC ₂ _Spatialblock _i , …, SC _n _Spatialblock _i .

The next crucial step is to determine whether all elements of the n spatial pixel blocks are within the range of [-128, 127). If they are within the range, it means that the shadow DCT block generated in this round is a stable block and is saved directly; if any element exceeds the range of [-128, 127), it means that the generated shadow DCT block is an unstable block, and it returns to the polynomial-based shadow understandable secret sharing algorithm, and continues to screen random numbers until a stable shadow DCT block is generated. It is worth noting that there may not be a set of random numbers that make all shadow DCT blocks stable (the specific analysis will be given below), so the maximum number of screening times MAX is set here.

In the recovery stage, the obtained shadow images greater than or equal to k are entropy decoded to obtain their quantized DCT coefficients; the quantized DCT coefficients are divided into 8×8 blocks; each block is then arranged in a zigzag pattern, and the first num bits of the zigzag arranged data are extracted as the object to be recovered; according to the minimum shift value determined during the sharing process, all DCT coefficients are shifted to the positive range, restored using the Lagrange interpolation method, and then inversely shifted, and then 64 bits are padded with 64-num zeros, followed by entropy encoding, and finally saved as a secret image.

Experimental verification process:

In order to verify the effectiveness of the robust secret image sharing scheme based on the robust shadow image construction under stable block conditions, this application implements a local simulation experiment on the sharing algorithm and recovery method proposed above. The experimental images of this application are from BOSSbase1.0. Four grayscale images of size 256×256 are randomly selected and converted into JPEG images with a quality factor of 75. The read() function of the JPEGIO package is used to simulate entropy decoding, and the write() function of the JPEGIO package is used to simulate entropy encoding.

Two sets of experiments are shown here. Figure 2 shows the experimental results of robust secret image sharing based on robust carrier image construction based on stable block conditions with (3,3) threshold, δ=4, num=9, id=[11,13,19], QF=75. Figure 2(a) shows the input grayscale secret JPEG image S, size 256×256, QF=75. Figure 2(bd) shows the input three grayscale carrier JPEG images cover1, cover2 and cover3 of size 256×256, QF=75. The robust carrier JPEG images stable_SC1, stable_SC2 and stable_SC3 obtained by applying the proposed algorithm are shown in Figure 2(eg), and their size is also 256×256. Figure 2(hj) shows the three grayscale carrier JPEG images recom_SC1, recom_SC2 and recom_SC3 of size 256×256 after compression channel with compression quality factor 75. Figure 2(k) is the recovered secret JPEG image S ^* . It can be seen from the recovered secret image that the recovery of several blocks is abnormal. This is because when the screening times reach the maximum condition, no stable carrier image is screened out. Experiments show that the (3,3) threshold scheme of the present application is feasible, and the quality of the generated shadow image and the image quality of the recovered secret image are both relatively high.

Figure 3 shows the experimental results of constructing robust secret image sharing based on robust carrier images with stable block conditions with (2,2) threshold, δ=3, num=9, id=[11,13], QF=75. Figure 3(a) shows the input grayscale secret JPEG image S, with a size of 256×256 and QF=75. Figure 3(bc) shows the input two grayscale carrier JPEG images cover1 and cover2 with a size of 256×256 and QF=75. The robust carrier JPEG images stable_SC1, stable_SC2 and stable_SC3 obtained by applying the algorithm proposed in this application are shown in Figure 3(de), and their size is also 256×256. Figure 3(fg) shows two recompressed grayscale carrier JPEG images recom_SC1 and recom_SC2 with a size of 256×256 after compression channel with compression quality factor of 75. Figure 3(h) shows the recovered secret JPEG image S ^* . Similar to the previous experiment, it can be seen from the recovered secret image that the recovery of several blocks is abnormal. This is because when the screening times reach the maximum condition, no stable carrier image is screened out. The experiment shows that the (2,2) threshold scheme of the present application is feasible, and the quality of the generated shadow image and the image quality of the recovered secret image are both relatively high.

The second aspect of the present invention discloses a secret image sharing system for resisting JPEG recompression. The secret image to be shared is a JPEG image, the secret information contained in the JPEG image is a quantized DCT (Discrete Cosine Transform) coefficient, the JPEG recompression refers to the compression process performed on the JPEG image after the sharing process, and the system resists the compression process while sharing the JPEG image; the system comprises:

A first processing unit is configured to: extract the acquired n+1 images for preprocessing to extract a complete DCT coefficient list of each image in the n+1 images, wherein the n+1 images include one secret image to be shared and n carrier images;

The second processing unit is configured to: determine the DCT coefficient list to be shared of the secret image to be shared and the n DCT coefficient lists to be used corresponding to the n carrier images based on the n+1 complete DCT coefficient lists, and determine the prime number p according to the maximum DCT coefficient value in the DCT coefficient list to be shared and the n DCT coefficient lists to be used;

The third processing unit is configured to: use the DCT coefficient list to be shared, the n DCT coefficient lists to be used, the prime number p and the threshold value k to obtain, by calculation, n sharing value lists corresponding to the n DCT coefficient lists to be used and containing the secret information of the secret image to be shared;

The fourth processing unit is configured to: for each of the n sharing value lists, perform: forming B×B shadow DCT blocks according to each sharing value thereof, and decompressing the B×B shadow DCT blocks to obtain B×B shadow image spatial domain blocks;

A fifth processing unit is configured to: determine whether an element value in each image spatial domain block of a total of n×B×B shadow image spatial domain blocks obtained based on the n sharing value lists is within a specified range, and if so, use the B×B shadow image spatial domain blocks corresponding to each sharing value list as B×B shadow DCT blocks to resist the JPEG recompression;

The sixth processing unit is configured to: determine, for each of the B×B shadow DCT blocks corresponding to the sharing value list and resistant to the JPEG recompression, one shadow image resistant to the JPEG recompression, and obtain a total of n shadow images resistant to the JPEG recompression;

The sender shares the secret image while resisting the JPEG recompression by sending n shadow images resisting the JPEG recompression to the receiver;

Wherein, n, p, k, and B are all positive integers, k≤n, and the threshold value k represents the minimum number of shadow images required to restore the secret image.

According to the system of the second aspect of the present invention, the preprocessing specifically includes performing the following steps on each of the n+1 images:

Extracting a quantized DCT coefficient matrix of the current image by entropy decoding, the DCT coefficient matrix comprising M×M DCT coefficients, performing block processing on the DCT coefficient matrix into B×B DCT blocks, each of which comprises A×A DCT coefficients, wherein M=B×A;

For each DCT block containing A×A DCT coefficients, extract the first C DCT coefficients in a zigzag order to obtain a DCT coefficient list of each DCT block, thereby constructing a complete DCT coefficient list of the current image, the length of the DCT coefficient list of each DCT block is C, and the length of the complete DCT coefficient list of the current image is C×B×B;

Among them, M, A, and C are all positive integers.

According to the system of the second aspect of the present invention, the second processing unit is specifically configured as follows:

Determine whether the minimum DCT coefficient in the n+1 complete DCT coefficient lists is greater than 0;

If yes, one of the n+1 complete DCT coefficient lists of the secret image to be shared is used as the DCT coefficient list to be shared, and n of the n+1 complete DCT coefficient lists of the carrier image are used as the n DCT coefficient lists to be used;

If not, perform value shift on all DCT coefficients in the n+1 complete DCT coefficient lists, the shift amount of the value shift is the absolute value of the minimum DCT coefficient, and use the complete DCT coefficient list of the secret image to be shared after the value shift as the DCT coefficient list to be shared, and use the complete DCT coefficient lists of the n carrier images after the value shift as the n DCT coefficient lists to be used;

The maximum DCT coefficient value in the DCT coefficient list to be shared and the n DCT coefficient lists to be used is obtained, and the minimum prime number greater than the maximum DCT coefficient is taken as the prime number p.

According to the system of the second aspect of the present invention, the length of the DCT coefficient list to be shared, the length of each of the n DCT coefficient lists to be used, and the length of each of the n shared value lists are all C×B×B; the second processing unit is specifically configured as follows:

For each position in each of the n shared value lists, calculate its DCT shadow value using the formula f(x)=s+a ₁ x+a ₂ x ² +…+ak _-1 x ^k-1 (mod p);

Wherein, f(x) is the DCT shadow value at the current position in the current list in the n shared value lists, s is the DCT coefficient at the position in the DCT coefficient list to be shared corresponding to the current position in the current list, a ₁ , a ₂ , ..., a _k-1 are arbitrarily selected random numbers, x is a selected value, and (mod p) represents a modulo p operation;

Determine whether the high δ bits of f(x) are equal to the high δ bits of the DCT coefficient at the position corresponding to the current position in the current list in the n DCT coefficient lists to be used, wherein

If so, the DCT shadow value f(x) is used as the shared value at the current position in the current list of the n shared value lists at the current position;

If not, adjust _a1 , _a2 , ..., _ak-1 and recalculate f(x) until its high δ bits are equal to the high δ bits of the DCT coefficient at the position corresponding to the current position in the current list in the n DCT coefficient lists to be used, and obtain the sharing value at the current position.

According to the system of the second aspect of the present invention, for each position in the current list, when calculating its DCT shadow value, x remains unchanged, and the selected values x of the n shared value lists are different, and the value ranges of f(x), x, and _a1 , _a2 , ..., _ak-1 are integers on [0, p-1].

According to the system of the second aspect of the present invention, the fourth processing unit is specifically configured as follows:

For each of the n shared value lists: extract C shared values each time, and concatenate them with the C+1th to A×Ath DCT coefficients in the corresponding DCT block of the corresponding carrier image in the n carrier images to form a complete shadow DCT list; repeat the above operation to obtain n complete shadow DCT lists;

For each of the n shadow DCT lists: obtain B×B shadow DCT blocks of size A×A by inverse zigzag arrangement, decompress the B×B shadow DCT blocks respectively, wherein the decompression process includes inverse DCT transformation and rounding process, thereby obtaining B×B shadow image spatial domain blocks; repeat the above operation to obtain a total of n×B×B shadow image spatial domain blocks;

Before executing the inverse zigzag arrangement, it is determined whether all DCT coefficients in the n+1 complete DCT coefficient lists have been value shifted in step S2. If so, all shared values and all DCT values in the n shadow DCT lists are inversely value shifted, and the shift amount of the inverse value shift is the absolute value of the minimum DCT coefficient.

According to the system of the second aspect of the present invention, the specified range is [-128, 127); the fifth processing unit is specifically configured to: if the element value in each image spatial domain block of a total of n×B×B shadow image spatial domain blocks obtained based on n sharing value lists is not within the specified range, adjust a ₁ , a ₂ , ..., a _k-1 and re-execute steps S3-S5 until the element value in each image spatial domain block is within the specified range.

According to the system of the second aspect of the present invention, the sixth processing unit is specifically configured as follows:

For the B×B shadow DCT blocks corresponding to each of the sharing value lists that resist the JPEG recompression, the shadow DCT matrix is formed by splicing, and the shadow DCT matrix is entropy encoded to obtain a shadow image that resists the JPEG recompression; repeat the above operation to obtain a total of n shadow images that resist the JPEG recompression;

Obtaining selected values x ₁ , x ₂ , ..., x _n of n shared value lists, the sender sending the selected values x ₁ , x ₂ , ..., x _n together with the n shadow images to the receiver;

The receiver recovers the secret image based on the received l shadow images and the selected values x ₁ , x ₂ , . . . , x _n , where k≤l≤n.

The third aspect of the present invention discloses an electronic device. The electronic device includes a memory and a processor, the memory stores a computer program, and when the processor executes the computer program, the steps of any one of the secret image sharing methods for resisting JPEG recompression described in the first aspect of the present disclosure are implemented.

FIG4 is a block diagram of an electronic device according to an embodiment of the present invention. As shown in FIG4 , the electronic device includes a processor, a memory, a communication interface, a display screen, and an input device connected via a system bus. Among them, the processor of the electronic device is used to provide computing and control capabilities. The memory of the electronic device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system and a computer program. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The communication interface of the electronic device is used to communicate with an external terminal in a wired or wireless manner, and the wireless manner can be implemented through WIFI, an operator network, near field communication (NFC) or other technologies. The display screen of the electronic device can be a liquid crystal display screen or an electronic ink display screen, and the input device of the electronic device can be a touch layer covered on the display screen, or a key, trackball or touchpad provided on the housing of the electronic device, or an external keyboard, touchpad or mouse, etc.

Those skilled in the art will understand that the structure shown in FIG. 4 is merely a structural diagram of the portion related to the technical solution of the present disclosure, and does not constitute a limitation on the electronic device to which the technical solution of the present application is applied. The specific electronic device may include more or fewer components than shown in the figure, or combine certain components, or have a different arrangement of components.

The fourth aspect of the present invention discloses a computer-readable storage medium having a computer program stored thereon, and when the computer program is executed by a processor, the steps of any one of the secret image sharing methods for resisting JPEG recompression described in the first aspect of the present disclosure are implemented.

In summary, the technical solution provided by the present invention applies secret image sharing technology to social networks to achieve covert transmission and storage of secret information, meet the needs of the state and society for convenient and secure communication, and have important value in ensuring information security. The solution proposed by the present invention implements a white-box robust solution for JPEG recompression, and realizes (k,n) threshold and understandable shadow images. The solution can be applied to the field of covert communication for social networks.

Please note that the technical features of the above embodiments can be combined arbitrarily. In order to make the description concise, all possible combinations of the technical features in the above embodiments are not 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. The above-mentioned embodiments only express several implementation methods of the present application, and their descriptions are relatively specific and detailed, but they cannot be understood as limiting the scope of the invention patent. It should be pointed out that for ordinary technicians in this field, without departing from the concept of the present application, several variations and improvements can be made, which all belong to the scope of protection of the present application. Therefore, the scope of protection of the patent in this application shall be based on the attached claims.

Claims (10)

1. A secret image sharing method for resisting JPEG heavy compression, it is characterized in that, the secret image to be shared is a JPEG image, and the secret information contained in the JPEG image is a quantized DCT (Discrete Cosine Transform, discrete cosine transform ) coefficient, the JPEG heavy compression refers to the compression processing performed after the JPEG image is shared and processed, and the method resists the compression processing while sharing the JPEG image; the method includes: Step S1, extracting the acquired n+1 images for preprocessing, so as to extract a complete list of DCT coefficients for each of the n+1 images, the n+1 images including one of the pending Shared secret image and n carrier images; Step S2, based on the n+1 complete DCT coefficient lists, determine the DCT coefficient lists to be shared of the secret image to be shared, and the n DCT coefficient lists to be used corresponding to the n carrier images, and according to the The maximum DCT coefficient value in the list of DCT coefficients to be shared and the n pieces of DCT coefficient lists to be used determines the prime number p; Step S3, using the list of DCT coefficients to be shared, the list of n DCT coefficients to be used, the prime number p and the threshold value k, obtain by calculation corresponding to the n lists of DCT coefficients to be used and including all A list of n sharing values describing the secret information of the secret image to be shared; Step S4, for each shared value list in the n shared value lists, execute: form B×B shadow DCT blocks according to their respective shared values, and decompress the B×B shadow DCT blocks to obtain B×B shadow image spatial blocks; Step S5. Determine whether the element values in each of the n×B×B shadow image spatial blocks obtained based on n shared value lists are all within the specified range, and if so, for each shared value The B×B shadow image spatial domain blocks corresponding to the list are used as B×B shadow DCT blocks against the JPEG re-compression; Step S6, for the B×B shadow DCT blocks against the JPEG re-compression corresponding to each shared value list, determine one shadow image against the JPEG re-compression, and obtain a total of resistance against the JPEG re-compression n shadow images, the sender sends n shadow images against the JPEG re-compression to the receiver to share the secret image while resisting the JPEG re-compression; Wherein, n, p, k, and B are all positive integers, k≤n, and the threshold k represents the minimum number of shadow images required to restore the secret image. 2. A secret image sharing method for resisting JPEG re-compression according to claim 1, characterized in that, in the step S1, the preprocessing specifically includes, among the n+1 images For each image of the execute: The quantized DCT coefficient matrix of the current image is extracted by entropy decoding, the DCT coefficient matrix includes M×M DCT coefficients, and the DCT coefficient matrix is divided into B×B DCT blocks, each of which The DCT block includes A×A DCT coefficients, where M=B×A; For each DCT block containing A×A DCT coefficients, extract the first C DCT coefficients in zigzag order to obtain a DCT coefficient list of each DCT block, thereby constructing a complete DCT coefficient list of the current image, The length of the DCT coefficient list of each DCT block is C, and the length of the complete DCT coefficient list of the current image is C×B×B; Wherein, M, A, and C are all positive integers. 3. A kind of secret image sharing method for resisting JPEG heavy compression according to claim 2, it is characterized in that, described step S2 specifically comprises: Judging whether the minimum DCT coefficient in the n+1 complete DCT coefficient list is greater than 0; If so, use one of the complete DCT coefficient lists of the secret image to be shared in the n+1 complete DCT coefficient lists as the to-be-shared DCT coefficient list, and use the n+1 complete DCT coefficient lists The complete DCT coefficient lists of the n pieces of the carrier image in the n pieces are used as the n pieces of DCT coefficient lists to be used; If not, then perform value translation on all the DCT coefficients in the n+1 complete DCT coefficient list, the translation amount of the value translation is the absolute value of the minimum DCT coefficient, and the 1 after the value translation The complete DCT coefficient lists of the secret images to be shared are used as the DCT coefficient lists to be shared, and the complete DCT coefficient lists of the n carrier images after the value translation are used as the n DCT coefficients to be used. list; Obtain the maximum DCT coefficient value in the DCT coefficient list to be shared and the n DCT coefficient lists to be used, and take the smallest prime number greater than the maximum DCT coefficient as the prime number p. 4. A kind of secret image sharing method for resisting JPEG heavy compression according to claim 3, it is characterized in that, the length of the DCT coefficient list to be shared, each of the n DCT coefficient lists to be used The length of the list and the length of each list in the n shared value lists are C×B×B; the step S3 specifically includes: For each position in each of the n shared value lists, use the formula f(x)=s+a ₁ x+a ₂ x ² +...+a _k-1 x ^k-1 (mod p ) to calculate its DCT shadow value; Wherein, f(x) is the DCT shadow value at the current position in the current list in the n shared value lists, and s is at the position corresponding to the current position in the current list in the DCT coefficient list to be shared The DCT coefficients of , a ₁ , a ₂ ,..., a _k-1 are randomly selected random numbers, x is a selected value, and (mod p) represents a modulo p operation; Judging whether the high δ bit of f(x) is equal to the high δ bit of the DCT coefficient at the position corresponding to the current position in the current list in the n DCT coefficient lists to be used, wherein

If so, then use the DCT shadow value f(x) as the shared value at the current position in the current list in the n shared value lists of the current position; If not, adjust a ₁ , a ₂ , ..., a _k-1 and recalculate f(x), until its high δ bit is the same as that in the n DCT coefficient lists to be used and in the current list The high δ bits of the DCT coefficients at the position corresponding to the current position are equal, and the shared value at the current position is obtained. 5. A kind of secret image sharing method for resisting JPEG heavy compression according to claim 4, it is characterized in that, in described step S3, for each position in the described current list, calculate its DCT shadow value , x remains unchanged, and the selected value x of the n shared value lists is different, and the value ranges of f(x), x, and a ₁ , a ₂ ,..., a _k-1 is an integer on [0,p-1]. 6. A kind of secret image sharing method for resisting JPEG heavy compression according to claim 5, is characterized in that, described step S4 specifically comprises: For each shared value list in the n shared value lists: every time C shared values are extracted, compare them with the C+1th to A×Ath DCT blocks of the corresponding carrier images in the n carrier images The DCT coefficients are spliced to form a complete shadow DCT list; repeat the above operations to obtain n complete shadow DCT lists; For each DCT list in the n shadow DCT lists: obtain B×B shadow DCT blocks with a size of A×A by reverse zigzag arrangement, and decompress the B×B shadow DCT blocks respectively , the decompression processing includes inverse DCT transform and rounding processing, thereby obtaining B×B shadow image spatial blocks; repeating the above operations to obtain a total of n×B×B shadow image spatial blocks; Wherein, before performing the inverse zigzag arrangement, it is judged in step S2 whether all DCT coefficients in the n+1 complete DCT coefficient lists have been shifted in value, and if so, the n shadow DCT lists All the shared values and all DCT values in are subjected to inverse value translation, and the translation amount of the inverse value translation is the absolute value of the minimum DCT coefficient. 7. A kind of secret image sharing method for resisting JPEG heavy compression according to claim 6, is characterized in that: In said step S5: The specified range is [-128,127); If the element values in each of the n×B×B shadow image spatial blocks obtained based on n shared value lists are not all within the specified range, then adjust a ₁ , a ₂ , ..., a _k-1 and re-execute steps S3-S5, until the element values in each image spatial domain block are within the specified range; In said step S6: For the B×B shadow DCT blocks against the JPEG recompression corresponding to each shared value list, a shadow DCT matrix is formed by splicing, and entropy coding is performed on the 1 shadow DCT matrix, so as to obtain Described 1 shadow image of JPEG heavy compression; Repeat above-mentioned operation, obtain altogether the n shadow images of resisting described JPEG heavy compression; Obtain n selected values x ₁ , x ₂ , ..., x _n of the shared value list, and the sender combines the selected values x ₁ , x ₂ , ..., x _n with the The n shadow images are sent to the receiver together, and the receiver recovers the secret based on the received l shadow images and the selected values x ₁ , x ₂ , ..., x _n image, where k≤l≤n. 8. A secret image sharing system for resisting JPEG heavy compression, characterized in that, the secret image to be shared is a JPEG image, and the secret information contained in the JPEG image is a quantized DCT (Discrete Cosine Transform, discrete cosine transform ) coefficient, the JPEG heavy compression refers to the compression processing performed after the JPEG image is shared and processed, and the system resists the compression processing while sharing the JPEG image; the system includes: The first processing unit is configured to: extract the acquired n+1 images for preprocessing, so as to extract a complete list of DCT coefficients for each of the n+1 images, the n+1 images Including 1 secret image to be shared and n carrier images; The second processing unit is configured to: based on the n+1 complete DCT coefficient lists, determine the DCT coefficient list to be shared of the secret image to be shared, and the n DCT coefficients to be used corresponding to the n carrier images List, and determine the prime number p according to the maximum DCT coefficient value in the DCT coefficient list to be shared and the n DCT coefficient lists to be used; The third processing unit is configured to: use the list of DCT coefficients to be shared, the list of n DCT coefficients to be used, the prime number p, and the threshold value k to acquire and obtain the n DCT coefficients to be used by calculation n shared value lists corresponding to the list and containing the secret information of the secret image to be shared; The fourth processing unit is configured to: for each shared value list in the n shared value lists, perform: form B×B shadow DCT blocks according to their respective shared values, and perform the following operations on the B×B shadow DCT blocks The DCT block is decompressed to obtain B×B shadow image spatial blocks; The fifth processing unit is configured to: determine whether the element values in each of the n×B×B shadow image spatial blocks obtained based on n shared value lists are all within the specified range, and if so, for The B×B shadow image space blocks corresponding to each shared value list are used as B×B shadow DCT blocks against the JPEG re-compression; The sixth processing unit is configured to: for the B×B shadow DCT blocks against the JPEG recompression corresponding to each shared value list, determine a shadow image against the JPEG recompression, and obtain a total of The n shadow images of the JPEG re-compression; Wherein, the sender realizes sharing the secret image by sending n shadow images against the JPEG recompression to the receiver while resisting the JPEG recompression; Wherein, n, p, k, and B are all positive integers, k≤n, and the threshold k represents the minimum number of shadow images required to recover the secret image. 9. An electronic device, characterized in that the electronic device comprises a memory and a processor, the memory stores a computer program, and when the processor executes the computer program, any one of claims 1-7 is realized The steps in the described secret image sharing method for resisting JPEG heavy compression. 10. A computer-readable storage medium, wherein a computer program is stored on the computer-readable storage medium, and when the computer program is executed by a processor, the method described in any one of claims 1-7 is realized. Steps in a method for secret image sharing against JPEG recompression.

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