Reversible information hiding method in ciphertext domain based on secret sharing and secure multi-party computation

Abstract

The invention relates to the technical field of information hiding, and in particular to a ciphertext domain reversible information hiding method based on secret sharing and secure multi-party computing, image encryption: using an image block scrambling method based on high-speed scrambling, using CRT-based secret sharing and adding random numbers during encryption to solve the residual problem of image sharing; multi-party secure embedding: using a secure multi-party embedding protocol to calculate pixel prediction errors and embed information; image decryption: the receiver simultaneously holds a key of CRT secret sharing and a key of image block scrambling to decrypt a secret image; information extraction: after obtaining the secret image, extracting information according to an extraction rule of a prediction error histogram shift and auxiliary information embedded in the image; through the method, the invention uses secret sharing to reduce the computational complexity of image encryption, and uses secure multi-party computing to protect image privacy while completing multi-party information embedding, and obtains a higher embedding capacity and carrier visual quality.

Description

Technical Field

[0001] The present invention relates to the technical field of information hiding, and in particular to a ciphertext domain reversible information hiding method based on secret sharing and secure multi-party computing. Background Art

[0002] With the rapid development of digital technology, a large amount of digital media information needs to be transmitted quickly in the network, and the secret information that needs to be transmitted may be stolen or tampered with. In order to realize functions such as covert communication and copyright identification in practical applications, information hiding technology is widely used.

[0003] Traditional information hiding technology embeds secret information into a carrier (such as an image) to obtain a secret carrier. The embedded information will not affect the observer's understanding of the carrier information itself, and the receiver can extract the secret information from the secret carrier. Later, after improvements, reversible information hiding technology was proposed: this type of method allows the receiver to not only extract information from the secret carrier, but also restore the image carrier losslessly. However, when the secret carrier is transmitted in the network, there is still a risk of privacy theft. In order to protect the privacy of the carrier image, cipher domain reversible information hiding was proposed: the image owner first encrypts the image carrier, then the information hider embeds the secret information in the encrypted image, and sends the secret encrypted image to the receiver. Finally, the receiver can extract the secret information, decrypt and restore the original image carrier.

[0004] However, the existing reversible information in the ciphertext domain still has some shortcomings. For example, the computational complexity of the encryption algorithm is high, and the amount of information embedded and the visual quality of the carrier need to be improved. More importantly, in application scenarios involving multiple parties (such as multi-party copyright), it is necessary to complete multi-party information embedding while protecting the rights and interests of all parties. This requires the introduction of multiple information embedders and the use of secure computing protocols to complete secure multi-party embedding. This requirement is also difficult to meet in traditional reversible information hiding in the ciphertext domain. Summary of the invention

[0005] The purpose of the present invention is to provide a reversible information hiding method in a ciphertext domain based on secret sharing and secure multi-party computing to solve the problems raised in the above background technology.

[0006] The technical solution of the present invention is: a ciphertext domain reversible information hiding method based on secret sharing and secure multi-party computing, comprising the following specific steps:

[0007] S1. Image encryption: Use the image block scrambling method based on high-speed scrambling, use CRT-based secret sharing and add random numbers during encryption to solve the residual problem of image sharing;

[0008] S2. Multi-party secure embedding: Use the secure multi-party embedding protocol to calculate the pixel prediction error and perform information embedding;

[0009] S3. Image decryption: The receiver holds both the key of the CRT secret sharing and the key of the image block scrambling, and decrypts the encrypted image;

[0010] S4. Information extraction: After obtaining the encrypted image, according to the extraction rule of the prediction error histogram translation and the auxiliary information embedded in the image, extract the information.

[0011] Preferably, in the above S1, the specific steps of image encryption are as follows:

[0012] S11. Block scrambling encryption: First, divide the image into non-overlapping 2×2 blocks, and then use the image block scrambling method to shuffle the order of each divided image block, thus achieving the first step of image encryption;

[0013] S12. Encrypt the image using CRT secret sharing: Set the threshold of secret sharing as (k,n), and select a set of integers {128 < p1 < p2 < … < p n ≤ 256 < p}, and these integers also need to meet the following conditions:

[0014] gcd(p i , p j ) = 1, i ≠ j;

[0015] gcd(p i , p) = 1, i = 1, 2, …, n.

[0016] Where For a pixel x(h,w) in the image, h ∈ [1, Μ], w ∈ [1, N] (assuming the size of the carrier image is Μ×N), select a random number Calculate y(h,w) = x(h,w) + A × p and perform CRT sharing:

[0017] y(h,w) ≡ s1(h,w) (mod p1)

[0018] y(h,w) ≡ s2(h,w) (mod p2)

[0019] …

[0020] y(h,w) ≡ s n (h,w) (mod p n )

[0021] Where s i (h,w), i = 1, 2, …, n are the pixel values in the encrypted image shares obtained after secret sharing.

[0022] Preferably, in S12, the (k, n) threshold requirement in secret sharing is: the secret cannot be reconstructed with less than k shares, and the secret can be reconstructed with any k shares.

[0023] Preferably, in S2, the algorithm of the secure multi-party embedding protocol is as follows:

[0024] Input: Encrypted Shares ij (h,w),s ij (h,w+1),s ij (h+1,w),s ij (h+1,w+1),j=1,2,…,k; secret sharing parameter p ij ,p;

[0025] Output: prediction error e m ;

[0026] S21. Individual information hiders Perform the following calculations:

[0027] e ij (h,w)

[0028] =5s ij (h,w)-2s ij (h,w+1)-2s ij (h+1,w)-s ij (h1,w+1);

[0029] S22, E ij (h,w) sent to

[0030] S23, By CRT calculation, solve for e A (h,w):

[0031]

[0032] S24, Calculate the raw prediction error value:

[0033]

[0034]

[0035] S25, Output the prediction error e m .

[0036] Preferably, in S2, the information embedding operation is as follows:

[0037] Assume that the resulting prediction error set is E = (e1, e2, ..., e MN / 4 ), based on this set, calculate the threshold T l , T r :

[0038] The information is embedded based on the prediction error, and the method used is the prediction error histogram translation:

[0039]

[0040] where g∈{0,1} is the secret bit to be embedded, is the resulting secret encrypted shared pixel value.

[0041] Preferably, the information hider embeds the auxiliary information required for information extraction into the encrypted share, and the embedding method can use a traditional reversible information hiding method.

[0042] Preferably, in S3, the specific steps of image decryption are as follows:

[0043] S31, after the receiver collects k encrypted shares, it uses CRT calculation to reconstruct the encrypted pixels;

[0044] S32. After the CRT reconstruction is completed, the secret image is obtained by using inverse scrambling.

[0045] Preferably, in S31, according to the CRT theorem, the following equation can be solved:

[0046]

[0047] Then calculate And according to the public parameter p, the final dense pixel value can be obtained;

[0048]

[0049] Preferably, in S4, when extracting information after the receiver has obtained the encrypted pixel by decryption, the prediction error value in each block is first calculated.

[0050] e b (h,w)

[0051] =x b' (h,w)-0.4x b' (h,w+1)-0.4x b' (h+1,w)-0.2x b' (h+1,w+1)

[0052] , and then obtain the threshold required for extraction based on the auxiliary information contained in the image.

[0053] The method is:

[0054]

[0055] Where g is the secret bit extracted from the block.

[0056] Preferably, in S4, after extracting the secret information, the receiver performs a reverse shift on the histogram according to the rule of prediction error histogram shift to restore the original pixel information;

[0057]

[0058] Finally, the receiver recovers the lossless original image carrier.

[0059] The present invention provides a ciphertext domain reversible information hiding method based on secret sharing and secure multi-party computing through improvement, which has the following improvements and advantages compared with the prior art:

[0060] First: In terms of embedding capacity, the present invention proposes a secure multi-party embedding protocol, which allows information hiders to flexibly calculate prediction error information, so that multi-layer and multi-round prediction error histogram shift in the image ciphertext domain can be realized, thereby achieving a higher embedding capacity.

[0061] Secondly: in terms of the visual quality of the encrypted image, the prediction error histogram shift used in the ciphertext domain of the present invention can be basically consistent with the prediction error histogram shift method in the plaintext domain, and compared with the related methods in the plaintext domain, the present invention can also achieve functions such as image privacy protection and multi-party security embedding; compared with the existing reversible information hiding in the ciphertext domain, the visual quality of the encrypted image of the present invention is higher.

[0062] Thirdly, in terms of security, the present invention uses CRT secret sharing and block scrambling for dual encryption, which not only ensures the privacy of pixel values, but also disrupts the correlation between pixels and protects the high-frequency information of the image. The security of the encrypted image can be proved when NPCR is used as an evaluation index for testing;

[0063] Fourthly, in terms of encryption complexity, the computational complexity of CRT secret sharing is lower than that of polynomial-based secret sharing, and the computational complexity of block scrambling is also lower than that of homomorphic encryption and other methods. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] The present invention will be further explained below in conjunction with the accompanying drawings and embodiments:

[0065] Figure 1 It is a scheme framework diagram of the present invention;

[0066] Figure 2Specific example diagram of multi-party embedding of the present invention;

[0067] Figure 3 Encryption result diagram of the present invention. Specific implementation manner

[0068] The present invention will be described in detail below. The technical solutions in the embodiments of the present invention are clearly and completely described. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0069] The present invention provides an improved reversible information hiding method in the ciphertext domain based on secret sharing and secure multi-party computation. The technical solution of the present invention is as follows:

[0070] As Figure 1 shown, the reversible information hiding method in the ciphertext domain based on secret sharing and secure multi-party computation includes the following specific steps:

[0071] S1. Image encryption: Use the image block scrambling method based on High-speed scrambling, use the secret sharing based on CRT and add random numbers during encryption to solve the residual problem of image sharing;

[0072] Among them, the specific steps of image encryption are as follows:

[0073] S11. Block scrambling encryption: First, divide the image into non-overlapping 2×2 blocks, and then use the image block scrambling method to scramble the order of each divided image block to achieve the first step of image encryption;

[0074] S12. Encrypt the image using CRT secret sharing: Set the threshold of secret sharing as (k, n), and select a set of integers {128 < p1 < p2 < … < p n ≤ 256 < p}, and these integers also need to meet the following conditions:

[0075] gcd(p i , p j ) = 1, i ≠ j;

[0076] gcd(p i , p) = 1, i = 1, 2, …, n.

[0077] Among them For a pixel x(h, w) in the image, h ∈ [1, Μ], w ∈ [1, N] (assuming the size of the carrier image is Μ × N), select a random number Calculate y(h,w)=x(h,w)+A×p and perform CRT sharing:

[0078] y(h,w)≡s1(h,w)(mod p1)

[0079] y(h,w)≡s2(h,w)(mod p2)

[0080] …

[0081] y(h,w)≡s n (h,w)(mod p n )

[0082] where s i (h,w),i=1,2,…,n are the pixel values ​​in the encrypted image sharing obtained after secret sharing; the encrypted image sharing obtained not only meets the (k,n) threshold requirement in secret sharing (less than k shares cannot reconstruct the secret, but any k shares can reconstruct the secret), but also uses block scrambling to further protect the privacy information of the correlation between pixels. Using CRT secret sharing and block scrambling as encryption methods, its computational complexity is also lower than many existing encryption methods in cipher domain reversible information hiding (such as homomorphic encryption);

[0083] S2, multi-party secure embedding: Calculate pixel prediction errors and embed information using a secure multi-party embedding protocol;

[0084] Among them, when the information hider After receiving the encrypted image sharing, any information hider cannot steal the private information of the original image. This is because the nature of secret sharing determines that less than k shares cannot reconstruct any secret. In order for the information hider to complete the task of information embedding, a multi-party secure computing protocol must be designed. Through this protocol, the information hider only obtains the necessary data required for embedding (prediction error information) without exposing the privacy of the carrier image. The present invention designs a secure multi-party embedding protocol (SME) for pixel prediction error calculation. The algorithm of the protocol is described as follows:

[0085] Input: Encrypted Shares ij (h,w),s ij (h,w+1),s ij (h+1,w),s ij (h+1,w+1),j=1,2,…,k; secret sharing parameter p ij ,p;

[0086] Output: prediction error e m ;

[0087] S21. Individual information hiders Perform the following calculations:

[0088] e ij (h,w)

[0089] =5s ij (h,w)-2s ij (h,w+1)-2s ij (h+1,w)-s ij (h1,w+1);

[0090] S22, E ij (h,w) sent to

[0091] S23, By CRT calculation, solve for e A (h,w):

[0092]

[0093] S24, Calculate the raw prediction error value:

[0094]

[0095] S25, Output the prediction error e m ;

[0096] The information embedding operation is as follows:

[0097] Assume that the resulting prediction error set is E = (e1, e2, ..., e MN / 4 ), based on this set, calculate the threshold T l , T r :

[0098] The information is embedded based on the prediction error, and the method used is the prediction error histogram translation:

[0099]

[0100] where g∈{0,1} is the secret bit to be embedded, is the obtained secret encrypted shared pixel value; in addition to the secret information, the information hider will also embed the auxiliary information required for information extraction into the encrypted share. The embedding method can use traditional reversible information hiding methods such as difference expansion;

[0101] In the attached Figure 2In the figure, a specific example of multi-party embedding is shown. The secret sharing threshold is (3, 4). There are three information hiders who calculate the prediction error values ​​in their respective image blocks. According to the prediction error values ​​in the three ciphertext domains, the original prediction error can be reconstructed according to the CRT calculation (as shown in Figure e m =-1). Then, according to the corresponding threshold and secret bit, all information hiders will perform pixel modification operations on their own encrypted image shares. It should be noted that after the secret information is hidden, the embedder also needs to embed necessary auxiliary information (such as pixel overflow information, the number of embedding layers and rounds of prediction error histogram shift, threshold T l ,T r , the embedding amount of the last round of histogram shift). After the embedding is completed, the secret encrypted sharing can be obtained;

[0102] S3, Image decryption: The receiver holds both the CRT secret sharing key and the image block scrambling key, and decrypts the secret image;

[0103] The specific steps are as follows:

[0104] S31. After the receiver collects k encrypted shares, it uses CRT calculation to reconstruct the secret pixels. According to the CRT theorem, the following equation can be solved:

[0105]

[0106] Then calculate And according to the public parameter p, the final dense pixel value can be obtained;

[0107]

[0108] S32, after the CRT reconstruction is completed, the correlation between the obtained secret pixels is still disrupted by the block scrambling. In order to obtain the secret image, inverse scrambling is required; the specific operation of inverse scrambling depends on the scrambling method (such as high-speed scrambling) used in the encryption step and the key set therefor; the receiver can decrypt the image according to the corresponding key and the inverse scrambling rule, and finally obtain the secret image;

[0109] S4, information extraction: After obtaining the encrypted image, the information is extracted according to the extraction rule of the prediction error histogram shift and the auxiliary information embedded in the image.

[0110] It should be noted that the receiver can also extract information before inverse scrambling, because information extraction is performed in units of image blocks, and block scrambling does not disrupt the difference information within the pixel block. Assuming that the receiver has obtained the encrypted pixels through decryption, when extracting information, the prediction error value within each block is first calculated.

[0111] e b (h,w)=x b' (h,w)-0.4x b' (h,w+1)-0.4x b' (h+1,w)-0.2x b' (h+1,w+1)

[0112] , and then obtain the threshold required for extraction based on the auxiliary information contained in the image. The extraction method is:

[0113]

[0114] Where g is the secret bit extracted from the block;

[0115] After extracting the secret information, the receiver performs a reverse shift on the histogram according to the rule of prediction error histogram shift to restore the original pixel information;

[0116]

[0117] Finally, the receiver recovers the lossless original image carrier.

[0118] The present invention uses secret sharing to reduce the computational complexity of image encryption through this method, and uses secure multi-party computing to protect image privacy while completing multi-party information embedding, and obtains higher embedding capacity and carrier visual quality.

[0119] The above description enables those skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but will conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A reversible information hiding method in ciphertext domain based on secret sharing and secure multi-party computation, characterized by: The specific steps include: S1. Image encryption: Use the image block scrambling method based on high-speed scrambling, use CRT-based secret sharing and add random numbers during encryption to solve the residual problem of image sharing. The specific steps of image encryption are as follows: S11, block scrambling encryption: first divide the image into 2×2 non-overlapping blocks, and then use the image block scrambling method to scramble the order of the divided image blocks, so as to achieve the first step of image encryption; S12. Encrypt the image using CRT secret sharing: Set the threshold of secret sharing as (k, n), and select a set of integers {128 < p1 < p2 < … < p n ≤ 256 < p}, and these integers also need to satisfy the following conditions: gcd(p i ,p j )=1,i≠j; gcd(p i ,p)=1,i=1,2,…,n; in For a pixel x(h,w) in the image, h∈[1,Μ],w∈[1,N] (assuming the carrier image size is Μ×N), select a random number Calculate y(h,w)=x(h,w)+A×p and perform CRT sharing: y(h,w)≡s1(h,w)(mod p1) y(h,w)≡s2(h,w)(mod p2) … y(h,w)≡s n (h,w)(mod p n ) where s i (h,w),i=1,2,…,n is the pixel value in the encrypted image shared after secret sharing; S2. Multi-party secure embedding: Pixel prediction error using secure multi-party embedding protocol Calculate and embed information, and the algorithm of the secure multi-party embedding protocol is as follows: Input: Encrypted Shares ij (h,w),s ij (h,w+1),s ij (h+1,w), s ij (h+1,w+1),j=1,2,…,k; secret sharing parameter p ij ,p; Output: prediction error e m ; S21. Individual information hiders Perform the following calculations: have been ij (h,w) =5s ij (h,w)-2s ij (h,w+1)-2s ij (h+1,w)-s ij (h1,w+1); S22, E ij (h,w) sent to S23, By CRT calculation, solve for e A (h,w): S24, Calculate the raw prediction error value: e(h,w)≡e' A (h,w)(mod p) S25, Output the prediction error e m ; S3, Image decryption: The receiver holds both the CRT secret sharing key and the image The block scrambled key is used to decrypt the encrypted image. The specific steps of image decryption are as follows: S31, after the receiver collects k encrypted shares, it uses CRT calculation to reconstruct the encrypted pixels; S32, after the CRT reconstruction is completed, the secret image is obtained by using the inverse scrambling; S4, information extraction: After obtaining the encrypted image, extract the information according to the extraction rules of the prediction error histogram shift and the auxiliary information embedded in the image. When the receiver has obtained the encrypted pixels through decryption, the prediction error value in each block is first calculated. have been b (h,w) =x b' (h,w)-0.4x b' (h,w+1)-0.4x b' (h+1,w)-0.2x b' (h+1,w+1), Then, according to the auxiliary information contained in the image, the threshold required for extraction is obtained. The extraction method is: Where g is the secret bit extracted from the block.

2. The method for reversible information hiding in ciphertext domain based on secret sharing and secure multi-party computation according to claim 1 is characterized in that: In S12, the secret sharing The (k,n) threshold requirement is: less than k shares cannot reconstruct the secret, and any k shares can reconstruct the secret.

3. The method for reversible information hiding in ciphertext domain based on secret sharing and secure multi-party computation according to claim 2 is characterized in that: In S2, the information embedding operation is as follows: Assume that the resulting prediction error set is E = (e1, e2, ..., e MN / 4 ), based on this set, calculate the threshold T l , T r : where h E (e) is the number of prediction error values ​​equal to e in the set E; then the information hider embeds information based on the prediction error, using the method of prediction error histogram shift: where g∈{0,1} is the secret bit to be embedded, is the resulting secret encrypted shared pixel value.

4. The method for reversible information hiding in ciphertext domain based on secret sharing and secure multi-party computation according to claim 3 is characterized in that: The information hider embeds the auxiliary information required for information extraction into the encrypted share, and the embedding method can use a traditional reversible information hiding method.

5. The method for reversible information hiding in ciphertext domain based on secret sharing and secure multi-party computation according to claim 4 is characterized in that: In S31, according to the CRT theorem, the following equation can be solved: … Then calculate And according to the public parameter p, the final dense pixel value can be obtained; 6. The method for reversible information hiding in ciphertext domain based on secret sharing and secure multi-party computation according to claim 5 is characterized in that: In S4, after extracting the secret information, the receiver performs a reverse shift on the histogram according to the rule of prediction error histogram shift to restore the original pixel information; Finally, the receiver recovers the lossless original image carrier.

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