CN113190807B - Ciphertext domain reversible information hiding method based on image secret sharing - Google Patents
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Abstract
The invention discloses a ciphertext domain reversible information hiding method based on image secret sharing, which comprises the following steps: encrypting the original image to obtain a ciphertext image; embedding two layers of secret information by redundancy of polynomials and utilizing homomorphism property of secret sharing to obtain a secret image; by acquiring a second key corresponding to the second layer secret information; directly extracting second-layer secret information from the second secret-carrying text image through the second secret key; and collecting a plurality of different second ciphertext-carrying images; the Lagrangian interpolation polynomial is utilized to recover the secret, and then homomorphic decryption is carried out on the second secret carrying text image; and after homomorphic decryption, recovering the original image by adopting a first key corresponding to the first layer secret information and a third key corresponding to the ciphertext image, and extracting the first layer secret information. The invention enhances the fault tolerance and disaster resistance of the encrypted text image, improves the embedding capacity of the reversible information hiding algorithm of the encrypted text domain, and ensures the safety of the carrier image and the secret information.
Description
Technical Field
The invention relates to the field of image processing, in particular to a ciphertext domain reversible information hiding method based on image secret sharing.
Background
Ciphertext domain reversible information hiding (Reversible data hiding in encrypted domain, RDH-ED) is an important branch of information hiding technology, which can embed secret information in ciphertext data and can recover the original carrier without loss. The ciphertext domain information processing technology and the information hiding technology are organically integrated, so that the dual functions of information encryption protection and secret information transmission are realized, and a method is provided for the fields of military, medical treatment and the like which both require carrier safety and ensure carrier undistorted recovery.
The existing ciphertext domain reversible information hiding technology is mainly divided into three types: redundancy is generated based on encryption, redundancy is generated based on encryption and a ciphertext domain embedding scheme is generated based on encryption process redundancy. The method for generating redundancy after encryption mainly utilizes ciphertext lossless compression or homomorphic encryption technology to generate redundancy in a ciphertext domain, and has the problems of low embedding rate, poor separability and the like. The method for generating redundancy before encryption mainly generates redundancy through complex preprocessing operation before encryption, in practical application, an image owner is difficult to execute related operation, certain application limitations exist, and representative algorithms mainly comprise: based on lossless compression techniques and based on pixel prediction techniques. The redundancy method in the encryption process mainly utilizes redundancy to formulate an embedding strategy by exploring redundancy information existing in the encryption process.
Secret sharing (Secret sharing scheme, SSS) is an important encryption technique that is widely used in many fields such as key management, digital watermarking, and distributed storage. The secret sharing scheme is introduced into reversible information hiding of a ciphertext domain, the existing algorithm mainly utilizes the techniques of difference expansion and difference histogram translation to embed secret information into a shadow image, but the separability of image decryption and secret extraction cannot be realized, and meanwhile, the technical advantages of secret sharing cannot be reserved.
Image secret sharing (Secret images sharing, SIS) is an extended application of secret sharing, where secret images are split into multiple shadow images and distributed to different participants, and the secret images can be restored without loss only if enough shadow images are collected. The main categories are two: a scheme for secret sharing of images based on visual cryptography and based on polynomials. The visual cryptography-based scheme is characterized in that the visual quality of the image is not high through overlapping a plurality of shadow images to be recognized and recovered by human eyes. The scheme based on the polynomial not only can realize the secret segmentation and compression of the image, but also can recover the secret image in a lossless manner. Many advantages of image secret sharing are worth information hiding reference, for example, SIS has the requirement of lossless recovery of images, reversibility of RDH-ED is met, a large amount of redundant information exists after SIS compression, redundancy of RDH-ED is met, and the like. However, the combination of the secret sharing and the information hiding of the current image is not tight, and the correctness and the integrity of the shadow image are verified mainly by using digital watermarks.
In summary, the conventional RDH-ED algorithm mainly utilizes redundancy of the carrier image to perform reversible embedding of secret information, and the embedding property is limited by the original carrier. Meanwhile, when the portable secret text is attacked or damaged, the embedded information cannot be accurately extracted and the original image cannot be restored without damage.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a ciphertext domain reversible information hiding method based on image secret sharing.
In order to achieve the above purpose, the present invention adopts the following technical scheme:
a ciphertext domain reversible information hiding method based on image secret sharing, the method comprising:
encrypting the original image to obtain a ciphertext image;
embedding first-layer secret information into the ciphertext image through redundancy of the polynomial to obtain a secret image;
dividing the secret image into a plurality of first secret carrying images;
and embedding second-layer secret information into the plurality of first secret-carrying images respectively by utilizing the homomorphism property of secret sharing so as to obtain a plurality of second secret-carrying images.
The further technical scheme is as follows: the method further comprises the steps of:
acquiring a second key corresponding to the second-layer secret information;
directly extracting second-layer secret information from the second secret-carrying text image through the second secret key;
the method comprises the steps of,
collecting a plurality of different second ciphertext-carrying images;
the Lagrangian interpolation polynomial is utilized to recover the secret, and then homomorphic decryption is carried out on the second secret carrying text image;
and after homomorphic decryption, recovering the original image by adopting a first key corresponding to the first layer secret information and a third key corresponding to the ciphertext image, and extracting the first layer secret information.
The further technical scheme is as follows: in the step of embedding the first layer of secret information into the ciphertext image through redundancy of the polynomial to obtain the secret image, the polynomial is:
F(x)＝a 1 +...+a w x w-1 +b 1 x w +...+b k-w x k-1 (modq); wherein a is 1 ,...,a w Is a ciphertext image pixel, b 1 ,...,b k-w Is first layer secret information.
The further technical scheme is as follows: in the step of dividing the secret image into a plurality of first secret-carrying text images, the secret image division needs to satisfy the following equation set:
The further technical scheme is as follows: embedding second-layer secret information into the plurality of first secret-carrying images respectively by utilizing homomorphism property of secret sharing so as to obtain a plurality of second secret-carrying images, wherein homomorphism embedding of the second-layer secret information is required to meet the following equation set;
The further technical scheme is as follows: after homomorphic decryption, recovering an original image by adopting a first key corresponding to the first layer secret information and a third key corresponding to the ciphertext image, and extracting the first layer secret information, wherein the recovered polynomial and the second secret carrying ciphertext image need to meet the following equation set;
Compared with the prior art, the invention has the beneficial effects that: the invention uses the characteristic of the image secret sharing scheme to divide the secret image into a plurality of secret-carrying text images, and when part of the secret-carrying text images are damaged or lost, the other k secret-carrying text images can be used for lossless recovery and extraction, so that the original image and secret information have stronger fault tolerance. The first layer secret information is embedded by utilizing the redundancy parameters in the encryption process, the second layer secret information is carried out by utilizing the homomorphic characteristic of the encryption algorithm, the embedding capacity of the algorithm is effectively improved, and the embedding capacity of the algorithm is not limited by the carrier image. After the secret image is divided into a plurality of parts by the characteristics of the secret sharing scheme, the secret image is stored by different participants, so that the secret is prevented from being too concentrated, and the safe storage and risk dispersion of the secret are realized. In addition, each information hiding participant holds different secret-carrying images, and can respectively and independently embed secondary secret information, and the embedded secret-carrying images cannot influence the extraction of primary embedded secret information and the recovery of an original image. In addition, according to the homomorphic characteristic of addition of the two-layer embedding mode and the secret sharing scheme, secret information can be extracted without error before and after decryption of the secret carrying text image, the separability of the algorithm is realized, the ciphertext expansion is reduced under the condition of ensuring high embedding capacity, the secret carrying text image generated by segmentation is compressed to half of the original secret carrying text image by utilizing the compression characteristic of the image secret sharing technology, the space for storing the ciphertext is effectively saved, and meanwhile, the high embedding capacity of the algorithm is also ensured.
The foregoing description is only an overview of the present invention, and is intended to be more clearly understood as being carried out in accordance with the following description of the preferred embodiments, as well as other objects, features and advantages of the present invention.
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In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for the description of the embodiments will be briefly described below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flowchart of an embodiment of a method for reversible information hiding in ciphertext domain based on image secret sharing according to the present invention;
FIG. 2 is a diagram of an algorithm framework of the present invention;
FIG. 3 is a schematic diagram of a secret information embedding process of the present invention;
FIG. 4 is a schematic diagram of the secret information extraction and original image restoration process of the present invention;
FIG. 5 is a schematic diagram of an image organization of a portable ciphertext according to the present invention;
FIG. 6 is a rena image restored before and after homomorphic decryption according to the present invention;
FIG. 7 is a first ciphertext-bearing image of the present invention having first layer secret information embedded therein;
FIG. 8 is a second ciphertext-carrying image of the present invention having second layer secret information embedded therein;
FIG. 9 is a graph of the embedding rate under various parameters of the present invention;
FIG. 10 is a graph of the effect of twice information embedding on the image security of a Lena carrier according to the present invention;
fig. 11 is a graph of the quality of the restored image before and after homomorphic decryption.
Detailed Description
The technical solutions of the present invention will be clearly and completely described below in conjunction with specific embodiments of the present invention, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
It should be understood that the terms "comprises" and "comprising," when used in this specification and claims, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof.
It is also to be understood that the terminology used in the description of the invention herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. As used in this specification and the appended claims, the singular forms "a," "an," and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise.
It should be further understood that the term "and/or" as used in the present specification and the appended claims refers to any and all possible combinations of one or more of the associated listed items, and includes such combinations.
The invention aims to fully combine the technical advantages of image secret sharing with the reversible information hiding algorithm of the ciphertext domain, and the invention uses the disaster tolerance characteristic of the secret sharing technology to enhance the fault tolerance and disaster resistance of the image carrying the ciphertext and improve the embedding capacity of the reversible information hiding algorithm of the ciphertext domain in order to solve the problems that the reversible information hiding algorithm of the current ciphertext domain cannot meet the information hiding requirement of multiple users, the fault tolerance and disaster resistance of the image carrying the ciphertext are not strong, the original image cannot be reconstructed and the secret information cannot be recovered once the image is attacked or damaged, and the like; the separability of the secret information before and after the decryption of the image carrying the secret document is realized by utilizing the homomorphic characteristic of the addition, and the safety of the carrier image and the secret information is ensured. The invention is described below by means of specific examples.
Referring to fig. 1, the method for hiding reversible information in ciphertext domain based on image secret sharing includes the following steps:
s10, encrypting the original image to obtain a ciphertext image;
s20, embedding first-layer secret information into the ciphertext image through redundancy of the polynomial to obtain a secret image;
s30, dividing the secret image into a plurality of first secret carrying text images;
s40, respectively embedding second-layer secret information into the plurality of first secret-carrying images by utilizing the homomorphism property of secret sharing so as to obtain a plurality of second secret-carrying images.
S50, acquiring a second secret key corresponding to the second-layer secret information;
s60, directly extracting second-layer secret information from the second secret-carrying text image through a second secret key;
the method comprises the steps of,
s70, collecting a plurality of different second encrypted text-carrying images;
s80, homomorphic decryption is carried out on the second secret-carrying text image after secret recovery by utilizing the Lagrange interpolation polynomial;
s90, after homomorphic decryption, recovering the original image by adopting a first key corresponding to the first layer secret information and a third key corresponding to the ciphertext image, and extracting the first layer secret information.
Specifically, steps S10 to S40 are encryption processes, steps S50 to S60 are decryption processes performed when only one second ciphertext-carrying image is collected, and steps S70 to S90 are decryption processes performed when a plurality of second ciphertext-carrying images are collected. Referring to fig. 4, fig. 4 is an algorithm frame diagram of the present invention, and symbols in the diagram specifically have the following meanings: i is an original image; i e Is a ciphertext image; msg (Msg) a Is the secret information to be embedded (i.e. the first layer secret information in the steps of the method); msg (Msg) b ＝{Msg b-1 ,Msg b-2 ,...,Msg b-n Secret information to be embedded (i.e. second layer secret information in the above method steps) for n hidden participants; k (K) e Encrypting a key for the image (i.e., a third key in the method steps described above); k (K) d Hiding the key (i.e. the first key in the above method steps) for the information; k (K) ds ＝{K ds-1 ,...,K ds-n Information hiding keys (i.e. second keys in the above method steps) for n hidden participants; SIS key= { SIS Key 1 ,...,SIS Key n -participant attribute tags; i em ＝{I em-1 ,I em-2 ,...,I em-n The n-piece secret document image after the polynomial embedding (namely the above-mentioned party)A first image of the carried ciphertext in the method step);
k copies of the homomorphism embedded secret-coded text image are carried; i ems ＝{I ems-1 ,I ems-2 ,...,I ems-n And n secret document images (namely the second secret document image in the method step) after homomorphism embedding.
Referring to fig. 2, the image owner encrypts the original image I and transmits the ciphertext image I using any symmetric encryption algorithm e To the information hiding person. The information concealer first embeds the secret information Msg using the redundancy of the polynomials a And dividing the secret image into a plurality of secret-carrying images I em ＝{I em-1 ,I em-2 ,...,I em-n Multiple information hiding participants re-use homomorphic property of secret sharing, embed secret information Msg b ＝{Msg b-1 ,Msg b-2 ,...,Msg b-n Obtaining a secondary embedded secret document-carrying image I ems ＝{I ems-1 ,I ems-2 ,...,I ems-n }. The receiver based on the corresponding key K ds Can be directly from I ems Extracting Msg from the extract b But to recover I, or to extract the secret Msg a Then k different images of the portable secret document are collected first
Recovering the secret by using Lagrangian interpolation polynomials, then homomorphic decryption is carried out, and finally, the image encryption key K is respectively used e Hidden key K with information d Restoring original image and extracting secret information Msg a 。
Fig. 3 is a process of embedding secret information: the method comprises the steps of embedding secret information into a polynomial redundancy by utilizing a secret sharing method, dividing a ciphertext image and the secret information into a plurality of ciphertext-carrying images and distributing the ciphertext image and the secret information to different users, wherein the method is required to extract information after secret recovery; secondly, each user can independently embed the self-managed secret carrying text image in the same state, and the information extraction is completed before secret recovery. The embedding of the information does not affect the restoration of the original image, i.e. the reconstructed image is undistorted.
For the first phase, first, the first phase is performed in the finite field GF (2 8 ) Constructing a Shamir (k, n) threshold image secret sharing scheme and generating a k-1 th order polynomial F (x) =a 0 +a 1 x+...+n k-1 x k-1 (modq) the polynomial has k available coefficients, and distributes a replacement coefficient for the ciphertext image and the secret information according to the image compression coefficient w, and distributes the ciphertext image I e And secret information Msg a Embedded into the following polynomial coefficients:
F(x)＝a 1 +...+a w x w-1 +b 1 x w +...+b k-w x k-1 (modq); wherein a is 1 ,...,a w Is ciphertext pixel, b 1 ,...,b k-w Secret information Msg a The secret information is usually hidden by using an information hiding key K before embedding d Encryption.
Hiding a shared Key SIS Key of a participant from information i Dividing the secret to obtain multiple secret-carrying text images I which are different from each other em-i And distributed to the corresponding information concealer p i . When secret segmentation is performed, the following equation set is satisfied:
By taking advantage of homomorphic nature of secret sharing technique, by carrying secret document image I em Homomorphic addition operation of secret information is realized. When embedding, the function psi (·) is utilized to transform the secret information Msg b Then, with I em-i Homomorphic addition operation is carried out to obtain a secret carrying text I after secondary embedding ems ：
In order to improve the embedding efficiency, i.e. to embed as much secret information as possible with less modifications, a steganography method of matrix coding is used. The embedding process is as follows: constructing corresponding matrix codes by (7, 4) error correcting codes, from I em-i 7 bits of a block of pixels are selected to form a packet x= (x) 1 ,...,x 7 ) T As an embedding carrier, an embedding message m= (m 1 ,...,m 4 ) T Calculating the syndrome s=m-Hx, and finding a corresponding coset leader e in the coding table, wherein the requirements are as follows: he=s=m-Hx; calculating y=x+e, resulting in an embedded packet y.
Fig. 4 is a secret information extraction process, and according to the number of secret images involved in recovery, the secret information extraction process can be mainly divided into the following two cases:
collecting only 1 part of image I carrying cipher text ems-i When the key K is hidden according to the information ds-i Can extract secret information Msg b-i The portable secret document image I can be recovered by the auxiliary information em-i 。
From the embedded packet y and the check matrix H, an embedded message m can be extracted:
Hy＝H(x+e)＝Hx+He
＝m-s+s
＝m；
collecting k parts of image carrying the dense text
When the method is used, firstly, attribute tags SIS Key of information hiding participants are utilized to construct Lagrange interpolation polynomials to recover secrets, and a ciphertext image I containing noise is obtained e ' and secret information Msg a 'A'; then, homomorphic decryption is performed based on the auxiliary information to eliminate noise.
Recovering multiple items according to addition homomorphism characteristic of secret sharingSecret carrying text I after secondary embedding ems The following relationship is satisfied:
FIG. 5 is a portable compact document image I ems Is mainly composed of two parts, namely, pixels carrying dense text
And auxiliary information. In homomorphic embedding process, I is used as em Embedding as carrier to obtain a pixel with secret>
While generating auxiliary information.
The invention uses the characteristic of the image secret sharing scheme to divide the secret image into a plurality of secret-carrying text images, and when part of the secret-carrying text images are damaged or lost, the other k secret-carrying text images can be used for lossless recovery and extraction, so that the original image and secret information have stronger fault tolerance. The first layer secret information is embedded by utilizing the redundancy parameters in the encryption process, the second layer secret information is carried out by utilizing the homomorphic characteristic of the encryption algorithm, the embedding capacity of the algorithm is effectively improved, and the embedding capacity of the algorithm is not limited by the carrier image. After the secret image is divided into a plurality of parts by the characteristics of the secret sharing scheme, the secret image is stored by different participants, so that the secret is prevented from being too concentrated, and the safe storage and risk dispersion of the secret are realized. In addition, each information hiding participant holds different secret-carrying images, and can respectively and independently embed secondary secret information, and the embedded secret-carrying images cannot influence the extraction of primary embedded secret information and the recovery of an original image. In addition, according to the homomorphic characteristic of addition of the two-layer embedding mode and the secret sharing scheme, secret information can be extracted without error before and after decryption of the secret carrying text image, the separability of the algorithm is realized, the ciphertext expansion is reduced under the condition of ensuring high embedding capacity, the secret carrying text image generated by segmentation is compressed to half of the original secret carrying text image by utilizing the compression characteristic of the image secret sharing technology, the space for storing the ciphertext is effectively saved, and meanwhile, the high embedding capacity of the algorithm is also ensured.
Fig. 6 shows the Lena images restored before and after homomorphic decryption, wherein (a) is the original image, (b) is the noise-containing image restored before homomorphic decryption, and (c) is the noise-removed image after homomorphic decryption, which is identical to the original image, indicating that the method has the complete reversibility of image restoration.
Based on Shamir (3, 4) threshold and image compression rate of 50%, fig. 7 and 8 show the secret-information-embedded ciphertext images after the first and second embedding. Fig. 9 is an embedding rate under different parameters, where n represents the total number of shares after splitting the secret, k represents the minimum value up to the threshold, and 1/w represents the compression rate of the split secret shares. Fig. 10 shows the effect of the twice embedded information on the security of the Lena carrier image, compared with the PSNR and the information entropy of the ciphertext image, the twice embedded secret-carrying images both conform to the characteristics of the ciphertext image, and any information related to the carrier image cannot be revealed, so that the security of the carrier image is ensured. Fig. 11 shows the quality of restored images before and after homomorphic decryption, and only the homomorphic decrypted images can restore the original images.
While the invention has been described with reference to certain preferred embodiments, it will be understood by those skilled in the art that various changes and substitutions of equivalents may be made and equivalents will be apparent to those skilled in the art without departing from the scope of the invention. Therefore, the protection scope of the invention is subject to the protection scope of the claims.
Claims (3)
1. The ciphertext domain reversible information hiding method based on image secret sharing is characterized by comprising the following steps:
encrypting the original image to obtain a ciphertext image;
embedding first-layer secret information into the ciphertext image through redundancy of the polynomial to obtain a secret image;
dividing the secret image into a plurality of first secret carrying images;
respectively embedding second-layer secret information into the plurality of first secret-carrying images by utilizing the homomorphism property of secret sharing so as to obtain a plurality of second secret-carrying images;
in the step of embedding the first layer of secret information into the ciphertext image through redundancy of the polynomial to obtain the secret image, the polynomial is:
F(x)＝a 1 +...+a w x w-1 +b 1 x w +...+b k-w x k-1 (mod q); wherein a is 1 ,...,a w Is a ciphertext image pixel, b 1 ,...,b k-w The method is characterized in that the method is first-layer secret information, w is a shadow image compression coefficient, k is a threshold parameter, and q is a prime number;
in the step of dividing the secret image into a plurality of first secret-carrying text images, the secret image division needs to satisfy the following equation set:
embedding second-layer secret information into the plurality of first secret-carrying images respectively by utilizing homomorphism property of secret sharing so as to obtain a plurality of second secret-carrying images, wherein homomorphism embedding of the second-layer secret information is required to meet the following equation set;
2. The ciphertext domain reversible information hiding method based on image secret sharing of claim 1, further comprising:
acquiring a second key corresponding to the second-layer secret information;
directly extracting second-layer secret information from the second secret-carrying text image through the second secret key;
the method comprises the steps of,
collecting a plurality of different second ciphertext-carrying images;
the Lagrangian interpolation polynomial is utilized to recover the secret, and then homomorphic decryption is carried out on the second secret carrying text image;
and after homomorphic decryption, recovering the original image by adopting a first key corresponding to the first layer secret information and a third key corresponding to the ciphertext image, and extracting the first layer secret information.
3. The method for hiding reversible information in ciphertext domain based on image secret sharing as claimed in claim 2, wherein, after homomorphic decryption, the following equation set is satisfied between the restored polynomial and the second secret carrying image in the steps of restoring the original image and extracting the first layer secret information by using the first key corresponding to the first layer secret information and the third key corresponding to the ciphertext image;
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| CN113992327B (en) * | 2021-11-16 | 2023-10-20 | 陕西师范大学 | Lossless approximate split-memory recovery method and system based on prime number decomposition |
| CN114301583B (en) * | 2021-12-22 | 2023-10-24 | 阿里巴巴（中国）有限公司 | Ciphertext compression method, ciphertext compression device, ciphertext compression equipment and storage medium |
| CN114913048A (en) * | 2022-04-22 | 2022-08-16 | 北京印刷学院 | Halftone secret sharing method and halftone secret extraction method based on optimized data distribution |
| CN115242930B (en) * | 2022-05-26 | 2023-07-07 | 辽宁师范大学 | Secret sharing-based ciphertext domain extreme prediction double-layer reversible information hiding method |
| CN115225771B (en) * | 2022-07-08 | 2023-07-28 | 广东技术师范大学 | Method and device for hiding reversible information of encrypted image and computer equipment |
| CN117499030B (en) * | 2023-10-31 | 2024-06-18 | 广东技术师范大学 | Ciphertext domain multi-party mobile information hiding method and system based on hybrid encryption |
| CN117240435B (en) * | 2023-11-10 | 2024-02-09 | 广东技术师范大学 | Decoupled multiparty encryption domain reversible information hiding method |
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