CN110337000B - Encryption domain reversible information hiding method based on double binary tree expansion and public key encryption - Google Patents

Encryption domain reversible information hiding method based on double binary tree expansion and public key encryption Download PDF

Info

Publication number
CN110337000B
CN110337000B CN201910624039.3A CN201910624039A CN110337000B CN 110337000 B CN110337000 B CN 110337000B CN 201910624039 A CN201910624039 A CN 201910624039A CN 110337000 B CN110337000 B CN 110337000B
Authority
CN
China
Prior art keywords
image
prediction error
secret information
pixel
encryption
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN201910624039.3A
Other languages
Chinese (zh)
Other versions
CN110337000A (en
Inventor
熊礼治
董丹萍
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Nanjing University of Information Science and Technology
Original Assignee
Nanjing University of Information Science and Technology
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Nanjing University of Information Science and Technology filed Critical Nanjing University of Information Science and Technology
Priority to CN201910624039.3A priority Critical patent/CN110337000B/en
Publication of CN110337000A publication Critical patent/CN110337000A/en
Application granted granted Critical
Publication of CN110337000B publication Critical patent/CN110337000B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/008—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols involving homomorphic encryption
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
    • H04N19/00—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals
    • H04N19/10—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding
    • H04N19/102—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding characterised by the element, parameter or selection affected or controlled by the adaptive coding
    • H04N19/12—Selection from among a plurality of transforms or standards, e.g. selection between discrete cosine transform [DCT] and sub-band transform or selection between H.263 and H.264
    • H04N19/122—Selection of transform size, e.g. 8x8 or 2x4x8 DCT; Selection of sub-band transforms of varying structure or type
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
    • H04N19/00—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals
    • H04N19/10—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding
    • H04N19/169—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding characterised by the coding unit, i.e. the structural portion or semantic portion of the video signal being the object or the subject of the adaptive coding
    • H04N19/17—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding characterised by the coding unit, i.e. the structural portion or semantic portion of the video signal being the object or the subject of the adaptive coding the unit being an image region, e.g. an object
    • H04N19/176—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding characterised by the coding unit, i.e. the structural portion or semantic portion of the video signal being the object or the subject of the adaptive coding the unit being an image region, e.g. an object the region being a block, e.g. a macroblock
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
    • H04N19/00—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals
    • H04N19/10—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding
    • H04N19/169—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding characterised by the coding unit, i.e. the structural portion or semantic portion of the video signal being the object or the subject of the adaptive coding
    • H04N19/182—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding characterised by the coding unit, i.e. the structural portion or semantic portion of the video signal being the object or the subject of the adaptive coding the unit being a pixel
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
    • H04N19/00—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals
    • H04N19/46—Embedding additional information in the video signal during the compression process
    • H04N19/467—Embedding additional information in the video signal during the compression process characterised by the embedded information being invisible, e.g. watermarking
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
    • H04N19/00—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals
    • H04N19/90—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using coding techniques not provided for in groups H04N19/10-H04N19/85, e.g. fractals
    • H04N19/96—Tree coding, e.g. quad-tree coding

Landscapes

  • Engineering & Computer Science (AREA)
  • Signal Processing (AREA)
  • Multimedia (AREA)
  • Physics & Mathematics (AREA)
  • Discrete Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Computer Security & Cryptography (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Image Processing (AREA)
  • Editing Of Facsimile Originals (AREA)

Abstract

The invention discloses an encryption domain reversible information hiding method based on double binary tree expansion and public key encryption, which comprises the steps of carrying out pixel overflow prevention preprocessing on an original image, reducing pixels on two sides of a pixel histogram of the original image according to the number of layers of a double binary tree, dividing the original image into a plurality of 2 multiplied by 2 first image blocks, carrying out original image encryption by adopting a homomorphic encryption public key encryption system, embedding secret information into a ciphertext image by utilizing a double binary tree traversal and prediction error expansion method, and realizing image recovery and information extraction in a ciphertext domain and/or a plaintext domain according to a data hiding key and a decryption key. The encryption domain reversible information hiding method based on double binary tree expansion and public key encryption greatly improves the aspects of encryption cost, capacity of embedded secret information, image quality after decryption and the like.

Description

Encryption domain reversible information hiding method based on double binary tree expansion and public key encryption
Technical Field
The invention relates to the technical field of encryption domain reversible information hiding technology and image content security, in particular to an encryption domain reversible information hiding method based on double binary tree expansion and public key encryption.
Background
With the rapid development and application of cloud computing, mass picture information is stored on a cloud server in a large quantity, and internet users can conveniently and rapidly access media information on the cloud storage, so that the number and the utilization rate of images are rapidly increased. However, in an open complex cloud environment, the problem of protecting image content is increasingly prominent. In order to realize information hiding and carrier image lossless recovery in a cloud environment, a reversible information hiding technology of an encryption domain is proposed. In this technique, the image provider encrypts the image and uploads it to the cloud server, the nature of the encryption algorithm allows the additional information to be embedded directly into the encrypted carrier image, from the encryption key, the additional information can be extracted in the ciphertext, and the original carrier image is obtained by the corresponding decryption key. This ensures that the cloud server performs analysis processing on the secret information without knowing the original content, thereby protecting the carrier image content.
Embedding rate and image quality are two important criteria for measuring reversible information hiding technical scheme of an encrypted domain. Generally, embedding more secret information is an important consideration, but as the amount of embedding increases, image quality is inevitably affected. Generally, the larger the embedding rate, the worse the image quality. How to find the balance between the two is the key point of research.
There are many current schemes for protecting image content based on symmetric encryption. Symmetric encryption requires the sender and receiver to share a common key, but this can lead to key distribution and management difficulties. Since each encryption process has uniqueness and confidentiality, a huge number of keys is generated. If the key of either party is broken, the image may be attacked and unprotected, which makes the security of the image challenging. Compared with symmetric encryption, an encryption key and a decryption key of a public key encryption system are respectively owned by a sender and a receiver, so that the problem of key management is solved. And the arithmetic operation of the data by directly executing homomorphic addition and homomorphic multiplication in the cryptograph domain can provide more safe and reliable protection for the image content. The public key encryption used by the existing method has the defects that the ciphertext is too long to expand, and better image quality cannot be ensured under the condition of high embedding rate.
In order to improve the storage space and the operation speed of a homomorphic encryption algorithm in an information hiding scheme, improve the secret information embedding rate and reduce the communication cost, an encryption domain reversible information hiding method based on double binary tree expansion and public key encryption is provided, and improvement is carried out on the aspects of ciphertext safety after carrier image encryption, secret information embedding rate, image quality after data embedding and the like.
Disclosure of Invention
The invention aims to provide an encryption domain reversible information hiding method based on double binary tree expansion and public key encryption, which comprises the steps of preprocessing an original image for preventing pixel overflow, reducing pixels on two sides of a pixel histogram of the original image according to the number of layers of a double binary tree, dividing the original image into a plurality of 2 multiplied by 2 first image blocks, encrypting the original image by adopting a homomorphic encryption public key encryption system, embedding secret information into a ciphertext image by utilizing a double binary tree traversal and prediction error expansion method, and realizing image recovery and information extraction in a ciphertext domain and/or a plaintext domain according to a data hiding key and a decryption key. The encryption domain reversible information hiding method based on double binary tree expansion and public key encryption greatly improves the aspects of encryption cost, capacity of embedded secret information, image quality after decryption and the like.
To achieve the above object, with reference to fig. 1, the present invention provides an encryption domain reversible information hiding method based on dual binary tree expansion and public key encryption, where the method includes:
s1: adopting the following formula, carrying out pixel overflow prevention preprocessing on an original image with the size of m multiplied by n, and reducing the pixels on two sides of a pixel histogram of the original image by 2 according to the double binary tree layer number LLAnd recording the positions of the reduced pixels to obtain a binary mapping position overflow map mapB:
Figure BDA0002126465730000021
wherein, Is(I, j) represents the image of the original pixel I (I, j) after the preprocessing of preventing the pixel overflow, L is the layer number of the binary tree, I, j are the abscissa and the ordinate of the original image, I belongs to [1, m ]]，j∈[1，n]。
The double binary tree is formed by taking a horizontal axis in a pixel histogram of an original image as a node.
S2: dividing an original image into a plurality of 2 multiplied by 2 first image blocks, and encrypting the original image by adopting a homomorphic encryption public key encryption system.
Encrypting each first image block using the following formula:
Figure BDA0002126465730000022
Figure BDA0002126465730000023
Figure BDA0002126465730000024
Figure BDA0002126465730000025
wherein x is1、x2、x3And x4Are four pixels, ct, in the same first image block of the original image1、ct2、ct3And ct4Are each x1、x2、x3And x4Ciphertext of a0U, t and g are parameters generated in the encryption algorithm.
The invention provides that, in order to ensure that the pixels in the same first image block maintain spatial correlation, four pixels in the same first image block are encrypted using the same parameters u, g, and t.
To ensure the security of the data hiding process, different first image blocks are encrypted using different parameters u, g, t and the public key pk.
S3: dividing the encrypted image into a plurality of 2 x 2 second image blocks, and calculating the prediction error e in each second image blockkWill predict the error ekSequentially arranging and forming a prediction error sequence E according to the sequence, and sequencing the prediction error sequence E according to the sequence of the elements in the binary tree from top to bottom to form a sequenced prediction error sequence EsortAnd embedding the secret information into the prediction error histogram by using a double binary tree traversal method.
Step S3 may be further broken down as follows:
s31: the image block dividing method in step S2 is adopted to divide the encrypted image into a plurality of 2 × 2 second image blocks.
S32: defining four encrypted pixels in the kth second image block as ct1(k)、ct2(k)、ct3(k)、ct4(k)；
Calculating the predicted value and the prediction error of the first encrypted pixel in the kth second image block by adopting the following formulas:
Figure BDA0002126465730000031
Figure BDA0002126465730000032
wherein, w2、w3、w4Is a weight coefficient and takes the value of [0, 1%]And w2+w3+w4＝1。
Calculating the prediction error e in each second image block in turnkWill predict the error ekSequentially arranging the prediction error sequences E-E (E)1，e2，...，eN) And N is the total number of the second image blocks.
S33: sequencing the prediction error sequence E according to the order of the elements in the binary tree from top to bottom to form a sequenced prediction error sequence Esort。
S34: embedding secret information into a prediction error histogram by using a double binary tree traversal method, comprising the following steps:
s341: determining a prediction error ekAt the location of the encrypted image embedding space,
(1) if the prediction error ekOn both sides of the encrypted image embedding space, move 2LThe unit is secret information embedded in the reserved space.
(2) If the prediction error ekEmbedding range-2 in encrypted image embedding spaceL，2L]The secret information is embedded in the prediction error histogram.
S342: the pixel is modified using the following equation:
Figure BDA0002126465730000033
wherein, ct'1(k) B is a bit of the secret information SM, which is the ciphertext image embedded with the secret information.
S343: and after the embedding of the secret information is finished, judging whether the prediction error sequence is completely traversed, if not, recording the position of the current pixel.
S35: and sending the ciphertext image comprising the embedded secret information and the edge information to an image receiver.
The edge information is represented by an 8-bit binary stream, including: the number of layers L of the binary tree, the position final (i, j) of the last embedded pixel and the length | SM |.
S4: and performing data extraction and image recovery on the ciphertext image containing the secret information according to the acquired information of the overflow map mapB for recording the position of the reduced pixel, the number L of the double binary tree layers, the position final (i, j) of the last embedded pixel and the length | SM | of the secret information.
The invention provides that the data extraction and the image recovery of the ciphertext image containing the secret information can comprise two types:
(1) and recovering the image and extracting the secret information in the ciphertext domain according to the data hiding key.
(2) And recovering the image and extracting the secret information in the plain text domain according to the data hiding key and the decryption key.
First, the image recovery and secret information extraction process in the ciphertext domain according to the data hiding key is as follows:
s41: the ciphertext image embedded with the secret information is divided into a plurality of 2 × 2 third image blocks by adopting the image blocking method in step S2.
S42: defining four pixels in the kth third image block as ct'1(k)、ct2(k)、ct3(k)、ct4(k) N is the total number of the third image blocks;
s43: calculating the first pixel ct 'in the kth third image block by adopting the following formula'1(k) Predicted value and prediction error of (2):
Figure BDA0002126465730000041
Figure BDA0002126465730000042
calculating prediction error e 'in each third image block in turn'kThe prediction error sequences E ' ═ E ' are sequentially arranged in the order of the sequences to constitute a prediction error sequence '1，e′2，...，e′N) A prediction error histogram is generated.
S44: the prediction error sequence E' is sorted in the order in which the secret information is embedded to form a sorted prediction error sequence Esort。
S45: according to formula b mod (e'kAnd 2) extracting the embedded secret information of each third image block, judging whether the process of extracting the embedded secret information advances to the final (i, j) position, and if so, indicating that the extraction of the last bit of the embedded secret information is finished.
S46: using the following formula, in accordance with EsortThe order of sorting, extract all ciphertext images:
Figure BDA0002126465730000043
wherein, ct1(k) And embedding the secret information into the first ciphertext pixel in the kth third image block after extraction, so as to obtain four ciphertext pixels of the kth third image block, and sequentially extracting the ciphertext image of each third image block until all the ciphertext images are extracted.
Second, the image restoration and secret information extraction process in the plain text domain according to the data hiding key and the decryption key is as follows:
s41': the ciphertext image embedded with the secret information is divided into a plurality of fourth image blocks of 2 × 2 by adopting the image blocking mode in step S2.
S42': and decrypting the ciphertext image embedded with the secret information according to the decryption key to obtain a decrypted image.
Decrypting the kth fourth image block using the following formula:
Figure BDA0002126465730000051
Figure BDA0002126465730000052
Figure BDA0002126465730000053
Figure BDA0002126465730000054
s43': calculating the first pixel ct 'in the kth fourth image block by adopting the following formula'1(k) Predicted value and prediction error of
Figure BDA0002126465730000055
Figure BDA0002126465730000056
Calculating prediction error e 'in each fourth image block in turn'kThe prediction error sequence E '═ E'1，e′2，...，e′N) A prediction error histogram is generated.
S44': the prediction error sequence E' is sorted in the order in which the secret information is embedded to form a sorted prediction error sequence Esort。
S45': according to formula b mod (e'kAnd 2) extracting the embedded secret information of each fourth image block and judging whether the embedded secret information is extracted or embeddedWhether the secret information process is advanced to final (i, j) position, if yes, it indicates that the last bit extraction of the embedded secret information is completed.
S46': the pixel embedding the secret information is recovered using the following formula:
Figure BDA0002126465730000057
s47': after the extraction of the embedded secret information and the recovery of the ciphertext image are finished, the image after the preprocessing of preventing the pixel overflow is recovered to the original image according to the position of the reduced pixel recorded on the overflow map mapB by adopting the following formula:
Figure BDA0002126465730000058
compared with the prior art, the technical scheme of the invention has the following remarkable beneficial effects:
(1) the image is encrypted by using the homomorphic encryption SHE, the SHE has the advantages of short and safe ciphertext in a public key cryptosystem, the ciphertext length is controlled to be 128 bits, the image security is ensured, meanwhile, the calculation complexity can be reduced, and the encryption efficiency is improved.
(2) The data is embedded by using a prediction error histogram expansion method, and the secret information is preferentially embedded into the pixels meeting the conditions by using a prediction error sequencing method, so that unnecessary pixel modification is avoided, the image quality is improved, and the peak signal-to-noise ratio is higher under the same embedding capacity.
(3) The use of a dual binary tree to indicate the movement of the peak points during the embedding process solves the problem of communicating multiple peak points to the receiver.
(4) Data can be extracted in a ciphertext domain and a plaintext domain, the data extraction is more flexible, and the method is more practical in an actual scene.
It should be understood that all combinations of the foregoing concepts and additional concepts described in greater detail below can be considered as part of the inventive subject matter of this disclosure unless such concepts are mutually inconsistent. In addition, all combinations of claimed subject matter are considered a part of the presently disclosed subject matter.
The foregoing and other aspects, embodiments and features of the present teachings can be more fully understood from the following description taken in conjunction with the accompanying drawings. Additional aspects of the present invention, such as features and/or advantages of exemplary embodiments, will be apparent from the description which follows, or may be learned by practice of specific embodiments in accordance with the teachings of the present invention.
Drawings
The drawings are not intended to be drawn to scale. In the drawings, each identical or nearly identical component that is illustrated in various figures may be represented by a like numeral. For purposes of clarity, not every component may be labeled in every drawing. Embodiments of various aspects of the present invention will now be described, by way of example, with reference to the accompanying drawings, in which:
FIG. 1 is a diagram of steps of an encryption domain reversible information hiding method based on binary tree expansion and public key encryption.
FIG. 2 is a flowchart of an encryption domain reversible information hiding method based on dual binary tree expansion and public key encryption.
FIG. 3 is a schematic diagram of a binary tree of the encryption domain reversible information hiding method based on binary tree expansion and public key encryption.
Detailed Description
In order to better understand the technical content of the present invention, specific embodiments are described below with reference to the accompanying drawings.
In this disclosure, aspects of the present invention are described with reference to the accompanying drawings, in which a number of illustrative embodiments are shown. Embodiments of the present disclosure are not necessarily defined to include all aspects of the invention. It should be appreciated that the various concepts and embodiments described above, as well as those described in greater detail below, may be implemented in any of numerous ways, as the disclosed concepts and embodiments are not limited to any one implementation. In addition, some aspects of the present disclosure may be used alone, or in any suitable combination with other aspects of the present disclosure.
With reference to fig. 1 and fig. 2, the present invention provides an encryption domain reversible information hiding method based on dual binary tree expansion and public key encryption, where the method includes:
s1: preprocessing the original image with the size of m multiplied by n to prevent pixel overflow, and reducing the pixels on two sides of the pixel histogram of the original image by 2 according to the double binary tree layer number LLThe unit, and the position of the reduced pixel is recorded to obtain a binary map position overflow map mapB, where 0 and 1 represent the unmoved and shifted elements, respectively. The following formula is used for preprocessing to prevent pixel overflow:
Figure BDA0002126465730000071
wherein, Is(I, j) represents the image of the original pixel I (I, j) after the pixel overflow prevention preprocessing, I, j are the abscissa and ordinate of the original image, I belongs to [1, m ]]，j∈[1，n]。
Referring to fig. 3, L is the number of levels of a binary tree, and the binary tree is formed by using the horizontal axis in the pixel histogram of the original image as a node.
The value of the boundary value pixel of the original image is adjusted to a reliable range through pixel overflow prevention preprocessing, and the pixel overflow problem after secret information is embedded is avoided.
S2: dividing an original image into a plurality of 2 multiplied by 2 first image blocks, and encrypting the original image by adopting a homomorphic encryption public key encryption system.
Encrypting each first image block using the following formula:
Figure BDA0002126465730000072
Figure BDA0002126465730000073
Figure BDA0002126465730000074
Figure BDA0002126465730000075
wherein x is1、x2、x3And x4Are four pixels, ct, in the same first image block of the original image1、ct2、ct3And ct4Are each x1、x2、x3And x4Ciphertext of a0U, t and g are parameters generated in the encryption algorithm.
In order to ensure that the four pixels in the same first image block maintain spatial correlation, encrypting the four pixels in the same first image block uses the same parameters u, g, and t for encryption.
To ensure the security of the data hiding process, different first image blocks should be encrypted using different parameters u, g, t and the public key pk.
S3: dividing the encrypted image into a plurality of 2 x 2 second image blocks, and calculating the prediction error e in each second image blockkWill predict the error ekSequentially arranging and forming a prediction error sequence E according to the sequence, and sequencing the prediction error sequence E according to the sequence of the elements in the binary tree from top to bottom to form a sequenced prediction error sequence EsortAnd embedding the secret information into the prediction error histogram by using a double binary tree traversal method.
According to the image blocking mode in the original image encryption process, the encrypted image is divided into a plurality of 2 × 2 second image blocks, and in this embodiment, it is assumed that there are N second image blocks in total.
Defining four encrypted pixels in the kth second image block as ct obtained from the ciphertext image in step S21(k)、ct2(k)、ct3(k)、ct4(k) And calculating the predicted value and the prediction error of the first encrypted pixel in the kth second image block by adopting the following formulas:
Figure BDA0002126465730000081
Figure BDA0002126465730000082
wherein, w2、w3、w4Is a weight coefficient and takes the value of [0, 1%]And w2+w3+w4In this embodiment, w is set to 12＝w3＝0.4、w4＝0.2。
Figure BDA0002126465730000084
For the target pixel ct of the ciphertext image1(k) Predicted value of ekIs a prediction error value. Due to the homomorphic nature of homomorphic encryption algorithms, the prediction error of four pixels encrypted with the same key remains the same as the value in the plain text domain.
Calculating the prediction error e in each second image block in turnkWill predict the error ekSequentially arranging the prediction error sequences E-E (E)1，e2，...，eN) The secret information is to be embedded in a prediction error histogram formed by the sequence of prediction errors.
In order to minimize the image pixel modification quantity after embedding the secret information, the prediction error sequence E is sequenced from top to bottom according to the elements in the binary tree layer, and the sequenced prediction error sequence E is formedsort. This ensures that the secret information is preferentially embedded in pixels with small modifiers. Under the same secret information embedding amount, the sequenced embedding can modify the original image pixels less, and the image recovery quality is improved.
Next, a dual binary tree traversal method is applied to the prediction error extended information hiding scheme. As shown in fig. 3, the corresponding relationship between the binary tree and the prediction error histogram is: the left binary tree corresponds to a negative half shaft of the histogram, and the right binary tree corresponds to a right half shaft of the histogram. Compared with a common single binary tree, the method has the advantage that the secret information can be embedded in both the positive half axis and the negative half axis of the histogram.
Determining a prediction error ekAt the location of the encrypted image embedding space,
(1) if the prediction error ekOn both sides of the encrypted image embedding space, move 2LThe unit is secret information embedded in the reserved space.
(2) If the prediction error ekEmbedding range-2 in encrypted image embedding spaceL，2L]The secret information is embedded in the prediction error histogram.
The pixel is modified using the following equation:
Figure BDA0002126465730000083
wherein, ct'1(k) B is a bit of the secret information SM, which is the ciphertext image embedded with the secret information.
And after the embedding of the secret information is finished, judging whether the prediction error sequence is completely traversed, if not, recording the position of the current pixel.
Recording the edge information after embedding the secret information, comprising: the number of binary tree levels L, the position final (i, j) of the last embedded pixel, the length of the secret information | SM |, which are all represented by a binary stream of 8 bits, requiring a total of 32 bits. And sending the ciphertext image containing the embedded secret information and the edge information to an image receiver, and entering an image recovery and secret information extraction link.
S4: according to the obtained information of the overflow map mapB for recording the position of the reduced pixel, the number L of the double binary tree layers, the position final (i, j) of the last embedded pixel and the length | SM | of the secret information, data extraction and image recovery are carried out on the ciphertext image containing the secret information, and the method can be divided into the following two types:
(1) and recovering the image and extracting the secret information in the ciphertext domain according to the data hiding key.
(2) And recovering the image and extracting the secret information in the plain text domain according to the data hiding key and the decryption key.
Firstly, according to the image recovery and secret information extraction in the ciphertext domain performed by the data hiding key, a ciphertext image and extracted secret information are obtained, and the method specifically comprises the following steps:
s41: the image blocking method when the secret information is embedded is adopted to divide the ciphertext image embedded with the secret information into a plurality of 2 × 2 third image blocks, and in the embodiment, it is assumed that N third image blocks are provided in total.
S42: defining four pixels in the kth third image block as ct'1(k)、ct2(k)、ct3(k)、ct4(k)，1＜＝k＜＝N。
S43: calculating the first pixel ct 'in the kth third image block by adopting the following formula'1(k) Predicted value and prediction error of
Figure BDA0002126465730000091
Figure BDA0002126465730000092
Calculating prediction error e 'in each third image block in turn'kThe prediction error sequences E ' ═ E ' are sequentially arranged in the order of the sequences to constitute a prediction error sequence '1，e′2，...，e′N) A prediction error histogram is generated.
S44: since the prediction errors are ordered in the process of embedding the secret information, in order to ensure the correctness of image recovery and secret information extraction, the prediction errors need to be ordered according to the sequence when embedding so as to form an ordered prediction error sequence Esort。
S45: the prediction error range of the embedded secret information is extended to-2L+1，2L+1) Mod (e 'according to the formula b'kAnd 2) extracting the embedded secret information of each third image block, and judging whether the process of extracting the embedded secret information advances to the last final (i, j) of the secret information embedded pixel) And if so, indicating that the last bit extraction of the embedded secret information is finished.
S46: then, the following formula is used to follow EsortThe order of sorting, extract all ciphertext images:
Figure BDA0002126465730000093
wherein, ct1(k) And embedding the secret information into the first ciphertext pixel in the kth third image block after extraction, so as to obtain four ciphertext pixels of the kth third image block, and sequentially extracting the ciphertext image of each third image block until all the ciphertext images are extracted.
Secondly, image restoration and secret information extraction in a plaintext domain are carried out according to the data hiding key and the decryption key to obtain a plaintext image and extracted secret information, and the specific steps are as follows:
s41': the image blocking method when the secret information is embedded is adopted to divide the ciphertext image embedded with the secret information into a plurality of 2 × 2 fourth image blocks, and in this embodiment, it is assumed that N fourth image blocks are total.
S42': and decrypting the ciphertext image embedded with the secret information according to the decryption key to obtain a decrypted image.
Decrypting the kth fourth image block using the following formula:
Figure BDA0002126465730000101
Figure BDA0002126465730000102
Figure BDA0002126465730000103
Figure BDA0002126465730000104
s43': calculating the first pixel ct 'in the kth fourth image block by adopting the following formula'1(k) Predicted value and prediction error of (2):
Figure BDA0002126465730000105
Figure BDA0002126465730000106
calculating prediction error e 'in each fourth image block in turn'kThe prediction error sequence E '═ E'1，e′2，...，e′N) A prediction error histogram is generated.
S44': since the prediction errors are ordered in the process of embedding the secret information, in order to ensure the correctness of image recovery and secret information extraction, the prediction error sequence E' needs to be ordered according to the order of embedding and the order of embedding the secret information so as to form an ordered prediction error sequence Esort。
S45': the prediction error range of the embedded secret information is extended to-2L+1，2L+1) Mod (e 'according to the formula b'kAnd 2) extracting the embedded secret information of each fourth image block, and judging whether the process of extracting the embedded secret information advances to the last final (i, j) position of the secret information embedded pixel, if so, indicating that the extraction of the last bit of the embedded secret information is finished.
S46': the pixel embedding the secret information is recovered using the following formula:
Figure BDA0002126465730000107
s47': after the extraction of the embedded secret information and the recovery of the ciphertext image are finished, the image after the pixel overflow prevention preprocessing is recovered to the original image according to an overflow map mapB for recording the reduced pixel position by adopting the following formula:
Figure BDA0002126465730000108
and performing the steps on each fourth image block to realize image recovery and information extraction in a plaintext domain, and obtaining a plaintext image and extracting secret information.
Although the present invention has been described with reference to the preferred embodiments, it is not intended to be limited thereto. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the invention. Therefore, the protection scope of the present invention should be determined by the appended claims.

Claims (6)

1. An encryption domain reversible information hiding method based on double binary tree expansion and public key encryption is characterized by comprising the following steps:
s1: carrying out pixel overflow prevention preprocessing on an original image with the size of m multiplied by n by adopting the following formula, and reducing the pixels on two sides of a pixel histogram of the original image by 2 according to the double binary tree layer number LLAnd recording the positions of the reduced pixels to obtain a binary mapping position overflow map mapB:
Figure FDA0003103836040000011
wherein, Is(I, j) represents the image pixel corresponding to the original pixel I (I, j) after the overflow processing, L is the layer number of the binary tree, I, j are the abscissa and ordinate of the original image, I belongs to [1, m ]]，j∈[1，n]；
The double binary tree is formed by taking a horizontal axis in a pixel histogram of an original image as a node;
s2: dividing an original image into a plurality of 2 multiplied by 2 first image blocks, and encrypting the original image by adopting a homomorphic encryption public key encryption system;
encrypting each first image block using the following formula:
Figure FDA0003103836040000012
Figure FDA0003103836040000013
Figure FDA0003103836040000014
Figure FDA0003103836040000015
wherein x is1、x2、x3And x4Are four pixels, ct, in the same first image block of the original image1、ct2、ct3And ct4Are each x1、x2、x3And x4U, t, f and g are parameters generated in the encryption algorithm; public key pk ═ a0，a1)；
S3: dividing the encrypted image into a plurality of 2 x 2 second image blocks, and calculating the prediction error e in each second image blockkDefining four encrypted pixels in the kth second image block as
Figure FDA0003103836040000016
Calculating the predicted value and the prediction error of the first encrypted pixel in the kth second image block by adopting the following formulas:
Figure FDA0003103836040000017
Figure FDA0003103836040000018
wherein, w2、w3、w4Is a weight coefficient and takes the value of [0, 1%]And w2+w3+w4＝1；
Figure FDA0003103836040000021
For target pixel of ciphertext image
Figure FDA0003103836040000022
The predicted value of (2); n is the total number of the second image blocks; will predict the error ekSequentially arranging and forming a prediction error sequence E according to the sequence, and sequencing the prediction error sequence E according to the sequence of the elements in the binary tree from top to bottom to form a sequenced prediction error sequence EsortEmbedding the secret information into a prediction error histogram by using a double binary tree traversal method;
s4: and performing data extraction and image recovery on the ciphertext image containing the secret information according to the acquired information of the overflow map mapB for recording the position of the reduced pixel, the number L of the double binary tree layers, the position final (i, j) of the last embedded pixel and the length | SM | of the secret information.
2. The encryption domain reversible information hiding method based on binary tree expansion and public key encryption as claimed in claim 1, wherein in step S2, the principle of using homomorphic encryption public key encryption system to encrypt original image includes:
(1) four pixels in the same first image block are encrypted by using the same parameters u, g and t;
(2) different first image blocks are encrypted using different parameters u, g, t and the public key pk.
3. The encryption domain reversible information hiding method based on the binary tree expansion and the public key encryption as claimed in claim 1, wherein in step S3,dividing the encrypted image into a plurality of 2 x 2 second image blocks, and calculating the prediction error e in each second image blockkWill predict the error ekSequentially arranging and forming a prediction error sequence E according to the sequence, and sequencing the prediction error sequence E according to the sequence of the elements in the binary tree from top to bottom to form a sequenced prediction error sequence EsortThe process of embedding secret information into the prediction error histogram using the dual binary tree traversal method can be decomposed into the following steps:
s31: dividing the encrypted image into a plurality of 2 × 2 second image blocks by adopting the image blocking mode in the step S2;
s32: defining four encrypted pixels in the kth second image block as ct1(k)、ct2(k)、ct3(k)、ct4(k)；
Calculating the predicted value and the prediction error of the first encrypted pixel in the kth second image block by adopting the following formulas:
Figure FDA0003103836040000023
Figure FDA0003103836040000024
wherein, w2、w3、w4Is a weight coefficient and takes the value of [0, 1%]And w2+w3+w4＝1；
Calculating the prediction error e in each second image block in turnkWill predict the error ekSequentially arranging the prediction error sequences E-E (E)1，e2，...，eN) N is the total number of the second image blocks;
s33: sequencing the prediction error sequence E according to the order of the elements in the binary tree from top to bottom to form a sequenced prediction error sequence Esort；
S34: embedding secret information into a prediction error histogram by using a double binary tree traversal method, comprising the following steps:
s341: determining a prediction error ekAt the location of the encrypted image embedding space,
(1) if the prediction error ekOn both sides of the encrypted image embedding space, move 2LThe unit is secret information embedded reserved space;
(2) if the prediction error ekEmbedding range-2 in encrypted image embedding spaceL，2L]Embedding the secret information into the prediction error histogram;
s342: the pixel is modified using the following equation:
Figure FDA0003103836040000031
wherein, ct'1(k) B is a bit of the secret information SM, namely the ciphertext image embedded with the secret information; an encrypted pixel ct1Comprises (c)10，c11) The two parts are provided with a plurality of grooves,
Figure FDA0003103836040000032
Figure FDA0003103836040000033
s343: after embedding of the secret information is completed, judging whether the prediction error sequence is completely traversed, if not, recording the position of the current pixel;
s35: sending the ciphertext image comprising the embedded secret information and the edge information to an image receiver;
the edge information is represented by an 8-bit binary stream, including: the number of layers L of the binary tree, the position final (i, j) of the last embedded pixel and the length | SM |.
4. The encryption domain reversible information hiding method based on dual binary tree expansion and public key encryption as claimed in claim 1, wherein in step S4, said performing data extraction and image recovery on the ciphertext image containing the secret information according to the obtained information of the overflow map mapB recording the reduced pixel position, the dual binary tree layer number L, the position final (i, j) of the last embedded pixel, and the secret information length | SM |:
(1) image recovery and secret information extraction in a ciphertext domain are carried out according to the data hiding key;
(2) and recovering the image and extracting the secret information in the plain text domain according to the data hiding key and the decryption key.
5. The encryption domain reversible information hiding method based on double binary tree expansion and public key encryption as claimed in claim 4, wherein said image recovery and secret information extraction in ciphertext domain according to data hiding key comprises the following steps:
s41: dividing the ciphertext image embedded with the secret information into a plurality of 2 x 2 third image blocks by adopting an image blocking mode in the step S2;
s42: defining four pixels in the kth third image block as ct'1(k)、ct2(k)、ct3(k)、ct4(k) N is the total number of the third image blocks;
s43: calculating the first pixel ct 'in the kth third image block by adopting the following formula'1(k) Predicted value and prediction error of (2):
Figure FDA0003103836040000041
Figure FDA0003103836040000042
calculating prediction error e 'in each third image block in turn'kThe prediction error sequences E ' ═ E ' are sequentially arranged in the order of the sequences to constitute a prediction error sequence '1，e′2，...，e′N) Generating a prediction error histogram;
s44: when the prediction error sequence E' is embedded in secret informationSequentially ordering to form an ordered prediction error sequence Esort；
S45: according to formula b mod (e'k2) extracting the embedded secret information of each third image block, judging whether the process of extracting the embedded secret information advances to the final (i, j) position, if so, indicating that the extraction of the last bit of the embedded secret information is finished;
s46: using the following formula, in accordance with EsortThe order of sorting, extract all ciphertext images:
Figure FDA0003103836040000043
wherein, ct1(k) The first ciphertext pixel and an encrypted pixel ct in the kth third image block after the secret information is embedded and extracted1Comprises (c)10，c11) The two parts are provided with a plurality of grooves,
Figure FDA0003103836040000044
Figure FDA0003103836040000051
and obtaining four ciphertext pixels of the kth third image block, and sequentially extracting the ciphertext image of each third image block until all ciphertext image extractions are completed.
6. The encryption domain reversible information hiding method based on double binary tree expansion and public key encryption as claimed in claim 4, wherein said image recovery and secret information extraction in plaintext domain according to data hiding key and decryption key comprises the following steps:
s41': dividing the ciphertext image embedded with the secret information into a plurality of fourth image blocks of 2 multiplied by 2 by adopting an image blocking mode in the step S2;
s42': decrypting the ciphertext image embedded with the secret information according to the decryption key to obtain a decrypted image;
decrypting the kth fourth image block using the following formula:
Figure FDA0003103836040000052
Figure FDA0003103836040000053
Figure FDA0003103836040000054
Figure FDA0003103836040000055
wherein the content of the first and second substances,
Figure FDA0003103836040000056
in the formula, x'1Is a decrypted plaintext pixel; δ is 1, a fixed parameter in SHE; c'1i(k) The ith ciphertext of the k image blocks; s is a decryption key; rqThe remainder of the rational number set in the real number set;
s43': calculating the first pixel ct 'in the kth fourth image block by adopting the following formula'1(k) Predicted value and prediction error of (2):
Figure FDA0003103836040000057
Figure FDA0003103836040000058
calculating prediction error e 'in each fourth image block in turn'kThe prediction error sequence E '═ E'1，e′2，...，e′N) Generating a prediction error histogram;
s44': the prediction error sequence E' is sorted in the order in which the secret information is embedded to form a sorted prediction error sequence Esort；
S45': according to formula b mod (e'k2) extracting the embedded secret information of each fourth image block, judging whether the process of extracting the embedded secret information advances to the final (i, j) position, if so, indicating that the extraction of the last bit of the embedded secret information is finished;
s46': the pixel embedding the secret information is recovered using the following formula:
Figure FDA0003103836040000061
s47': after the extraction of the embedded secret information and the recovery of the ciphertext image are finished, the image after the preprocessing of preventing the pixel overflow is recovered to the original image according to the position of the reduced pixel recorded on the overflow map mapB by adopting the following formula:
Figure FDA0003103836040000062
CN201910624039.3A 2019-07-11 2019-07-11 Encryption domain reversible information hiding method based on double binary tree expansion and public key encryption Active CN110337000B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201910624039.3A CN110337000B (en) 2019-07-11 2019-07-11 Encryption domain reversible information hiding method based on double binary tree expansion and public key encryption

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201910624039.3A CN110337000B (en) 2019-07-11 2019-07-11 Encryption domain reversible information hiding method based on double binary tree expansion and public key encryption

Publications (2)

Publication Number Publication Date
CN110337000A CN110337000A (en) 2019-10-15
CN110337000B true CN110337000B (en) 2021-07-27

Family

ID=68146199

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201910624039.3A Active CN110337000B (en) 2019-07-11 2019-07-11 Encryption domain reversible information hiding method based on double binary tree expansion and public key encryption

Country Status (1)

Country Link
CN (1) CN110337000B (en)

Families Citing this family (9)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN111932430B (en) * 2020-01-15 2023-05-26 南京信息工程大学 Image encryption method based on FPGA
CN111598766B (en) * 2020-05-09 2023-05-02 绍兴聚量数据技术有限公司 Encryption domain three-dimensional model reversible information hiding method based on prediction error expansion
CN111614640B (en) * 2020-05-09 2023-06-27 绍兴聚量数据技术有限公司 Reversible information hiding method for homomorphic encryption domain three-dimensional model with high capacity
CN112132732B (en) * 2020-09-10 2023-06-02 宁波大学科学技术学院 Pixel prediction method, reversible information hiding and extracting method, terminal and storage medium for stereoscopic image
CN112311954B (en) * 2020-10-29 2022-05-20 杭州电子科技大学 Ciphertext domain reversible information hiding method based on complementary code mark and bitmap embedding
CN112926087B (en) * 2021-03-09 2023-05-05 南京信息工程大学 Secret sharing method with verification function and high embedding capacity based on two-dimensional code
CN113079274B (en) * 2021-04-06 2023-03-07 绍兴图信物联科技有限公司 Encryption image reversible information hiding method of adaptive parameter binary tree mark
CN115134474A (en) * 2022-06-30 2022-09-30 西安理工大学 Pixel prediction-based parameter binary tree reversible data hiding method
CN115834789B (en) * 2022-11-24 2024-02-23 南京信息工程大学 Medical image encryption and recovery method based on encryption domain

Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106941402A (en) * 2017-04-01 2017-07-11 中国人民武装警察部队工程大学 A kind of reversible hidden method of homomorphism ciphertext domain
CN107395336A (en) * 2017-07-03 2017-11-24 安徽大学 Ciphertext domain reversible data embedding method based on pailliar public key encryps

Family Cites Families (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US9639912B2 (en) * 2014-12-30 2017-05-02 University Of Macau Method for reversible image data hiding

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106941402A (en) * 2017-04-01 2017-07-11 中国人民武装警察部队工程大学 A kind of reversible hidden method of homomorphism ciphertext domain
CN107395336A (en) * 2017-07-03 2017-11-24 安徽大学 Ciphertext domain reversible data embedding method based on pailliar public key encryps

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
《一种同态密文域可逆隐藏方案》;丁义涛等;《山东大学学报（理学版）》;20170731;全文 *
《同态公钥加密系统的图像可逆信息隐藏算法》;项世军等;《软件学报》;20160630;全文 *

Also Published As

Publication number Publication date
CN110337000A (en) 2019-10-15

Similar Documents

Publication Publication Date Title
CN110337000B (en) Encryption domain reversible information hiding method based on double binary tree expansion and public key encryption
Yi et al. Separable and reversible data hiding in encrypted images using parametric binary tree labeling
Puyang et al. Reversible data hiding in encrypted images with two-MSB prediction
Chai et al. TPE-GAN: Thumbnail preserving encryption based on GAN with key
CN110753226B (en) High-capacity ciphertext domain image reversible data hiding method
CN109803142B (en) Encrypted domain image reversible data hiding method based on neighborhood prediction
CN109617682B (en) Ciphertext domain reversible information hiding method based on histogram left-right shifting
CN109800585B (en) Image interpolation space completely reversible separable ciphertext domain information hiding algorithm
CN113114869B (en) Ciphertext domain high-capacity image reversible data hiding method based on MSB prediction
CN111898138B (en) Separable ciphertext domain reversible data hiding method
Anushiadevi et al. Uncover the cover to recover the hidden secret-a separable reversible data hiding framework
Ye et al. Noise-free thumbnail-preserving image encryption based on MSB prediction
CN106941402B (en) Homomorphic ciphertext domain reversible hiding method
Panchikkil et al. A pseudo-random pixel mapping with weighted mesh graph approach for reversible data hiding in encrypted image
Zhang et al. Vector-based efficient data hiding in encrypted images via multi-MSB replacement
Wang et al. TPE-ISE: approximate thumbnail preserving encryption based on multilevel DWT information self-embedding
Gao et al. High-performance reversible data hiding in encrypted images with adaptive Huffman code
CN113206926B (en) Method for balancing privacy and usability of image based on three-pixel-point encryption
Abhinav et al. An improved reversible data hiding on encrypted images by selective pixel flipping technique
Teotia et al. Enhancing audio and video steganography technique using hybrid algorithm
Kar et al. Chaos-based video steganography
Li et al. A Novel Scheme for the Preview of the Image Encryption Based on Chaotic Ikeda Map.
Najm et al. Steganography Method of the Bigger Size in WebP Image Using M2PAM Algorithm for Social Applications
Cao et al. A New Reversible Date‐Hiding Algorithm for Encrypted Images
Subramanian et al. Image Steganography Using HBV And Padded RSA

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant