CN117294799A - Ciphertext domain reversible hiding method based on image secret sharing and hierarchical embedding - Google Patents
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- H04N1/32149—Methods relating to embedding, encoding, decoding, detection or retrieval operations
- H04N1/32288—Multiple embedding, e.g. cocktail embedding, or redundant embedding, e.g. repeating the additional information at a plurality of locations in the image
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Abstract
The invention discloses a ciphertext domain reversible hiding method based on image secret sharing and hierarchical embedding, which comprises the following steps: the multi-level embedding method based on identity grading is divided into primary embedding and secondary embedding; based on the original image, performing first embedding in an image owner, and performing secret sharing by performing embedding through polynomial coefficient redundancy generated in the encryption process; combining secret sharing, performing secondary embedding on the image secret participants based on the secret share image, wherein the participants are divided into core users and common users according to identity levels; the core user performs secondary embedding by adopting a self-adaptive difference value reservation embedding method, and the common user performs secondary embedding by adopting a pixel bit replacement embedding method to complete information hiding; and combining information hiding, extracting embedded additional information, recovering the original image and completing authority management of users with different identity levels. The invention has the advantages of higher safety, higher reversibility, higher embedding rate and higher separability.
Description
Technical Field
The invention belongs to the technical field of reversible hiding of ciphertext domains, and particularly relates to a reversible hiding method of ciphertext domains based on image secret sharing and hierarchical embedding.
Background
Ciphertext domain reversible information hiding (RDH-ED, reversible Data Hiding in Encrypted Domain) refers to embedding additional information in an encrypted carrier. Depending on the source of redundancy, RDH-EDs can be categorized into three types, redundancy after encryption (VRAE, vacating Room After Encryption), redundancy before encryption (VRBE, vacating Room Before Encryption), and redundancy during encryption (VRIE, vacating Redundancy In Encryption). RDH-ED under VRAE framework embeds additional information by modifying ciphertext pixels. Since the correlation between ciphertext data is small, the ciphertext image information entropy has become maximized, and therefore the embedding rate is limited. The RDH-ED under the VRBE frame is used for preprocessing an original image mainly through pixel prediction, compression, encoding and other technologies, embedding is implemented by utilizing a redundant space generated by correlation among pixels, the embedding rate is usually large, but the preprocessing process is too complicated, and the application scene is limited. In order to solve the above problems, the VRIE framework has been developed, ke et al propose to apply LWE and R-LWE algorithms to RDH-ED for the first time, and by quantizing ciphertext space and exploiting redundancy in the encryption process, information hiding and cryptographic techniques can be organically fused, so that the security, reversibility and embedding rate of RDH-ED are improved, but the cryptographic algorithms applicable to VRIE are limited, and the design difficulty is high. With the popularization and application of cloud environments, designing an RDH-ED suitable for a distributed scene becomes a research hotspot. The threshold effect of Secret Sharing (SS) makes it have better disaster tolerance, and is suitable for distributed scenes. The cloud server, namely the secret owner, divides the secret into a plurality of secret shares, distributes the secret to n different users for distributed storage, and randomly distributes the secret to the n different usersCollecting k or more different shares can recover the secret, otherwise it cannot. Wu et al propose an RDH-ED algorithm based on secret sharing for the first time, and fully exert the disaster recovery effect. Ke has better separability based on RDH-ED proposed by China's remainder theorem and secret sharing. In order to solve the defect that the traditional secret sharing scheme does not have diffusion characteristic, two RDH-ED are proposed by Hua et al based on Cipher feedback secret sharing (CFSS, cipher-Feedback Secret Sharing), and higher embedding rate and security are realized by predictive coding of the pixel values of the ciphertext image. To improve the embedding rate, zhang et al propose a multiple embedding mechanism using polynomial secret sharing, performing polynomial embedding and homomorphic embedding. Qin et al propose Galois fields GF (p) and GF (2) based on secret sharing 8 ) The RDH-ED ensures consistency of correlation between pixels of the secret share image block and the original image block by adopting a differential protection secret sharing strategy, solves the problem of pixel overflow, however, a user needs to pre-select a threshold before embedding the secret, the application scene is limited, a large number of non-embeddable blocks exist, and the embedding capacity is low. However, in a real distributed environment, the identities of the participants usually have different grades, and corresponding rights are required to be given according to the identity grades, so as to ensure that each work operates safely and efficiently. For example, the secret owner needs to distribute the secret to a certain number of core users and common users, and agrees that the two-stage users embed additional information in different embedding manners, and in the secret reconstruction stage, the core users master more important information, and the different embedding manners are adopted here to ensure that the two-stage users play different roles in the secret reconstruction stage so as to realize corresponding rights management.
Disclosure of Invention
In order to solve the technical problems, the invention provides a ciphertext domain reversible hiding method based on image secret sharing and hierarchical embedding, which has the advantages of higher safety, stronger reversibility, higher embedding rate and stronger separability and is suitable for multiple embedding scenes in which multi-stage user identities participate.
In order to achieve the above object, the present invention provides a ciphertext domain reversible hiding method based on image secret sharing and hierarchical embedding, comprising:
the multi-level embedding method based on identity grading is divided into primary embedding and secondary embedding;
based on the original image, performing first embedding in an image owner, and performing secret sharing by performing embedding through polynomial coefficient redundancy generated in the encryption process;
combining secret sharing, performing secondary embedding on the image secret participants based on the secret share image, wherein the participants are divided into core users and common users according to identity levels;
the core user performs secondary embedding by adopting a self-adaptive difference value reservation embedding method, and the common user performs secondary embedding by adopting a pixel bit replacement embedding method to complete information hiding;
and combining information hiding, extracting embedded additional information, recovering the original image and completing authority management of users with different identity levels.
Optionally, the construction method of the image owner includes:
F(x)＝s+C 1 x+C 2 x 2 +…+C k-1 x k-1
where s is a secret, C 1 ,C 2 ,…,C k-1 For a random number, x is the corresponding participant, k is the selected threshold value, and F (x) is the secret share to which x corresponds.
Optionally, implementing embedding for secret sharing using polynomial coefficient redundancy generated in the encryption process includes:
converting each 8 bits of the secret which is embedded for the first time into decimal numbers, performing AES (advanced encryption standard) encryption on the secret which is embedded for the first time by using a key1 to generate a first key, and constructing a polynomial by using image block pixels and the key after block scrambling; and calculating and distributing secret shares according to the polynomial to complete secret sharing.
Optionally, in combination with secret sharing, secondary embedding is performed on the image secret participants, and the participants are divided into core users and common users according to identity levels, including:
the polynomials are as follows,
the core user calculates as follows,
handle x i ∈ID cor ＝{id 1 ,id 2 ,…,id n1 Substituted polynomial calculation n 1 The individual shares are distributed to corresponding users;
the average user calculates as follows,
handleSubstituting polynomial to calculate n 2 Individual shares, and distributed to users.
Optionally, the secondary embedding of the core user by adopting the adaptive difference value reservation embedding method includes:
after the core user carries out pixel modulation, providing a difference value between pixels of an original image block;
the maximum absolute value of the difference value between the z pixel and the 1 st pixel in the image block;
and dividing the maximum absolute value into a plurality of difference values, and coding to finish secondary embedding of the core user.
Optionally, the performing the secondary embedding by the common user by using the pixel bit replacement embedding method includes:
converting each 8 bits of the secret to be embedded into a decimal number, and performing AES (advanced encryption Standard) encryption by using an encryption key3 to generate a second key;
for each image block share, reserving a first pixel value, replacing other three pixel values with a second secret to be embedded, and sequentially executing the operation on all shares to finish the secondary embedding of the common user.
Optionally, extracting the additional information embedded by the image secret owner includes:
receiver arbitrary collection k 1 Individual core user shares, k 2 A common user share;
the core user firstly converts four pixels into binary, extracts corresponding difference values according to the difference value grades, extracts additional information, and obtains secret information through a decryption key 3;
the ordinary user directly extracts the last three pixels of each pixel block and decrypts the last three pixels by the decryption key3 to obtain secret information.
Optionally, the marked pixels of the original image block are restored by a lagrangian interpolation formula according to the marked pixels of the pixel block provided by the ordinary user, the first secret embedded in the polynomial coefficient is extracted, the first secret embedded is obtained after decryption by the decryption key1, and then all the pixels of the original image block are restored according to the pixel difference provided by the core user.
The invention has the technical effects that: the invention discloses a ciphertext domain reversible hiding method based on image secret sharing and hierarchical embedding, which aims at solving the problem that a ciphertext domain reversible information hiding algorithm cannot endow corresponding rights according to user identity levels in the current distributed environment. A multiple embedding scheme is then proposed based on the improved secret sharing and the identity level of the participants. The secret owner utilizes the polynomial coefficient redundancy generated in the secret sharing encryption process to embed the image copyright information, so that the embedding rate is improved, and meanwhile, the authenticability of the carrier image is ensured. The core participant adopts a self-adaptive difference value retaining embedding method, and the common participant adopts a pixel bit replacing embedding method. In the image reconstruction stage, a certain number of core users are needed to reconstruct images and extract image copyright information among participants reaching the threshold condition, so that rights management of different identity levels is realized. The invention has higher safety, stronger reversibility, larger embedding rate and stronger separability, and is suitable for multiple embedding scenes in which the multi-stage user identity participates.
Drawings
The accompanying drawings, which are included to provide a further understanding of the application, illustrate and explain the application and are not to be construed as limiting the application. In the drawings:
FIG. 1 is a flow chart of a ciphertext domain reversible hiding method based on image secret sharing and hierarchical embedding according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of a core user embedding scheme according to an embodiment of the present invention;
FIG. 3 is a numerical example schematic view of an embodiment of the present invention;
fig. 4 is a schematic diagram of experimental test pictures according to an embodiment of the present invention, wherein the pictures (a) to (h) are Lena, jetplane, pappers, goldhill, baboon, boats, man, airplane respectively;
fig. 5 shows a Baboon histogram of each stage of the present invention, where fig. s (a) - (D) are the original image, the ciphertext image, the secret image, and the reconstructed image of Lena, (e) - (h) are corresponding plane histograms, (i) - (l) are corresponding pixel distribution scatter histograms, and (m) - (p) are corresponding 3D histograms;
FIG. 6 is a graph showing the contrast of the embedding rates of different images under different thresholds according to the embodiment of the present invention, wherein the graphs (a) - (f) are respectively the contrast of the embedding rates of different schemes when the thresholds are (2, 2), (3, 3), (4, 4), (2, 3), (3, 4) and (4, 5);
FIG. 7 shows the embedding rate of 1000 images (3, 4) selected randomly in BOWS_2 according to the embodiment of the invention;
FIG. 8 is an error diagram of embodiments S1, S2 and S3 of the present invention, wherein diagrams (a) - (c) are respectively the extracted S after secret embedding of Airplane under threshold (3, 4) 1 ,S 2 And S is 3 Bit-by-bit comparison with the original data is performed.
Detailed Description
It should be noted that, in the case of no conflict, the embodiments and features in the embodiments may be combined with each other. The present application will be described in detail below with reference to the accompanying drawings in conjunction with embodiments.
It should be noted that the steps illustrated in the flowcharts of the figures may be performed in a computer system such as a set of computer executable instructions, and that although a logical order is illustrated in the flowcharts, in some cases the steps illustrated or described may be performed in an order other than that illustrated herein.
As shown in fig. 1, the embodiment provides a ciphertext domain reversible hiding method based on image secret sharing and hierarchical embedding, which comprises the following steps:
the multi-level embedding method based on identity grading is divided into primary embedding and secondary embedding;
based on the original image, performing first embedding in an image owner, and performing secret sharing by performing embedding through polynomial coefficient redundancy generated in the encryption process;
combining secret sharing, performing secondary embedding on the image secret participants based on the secret share image, wherein the participants are divided into core users and common users according to identity levels;
the core user adopts a self-adaptive difference value reserved embedding method to carry out secondary embedding, and the common user adopts a pixel bit replacement embedding method to carry out secondary embedding so as to complete information hiding;
and combining information hiding, extracting embedded additional information, recovering an original image and completing rights management of users with different identity levels.
Improved image secret sharing based on pixel difference preservation
The (k, n) secret sharing scheme based on Lagrange interpolation polynomials, proposed by Shamir, wherein a secret owner divides a secret into n parts by constructing a unitary polynomial, and a receiving party collects any more than or equal to k parts to reconstruct the polynomial to recover the secret.
Theorem 1 optionally k (x i ,f(x i ) The k-1 th order polynomial can be uniquely determined by Lagrange interpolation formula as shown in formula (1):
wherein the secret owner constructs a formula as shown in formula (2):
F(x)＝s+C 1 x+C 2 x 2 +…+C k-1 x k-1 (2)
where s is a secret, C 1 ,C 2 ,…,C k-1 As a random number, the sender calculates the secret share f i ＝F(i),i＝1,2,…,n, and f i Distribution to n different users P i . From theorem 1, k fi are arbitrarily collected, F (x) can be reconstructed, and since each coefficient of F (x) can be reconstructed, a secret can be embedded on the coefficient. If the image is used as a secret, the pixel is used as a polynomial coefficient, and the secret sharing can be performed on the image.
In order to keep the difference between the pixels of the image block share after encryption consistent with the difference between the pixels of the image block before encryption, qin et al propose in the scheme an image secret sharing scheme based on pixel difference preservation, the encryption process of which is as follows:
assume that the image block has a size of 2×2 and a pixel value of p z (z=2, 3, 4), the threshold is (k, n). G below 1 (x) 1 st pixel, g, of the share image block z (x) Is the z-th pixel of the share image block. The secret owner constructs 4 k-1 degree polynomials over GF (251) as shown in equation (3):
h in 1 ,h 2 ,…,h k-1 Are random numbers. From formula (3), as shown in formula (4):
where r is 1 ,r z Is a non-negative integer, and thus can be expressed as formula (5):
Δ＝g 1 (x)-g z (x)＝(g 1 (x)+251r 1 )mod251-(g z (x)+251r z )mod251 (5)
where Δ is the 1 st pixel g of the share image block 1 (x) And the z-th pixel g z (x) Difference between them. Because of the high similarity between pixels of the same image block, in most cases: g I 1 (x)-g z (x)|<128, at this time r 1 ＝r z ,Δ＝g 1 (x)-g z (x)＝g 1 (x)+251r 1 -g z (x)+251r z But when |g 1 (x)-g z (x) When the I is more than or equal to 128, r 1 -r z = ±1. When r is 1 -r z When=1, p 1 -p z ＝g 1 (x)+251r 1 -g z (x)+251r z =Δ+251; when r is 1 -r z When= -1, p 1 -p z ＝g 1 (x)+251r 1 -g z (x)+251r z =Δ -251, and thus the formula shown in formula (6) can be obtained:
in p 1 ，p z Original image pixels, g 1 (x)，g z (x) For the original share, p is chosen prime 251. Therefore, whether the difference value between the pixels of the secret share and the original pixel is equal or not can be determined according to whether the absolute value of the difference value between the z pixel value and the 1 st pixel value in the secret share exceeds 128, if the difference value between the z pixel value and the 1 st pixel value is smaller than 128, the difference value between the pixels is not changed. In order to keep the correlation between the pixels of the encrypted image completely consistent with the correlation between the original pixels, the secret sharing in the scheme is improved through pixel modulation, and the pixel modulation mode is shown as a formula (7):
g in z (x) G 'as the original share' z (x) For the share after pixel modulation, the potential safety hazard that is easy to attack exists in data management in the cloud environment, and in the information transmission process, a user not only requires the confidentiality of information content, but also ensures that the information transmission behavior is not revealed, so that secret information is hidden in a carrier for transmission. Meanwhile, partial image owners also need to effectively protect the confidentiality and the integrity of the carrier image, and corresponding copyright, identity mark and other authentication information needs to be added into the carrier image, so the image owners need to encryptIs embedded with corresponding information in the polynomial coefficients. As shown in figure 1, when in secret embedding, a core user must reserve the difference between pixels in order to ensure the correct recovery of an original image, and meanwhile, in order to improve the embedding capacity, an adaptive difference coding embedding method is adopted to improve the number of embeddable blocks as much as possible; the ordinary user can directly replace the non-tag bit pixel value in the secret share with the encrypted secret information. In the stage of secret extraction and image reconstruction, k share marked pixels provided by a participant can restore marked pixels of an image block before encryption while secret information is extracted, and then the pixel value before encryption is restored according to the pixel difference value provided by a core user.
Image preprocessing
To improve the security of the algorithm, a 512×512 gray image is first divided into image blocks of size 2×2, and then the image is double reset scrambled. The inter-block scrambling is performed by using a scrambling key Scrkey1 to scramble the positions of the image blocks, and then the intra-block pixel scrambling is performed by using a scrambling key Scrkey2 to scramble the positions of the pixels in the image blocks.
Generating session keys
According to n 1 Identity number { i } of individual core user 1 |i 1 ＝1,2,…,n 1 }、n 2 Common user identity number { i } 2 |i 2 ＝n 1 +1,n 1 +2,…,n 1 +n 2 Sum seed key h i Generating n using a pseudo-random number generator 1 Number of markAnd n 2 Personal sign->As a session key and distributed to users, wherein id i ≠id j 。
Secret sharing encryption
The invention uses the image secret sharing scheme based on pixel difference value reservation, and embeds the copyright authentication information of the carrier in the encryption process. Assume that the image block pixels after block scrambling are a=a, b, c, dFirst embedded secret S 1 ＝{0,1} N 。
a. Construction polynomial
Will S 1 Every 8 bits are converted into decimal numbers, and the key encryption key1 is used for S 1 AES encryption is performed to generate E (S) 1 )＝{b 1 ,b 2 ,…,b k-1 Using A and E (S) 1 ) A polynomial (8) is constructed, this process being performed over GF (251).
b. Calculating and distributing secret shares
n 1 The core users: handle x i ∈ID cor ＝{id 1 ,id 2 ,…,id n1 Substituted formula (8) to calculate n 1 Individual shares and distributed to corresponding users. Such as: user id 1 The resulting fraction is f 1 (id 1 )、f 2 (id 1 )、f 3 (id 1 )、f 4 (id 1 )。
n 2 Individual average users: handleSubstituting formula (8) to calculate n 2 Individual shares, and distributed to users.
This operation is performed on all image blocks in turn, as this process is performed over GF (251), a direct substitution of 250 for original pixel values greater than 250, and embedding the original pixel values and corresponding positions as side information in polynomial coefficients for transmission to the receiver.
Information hiding
a. Difference preserving embedding
After the core user carries out pixel modulation, the difference value between the pixels of the original image block can be accurately provided. Core user embedding rules are shown in FIG. 2 and Table 1, |d max The i refers to the absolute maximum value of the difference between the z (z=2, 3, 4) th pixel and the 1 st pixel in the image block, and the inter-pixel i d is the result of the pixel transformation performed by the core user max Not exceeding I128 th, d max The I is divided into 7 difference levels and encoded, and is expressed by 3 bits, dc max Is |d max And (3) encoding corresponding to the I. Due to the difference d max The positive and negative values are represented by 1 bit, wherein 1 represents the positive value of the difference value, and 0 represents the negative value of the difference value. As can be seen from Table 1, if |d| max ∈[32，127]The block is a non-embeddable block when |d| | max ∈[64，127]When the absolute value of the difference is stored, 21 bits and 3 signs are needed, 3 bits are overflowed, and the overflowed part is embedded into the embeddable block as a load, so that the difference between pixels is restored in a lossless manner.
TABLE 1
b. Pixel bit replacement embedding
n 2 Individual average users: will be embedded secret S 2 ＝{0,1} N Is converted into decimal numbers every 8 bits, and AES-encryption is performed with encryption key encrypy-tion key3 to generate E (S 2 ). For each image block share, the first pixel value is reserved, the other three pixel values are used with E (S 2 ) And (5) replacing. Such as: user' sThe resulting fraction is->User reservation->By E (S) 2 ) Secret substitution-> The operation is sequentially carried out on all the shares, and the information embedding can be completed by the common user.
Secret extraction and image recovery
Receiver arbitrary collection k 1 Personal core user sharesSum of the amounts and k 2 A common user share, where k 1 +k 2 ≥k,k 1 ≥1。
For the core user, firstly converting four pixels into binary, extracting corresponding difference values according to the difference value grades, extracting additional information, obtaining secret information through decrypting the key3, and for the share image block with the difference value grade of 110, extracting overflowed last 3 bits from the embeddable block.
For an ordinary user, the last three pixels of each pixel block are directly extracted, and secret information is obtained through decryption by a decryption key 3.
According to k 1 +k 2 The marked pixels of the pixel block provided by the individual user can be restored to the marked pixels of the original image block by the lagrangian interpolation formula, and the secret E embedded in the polynomial coefficient is extracted (S 1 ) S can be obtained after decryption by the decryption key1 1 And then, according to the pixel difference value provided by the core user, all pixels of the original image block can be restored. This is performed on all image blocks, i.e. the original image is restored and the embedded secret is extracted.
Numerical examples
As shown in fig. 3, assuming that the pixel value of the received image block with secret is {65,198,66,63}, the receiver first changes {65,198,66,63} to {65,70,66,63}, and the difference between the z (z=2, 3, 4) th pixel and the 1 st pixel of the original image block is: +5, +1, -2, because its absolute value is 5, the corresponding level is encoded as 010, and the corresponding difference is expressed as: 1101. 1001, 0010, the extra data that can be embedded at this time is 9 bits, the pixels that carry the dense image block are {65,91,37,85}. After the receiver receives 65,91,37,85, it first converts it to binary and then calculates the difference from the difference level, while extracting the secret and obtaining the marked pixel and the difference size.
Experimental results and analysis
Experiments were performed on Windows 10 operating system, programmed with Matlab R2021b, and the experimental setup was configured as Intel (R) Core (TM) i7-11800H 2.30GHz,32GB. The test data selected in the experiment are BOWS_2 data sets containing 10000 gray images, 3000 pieces of the BOWS_2 data sets are randomly selected from the BOWS_2 data sets to form 3 sub data sets BOWS_2_1, BOWS_2_2 and BOWS_2_3, the sub data sets respectively contain 1000 images, part of the test data are shown in FIG. 4, and FIGS. 4 (a) - (f) are Lena, jetplane, pappers, goldhill, baboon, boats, man, airplane respectively.
Security analysis
The algorithm security is analyzed from the aspects of key space, visual quality, histogram distribution, related parameter analysis, attack resistance and the like, and the selected threshold is (3, 4), k 1 The encrypted image referred to in the present invention is the 1 st secret share, and the secret-carried image is the image with the 1 st secret share embedded with additional information again.
Key space
The key space refers to the total number of keys which can be used in the algorithm, and when the key space is large enough, attacks such as brute force cracking can be effectively resisted. The size of the selected image is 512 multiplied by 512, the size of each image block is 2 multiplied by 2, and 65536 image blocks are all arranged. According to the image double-reset scrambling rule, inter-block scrambling is performed first, and since 65536 blocks are shared, inter-block scrambling shares 65536 ≡! In this case. Further intra-block pixel scrambling, since there are 4 pixels per image block, there are 4 ≡ per image block! In this case. Therefore, the image is double reset, sharing 65536-! X 4-! 65536 The case where the total scrambling key space size is 65536-! X 4-! 65536 Its value is far greater than 2 100 Is sufficient to resist brute force attacks.
Histogram distribution
The histogram can intuitively show the pixel value distribution of the image. If the histograms are uniformly distributed, the higher the algorithm security is, the statistical analysis attack can be effectively resisted. Fig. 5 (a) - (D) are original, ciphertext, secret, and reconstructed images of Lena, (e) - (h) are corresponding planar histograms, (i) - (l) are corresponding pixel distribution scatter histograms, and (m) - (p) are corresponding 3D histograms. As can be seen from fig. 5, the histogram distribution of the ciphertext image and the ciphertext-carrying image is uniform and gentle, and the histogram distribution of the original image and the reconstructed image is completely consistent. It can be seen that an attacker cannot obtain relevant information from the pixel distribution rule, and the encryption algorithm and the embedding algorithm have higher security.
Correlation parameter analysis
a. Information entropy
Information entropy is defined as an uncertainty measure of a discrete random variable, and is an index for measuring complexity and information richness of an image. The more uniform the pixel values, the greater the information entropy value; conversely, if the pixel values are more random, the information entropy is smaller. The calculation method of the information entropy is shown in the formula (9).
H(X)＝-ΣP(x)log 2 P(x) (9)
Where H (X) represents the entropy of the random variable X and P (X) represents the probability of occurrence of the event X. The image entropy may take a maximum value of 8 when each pixel in the image has an equal probability. The table 2 shows the entropy of different stages of information of different images, and the entropy values of the ciphertext share and the secret share of the test image are close to 8, and compared with the prior art, the entropy value of the ciphertext image is closer to 8, so that the algorithm can effectively resist entropy analysis attack.
TABLE 2
PSNR and SSIM
Peak signal-to-noise ratio (PSRN) and Structural Similarity (SSIM) can be used to evaluate differences in images before and after encryption. The larger the PSNR value is, the smaller the image distortion degree is, when PSNR is more than 35dB, the human eyes cannot perceive obvious distortion, and when PSNR is less than 10dB, the larger the difference between the images before and after encryption is shown. The closer the SSIM is to 1, the higher the similarity between the images, and when the SSIM value is 1, the images are identical. The experiment carried out tests on 8 images, and the results are shown in table 3, wherein the PSNR and SSIM mean values of the ciphertext image and the original image are respectively close to 4.7988 and 0.0154, and the PSNR and SSIM mean values of the secret image and the original image are respectively close to 7.5858 and 0.0243. The smaller PSNR and SSIM indicate that the ciphertext image and the secret-carrying image have larger difference from the original image, and indicate that the encryption algorithm and the embedding algorithm have higher security.
TABLE 3 Table 3
Embedding rate
The embedding rate refers to the number of additional information bits that are embedded in a unit pixel on average, and in this embodiment, the embedding capacity is defined by a polynomial embedding capacity (EC 1 ) Core user embedded capacity (EC 2 ) And the common user embedded capacity (EC 3 ) Co-composition, EC 1 And EC (EC) 3 Irrespective of the texture of the carrier image, only the size of the carrier image and the parameter selection of the embedding algorithm are related, and after secret sharing, the pixel quantity of the ciphertext is expanded to 512 multiplied by n. The embedding rate is thus expressed as shown in formula (10):
experiment 8 images as shown in FIG. 4 were first tested at different thresholds, when k 1 When k=n, the embedding rate is large, but the disaster recovery characteristic of secret sharing cannot be exhibited at this time, as shown in table 4. The algorithm of the invention also has better embedding performance for the common thresholds (3, 4) and (4, 5). To illustrate the superiority of the algorithm, the algorithm is compared with the current advanced similar algorithm, the comparison result is shown in fig. 6, and the comparison results in fig. 6 (a) - (f) are respectively the embedding rate comparison of different schemes when the thresholds are (2, 2), (3, 3), (4, 4), (2, 3), (3, 4) and (4, 5), and the average value of the embedding rate of the algorithm is the largest under 6 different thresholds. The comparison schemes are RDH-ED based on secret sharing, and Wu et al propose two schemes, and the comparison is performed by using a large embedding rate. The embedding rate of the scheme of Chen et al is 7/n, which decreases with increasing n. CFSS RDH-ED and MSS RDH-ED proposed by Hua et al, by embedding ciphertext image pixel value predictive coding, due to the small correlation between encrypted ciphertext image pixels, result in the limitation of the embedding rate of CFSS scheme and MSS scheme, qin et alThe adoption of a differential protection secret sharing strategy ensures consistency of correlation between pixels of the secret share image block and the original image block, but a threshold value is required to be preselected before the secret is embedded, so that a large number of non-embeddable blocks exist, and the embedding capacity is low.
TABLE 4 Table 4
In order to further verify the performance advantage of the algorithm provided by the invention, the experiment randomly selects 1000 images from BOWS_2 and performs embedding performance test on the threshold (3, 4), and as shown in the result of FIG. 7, the embedding rate of the algorithm in different test images is slightly different, but the embedding performance of the algorithm in the invention generally fluctuates up and down around 4.3bpp, which proves that the embedding performance of the algorithm in the invention is relatively stable.
Reversibility of
Correlation parameter analysis
Reversibility refers to whether the original image can be completely restored and additional information can be extracted in a lossless manner after the carrier image is encrypted and the additional information is embedded, and is an important index for measuring the performance of an RDH-ED algorithm. PSRN, SSIM and mean variance MSE and can be used to evaluate the degree of reversible recovery of RDH-ED reconstructed images. The 3 sub-data sets were tested in the experiment, and the results are shown in table 5, in the 3 data sets, the MSE of the reconstructed image and the original image are all 0, the psnr is ++ -infinity, and the SSIM is all 1, which indicates that the reconstructed image and the original image have no difference. The algorithm of the invention adopts Lagrange interpolation to reconstruct the image, and polynomial coefficients of the Lagrange interpolation can be restored in a lossless manner, so that the marked pixels can be restored in a lossless manner, and the core user can accurately provide the difference value between the pixels of the image blocks, so that the original image can be restored in a lossless manner, and the scheme is proved to have complete reversibility.
TABLE 5
Extracting secret error map
The error map refers to a bit-by-bit comparison of the processed data with the original data, equal to 0, and vice versa, equal to 1. FIGS. 8 (a) - (c) show the extraction of S after secret embedding of Airplane under threshold (3, 4) 1 ,S 2 And S is 3 As can be seen from fig. 8, the error map values between the extracted secret information and the original secret data are all 0, which indicates that the scheme can realize reversible extraction of the secret.
Data expansion
The data expansion refers to that the size of the ciphertext image is larger than that of the original image, the data expansion rate refers to the ratio between the size of the ciphertext image and that of the original image, and the calculation method is shown in the formula (11).
The invention encrypts the carrier image into n shares using secret sharing, with 1 share per participant, and for a single embedder, the relative data expansion rates are all 1, but the overall expansion rate of the scheme depends on the threshold size. When the value of n is not very large, the overall expansion ratio of the present invention is acceptable. Table 6 shows the expansion ratio comparison results of different schemes, only 1 encrypted image is generated, the relative expansion ratio is equal to the total expansion ratio, but the homomorphic encryption is adopted to generate larger data expansion, and the multi-secret sharing and lightweight encryption method is adopted, wherein the data expansion ratio is 1. The prior art and the scheme of the invention both use secret sharing to generate secret shares, and the relative expansion rate is 1 although the total expansion rate depends on the threshold size n. With secret sharing encryption, the data expansion can be extended within an acceptable range by controlling the value of the threshold.
TABLE 6
The invention provides a multiple embedding scheme based on image secret sharing and multi-level user identity, and in order to improve the safety of an algorithm, the original image is subjected to double replacement to destroy the strong correlation among pixels. And then, the image copyright information is embedded by utilizing polynomial coefficient redundancy generated in the secret sharing encryption process, so that the embedding rate is improved and the integrity of the carrier image is ensured. The invention provides a multi-level embedding algorithm based on identity grading, which divides participants into core users and common users, wherein the core users adopt a self-adaptive difference value retaining embedding method, the common users adopt a pixel replacing embedding method, and in an image reconstruction stage, a certain number of core users are required to reconstruct images and extract image copyright information in the participants reaching threshold conditions, so that rights management on different identity grades is realized. Experimental results show that the algorithm has high embedding rate, high safety and reversibility, and strong separability, secret extraction and image recovery are independent processes, and the algorithm is suitable for multiple embedding scenes with multi-stage user identity participation.
The foregoing is merely a preferred embodiment of the present application, but the scope of the present application is not limited thereto, and any changes or substitutions easily conceivable by those skilled in the art within the technical scope of the present application should be covered in the scope of the present application. Therefore, the protection scope of the present application shall be subject to the protection scope of the claims.
Claims (8)
1. The ciphertext domain reversible hiding method based on image secret sharing and hierarchical embedding is characterized by comprising the following steps of:
the multi-level embedding method based on identity grading is divided into primary embedding and secondary embedding;
based on the original image, performing first embedding in an image owner, and performing secret sharing by performing embedding through polynomial coefficient redundancy generated in the encryption process;
combining secret sharing, performing secondary embedding on the image secret participants based on the secret share image, wherein the participants are divided into core users and common users according to identity levels;
the core user performs secondary embedding by adopting a self-adaptive difference value reservation embedding method, and the common user performs secondary embedding by adopting a pixel bit replacement embedding method to complete information hiding;
and combining information hiding, extracting embedded additional information, recovering the original image and completing authority management of users with different identity levels.
2. The ciphertext domain reversible hiding method based on image secret sharing and hierarchical embedding of claim 1, wherein the image owner constructing method comprises:
F(x)＝s+C 1 x+C 2 x 2 +…+C k-1 x k-1
where s is a secret, C 1 ,C 2 ,…,C k-1 For a random number, x is the corresponding participant, k is the selected threshold value, and F (x) is the secret share to which x corresponds.
3. A ciphertext domain reversible hiding method based on image secret sharing and hierarchical embedding as claimed in claim 1, wherein implementing embedding with polynomial coefficient redundancy generated in encryption process comprises:
converting each 8 bits of the secret which is embedded for the first time into decimal numbers, performing AES (advanced encryption standard) encryption on the secret which is embedded for the first time by using a key1 to generate a first key, and constructing a polynomial by using image block pixels and the key after block scrambling; and calculating and distributing secret shares according to the polynomial to complete secret sharing.
4. The ciphertext domain reversible hiding method based on image secret sharing and hierarchical embedding as claimed in claim 1, wherein secondary embedding is performed at image secret participants in combination with secret sharing, the participants being divided into core users and ordinary users according to identity levels, comprising:
the polynomials are as follows,
the core user calculates as follows,
handle x i ∈ID cor ＝{id 1 ,id 2 ,…,id n1 Substituted polynomial calculation n 1 The individual shares are distributed to corresponding users;
the average user calculates as follows,
handleSubstituting polynomial to calculate n 2 Individual shares, and distributed to users.
5. The ciphertext domain reversible hiding method based on image secret sharing and hierarchical embedding of claim 1, wherein the core user performing secondary embedding by adopting an adaptive difference reservation embedding method comprises:
after the core user carries out pixel modulation, providing a difference value between pixels of an original image block;
the maximum absolute value of the difference value between the z pixel and the 1 st pixel in the image block;
and dividing the maximum absolute value into a plurality of difference values, and coding to finish secondary embedding of the core user.
6. The ciphertext domain reversible hiding method based on image secret sharing and hierarchical embedding of claim 1, wherein said secondary embedding by the ordinary user using a pixel bit substitution embedding method comprises:
converting each 8 bits of the secret to be embedded into a decimal number, and performing AES (advanced encryption Standard) encryption by using an encryption key3 to generate a second key;
for each image block share, reserving a first pixel value, replacing other three pixel values with a second secret to be embedded, and sequentially executing the operation on all shares to finish the secondary embedding of the common user.
7. A ciphertext domain reversible hiding method based on image secret sharing and hierarchical embedding as claimed in claim 1, wherein extracting the additional information embedded by the image secret owner comprises:
receiver arbitrary collection k 1 Individual core user shares, k 2 A common user share;
the core user firstly converts four pixels into binary, extracts corresponding difference values according to the difference value grades, extracts additional information, and obtains secret information through a decryption key 3;
the ordinary user directly extracts the last three pixels of each pixel block and decrypts the last three pixels by the decryption key3 to obtain secret information.
8. The ciphertext domain reversible hiding method based on image secret sharing and hierarchical embedding of claim 1, wherein the marked pixels of the original image block are restored by a lagrangian interpolation formula according to the marked pixels of the pixel block provided by the common user, the first secret embedded in the polynomial coefficient is extracted, the first embedded secret is obtained after decryption by a decryption key1, and then all pixels of the original image block are restored according to the pixel difference provided by the core user.
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| CN118488147A (en) * | 2024-07-09 | 2024-08-13 | 合肥国家实验室 | Robust secret reconstruction and information hiding method based on robust Chinese remainder theorem |
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| CN118114774B (en) * | 2024-04-30 | 2024-07-02 | 哈尔滨工业大学(深圳)(哈尔滨工业大学深圳科技创新研究院) | Large model inference method, large model inference device, electronic device, storage medium, and program product |
| CN118488147A (en) * | 2024-07-09 | 2024-08-13 | 合肥国家实验室 | Robust secret reconstruction and information hiding method based on robust Chinese remainder theorem |
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