A reversible information hiding method and system for JPEG images based on Paillier homomorphic encryption

Abstract

The present invention belongs to the field of image encryption and decryption, and provides a JPEG image reversible information hiding method and system based on Paillier homomorphic encryption. If the method is applied to the sender, it includes: reading the quantized DCT coefficients in the original JPEG image, the DCT coefficients include DC coefficients and AC coefficients; the DC coefficients are chaotically encrypted, the AC coefficients are encrypted using Paillier encryption and the multiplication characteristics of Paillier homomorphic encryption to embed secret information, construct DCT coefficient ciphertext blocks, and obtain a ciphertext image containing secret information; and the ciphertext image containing secret information is sent to the receiver, so that the receiver can perform separable extraction of the ciphertext image containing secret information to obtain the secret information. The present invention effectively improves the data embedding capacity and image encryption quality.

Description

Technical Field

[0001] The present invention belongs to the field of image encryption and decryption, and in particular relates to a JPEG image reversible information hiding method and system based on Paillier homomorphic encryption. Background Art

[0002] The statements in this section merely provide background information related to the present invention and do not necessarily constitute prior art.

[0003] Reversible Data Hiding (RDH) is a method of hiding hidden information in a carrier, such as an image, audio, or video. RDH focuses on being able to completely restore the embedded message after image processing. The embedded carrier image and the original image must be exactly the same, so that the image and hidden information can be reversible. At present, reversible data hiding based on JPEG images can be divided into three categories: 1. RDH based on quantization table modification. 2. RDH based on Huffman code modification. 3. RDH based on quantized DCT coefficients.

[0004] For traditional encryption algorithms, such as stream ciphers and DES, these traditional encryption algorithms are directly used in encryption. Although the security of plaintext is determined, the information cannot be modified in the ciphertext, and the ciphertext needs to be decrypted before operation. For homomorphic encryption, the information can be embedded under the premise of ensuring the security of plaintext. In the cloud, the properties of homomorphic encryption can be used to perform a series of algebraic operations, and the operation results in the ciphertext domain are the same as the corresponding operation results in the plaintext domain. Based on this good property, users can hand over the homomorphically encrypted data to the cloud platform for labeling and other actions to better protect their privacy. In the past, homomorphic encryption has made significant progress. This algorithm can be used to process data directly in the encrypted domain. For modern communication systems, decryption is not required when processing the ciphertext domain, so the privacy and integrity of users can be guaranteed. However, few algorithms for reversible information hiding in the encrypted domain have been proposed in the transform domain of JPEG images.

[0005] With the rapid development of convenient cloud storage, data privacy infringement issues are becoming increasingly prominent. Reversible data hiding (RDH) can be used to embed additional data in encrypted data stored in the cloud. Most encrypted RDH algorithms are performed on uncompressed images and have not been widely used in popular JPEG images. Summary of the invention

[0006] In order to solve the technical problems existing in the above-mentioned background technology, the present invention provides a reversible information hiding method and system for JPEG images based on Paillier homomorphic encryption; it first extracts the distribution characteristics of DCT coefficients, and then encrypts the DCT coefficients using chaotic encryption; then calculates the number of AC coefficient "0" in each DCT block to generate an embedding sequence in descending order; and embeds the AC coefficients using the multiplication characteristics of Paillier encryption and homomorphic encryption; the present invention effectively improves the data embedding capacity and image encryption quality.

[0007] In order to achieve the above object, the present invention adopts the following technical solution:

[0008] The first aspect of the present invention provides a reversible information hiding method for JPEG images based on Paillier homomorphic encryption.

[0009] A reversible information hiding method for JPEG images based on Paillier homomorphic encryption, applied to the sender, includes:

[0010] Read the quantized DCT coefficients in the JPEG original image, the DCT coefficients include DC coefficients and AC coefficients; the DC coefficients are chaotically encrypted, the AC coefficients are encrypted using Paillier encryption and the multiplication characteristics of Paillier homomorphic encryption are used to embed secret information, a DCT coefficient ciphertext block is constructed, and a ciphertext image containing secret information is obtained;

[0011] The ciphertext image containing the secret information is sent to a receiver, so that the receiver can detachably extract the ciphertext image containing the secret information to obtain the secret information.

[0012] The second aspect of the present invention provides a JPEG image reversible information hiding system based on Paillier homomorphic encryption.

[0013] A JPEG image reversible information hiding system based on Paillier homomorphic encryption, applied to the sender, includes:

[0014] The encryption module is configured to: read the quantized DCT coefficients in the JPEG original image, wherein the DCT coefficients include DC coefficients and AC coefficients; perform chaotic encryption on the DC coefficients, and use Paillier encryption and the multiplication characteristics of Paillier homomorphic encryption to embed secret information on the AC coefficients, construct a DCT coefficient ciphertext block, and obtain a ciphertext image containing secret information;

[0015] The decryption module is configured to: send the ciphertext image containing the secret information to a receiver, so that the receiver can detachably extract the ciphertext image containing the secret information to obtain the secret information.

[0016] The third aspect of the present invention provides a reversible information hiding method for JPEG images based on Paillier homomorphic encryption.

[0017] A reversible information hiding method for JPEG images based on Paillier homomorphic encryption, applied to the receiving and sending parties, includes:

[0018] Receiving a ciphertext image containing secret information, and performing separable extraction on the ciphertext image containing the secret information to obtain the secret information;

[0019] The ciphertext image containing secret information is obtained by embedding the secret information into the AC coefficient. The AC coefficient uses the multiplication characteristics of Paillier encryption and Paillier homomorphic encryption to embed the secret information, and the DC coefficient is chaotically encrypted to obtain a DCT coefficient ciphertext block. The AC coefficient and DC coefficient both belong to the DCT coefficient, and the DCT coefficient is obtained by reading the JPEG original image and quantizing it.

[0020] A fourth aspect of the present invention provides a JPEG image reversible information hiding system based on Paillier homomorphic encryption.

[0021] A reversible information hiding system for JPEG images based on Paillier homomorphic encryption, comprising:

[0022] A decryption module is configured to: receive a ciphertext image containing secret information, and perform separable extraction on the ciphertext image containing secret information to obtain the secret information;

[0023] The encryption module is configured as follows: the ciphertext image containing secret information is obtained by embedding the secret information into the AC coefficient, the AC coefficient uses the multiplication characteristics of Paillier encryption and Paillier homomorphic encryption to embed the secret information, and the DC coefficient is chaotically encrypted to obtain a DCT coefficient ciphertext block, the AC coefficient and the DC coefficient both belong to the DCT coefficient, and the DCT coefficient is obtained by reading the JPEG original image and quantizing it.

[0024] A fifth aspect of the present invention provides a computer-readable storage medium.

[0025] A computer-readable storage medium stores a computer program, which, when executed by a processor, implements the steps in the JPEG image reversible information hiding method based on Paillier homomorphic encryption as described in the first aspect or the third aspect.

[0026] A sixth aspect of the present invention provides a computer device.

[0027] A computer device comprises a memory, a processor and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, the steps in the reversible information hiding method for JPEG images based on Paillier homomorphic encryption as described in the first aspect or the third aspect are implemented.

[0028] Compared with the prior art, the present invention has the following beneficial effects:

[0029] The present invention first constructs a multi-coefficient encryption model by reading the DCT coefficients in the JPEG image, and uses the highly secure chaotic encryption to encrypt the DC coefficients. The AC coefficients are divided into two categories, one is the AC coefficients to be embedded with information, and the coefficients of this part are embedded by the Paillier homomorphic encryption at the same time, and the other is the DC coefficients for the chaotic encryption operation. The quantized DCT coefficients have a certain size range, and the encrypted data is overflow processed. When encrypting, the threshold T and the parameter r are used to control the encrypted value size, so that separable extraction data can be realized. The algorithm has good embedding capacity while being able to better ensure the security of the plaintext. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] The accompanying drawings in the specification, which constitute a part of the present invention, are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0031] Figure 1 It is a flowchart of a JPEG image reversible information hiding method based on Paillier homomorphic encryption shown in the first embodiment of the present invention;

[0032] Figure 2 Schematic diagram of the start and end bits of homomorphic encryption of AC coefficients shown in the first embodiment of the present invention;

[0033] Figure 3 Schematic diagram of the encryption of plain text by different values ​​of r according to the first embodiment of the present invention;

[0034] Figure 4 is a schematic diagram of a multi-coefficient encryption model result shown in the first embodiment of the present invention;

[0035] Figure 5 is a decryption and extraction flow chart shown in the first embodiment of the present invention;

[0036] FIG6( a ) is an original image shown in the first embodiment of the present invention;

[0037] FIG6( b ) is a ciphertext image embedded with secret information shown in the first embodiment of the present invention;

[0038] FIG6( c ) is a decrypted image shown in the first embodiment of the present invention;

[0039] FIG. 7( a ) is a plaintext image to be operated on according to the first embodiment of the present invention;

[0040] FIG. 7( b ) is an image after the DC coefficient in the plaintext image is extracted according to the first embodiment of the present invention;

[0041] FIG. 7( c ) is a diagram showing the DC coefficient after chaotic encryption according to the first embodiment of the present invention;

[0042] FIG8( a ) is an Airplane diagram shown in Embodiment 1 of the present invention;

[0043] FIG8( b ) is a Baboon diagram shown in Embodiment 1 of the present invention;

[0044] FIG8( c ) is a Lena diagram shown in Embodiment 1 of the present invention;

[0045] FIG8( d ) is a Peppers diagram shown in the first embodiment of the present invention;

[0046] FIG8(e) is an encrypted image of the airplane image after being processed by the algorithm shown in the first embodiment of the present invention;

[0047] FIG8( f ) is an encrypted image of the Baboon graph after being processed by the algorithm shown in the first embodiment of the present invention;

[0048] FIG8(g) is an encrypted image of the Lena image after being processed by the algorithm shown in the first embodiment of the present invention;

[0049] FIG8(h) is an encrypted image of the Peppers graph after being processed by the algorithm shown in the first embodiment of the present invention;

[0050] FIG9( a ) is an embedding capacity of 337 random images in the BOSS image library according to the first embodiment of the present invention, where the quality factor is QualityFactor (QF)=50;

[0051] FIG9( b ) is an embedding capacity of 337 random images in the BOSS image library according to the first embodiment of the present invention, where the quality factor is QualityFactor (QF)=60;

[0052] FIG9( c ) is an embedding capacity of 337 random images in the BOSS image library shown in the first embodiment of the present invention, and the quality factor is QualityFactor (QF)=70;

[0053] FIG9( d ) is an embedding capacity of 337 random images in the BOSS image library shown in the first embodiment of the present invention, and the quality factor is QualityFactor (QF)=80;

[0054] FIG. 10( a ) is a diagram showing the embedding capacity effect of a Baboon image under different quality factors according to the first embodiment of the present invention;

[0055] FIG10( b ) is a diagram showing the embedding capacity effect of the Boat image under different quality factors according to the first embodiment of the present invention;

[0056] FIG10( c ) is a diagram showing the embedding capacity effect of the Couple image under different quality factors according to the first embodiment of the present invention;

[0057] FIG. 10( d ) is a diagram showing the embedding capacity effect of the Lena image under different quality factors according to the first embodiment of the present invention. DETAILED DESCRIPTION

[0058] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0059] It should be noted that the following detailed descriptions are all illustrative and intended to provide further explanation of the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meanings as those commonly understood by those skilled in the art to which the present invention belongs.

[0060] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit exemplary embodiments according to the present invention. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the term "comprising" is used in this specification, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof.

[0061] It should be noted that the flowcharts and block diagrams in the accompanying drawings illustrate the possible implementation architecture, functions and operations of the methods and systems according to various embodiments of the present disclosure. It should be noted that each box in the flowchart or block diagram can represent a module, a program segment, or a part of a code, and the module, program segment, or a part of a code may include one or more executable instructions for implementing the logical functions specified in each embodiment. It should also be noted that in some alternative implementations, the functions marked in the box can also occur in an order different from that marked in the accompanying drawings. For example, two boxes represented in succession can actually be executed substantially in parallel, or they can sometimes be executed in the opposite order, depending on the functions involved. It should also be noted that each box in the flowchart and / or block diagram, and the combination of boxes in the flowchart and / or block diagram can be implemented using a dedicated hardware-based system that performs a specified function or operation, or can be implemented using a combination of dedicated hardware and computer instructions.

[0062] Embodiment 1

[0063] like Figure 1 As shown, this embodiment provides a JPEG image reversible information hiding method based on Paillier homomorphic encryption, which is applied to the sender and includes:

[0064] Read the quantized DCT coefficients in the JPEG original image, the DCT coefficients include DC coefficients and AC coefficients; the DC coefficients are chaotically encrypted, the AC coefficients are encrypted using Paillier encryption and the multiplication characteristics of Paillier homomorphic encryption are used to embed secret information, a DCT coefficient ciphertext block is constructed, and a ciphertext image containing secret information is obtained;

[0065] The ciphertext image containing the secret information is sent to a receiver, so that the receiver can detachably extract the ciphertext image containing the secret information to obtain the secret information.

[0066] Specifically, this embodiment first operates on the quantized DCT coefficients (DCT Discrete Consine Transform) in the JPEG image, and divides the DCT coefficients into two categories, one is the direct current coefficient (DC coefficient: Direct Coefficient), which is subjected to chaotic encryption; the other is the alternating current coefficients (AC coefficient Alternating Current coefficients). At the sender, it is assumed that when encountering an AC coefficient to be embedded, it is EA after Paillier encryption. At this time, the secret information is B, and the secret information is encrypted into EB using Paillier. Embedding the secret information in the AC coefficient is to utilize the multiplication property of Paillier encryption: multiplication in the ciphertext domain is equivalent to addition in the plaintext, and the operation performed in the ciphertext domain is EC=EA×EB, which is equivalent to A+B in the plaintext domain; at the receiver, after receiving the ciphertext image, the secret information can be extracted separably: decryption first and then extraction, and after obtaining the ciphertext EC, Paillier decryption is directly performed to obtain A+B, and then the secret information is extracted.

[0067] Extract first and then decrypt, first use the operators λ(n) and μ in the key (the operator is given by the key), and calculate L([EC] λ(n) mod n 2 )×μ calculates the plaintext A+B, extracts the secret information, and then decrypts it to restore the original image.

[0068] The technical solution of this embodiment mainly includes three parts. The first part: a brief introduction to the Paillier homomorphic encryption algorithm; the second part: an introduction to the flowchart and main innovation points of the reversible information hiding method for JPEG images based on Paillier homomorphic encryption; the third part: experimental results and experimental analysis.

[0069] I. A brief introduction to the Paillier homomorphic encryption algorithm

[0070] 1. Paillier homomorphic encryption

[0071] In a homomorphic encryption system, arithmetic operations can be directly performed on ciphertexts, and the resulting result is the same as the result of the corresponding operation in the plaintext domain. Encryption technologies with both homomorphic and probabilistic properties have been widely applied in the fields of encrypted signal processing or third-party data processing. The Paillier encryption system is an additive homomorphic public-key encryption system, and its encryption and decryption mechanisms are as follows:

[0072] 1.1 Key generation

[0073] First, select two large prime numbers p and q to ensure that the greatest common divisor of p×q and (p - 1)×(q - 1), that is, it conforms to the following formula:

[0074] gcd(pg, (p - 1)(q - 1)) = 1

[0075] This can ensure that the two prime numbers are equal. Calculate n = pq and λ = lcm(p - 1, q - 1), where lcm(a, b) represents a and b. Randomly select an integer such that n can satisfy that the order of g is divisible. After a series of calculations, the public key is (n, g), and the private key is λ, where it is necessary to satisfy gcd(L(g λ mod n 2 ), n) = 1, where represents fractional division.

[0076] 1.2 Encryption process

[0077] Let the plaintext m be a positive integer between 0 and n, and randomly select r such that r satisfies two conditions: 1. 0 < r < n; 2. r has a multiplicative inverse in the residue system of Encrypt m into c according to the following formula.

[0078] c = E[m, r] = g m r N mod N 2

[0079] Among them, m represents plain text, parameter r is the parameter in the secret key, which is not required on the decryption side, (N,g) is the public key, and c is the encrypted value.

[0080] 1.3 Decryption process

[0081] The decryption process for ciphertext c is as follows:

[0082]

[0083] Among them, c is the ciphertext, (N,g) is the public key, and m is the final decrypted plaintext.

[0084] Additive Homomorphic Features

[0085] Choose two arbitrary plaintexts m 1 and m 2 , randomly select parameter r 1 and r 2 Encrypt, and then encrypt to E[m 1 ,r 1 ],E[m 2 ,r 2 ], with the following formula features:

[0086]

[0087] D[E[m 1 ,r 1 ]·[m 2 ,r 2 ]modN 2 ]=m 1 +m 2 mod N

[0088] From the formula we can know that the multiplication of two ciphertexts is equal to the addition of the plaintext fields.

[0089] Theorem (I): That is There is a unique c=E[m,r] corresponding to each of them. This theorem is used in the embedding process of the encrypted coefficients in this algorithm and is clearly explained below.

[0090] 2. Chaos Code

[0091] Chaotic systems have several characteristics: pseudo-randomness, convenience, determinism, and sensitivity to initial conditions. These characteristics are consistent with many requirements of cryptography, and the inevitable connection between chaos theory and cryptography has also formed chaotic cryptography.

[0092] The method of chaos encryption mainly uses the sequence iterated from the chaotic system and regards this sequence as a factor sequence of encryption exchange. Among them, the theoretical basis of chaos encryption is the self-similar characteristics in the chaotic system, so as to achieve the purpose of similarity between the locally selected chaotic key and the redistribution form and the whole. The existing technology sets the encryption parameters through chaotic encryption, and then uses the encryption parameters to encrypt the image, and inserts the least significant bit (LSB) after encryption into the ciphertext image. Due to the double-layer security, it is difficult for eavesdroppers to attack this algorithm.

[0093] The important point that the chaos series can achieve security is that even if an illegal person has mastered the equation of the chaos sequence, it is difficult to guess the initial value of the chaos sequence and the parameters used in the chaos sequence. In contrast, logistic chaos encryption is a simple and important nonlinear iterative equation, in which the logistic map is a dynamic system of statistical population, and its equation can be written as follows:

[0094]

[0095] Among them, x n is the mapping variable, μ is the system parameter, and their value range is -1 <x n <1, 0<μ<2.

[0096] The basic principle of chaos encryption is to use the chaotic series generated by the chaotic system as a key sequence to encrypt the plaintext. The chaos is deterministic and is determined by the equations, initial conditions and parameters of the nonlinear system. When the system parameters and initial conditions are the same, it can be completely reconstructed. The receiver can use chaos synchronization to decrypt the plaintext signal.

[0097] 2. RDH-EI algorithm for JPEG images based on Paillier homomorphic encryption

[0098] In this embodiment, a new Paillier homomorphic encryption separable RDH algorithm will be described in detail. The three major innovations of this algorithm are described in 1, 2, and 3, including the embedding of secret information while using homomorphic encryption, the parameter r controlling the size of the encrypted AC coefficient so that overflow does not occur, and the model of multi-coefficient encryption. The framework of this algorithm is as follows Figure 1 shown.

[0099] 1. Paillier encryption and information embedding

[0100] The data owner divides the original image I into several non-overlapping 8×8 blocks, and sorts the quantized DCT blocks according to the number of zero coefficients. There are DC components and AC components in each block. For JPEG images, the low-frequency DC component contains most of the image information, and we embed the information into the AC component. Figure 2 shown.

[0101] First, pre-operation is performed. After the DCT AC coefficients select the KEY to be embedded, the coefficients with absolute values ​​greater than the embedded position are moved one position in the direction of increasing values ​​to make room for embedding. This ensures that the embedded information can be extracted separately. In this algorithm, data is embedded by using homomorphic properties. Suppose the embedded secret information is used. Based on the formula, the secret information can be converted into a form that can be embedded using homomorphism.

[0102] c=E[m,r]=g m r N mod N 2

[0103] The encrypted secret information is converted to c, where m is the information to be encrypted, r is the parameter in encryption, and g is the public key.

[0104] Assume A is an initial image sequence of size N*N. We will extract the matrix of DC coefficients and embed it using the characteristics of homomorphic encryption. We will perform a zigzag scan and embed it when we encounter the position of AC coefficients.

[0105]

[0106] D[E[m 1 ,r 1 ]·E[m 2 ,r 2 ]mod N 2 ]=m 1 +m 2 mod N

[0107] Among them, m 1 、m 2 Represents two different ciphertexts, r 1 、r 2 They are their parameters respectively, (N,g) represents the public key in the cryptographic system, E[.] represents the encryption operation, and D[.] represents the decryption operation.

[0108] The AC coefficients on the embedded bits and the encrypted secret information are embedded using the multiplication homomorphism property and brought into the formula for multiplying two numbers.

[0109] In order to enable the image in the ciphertext domain to be directly decrypted, the threshold T and parameter r are used in Paillier encryption to make the encrypted data conform to the range of quantized DCT coefficients (-1024, 1024). When using Paillier multiplication homomorphism for embedding, the size of the embedded number cannot be controlled. In this algorithm, the embedded AC coefficient is controlled between (-128, 128).

[0110]

[0111] As shown in the above formula, the embedded data is encrypted within the coefficient range according to the threshold T and the parameter r.

[0112] In this way, the embedded encrypted data can be separated within a certain range when the recipient extracts the information, that is, the information can be extracted from the ciphertext or from the decrypted plaintext.

[0113] 2. Control of the encrypted value by parameter r in homomorphic encryption

[0114] 2.1 Mapping characteristics of plaintext and ciphertext in homomorphic encryption

[0115] In the encryption process, the process of generating public and private keys is fixed, but for image pixels, the ciphertext generated by this encryption method will produce the same waveform as the pixel histogram statistics of the plaintext. In addition, for JPEG images, the range of coefficients in the quantized DCT coefficients is [-1024, 1024]. When the secret key parameters are the same, the plaintext and ciphertext after homomorphic encryption are mapped one to one.

[0116] When the parameter r is fixed: for example, the secret key is N = p × q = 11 × 13 = 143, g = 8400, that is, the public key of the cryptographic system is (143, 8400), and the encrypted plaintext is m = 11, m = 12, m = 13, when r = 3, the encrypted value is c m＝11 =13180,c m＝12 =1114,c m＝13 =12407.

[0117] In the process of Paillier homomorphic encryption, random parameters g and r are selected. The order of parameter g is a non-zero multiple of n. Parameter g participates in the encryption and decryption process of data, so this algorithm fixes the value of g and operates on the encrypted parameter r. In order to solve the problem of consistent image waveform and make the encrypted image more meaningful, we will select different parameter r values ​​for encryption. When r takes different parameters, the encrypted value is different.

[0118] Each time encryption is performed, a random number r is generated for encryption. The parameter r is a number in the range of 2 to n that is relatively prime to n, that is, r∈[2,n]. At the encryption end, r is cycled from 2 to n for encryption, and the size of the encrypted AC coefficient can be controlled by using different parameters r.

[0119] When the parameter r changes: for example, the key is n = p × q = 11 × 13 = 143, g = 8400, and the encrypted value is 10, when r = 2, 3, 4, the encrypted value is c r＝2 =5101,c r＝3 =19915,c r＝4 =20029.

[0120] 2.2 Using parameter r to control the ciphertext size

[0121] The parameter r only exists in the encryption formula. The value of the parameter r is no longer needed in the decryption formula. This embodiment is to control the size of the encrypted data. If the parameter r is a fixed value, the encrypted image histogram will be similar to the plaintext image histogram waveform before encryption. The encrypted coefficient histogram is the same as the unencrypted histogram waveform, which is easy to identify attacks. Therefore, in order to keep the encrypted ciphertext within the maximum range of the DCT coefficients and to have good ciphertext properties, encryption is performed within r∈[2,n] during the encryption process.

[0122] like Figure 3 As shown, where m 1 、m 2 、m 3 、m 4 、m 5 All are in plain text, and the ones marked by asterisks are 3 It is the position to be embedded. The size range of the ciphertext is adjusted by operating the parameter r. 3 You can choose different parameters r c 、r d 、r e Then generate different encrypted ciphertexts to determine the encrypted ciphertext c 3rc 、c 3rd 、c 3re The range of , so that the overflow operation in this embodiment can be used to control the range of the ciphertext to be between (-128, 128). Where m represents the plaintext coefficient, the black curve is used to represent the quantity, and E(m) represents the encrypted numerical curve. D(E(m)) represents the numerical curve after decrypting the encrypted water ciphertext data.

[0123] 3. Multi-coefficient encryption model

[0124] exist Figure 4In the figure, the quantized DCT coefficients are obtained from the original plaintext image. It can be seen from the figure that the original plaintext image is divided into 8×8 blocks. One of the blocks is used for demonstration operation. In the 8×8 DCT demonstration block, the dark part is the DC coefficient for chaotic encryption, the light part is the AC coefficient to be embedded with secret information, and the other white parts are other AC coefficients. Among them, Paillier encryption is performed in the AC coefficient. The tributary coefficients to be embedded are marked with a five-pointed star in the AC coefficient distribution diagram. This part is encrypted with Paillier and the secret information is embedded at the same time. The other green parts are DC coefficients that are not embedded. This part is only encrypted with Paillier.

[0125] 4. Framework of RDH-EI

[0126] The JPEG homomorphic encryption reversible information hiding algorithm proposed in this embodiment is as follows: Figure 1 As shown, first read the DCT coefficients of the quantized JPEG image, and encrypt the DC and AC coefficients respectively. The DC coefficient is chaotically encrypted, and the AC coefficient is homomorphically encrypted and embedded using its multiplication characteristics. The detailed steps are pointed out below.

[0127] 5. Separable and extractable

[0128] exist Figure 5 A brief description of extracting secret information and restoring the original image is given in the paper. The algorithm can separate the extracted information (a) representing the ciphertext image containing secret information. First, the ciphertext image (b) is generated by extracting the private information, and then the plaintext image can be obtained by decryption. If the image (a) is decrypted first, the plaintext image (d) containing the secret information will be generated, from which the private information can be extracted. The specific steps are described in the following two subsections.

[0129] 5.1 Extract first and then decrypt

[0130] Similar to the embedding process, the receiver first divides the quantized DCT coefficients of the ciphertext image containing the secret information into 8×8 blocks, sorts them according to the number of 0 coefficients in each block, and decrypts them according to the range of the coefficients of the embedded information. The following is the derivation process:

[0131] set up

[0132] Then

[0133] at this time Therefore This is the encryption of a new message, m 1 +m 2 , with a random element r 1 ·r 2. Decryption c 1 and c 2 The product of (c 1 ·c 2 ) to the power of λ(n):

[0134] From Carmichael's theorem, we know that (r 1 ·r 2 ) nλ(n) ≡1mod n 2 :

[0135]

[0136] g λ(n) =(1+n) λ(n)[g](1+n) mod n 2

[0137] (c 1 ·c 2 ) λ(n) =(1+n) λ(n)[g](1+n) =1+(m 1 +m 2 )·λ(n)[g](1+n)·n mod n 2

[0138] Therefore, L((c 1 ·c 2 ) λ(n) mod n 2 )=(m 1 +m 2 )·λ(n)[g](1+n)mod n and μ is still the inverse of {λ(n)[g](1+n)}, so the decryption process is completed by multiplying by μ, and the result is m 1 +m 2 mod n.

[0139] Example: Assume that public key (n, g) = (11×13, 20049) = (143, 20449), λ(n) = 60, μ = 114 has been proposed. If someone encrypts two messages, such as (m 1 , r 1 )=(2,4) and (m 1 , r 2 )=(3,7), the ciphertext obtained will be E(m 1 )=19460 and E(m 2 )=12170.

[0140] The product of these ciphertexts E(m 1 )·E(m 2 )for

[0141] E(m1 )·E(m 2 )=19460×12170=236828200=8331mod 20449

[0142] The decryption process starts with calculating L([E(m 1 )·E(m 2 )] λ(n) mod n 2 )start:

[0143] L(8331 60 mod 20449)=L(8438)=8437 / 143=59mod 143

[0144] Finally, multiply the above result by μ = 114 to complete the decryption process:

[0145] L(8331 60 mod 20449)·μ=59×114=6726mod143=5=2+3=m 1 +m 2 mod 143

[0146] In this way, the algorithm can perform the above operations to extract secret information in the ciphertext domain without destroying the ciphertext.

[0147] 5.2 Decryption before extraction

[0148] First, decrypt the ciphertext image with privacy information. First, perform chaotic decryption on the DC coefficient in the quantized DCT coefficient, and the high-frequency information in the image can be restored to its original position, which contains a lot of information about the key points of the image. Then, perform Paillier decryption directly on the AC coefficient:

[0149]

[0150] Then, based on the embedded secret key KEY, the information is extracted, and the image is restored while the information is extracted, thus achieving completely reversible information hiding.

[0151] 6. Overflow handling

[0152] When quantized DCT coefficients are encrypted, an image must maintain the same cryptographic system. After the key is selected, the AC coefficients in the quantized DCT coefficients are encrypted. For natural images, the value range of the pixel AC coefficients is between [-1024, 1024]. When we encrypt beyond this range, we cannot write the encrypted AC coefficients into the JPEG image, so we determine a threshold T. Because the same AC coefficient can be encrypted into different numbers depending on the value of r mentioned above, we take the remainder of the encrypted AC coefficient. If the coefficient after taking the remainder is between [-128, 128], the encrypted AC coefficient can be written into the JPEG image. The remainder of the encrypted number must be T, so that it can be decrypted according to the remainder T during decryption.

[0153] c=e mod 128

[0154]

[0155] Among them, e is the encrypted AC coefficient, c represents the encrypted AC coefficient after taking the remainder, and T represents the remainder of the encrypted AC coefficient.

[0156] Table 1 Encrypted coefficients in the range (-128, 128) obtained with different parameters r

[0157]

[0158] For example, the public key cryptosystem is (n, g) = (143, 9622). When the peaks in the DCT coefficients are 1 and -1, we embed them. Assuming that the embedded secret information is '1', for the peak '1' in the AC coefficient, we need to encrypt the AC coefficient and the embedded secret information separately, and then use the multiplication property of homomorphic encryption to embed the secret information. At the same time, the encrypted value must also comply with the overflow handling operation. For example, when the encrypted AC coefficient is c 1 =12884, which satisfies the overflow processing. The encrypted embedded information is c 2 =12884, perform embedding operation:

[0159] c e =c 1 c 2 =12884×12884mod n 2 =12923mod n 2

[0160] c e '=c e mod128=12923mod128=123

[0161] When decrypting, the range between [-128, 128] contains secret information. For example, the value c with secret information e '=123, at the extraction end, the value before the control coefficient size is restored according to the threshold T.

[0162] 7. Avoid ciphertext collision processing

[0163] In the Paillier homomorphic encryption system, for a certain value, the determination of the parameter r ensures a one-to-one mapping between plaintext and ciphertext. However, for images, multiple coefficients need to be operated. For example, the coefficient with the highest peak value in an image is determined as KEY. Assuming that the embedded coefficient is '1', the one-to-one mapping between plaintext and ciphertext in the same encryption system can ensure its security. However, the waveform of the statistical histogram of the plaintext image and the statistical histogram of the ciphertext image are the same, which is not conducive to secure transmission. Therefore, the waveform transformation is adjusted by adjusting multiple parameters r. Because Paillier encryption is also required for other non-embedded AC coefficients, ciphertext collisions may occur at this time. For example, when n=11×13=143, g=9927, λ=60, and AC coefficient AC=4, when r=39, the generated ciphertext is 9633, but the decrypted value is 101. This means that the encrypted ciphertext of the plaintext value "4" and the encrypted ciphertext of the plaintext value "101" have collided. This is because we need to control the encrypted ciphertext within a certain range, so that the range after Paillier encryption becomes smaller, so a ciphertext collision will occur. In order to avoid this situation, we first screen the values ​​of r∈[2,n] before encryption to eliminate values ​​that will cause ciphertext collisions, such as r=39.

[0164] Table 2 Demonstration table of collision control of some coefficient ciphertexts with different parameters r

[0165]

[0166]

[0167] From Table 2, we can see that the DCT coefficients after different quantization are -5, -4, -3, -2, -1, 1, 2, 3, 4, 5; in order to control the size of the encrypted coefficient, the threshold T=75 is taken, and the values ​​of the parameter r are determined by the screened value range to be 98, 64, 38, 36, 136, 95, 95, 136, 36, 38, 64, 98 respectively; the values ​​of the encrypted coefficients are -9701, -9619, -9641, -9629, -9635, -9604, 9604, 9635, 9629, 9641, 9619, 9701; the encrypted values ​​are modulo 128 and are: -101, -19, -41, -29, -35, -4, 4, 35, 29, 41, 19, 101.

[0168] 3. Experiment and results analysis

[0169] In the experiment of the embodiment, we downloaded some commonly used 512*512 images from the USC-SIPI image database, including Baboon, Couple, Boat, and Lena. At the same time, 337 images were randomly selected from the BOSS image library to analyze the feasibility of the algorithm.

[0170] 1. Algorithm feasibility

[0171] 1.1 Algorithm Verification on a Single Image

[0172] This experiment first selects the image lena to verify the feasibility of the algorithm. The image size is 512*512 8-bit grayscale image (as shown in Figure a). The DC coefficient and AC coefficient of the quantized DCT transform are processed separately. The DC coefficient is extracted separately and then chaotic encryption is performed. The AC coefficient is extracted and Paillier encryption is performed while information is embedded. The parameters of the Paillier encryption system are p=13 and q=17. The upper limit value of the plaintext that can be encrypted is N=p*q=221.r∈[2,n]. The content owner hides the secret information in the AC coefficient. The specific experimental results are as follows: Figure 6(a)-Figure 6(c) as follows:

[0173] First, Figure 6(a) is divided into 8×8 blocks, and the quantized AC coefficients are homomorphically encrypted using Paillier, while embedding information. This method implements the ciphertext image of RDH, and Figure 6(c) is the encrypted image after decryption.

[0174] Figure 7(a)-Figure 7(c)This is the effect diagram after chaotic encryption of the DC coefficient in the algorithm. Figure 7(a) is the plaintext image to be operated, and Figure 7(b) is the image after the DC coefficient in the plaintext image is extracted. The image maintains the basic outline of the plaintext image and is still easy to recognize. Figure 7(c) is the DC coefficient after chaotic encryption, and its PSNR is 22.8.

[0175] In order to further evaluate the performance of this algorithm, the experiment selected Figure 8(a)-Figure 8(d) The four 8-bit grayscale images with a size of 512*512 are used as carriers for testing. In the experiment, the four carrier images are divided into 8×8 blocks. When the QF quality factor is 50, the embedded secret information is a comparison chart of a pseudo-random series of 2500 bits.

[0176] When the Airplane graph in Figure 8(a) is embedded with 2500 bits, the PSNR value is 9.73. When the Baboon graph in Figure 8(b) is embedded with 2500 bits, the PSNR value is 6.606. When the Lena graph in Figure 8(c) is embedded with 2500 bits, the PSNR value is 6.102. When the Peppers graph in Figure 8(d) is embedded with 2500 bits, the PSNR value is 5.749. Figure 8(e)-Figure 8(h) Corresponding to Figure 8(a)-Figure 8(d) The encrypted images of the four pictures after using this algorithm.

[0177] 1.2 Algorithm Verification in BOSS Database

[0178] exist Figure 9(a)-Figure 9(d) In the figure, 337 512*512 grayscale images are randomly selected from the BOSS image library, and their embedding capacity after compression into JPEG images is counted. The quality factor is QualityFactor (QF) = 50, 60, 70, and 80, and the maximum embedding capacity of each image. Figure 9 (a) shows the embedding capacity distribution when QF = 50, and the minimum embedding capacity represented by the straight line is 6912 bits. Figure 9 (b) shows the embedding capacity distribution when QF = 60, and the minimum embedding capacity represented by the straight line is 7697 bits. Figure 9 (c) shows the embedding capacity distribution when QF = 70, and the minimum embedding capacity represented by the straight line is 8473 bits. Figure 9 (d) shows the embedding capacity distribution when QF = 80, and the minimum embedding capacity represented by the straight line is 9610 bits. Figure 9(a)-Figure 9(d) It can be seen that as the quality factor increases, the effective bits in the DC coefficient will increase. This algorithm is also applicable to images in other galleries and has good results.

[0179] 2. Experimental analysis

[0180] The performance of the algorithm of this embodiment in terms of embedding capacity, file increment, PSNR value, etc. is analyzed below:

[0181] 2.1 Embedding Capacity

[0182] In the solution of this embodiment, the size of the encryption key determines the blocks that cannot be embedded, but in the quantized DCT coefficients, the coefficients must be less than N to ensure accurate decryption of the plaintext. We have counted the maximum AC coefficients of different quality factors for four images. As shown in Table 3:

[0183] Table 3 Values ​​of the maximum AC coefficients of four images at different quality factors

[0184] Image QF=50 QF=60 QF=70 QF=80 Couple 48 60 80 122 Baboon 27 32 45 67 Boat 42 51 71 111 Lena 58 71 91 159

[0185] It can be seen from Table 3 that the maximum value of the AC coefficient is when the quality factor QF=80. In the lena graph, the maximum value is 159 when QF=80. That is to say, when the value of the secret key N is greater than 159, it can ensure that the ciphertext can be completely decrypted without any error. This is also an important reason why this algorithm has a larger embedding capacity than other methods.

[0186] Under the premise of quality factor 80, the comparison of the number of embedded blocks of different algorithms is shown in Table 4:

[0187] Table 4 Comparison of the number of embedded blocks in different algorithms

[0188]

[0189] From the above table, we can conclude that after being divided into 8*8 blocks, DCT coefficient blocks are divided into three forms: regular blocks, singular blocks, and non-embeddable blocks. Regular blocks are blocks that can be fully used, singular blocks are blocks that can be embedded under certain conditions, and non-embeddable blocks are blocks that cannot embed any data. For this algorithm, a 512*512 image is divided into 4096 DCT coefficient blocks. This algorithm can fully use these blocks, so the embedding capacity is better than that of other algorithms.

[0190] Figure 10(a)-Figure 10(d)The comparison of the embedding capacity of the algorithm proposed in this embodiment and other algorithm frameworks is shown. When the quality factor is QF=50, QF=60, QF=70 and QF=80, it is compared with Figure 10(a) Baboon, Figure 10(b) Boat, Figure 10(c) Couple, and Figure 10(d) Lena. From the implementation results, it can be seen that the overall embedding capacity of the baboon with more complex texture is the largest. As the quality factor increases, the embedding capacity also increases. The embedding capacity of the other three images also increases with the increase of the quality factor, and the embedding capacity of the algorithm proposed in this embodiment is better than that of other algorithms. In the algorithm of this embodiment, no matter how large the embedding capacity is, there will be no embedding failure. This can ensure the effect of high embedding capacity, but in order to obtain higher embedding capacity, the cost of the file will increase significantly.

[0191] This embodiment proposes a reversible information hiding algorithm in the Paillier homomorphic encryption domain of JPEG images based on quantized DCT coefficients. Experimental results and analysis show that the performance of this scheme is better than other schemes. The main contributions of this method are as follows:

[0192] 1. It is proposed to double encrypt the quantized DCT coefficients, perform relatively secure chaotic encryption on the DC coefficients, perform additive homomorphic encryption on the AC coefficients, and use the characteristics of Paillier homomorphic encryption (the multiplication characteristic is that the multiplication operation in the ciphertext domain is equivalent to the addition operation in the plaintext domain) to process the data.

[0193] 2. The proposed encrypted JPEG quantized DCT coefficient RDH scheme sorts the number of AC 0 coefficients in each 8*8 quantized DCT block, first selects the smooth block for embedding, and performs histogram shift in the embedded block, so that the invalid histogram in other unembedded blocks can be shifted.

[0194] 3. When encrypting, think in reverse and generate ciphertext that meets the range of DCT based on the threshold T and parameter r, which can meet both the conditions of Paillier homomorphic encryption and the size range of DCT. According to the multiplication characteristics of Paillier homomorphic encryption, information can be embedded while encrypting. In the future, a more optimized solution can be selected in the embedding scheme for Paillier homomorphic encryption to achieve a balance between file increment and embedding capacity.

[0195] Embodiment 2

[0196] This embodiment provides a JPEG image reversible information hiding system based on Paillier homomorphic encryption.

[0197] A JPEG image reversible information hiding system based on Paillier homomorphic encryption, applied to the sender, includes:

[0198] The encryption module is configured to: read the quantized DCT coefficients in the JPEG original image, wherein the DCT coefficients include DC coefficients and AC coefficients; perform chaotic encryption on the DC coefficients, and use Paillier encryption and the multiplication characteristics of Paillier homomorphic encryption to embed secret information on the AC coefficients, construct a DCT coefficient ciphertext block, and obtain a ciphertext image containing secret information;

[0199] The decryption module is configured to: send the ciphertext image containing the secret information to a receiver, so that the receiver can detachably extract the ciphertext image containing the secret information to obtain the secret information.

[0200] It should be noted that the examples and application scenarios implemented by the above encryption module and decryption module are the same as those in the steps of Embodiment 1, but are not limited to the contents disclosed in the above Embodiment 1. It should be noted that the above modules as part of the system can be executed in a computer system such as a set of computer executable instructions.

[0201] Embodiment 3

[0202] This embodiment provides a reversible information hiding method for JPEG images based on Paillier homomorphic encryption.

[0203] A reversible information hiding method for JPEG images based on Paillier homomorphic encryption, applied to the receiving and sending parties, includes:

[0204] Receiving a ciphertext image containing secret information, and performing separable extraction on the ciphertext image containing the secret information to obtain the secret information;

[0205] The ciphertext image containing secret information is obtained by embedding the secret information into the AC coefficient. The AC coefficient uses the multiplication characteristics of Paillier encryption and Paillier homomorphic encryption to embed the secret information, and the DC coefficient is chaotically encrypted to obtain a DCT coefficient ciphertext block. The AC coefficient and DC coefficient both belong to the DCT coefficient, and the DCT coefficient is obtained by reading the JPEG original image and quantizing it.

[0206] The specific implementation steps of the technical solution in this example are the same as those in Example 1 and will not be repeated here.

[0207] Embodiment 4

[0208] This example provides a reversible information hiding system for JPEG images based on Paillier homomorphic encryption.

[0209] A reversible information hiding system for JPEG images based on Paillier homomorphic encryption, comprising:

[0210] A decryption module is configured to: receive a ciphertext image containing secret information, and perform separable extraction on the ciphertext image containing secret information to obtain the secret information;

[0211] The encryption module is configured as follows: the ciphertext image containing secret information is obtained by embedding the secret information into the AC coefficient, the AC coefficient uses the multiplication characteristics of Paillier encryption and Paillier homomorphic encryption to embed the secret information, and the DC coefficient is chaotically encrypted to obtain a DCT coefficient ciphertext block, the AC coefficient and the DC coefficient both belong to the DCT coefficient, and the DCT coefficient is obtained by reading the JPEG original image and quantizing it.

[0212] Embodiment 5

[0213] This embodiment provides a computer-readable storage medium on which a computer program is stored. When the program is executed by a processor, the steps in the JPEG image reversible information hiding method based on Paillier homomorphic encryption as described in the above-mentioned embodiment 1 or embodiment 3 are implemented.

[0214] Embodiment 6

[0215] This embodiment provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, the steps in the reversible information hiding method for JPEG images based on Paillier homomorphic encryption as described in the above-mentioned embodiment 1 or embodiment 3 are implemented.

[0216] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0217] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A reversible information hiding method for JPEG images based on Paillier homomorphic encryption, characterized in that: Applicable to the sender, including: Read the quantized DCT coefficients in the original JPEG image, the DCT coefficients include DC coefficients and AC coefficients; the DC coefficients are chaotically encrypted, the AC coefficients are encrypted using Paillier encryption and the multiplication characteristics of Paillier homomorphic encryption to embed secret information, the embedding is pre-operated, after the DCT AC coefficients select the to-be-embedded bit KEY, the coefficients whose absolute values ​​are greater than the embedding bit are moved one position in the direction of increasing the value, leaving space for embedding to ensure that the embedded information can be extracted separately, the data is embedded using homomorphic properties, set the embedded secret information, and convert the secret information into a form that can be embedded using homomorphism based on the formula, The encrypted secret information is converted to c, where m is the information to be encrypted, r is the parameter in encryption, and g is the public key; Assume A is an initial image sequence of size N*N. The matrix of the extracted DC coefficient is embedded using the characteristics of homomorphic encryption. A zigzag scan is performed and the position of the AC coefficient is embedded. Among them, m1 and m2 represent two different ciphertexts, r1 and r2 are their parameters, (N, g) represents the public key in the cryptographic system, E[.] represents the encryption operation, and D[.] represents the decryption operation; The AC coefficients on the embedded bits and the encrypted secret information are embedded using the multiplication homomorphism property and brought into the formula for multiplying two numbers. In order to enable the image in the ciphertext domain to be directly decrypted, the Paillier encryption has a threshold T and a parameter r to quantize the encrypted data so that the range of the DCT coefficients is between -1024 and 1024. When embedding using the Paillier multiplication homomorphism, the size of the embedded number cannot be controlled, and the AC coefficient after embedding is controlled between -128 and 128. Construct DCT coefficient ciphertext blocks to obtain ciphertext images containing secret information; The ciphertext image containing the secret information is sent to a receiver, so that the receiver can detachably extract the ciphertext image containing the secret information to obtain the secret information.

2. The reversible information hiding method for JPEG images based on Paillier homomorphic encryption according to claim 1 is characterized in that: The AC coefficients are embedded using the multiplication characteristics of Paillier encryption and Paillier homomorphic encryption, including: calculating the number of AC coefficient "0" in each DCT block to generate an embedding sequence in descending order.

3. The reversible information hiding method for JPEG images based on Paillier homomorphic encryption according to claim 1 is characterized in that: The method of enabling the receiving party to decrypt the ciphertext image containing the secret information includes: enabling the receiving party to extract the secret information to generate the ciphertext image, and obtaining the plaintext image by decrypting the ciphertext image; or enabling the receiving party to first decrypt to generate the plaintext image containing the secret information, and then extracting the secret information from the plaintext image.

4. A JPEG image reversible information hiding method based on Paillier homomorphic encryption as claimed in claim 1, characterized in that: Applicable to the sender, including: An encryption module is configured to: read quantized DCT coefficients in a JPEG original image, wherein the DCT coefficients include DC coefficients and AC coefficients; the DC coefficients are chaotically encrypted, and the AC coefficients are encrypted using Paillier encryption and the multiplication characteristics of Paillier homomorphic encryption to embed secret information, construct a DCT coefficient ciphertext block, and obtain a ciphertext image containing secret information; The decryption module is configured to: send the ciphertext image containing the secret information to a receiver, so that the receiver can detachably extract the ciphertext image containing the secret information to obtain the secret information.

5. A JPEG image reversible information hiding method based on Paillier homomorphic encryption as claimed in claim 1, characterized in that: Applicable to the pick-up and drop-off parties, including: Receiving a ciphertext image containing secret information, and performing separable extraction on the ciphertext image containing the secret information to obtain the secret information; The ciphertext image containing secret information is obtained by embedding the secret information into the AC coefficient. The AC coefficient uses the multiplication characteristics of Paillier encryption and Paillier homomorphic encryption to embed the secret information, and the DC coefficient is chaotically encrypted to obtain a DCT coefficient ciphertext block. The AC coefficient and DC coefficient both belong to the DCT coefficient, and the DCT coefficient is obtained by reading the JPEG original image and quantizing it.

6. The reversible information hiding method for JPEG images based on Paillier homomorphic encryption according to claim 5 is characterized in that: The AC coefficients are embedded using the multiplication characteristics of Paillier encryption and Paillier homomorphic encryption, including: calculating the number of AC coefficients "0" in each DCT block to generate an embedding sequence in descending order.

7. The reversible information hiding method for JPEG images based on Paillier homomorphic encryption according to claim 5 is characterized in that: The decrypting of the ciphertext image containing the secret information includes: extracting the secret information to generate the ciphertext image, and obtaining the plaintext image by decrypting the ciphertext image; or first decrypting to generate the plaintext image containing the secret information, and extracting the secret information from the plaintext image.

8. A JPEG image reversible information hiding method based on Paillier homomorphic encryption as claimed in claim 1, characterized in that: include: A decryption module is configured to: receive a ciphertext image containing secret information, and perform separable extraction on the ciphertext image containing secret information to obtain the secret information; The encryption module is configured as follows: the ciphertext image containing secret information is obtained by embedding the secret information into the AC coefficient, the AC coefficient uses the multiplication characteristics of Paillier encryption and Paillier homomorphic encryption to embed the secret information, and the DC coefficient is chaotically encrypted to obtain a DCT coefficient ciphertext block, the AC coefficient and the DC coefficient both belong to the DCT coefficient, and the DCT coefficient is obtained by reading the JPEG original image and quantizing it.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the steps in the JPEG image reversible information hiding method based on Paillier homomorphic encryption as described in any one of claims 1-3 or 5-7 are implemented.

10. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the program, the steps in the JPEG image reversible information hiding method based on Paillier homomorphic encryption as described in any one of claims 1-3 or 5-7 are implemented.

Images