CN115664653A - Ciphertext domain reversible information hiding method based on secret sharing and secure multi-party computation - Google Patents

Ciphertext domain reversible information hiding method based on secret sharing and secure multi-party computation Download PDF

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CN115664653A
CN115664653A CN202211287807.9A CN202211287807A CN115664653A CN 115664653 A CN115664653 A CN 115664653A CN 202211287807 A CN202211287807 A CN 202211287807A CN 115664653 A CN115664653 A CN 115664653A
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image
information
secret
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熊礼治
韩啸
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Nanjing University of Information Science and Technology
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Nanjing University of Information Science and Technology
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Abstract

The invention relates to the technical field of information hiding, in particular to a ciphertext domain reversible information hiding method based on secret sharing and safe multiparty computation, which comprises the following steps of: an image block scrambling method based on High-speed scrambling is used, secret sharing based on a CRT is used, random numbers are added during encryption, and the problem of residual errors of image sharing is solved; multi-party secure embedding: carrying out pixel prediction error calculation by utilizing a safe multi-party embedding protocol and carrying out information embedding; image decryption: the receiver simultaneously holds a secret key shared by the CRT and a secret key scrambled by the image block, and decrypts the secret image; information extraction: after a dense image is obtained, extracting information according to an extraction rule of prediction error histogram translation and auxiliary information embedded in the image; according to the method, the complexity of image encryption calculation is reduced by secret sharing, and the image privacy is protected while multi-party information embedding is completed by utilizing safe multi-party calculation, and higher embedding capacity and carrier visual quality are obtained.

Description

Ciphertext domain reversible information hiding method based on secret sharing and secure multi-party computation
Technical Field
The invention relates to the technical field of information hiding, in particular to a ciphertext domain reversible information hiding method based on secret sharing and safe multi-party computation.
Background
With the rapid development of the digitization technology, a large amount of digital media information needs to be rapidly transmitted in the network, and the secret information needing to be transmitted may be stolen or tampered. In order to implement functions such as covert communication and copyright identification in practical applications, information hiding techniques are widely used.
In the conventional information hiding technology, secret information is embedded into a carrier (such as an image) to obtain a secret carrier, the embedded information does not influence an observer to understand the carrier information, and a receiver can extract the secret information from the secret carrier. Later on, reversible information hiding techniques were proposed: such a method allows the recipient not only to extract information from the secret carrier but also to recover the image carrier without loss. However, there is still a risk of privacy being stolen when a secret-containing bearer is transmitted in the network. In order to protect the privacy of the carrier image, reversible information hiding in a ciphertext domain is proposed: the image owner first encrypts the image carrier, then the information-concealer embeds the secret information in the encrypted image and sends the encrypted image to the receiver. Finally, the receiver can extract the secret information, decrypt and restore the original image carrier.
However, the existing ciphertext domain invertible information still has some defects. For example, the computational complexity of the encryption algorithm is high, and the information embedding amount and the carrier visual quality are to be improved. More importantly, in an application scenario in which multiple parties participate (such as multi-party copyright), multi-party information embedding needs to be completed, and rights and interests of the parties are protected. This requires the introduction of multiple information embedders, while using secure computing protocols to accomplish secure multi-party embedding. This requirement is also difficult to satisfy in the traditional ciphertext domain reversible information hiding.
Disclosure of Invention
The invention aims to provide a ciphertext domain reversible information hiding method based on secret sharing and secure multi-party computation, so as to solve the problems in the background technology.
The technical scheme of the invention is as follows: the ciphertext domain reversible information hiding method based on secret sharing and secure multi-party calculation comprises the following specific steps of:
s1, image encryption: an image block scrambling method based on High-speed scrambling is used, secret sharing based on CRT is used, random numbers are added during encryption, and the problem of residual errors of image sharing is solved;
s2, multi-party secure embedding: carrying out pixel prediction error calculation by utilizing a safe multi-party embedding protocol and carrying out information embedding;
s3, image decryption: the receiver simultaneously holds a secret key shared by the CRT and a secret key scrambled by the image block, and decrypts the secret image;
s4, information extraction: and after a dense image is obtained, extracting information according to the extraction rule of the prediction error histogram translation and the auxiliary information embedded in the image.
Preferably, in S1, the image encryption includes the following specific steps:
s11, block scrambling and encryption: firstly, dividing an image into 2 multiplied by 2 non-overlapping blocks, and then using an image block scrambling method to scramble the sequence of each divided image block so as to achieve a first step of image encryption;
s12, secret sharing of the encrypted image by using a CRT: set the threshold for secret sharing to (k, n) and select a set of integers {128 < p 1 <p 2 <…<p n 256 < p), these integers also need to satisfy the following condition:
gcd(p i ,p j )=1,i≠j;
gcd(p i ,p)=1,i=1,2,...,n。
wherein
Figure BDA0003900091860000031
For one pixel x (h, w) in the image, h ∈ [1, μm],w∈[1,N](assuming the size of the carrier image is Mm × N), a random number is selected
Figure BDA00039000918600000311
Calculate y (h, w) = x (h, w) + a × p, and perform CRT sharing:
y(h,w)≡s 1 (h,w)(mod p 1 )
y(h,w)≡s 2 (h,w)(mod p 2 )
y(h,w)≡s n (h,w)(mod p n )
wherein s is i (h, w), i =1,2, \ 8230;, n is the pixel value in the encrypted image share resulting from the secret sharing.
Preferably, in S12, the (k, n) threshold requirement in secret sharing is: fewer than k shares cannot reconstruct the secret, any k shares can reconstruct the secret.
Preferably, in S2, the algorithm of the secure multiparty embedding protocol is as follows:
inputting: encrypted sharing
Figure BDA0003900091860000032
Figure BDA0003900091860000033
Secret sharing parameters
Figure BDA0003900091860000034
And (3) outputting: prediction error e m
S21, each information hiding person
Figure BDA0003900091860000035
The following calculations were performed:
Figure BDA0003900091860000036
S22、
Figure BDA0003900091860000037
will be provided with
Figure BDA0003900091860000038
Is sent to
Figure BDA0003900091860000039
S23、
Figure BDA00039000918600000310
By CRT calculation, solve for e A (h,w):
Figure BDA0003900091860000041
S24、
Figure BDA0003900091860000042
Calculate the original prediction error value:
Figure BDA0003900091860000043
e(h,w)≡e′ A (h,w)(mod p)
Figure BDA0003900091860000044
Figure BDA0003900091860000045
S25、
Figure BDA0003900091860000046
outputting the resulting prediction error e m
Preferably, in S2, the information embedding operation is as follows:
let the set of prediction errors be E = (E) 1 ,e 2 ,…,e MN/4 ) From this set, a threshold value T is calculated l ,T r
Figure BDA0003900091860000047
Wherein h is E (e) The number of prediction error values equal to E in the set E, then the information hider embeds the information according to the prediction error, and the used method is the translation of a prediction error histogram:
Figure BDA0003900091860000048
where g e 0,1 is the secret bit that needs to be embedded,
Figure BDA0003900091860000049
is the resulting encrypted shared pixel value.
Preferably, the information hider embeds the auxiliary information required by information extraction into the encrypted share, and the embedding method can use a traditional reversible information hiding method.
Preferably, in S3, the image decryption includes the following specific steps:
s31, after k secret-containing encryption shares are collected by a receiver, a CRT is used for calculating and reconstructing a secret-containing pixel;
and S32, after CRT reconstruction is finished, acquiring a secret image by using inverse scrambling.
Preferably, in S31, according to the CRT theorem, the following equation can be solved:
Figure BDA0003900091860000051
Figure BDA0003900091860000052
Figure BDA0003900091860000053
then calculate
Figure BDA0003900091860000054
And according to the disclosed parameter p, a final dense pixel value can be obtained;
Figure BDA0003900091860000055
preferably, in said S4, inWhen the receiver has obtained the information extraction with the dense pixels by decryption, the prediction error value e in each block is first calculated 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), and obtaining a threshold value required by extraction according to auxiliary information contained in the image, wherein the extraction method comprises the following steps:
Figure BDA0003900091860000056
where g is the secret bit extracted from the block.
Preferably, in S4, after the secret information is extracted, the receiver performs reverse translation on the histogram according to the rule of predicting error histogram translation, and restores the original pixel information;
Figure BDA0003900091860000061
finally, the receiver recovers the original image carrier without losses.
Compared with the prior art, the invention provides the reversible information hiding method of the ciphertext domain based on secret sharing and safe multi-party computation by improvement, and has the following improvements and advantages:
one is as follows: the invention provides a safe multi-party embedding protocol on the aspect of embedding capacity, so that an information hiding person can flexibly calculate the prediction error information, and the multi-layer multi-round prediction error histogram translation in the image cryptograph domain is realized, thereby achieving higher embedding capacity.
The second step is as follows: in the visual quality of the confidential image, the prediction error histogram translation used in the ciphertext domain can be basically consistent with the prediction error histogram translation method of the plaintext domain, and compared with the related method of the plaintext domain, the method can also realize the functions of image privacy protection, multi-party safe embedding and the like; compared with reversible information hiding of the existing ciphertext domain, the visual quality of the encrypted image is higher.
And thirdly: in the aspect of safety, CRT secret sharing and block scrambling double encryption are used, so that the privacy safety of pixel values is guaranteed, the correlation among pixels is disturbed, the high-frequency information of an image is protected, and the safety of the encrypted image can be proved when NPCR is used as an evaluation index for testing;
fourthly, the method comprises the following steps: in the encryption complexity, the calculation complexity of CRT secret sharing is lower than that of secret sharing based on a polynomial, and the calculation complexity of block scrambling is lower than that of homomorphic encryption and other methods.
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The invention is further explained below with reference to the figures and examples:
FIG. 1 is a block diagram of a solution of the present invention;
FIG. 2 is a diagram of a multi-party embedding embodiment of the present invention;
fig. 3 is a graph of the encryption result of the present invention.
Detailed Description
The present invention is described in detail below, and technical solutions in the embodiments of the present invention are clearly and completely described, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention provides a ciphertext domain reversible information hiding method based on secret sharing and safe multi-party computation through improvement, and the technical scheme of the invention is as follows:
as shown in fig. 1, the ciphertext domain reversible information hiding method based on secret sharing and secure multiparty computation includes the following specific steps:
s1, image encryption: an image block scrambling method based on High-speed scrambling is used, secret sharing based on a CRT is used, random numbers are added during encryption, and the problem of residual errors of image sharing is solved;
the image encryption method comprises the following specific steps:
s11, block scrambling and encryption: firstly, dividing an image into 2 multiplied by 2 non-overlapping blocks, and then using an image block scrambling method to scramble the sequence of each divided image block so as to achieve a first step of image encryption;
s12, secret sharing of the encrypted image by using a CRT: set the threshold for secret sharing to (k, n) and select a set of integers 128<p 1 <p 2 <…<p n ≤256<p, these integers also need to satisfy the following condition:
gcd(p i ,p j )=1,i≠j;
gcd(pi,p)=1,i=1,2,...,n。
wherein
Figure BDA0003900091860000081
For a pixel x (h, w) in the image, h e [1, M ∈],w∈[1,N](assuming the carrier image size is M N), a random number is selected
Figure BDA0003900091860000083
Calculate y (h, w) = x (h, w) + a × p, and perform CRT sharing:
y(h,w)≡s 1 (h,w)(mod p 1 )
y(h,w)≡s 2 (h,w)(mod p 2 )
y(h,w)≡s n (h,w)(mod p n )
wherein s is i (h, w), i =1,2, \8230;, n is the pixel value in the encrypted image share obtained after secret sharing; the obtained encrypted image shares not only meet the (k, n) threshold requirement in secret sharing (secret cannot be reconstructed if less than k shares, secret can be reconstructed if any k shares are available), but also further protect the privacy information of the correlation between pixels by using block scrambling. CRT secret sharing and block scrambling are used as encryption methods, and the computation complexity is lower than that of the encryption method (like state encryption) in reversible information hiding of many existing ciphertext domains;
s2, multi-party secure embedding: carrying out pixel prediction error calculation by utilizing a safe multi-party embedding protocol and carrying out information embedding;
wherein, when the information is hidden
Figure BDA0003900091860000082
After the encrypted image sharing is received, any information hiding person cannot steal the privacy information of the original image, and the reason is that in the property of secret sharing, it is determined that less than k shares cannot reconstruct any secret. In order to make the information hiding person complete the task of information embedding, a multi-party secure computing protocol must be designed, and the protocol enables the information hiding person to obtain only necessary data (prediction error information) required for embedding, and meanwhile, the privacy of the carrier image is not exposed. The invention designs a secure multi-party embedding protocol (SME) for pixel prediction error calculation, and the algorithm of the protocol is described as follows:
inputting: encrypted sharing
Figure BDA0003900091860000091
Figure BDA0003900091860000092
Secret sharing parameters
Figure BDA0003900091860000093
And (3) outputting: prediction error e m
S21, each information hiding person
Figure BDA0003900091860000094
The following calculations were performed:
Figure BDA0003900091860000095
S22、
Figure BDA0003900091860000096
will be provided with
Figure BDA0003900091860000097
Is sent to
Figure BDA0003900091860000098
S23、
Figure BDA0003900091860000099
By CRT calculation, solve for e A (h,w):
Figure BDA00039000918600000910
S24、
Figure BDA00039000918600000911
Calculate the original prediction error value:
Figure BDA00039000918600000912
e(h,w)≡e′ A (h,w)(mod p)
Figure BDA00039000918600000913
Figure BDA0003900091860000101
S25、
Figure BDA0003900091860000102
outputting the resulting prediction error e m
The information embedding operation is as follows:
let the set of prediction errors be E = (E) 1 ,e 2 ,…,e MN/4 ) From this set, a threshold value T is calculated l ,T r
Figure BDA0003900091860000103
Wherein h is E (e) The number of prediction error values equal to E in the set E, then the information hider embeds the information according to the prediction error, and the used method is the translation of a prediction error histogram:
Figure BDA0003900091860000104
where g e 0,1 is the secret bit that needs to be embedded,
Figure BDA0003900091860000105
is the resulting encrypted shared pixel value; besides secret information, the information hiding person can embed auxiliary information required by information extraction into encryption sharing, and the embedding method can use traditional reversible information hiding methods such as difference expansion;
in fig. 2, a specific example of multi-party embedding is shown, the secret sharing threshold is (3, 4), three information hiders respectively calculate the prediction error values in the respective image blocks, and the original prediction error (e.g. e in the figure) can be reconstructed by CRT calculation according to the prediction error values in the three ciphertext domains m = 1). And then according to the corresponding threshold value and the secret bit, all the information hiding persons can respectively carry out pixel modification operation required by embedding on the own held encrypted image share. It should be noted that after the secret information is hidden, the embedder needs to embed the necessary auxiliary information (such as pixel overflow information, the number of embedding layers and rounds of prediction error histogram translation, and the threshold T) l ,T r The embedding amount of the last round of histogram translation). After the embedding is finished, the secret encryption sharing can be obtained;
s3, image decryption: the receiver simultaneously holds a secret key shared by the CRT and a secret key scrambled by the image block, and decrypts the secret image;
the method comprises the following specific steps:
s31, after k secret-containing encryption shares are collected by a receiver, a CRT is used for calculating and reconstructing a secret-containing pixel, and according to the CRT theorem, the following equation can be solved:
Figure BDA0003900091860000111
Figure BDA0003900091860000112
Figure BDA0003900091860000113
then calculate
Figure BDA0003900091860000114
And according to the disclosed parameter p, a final dense pixel value can be obtained;
Figure BDA0003900091860000115
s32, after the CRT reconstruction is finished, the correlation between the obtained dense pixels is still disturbed by block scrambling, and inverse scrambling is needed to obtain a dense image; the specific operation of reverse scrambling depends on the scrambling method (such as High-speed scrambling) adopted in the encryption step and the set key thereof; the receiver can decrypt the image according to the corresponding key and the inverse scrambling rule to finally obtain the encrypted image;
s4, information extraction: and after a dense image is obtained, extracting information according to the extraction rule of the prediction error histogram translation and the auxiliary information embedded in the image.
It should be noted that the receiver may also perform information extraction before inverse scrambling, because the information extraction is performed in units of image blocks, and the block scrambling does not disturb the difference information in the pixel blocks. Assuming that the receiver has obtained the dense pixels through decryption, the prediction error value e in each block is first calculated in the information extraction 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), and obtaining a threshold value required by extraction according to auxiliary information contained in the image, wherein the extraction method comprises the following steps:
Figure BDA0003900091860000121
wherein g is the secret bit extracted from the block;
after extracting the secret information, the receiver carries out reverse translation on the histogram according to the rule of predicting error histogram translation, and original pixel information is recovered;
Figure BDA0003900091860000122
finally, the receiver recovers the original image carrier without loss.
According to the method, the complexity of image encryption calculation is reduced by secret sharing, and the image privacy is protected while multi-party information embedding is finished by utilizing safe multi-party calculation, so that higher embedding capacity and carrier visual quality are obtained.
The previous description is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims (10)

1. The ciphertext domain reversible information hiding method based on secret sharing and safe multiparty computation is characterized by comprising the following steps: the method comprises the following specific steps:
s1, image encryption: an image block scrambling method based on High-speed scrambling is used, secret sharing based on a CRT is used, random numbers are added during encryption, and the problem of residual errors of image sharing is solved;
s2, multi-party secure embedding: calculating pixel prediction errors by using a secure multi-party embedding protocol, and embedding information;
s3, image decryption: a receiver simultaneously holds a secret key shared by CRT (cathode ray tube) and a secret key scrambled by an image block and decrypts a secret image;
s4, information extraction: and after the dense image is obtained, extracting information according to the extraction rule of the prediction error histogram translation and the auxiliary information embedded in the image.
2. The ciphertext domain invertible information hiding method based on secret sharing and secure multiparty computation of claim 1, wherein: in S1, the image encryption specifically includes the following steps:
s11, block scrambling encryption: firstly, dividing an image into 2 multiplied by 2 non-overlapping blocks, and then using an image block scrambling method to scramble the sequence of each divided image block so as to achieve a first step of image encryption;
s12, secret sharing of the encrypted image by using a CRT: set the threshold for secret sharing to (k, n) and select a set of integers 128<p 1 <p 2 <…<p n ≤256<p, these integers also need to satisfy the following condition:
gcd(p i ,p j )=1,i≠j;
gcd(p i ,p)=1,i=1,2,…,n。
wherein
Figure FDA0003900091850000021
For one pixel x (h, w) in the image, h ∈ [1, μm],w∈[1,N](assuming the size of the carrier image is Mm × N), a random number is selected
Figure FDA0003900091850000027
Calculate y (h, w) = x (h, w) + a × p, and perform CRT sharing:
y(h,w)≡s 1 (h,w)(mod p 1 )
y(h,w)≡s 2 (h,w)(mod p 2 )
y(h,w)≡s n (h,w)(mod p n )
wherein s is i (h, w), i =1,2, \ 8230;, n is the pixel value in the encrypted image share resulting from the secret sharing.
3. The ciphertext domain invertible information hiding method based on secret sharing and secure multiparty computation of claim 2, wherein: in S12, the (k, n) threshold requirement in secret sharing is: fewer than k shares cannot reconstruct the secret, any k shares can reconstruct the secret.
4. The ciphertext domain invertible information hiding method based on secret sharing and secure multiparty computation of claim 3, wherein: in S2, the algorithm of the secure multiparty embedding protocol is as follows:
inputting: encrypted sharing
Figure FDA0003900091850000022
Figure FDA0003900091850000023
Secret sharing parameters
Figure FDA0003900091850000024
And (3) outputting: prediction error e m
S21, each information hiding person
Figure FDA0003900091850000025
The following calculations were performed:
Figure FDA0003900091850000026
S22、
Figure FDA0003900091850000031
will be provided with
Figure FDA0003900091850000032
Is sent to
Figure FDA0003900091850000033
S23、
Figure FDA0003900091850000034
By CRT calculation, solve for e A (h,w):
Figure FDA0003900091850000035
S24、
Figure FDA0003900091850000036
Calculate the original prediction error value:
Figure FDA0003900091850000037
e(h,w)≡e′ A (h,w)(mod p)
Figure FDA0003900091850000038
Figure FDA0003900091850000039
S25、
Figure FDA00039000918500000310
outputting the resulting prediction error e m
5. The ciphertext domain invertible information hiding method based on secret sharing and secure multiparty computation of claim 4, wherein: in S2, the information embedding operation is as follows:
let the set of prediction errors be E = (E) 1 ,e 2 ,…,e MN/4 ) From this set, a threshold value T is calculated l ,T r
Figure FDA00039000918500000311
Wherein h is E (e) The number of prediction error values equal to E in the set E is determined, then an information hider embeds information according to the prediction error, and the used method is prediction error histogram translation:
Figure FDA0003900091850000041
where g e 0,1 is the secret bit that needs to be embedded,
Figure FDA0003900091850000042
the resulting cryptographically encrypted shared pixel value.
6. The ciphertext domain reversible information hiding method based on secret sharing and secure multi-party computation according to claim 5, wherein: the information hiding person embeds the auxiliary information required by information extraction into the encrypted sharing, and the embedding method can use a traditional reversible information hiding method.
7. The ciphertext domain invertible information hiding method based on secret sharing and secure multiparty computation of claim 6, wherein: in S3, the image decryption specifically includes the following steps:
s31, after k secret-containing encryption shares are collected by a receiver, a CRT is used for calculating and reconstructing a secret-containing pixel;
and S32, after the CRT reconstruction is finished, acquiring a secret image by using inverse scrambling.
8. The ciphertext domain invertible information hiding method based on secret sharing and secure multiparty computation of claim 7, wherein: in S31, according to the CRT theorem, the following equation can be solved:
Figure FDA0003900091850000043
Figure FDA0003900091850000044
Figure FDA0003900091850000045
then calculate
Figure FDA0003900091850000046
And according to the disclosed parameter p, a final dense pixel value can be obtained;
Figure FDA0003900091850000051
9. the ciphertext domain reversible information hiding method based on secret sharing and secure multi-party computation of claim 8, wherein: in S4, when information extraction is performed in a case where the receiver has obtained a dense pixel by decryption, a prediction error value e in each block is first calculated 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), and obtaining a threshold value required by extraction according to auxiliary information contained in the image, wherein the extraction method comprises the following steps:
Figure FDA0003900091850000052
where g is the secret bit extracted from the block.
10. The ciphertext domain reversible information hiding method based on secret sharing and secure multiparty computation of claim 9, wherein: in the step S4, after the secret information is extracted, the receiver reversely translates the histogram according to the rule of predicting the error histogram translation, and the original pixel information is recovered;
Figure FDA0003900091850000053
finally, the receiver recovers the original image carrier without loss.
CN202211287807.9A 2022-10-20 2022-10-20 Ciphertext domain reversible information hiding method based on secret sharing and secure multi-party computation Pending CN115664653A (en)

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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116095245A (en) * 2023-04-07 2023-05-09 江西财经大学 Secret information sharing method, system, terminal and storage medium
CN117499030A (en) * 2023-10-31 2024-02-02 广东技术师范大学 Ciphertext domain multi-party mobile information hiding method and system based on hybrid encryption

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116095245A (en) * 2023-04-07 2023-05-09 江西财经大学 Secret information sharing method, system, terminal and storage medium
CN116095245B (en) * 2023-04-07 2023-06-23 江西财经大学 Secret information sharing method, system, terminal and storage medium
CN117499030A (en) * 2023-10-31 2024-02-02 广东技术师范大学 Ciphertext domain multi-party mobile information hiding method and system based on hybrid encryption

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