CN115208549A

CN115208549A - JPEG image reversible information hiding method and system based on Paillier homomorphic encryption

Info

Publication number: CN115208549A
Application number: CN202210544890.7A
Authority: CN
Inventors: 马宾; 张宝娜; 马睿和; 王春鹏; 李健; 周琳娜
Original assignee: Qilu University of Technology
Current assignee: Qilu University of Technology
Priority date: 2022-05-19
Filing date: 2022-05-19
Publication date: 2022-10-18

Abstract

The invention belongs to the field of image encryption and decryption, and provides a JPEG image reversible information hiding method and a JPEG image reversible information hiding system based on Paillier homomorphic encryption. If the method is applied to the sender, the method comprises the following steps: reading a quantized DCT coefficient in a JPEG original image, wherein the DCT coefficient comprises a DC coefficient and an AC coefficient; the DC coefficient is subjected to chaotic encryption, the AC coefficient is subjected to secret information embedding by utilizing Paillier encryption and multiplication characteristics of Paillier homomorphic encryption, and a DCT coefficient ciphertext block is constructed to obtain a ciphertext image containing secret information; and the ciphertext image containing the secret information is sent to the receiving party, so that the receiving party can extract the ciphertext image containing the secret information in a separable way to obtain the secret information. The invention effectively improves the data embedding capacity and the image encryption quality.

Description

JPEG image reversible information hiding method and system based on Paillier homomorphic encryption

Technical Field

The invention belongs to the field of image encryption and decryption, and particularly relates to a JPEG image reversible information hiding method and system based on Paillier homomorphic encryption.

Background

The statements in this section merely provide background information related to the present disclosure and may not constitute prior art.

Reversible information Hiding (Reversible Data Hiding RDH) is a method for Hiding hidden information into a carrier, wherein the carrier comprises an image, an audio frequency and a video frequency, the RDH pays attention to the fact that embedded information can be completely restored after image processing, and an embedded carrier image and an original image are completely the same, so that the reversibility of the image and the hidden information can be realized. At present, the reversible information hiding based on the JPEG image can be divided into three categories: 1. RDH modified based on quantization table. 2. RDH modified based on huffman codes. 3. Based on the RDH of the quantized DCT coefficients.

For conventional encryption algorithms such as stream cipher, DES, etc. These conventional encryption algorithms are directly used in encryption, and although the security of plaintext is determined, the information cannot be modified in the ciphertext, and the ciphertext needs to be decrypted and then operated. For homomorphic encryption, on the premise of ensuring the safety of plaintext, the information can be ensured to be embedded. A series of algebraic operations can be performed at the cloud by utilizing the property of homomorphic encryption, and the operation results in the ciphertext domain are the same as the operation results in the plaintext domain. According to the good property, the user can give the homomorphic encrypted data to the cloud platform for actions such as labeling and the like, so that the privacy of the user is protected. In the past, homomorphic encryption has made significant progress, and data can be processed directly in the encrypted domain using such algorithms. For modern communication systems, decryption is not required when the ciphertext domain is processed, so that both privacy and integrity of a user can be guaranteed. But few algorithms for encryption domain invertible information hiding have been proposed in the transform domain of JPEG images.

Along with the convenient and rapid development of cloud storage, the data privacy infringement problem is increasingly prominent. Reversible Data Hiding (RDH) may be used to embed additional data in encrypted data stored in the cloud. Most encrypted RDH algorithms are performed in uncompressed images and have not found widespread use in popular JPEG images.

Disclosure of Invention

In order to solve the technical problems in the background art, the invention provides a JPEG image reversible information hiding method and system based on Paillier homomorphic encryption; firstly, extracting the distribution characteristics of DCT coefficients, and then encrypting the DCT coefficients by using chaotic encryption; then calculating the number of AC coefficients '0' in each DCT block to generate an embedded sequence in a descending order; embedding an AC coefficient by utilizing multiplication characteristics of paillier encryption and homomorphic encryption; the invention effectively improves the data embedding capacity and the image encryption quality.

In order to achieve the purpose, the invention adopts the following technical scheme:

the invention provides a JPEG image reversible information hiding method based on Paillier homomorphic encryption.

A JPEG image reversible information hiding method based on Paillier homomorphic encryption is applied to a sender and comprises the following steps:

reading a quantized DCT coefficient in a JPEG original image, wherein the DCT coefficient comprises a DC coefficient and an AC coefficient; the DC coefficient is subjected to chaotic encryption, the AC coefficient is subjected to secret information embedding by utilizing Paillier encryption and multiplication characteristics of Paillier homomorphic encryption, and a DCT coefficient ciphertext block is constructed to obtain a ciphertext image containing secret information;

and the ciphertext image containing the secret information is sent to the receiver, so that the receiver can extract the ciphertext image containing the secret information in a separable way to obtain the secret information.

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

A JPEG image reversible information hiding system based on Paillier homomorphic encryption is applied to a sender and comprises the following components:

an encryption module configured to: reading a quantized DCT coefficient in a JPEG original image, wherein the DCT coefficient comprises a DC coefficient and an AC coefficient; the DC coefficient is subjected to chaotic encryption, the AC coefficient is subjected to secret information embedding by utilizing Paillier encryption and multiplication characteristics of Paillier homomorphic encryption, and a DCT coefficient ciphertext block is constructed to obtain a ciphertext image containing secret information;

a decryption module configured to: and the ciphertext image containing the secret information is sent to the receiver, so that the receiver can extract the ciphertext image containing the secret information in a separable way to obtain the secret information.

The third aspect of the invention provides a JPEG image reversible information hiding method based on Paillier homomorphic encryption.

A JPEG image reversible information hiding method based on Paillier homomorphic encryption is applied to a receiver and comprises the following steps:

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 the secret information is obtained by embedding the secret information into an AC coefficient, the AC coefficient utilizes multiplication characteristics of paillier encryption and paillier homomorphic encryption to embed the secret information, a DC coefficient is subjected to chaotic encryption 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 JPEG original image and quantizing the JPEG original image.

The fourth aspect of the invention provides a JPEG image reversible information hiding system based on Paillier homomorphic encryption.

A JPEG image reversible information hiding system based on Paillier homomorphic encryption comprises:

a decryption module configured to: receiving a ciphertext image containing the secret information, and performing separable extraction on the ciphertext image containing the secret information to obtain the secret information;

an encryption module configured to: the ciphertext image containing the secret information is obtained by embedding the secret information into an AC coefficient, the AC coefficient utilizes multiplication characteristics of paillier encryption and paillier homomorphic encryption to embed the secret information, a DC coefficient is subjected to chaotic encryption 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 JPEG original image and quantizing the JPEG original image.

A fifth aspect of the invention provides a computer-readable storage medium.

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

A sixth aspect of the invention provides a computer apparatus.

A computer device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the processor executes the program to implement the steps of the method for hiding reversible information in JPEG images based on Paillier homomorphic encryption as described in the first or third aspect.

Compared with the prior art, the invention has the beneficial effects that:

the method comprises the steps of firstly, reading DCT coefficients in JPEG images to construct a multi-number encryption model, and encrypting the direct current coefficients by using chaotic encryption with higher safety. The alternating current coefficients are divided into two types, one type is the alternating current coefficients to be embedded with information, the coefficients of the part are encrypted in a identical state by paillier and are simultaneously embedded, and the other type is the direct current coefficients for chaotic encryption. The quantized DCT coefficient has a certain size range, the encrypted data is subjected to overflow processing, and the value of the encrypted data is controlled by using a threshold value T and a parameter r during encryption, so that separable data extraction can be realized. The algorithm has good embedding capacity under the condition of better ensuring the safety of the plaintext.

Drawings

The accompanying drawings, which are incorporated in and constitute a part of this specification, are included to provide a further understanding of the invention, and are incorporated in and constitute a part of this specification, illustrate exemplary embodiments of the invention and together with the description serve to explain the invention and not to limit the invention.

FIG. 1 is a flowchart illustrating a JPEG image reversible information hiding method based on Paillier homomorphic encryption according to an embodiment of the present invention;

FIG. 2 is a schematic diagram illustrating the start and end bits of homomorphic encryption for AC coefficients according to an embodiment of the present invention;

fig. 3 is a schematic diagram illustrating encryption of plaintext by different values of r according to an embodiment of the present invention;

FIG. 4 is a diagram illustrating the result of a multi-number encryption model according to an embodiment of the present invention;

FIG. 5 is a flow chart illustrating decryption and extraction according to an embodiment of the present invention;

FIG. 6 (a) is an original image according to an embodiment of the present invention;

fig. 6 (b) is a secret ciphertext image embedded with secret information according to an embodiment of the present invention;

FIG. 6 (c) is a diagram of a decrypted image according to an embodiment of the present invention;

FIG. 7 (a) is a plaintext image illustrating an operation to be performed according to an embodiment of the invention;

fig. 7 (b) is an image after extracting dc coefficients from a plaintext image according to an embodiment of the present invention;

fig. 7 (c) shows dc coefficients after chaotic encryption according to an embodiment of the present invention;

fig. 8 (a) is an airplan diagram showing an embodiment of the present invention;

FIG. 8 (b) is a Baboon diagram illustrating one embodiment of the present invention;

FIG. 8 (c) is a Lena diagram illustrating an embodiment of the present invention;

FIG. 8 (d) is a diagram showing Peppers in accordance with the first embodiment of the present invention;

fig. 8 (e) is an encrypted image of the Airplane graph after the algorithm according to the embodiment of the present invention;

FIG. 8 (f) is an encrypted image of the Baboon diagram after the algorithm according to the embodiment of the present invention;

FIG. 8 (g) is an encrypted image of the Lena graph after the algorithm according to an embodiment of the present invention;

FIG. 8 (h) is an encrypted image of the Peppers graph after the algorithm according to the first embodiment of the present invention;

fig. 9 (a) illustrates an embedding capacity of 337 random pictures in the BOSS gallery, where the quality factor is QualityFactor (QF) =50;

fig. 9 (b) is an embedded capacity of 337 random pictures in the BOSS gallery according to an embodiment of the present invention, where the quality factor is QualityFactor (QF) =60;

fig. 9 (c) illustrates an embedding capacity of 337 random pictures in the BOSS gallery, where the quality factor is QualityFactor (QF) =70;

fig. 9 (d) shows an embedding capacity of 337 random pictures in the BOSS gallery, where the quality factor is QualityFactor (QF) =80;

fig. 10 (a) is a diagram illustrating the effect of embedding capacity of a babon image under different quality factors according to an embodiment of the present invention;

FIG. 10 (b) is a graph showing the embedded volume effect of Boat images at different quality factors according to an embodiment of the present invention;

FIG. 10 (c) is a graph showing the effect of embedding capacity of the Couple image under different quality factors according to an embodiment of the present invention;

fig. 10 (d) is a graph showing the embedding capacity effect of Lena images under different quality factors according to an embodiment of the present invention.

Detailed Description

The invention is further described with reference to the following figures and examples.

It is to be understood that the following detailed description is exemplary and is intended to provide further explanation of the invention as claimed. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs.

It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of exemplary embodiments according to the invention. As used herein, the singular forms "a", "an", and "the" are intended to include the plural forms as well, and it should be understood that when the term "comprising" is used in this specification, it indicates the presence of the feature, step, operation, device, component, and/or combination thereof.

It should be noted that the flowchart and block diagrams in the figures illustrate the architecture, functionality, and operation of possible implementations of methods and systems according to various embodiments of the present disclosure. It should be noted that each block in the flowchart or block diagrams may represent a module, segment, or portion of code, which comprises one or more executable instructions for implementing the logical function specified in the various embodiments. It should also be noted that, in some alternative implementations, the functions noted in the block may occur out of the order noted in the figures. For example, two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order, depending upon the functionality involved. It will also be noted that each block of the flowchart illustrations and/or block diagrams, and combinations of blocks in the flowchart illustrations and/or block diagrams, can be implemented by special purpose hardware-based systems which perform the specified functions or acts, or combinations of special purpose hardware and computer instructions.

Example one

As shown in fig. 1, the embodiment provides a method for hiding reversible information of JPEG images based on Paillier homomorphic encryption, which is applied to a sender and includes:

and the ciphertext image containing the secret information is sent to the receiving party, so that the receiving party can extract the ciphertext image containing the secret information in a separable way to obtain the secret information.

Specifically, the present embodiment first operates in the quantized DCT Coefficient (DCT discrete cosine transform) in the JPEG image, and divides the DCT Coefficient into two types, one type is a Direct current Coefficient (DC Coefficient), and this portion is chaotically encrypted; the other part is Alternating Current coefficients (AC coefficients), and in the sending party, assuming that EA is obtained after paillier encryption when an AC coefficient to be embedded is encountered, secret information is B, the secret information is EB by paillier encryption, and embedding the secret information into the AC coefficient is a multiplication characteristic by the paillier encryption: the ciphertext domain multiplication corresponds to addition in the plaintext, and the operation performed in the ciphertext domain is EC = EA × EB, which corresponds to a + B in the plaintext domain; on the receiving side, the secret information can be extracted separately after receiving the ciphertext image: and (3) firstly decrypting and then extracting to obtain a ciphertext EC, then directly carrying out paillier decryption to obtain A + B, and then extracting secret information.

Extracting first and then decrypting, and calculating L ([ EC ] by using the operators lambda (n) and mu (the operators are given by the key) in the key] ^λ(n) mod n ² ) And multiplying the multiplied mu to calculate a plaintext A + B, extracting the secret information, and then decrypting to recover the original image.

The technical scheme of the embodiment mainly comprises three parts, namely a first part: briefly introducing a Paillier homomorphic encryption algorithm; a second part: introducing a flow chart and main innovation points of a JPEG image reversible information hiding method based on Paillier homomorphic encryption; and a third part: experimental results and experimental analyses were performed.

1. Brief introduction to Paillier homomorphic encryption Algorithm

1. paillier homomorphic encryption

In a homomorphic encryption system, the cipher text can be directly subjected to arithmetic operation, and the obtained result is consistent with the result of the corresponding operation in the plain text domain. Encryption technologies with homomorphic and probabilistic properties have been widely used in the field of encrypted signal processing or third-party data processing. The Paillier encryption system is an addition homomorphic public key encryption system, and the encryption and decryption mechanisms of the Paillier encryption system are as follows:

1.1 Key Generation

Firstly, two large prime numbers p and q are selected, and the greatest common divisor of p × q and (p-1) × (q-1) is ensured to be in accordance with the following formula:

gcd(pg,(p-1)(q-1))＝1

thus canEnsuring that the two prime numbers are equal. N = pq and λ = lcm (p-1, q-1) were calculated, where lcm (a, b) represents a and b. Randomly selected integers

After a series of calculations, the order of n to satisfy the integer division g is (n, g) for the public key and λ for the private key, where gcd (L (g) is to be satisfied ^λ modn ² ) N) =1 wherein

Representing fractional division.

1.2 encryption Process

Let m be a positive integer between 0 and n, and randomly select r such that r satisfies two conditions: 1. 0 to<r<n; 2. r is at

Is the inverse of the multiplication, i.e.

M is encrypted to c according to the following formula.

c＝E[m,r]＝g ^m r ^N mod N ²

Where m represents plaintext, the parameter r is a parameter in the key, which is not needed at the decryption end, (N, g) is a public key, and c is an encrypted value.

1.3 decryption Process

The decryption process for ciphertext c is as follows:

where c is the ciphertext, (N, g) is the public key, and m is the plaintext that is ultimately decrypted.

Additive homomorphism features

Selecting two arbitrary plaintexts m ₁ And m ₂ Randomly selecting a parameter r ₁ And r ₂ Encrypting to E [ m ] respectively ₁ ,r ₁ ]，E[m ₂ ,r ₂ ]The following formula features:

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

we can learn by formula; the multiplication of the two ciphertexts is equal to the addition of the plaintext fields.

Theorem (I): namely that

With a unique c = E [ m, r ]]In one correspondence, the algorithm uses this theorem in the process of embedding the encrypted coefficients, and is explained explicitly below.

2. Chaos cipher

Chaotic systems have several characteristics: pseudo-randomness, convenience, certainty, and sensitivity to initial conditions. These properties are consistent with many requirements of cryptography, and the inevitable link between chaos theory and cryptography also forms chaotic ciphers.

The mixed theory encryption mode mainly utilizes a sequence iterated by a chaotic system and takes the sequence as a factor sequence of encryption exchange. The chaos encryption theory is the self-similarity characteristic of the chaos system, and achieves the aim of similarity with the whole in the form of locally selected chaos keys and redistribution. In the prior art, encrypted parameters are set through chaotic encryption, then an image is encrypted by utilizing the encrypted parameters, and the encrypted Least Significant Bit (LSB) is inserted into a ciphertext image.

The important point of the safety of the chaotic series is that even if an illegal person grasps the equation of the chaotic sequence, the initial value of the chaotic sequence and the parameters used in the chaotic sequence are difficult to guess. In contrast, the logistic chaotic encryption is a simple and significant nonlinear iterative equation, the logistic mapping is a dynamic system of statistical population, and the equation can be written as follows:

wherein x is _n Is a mapping variable, mu is a parameter of the system, and the value range of the variables is-1<x _n <1，0<μ<2。

The basic principle of chaotic encryption is to take a chaotic series generated by a chaotic system as a key sequence and encrypt a plaintext by using the key sequence. The chaos is determined by the equation, initial condition and parameters of the nonlinear system, and can be completely reconstructed when the parameters of the system are the same as the initial condition. The receiver can decrypt the plaintext signal by using chaotic synchronization.

2. JPEG image RDH-EI algorithm based on paillier homomorphic encryption

In the present embodiment, a new separable RDH algorithm for paillier homomorphic encryption will be described in detail. Three major innovation points of the algorithm are described in

priority

1, 2 and 3, wherein the three major innovation points comprise embedding of secret information while homomorphic encryption is utilized, a parameter r controls the size of an AC coefficient after encryption so that overflow cannot occur, and a model of multi-number encryption. The framework of the present algorithm is shown in fig. 1.

1. paillier encryption with information embedding

The data owner divides the original image I into a plurality of non-overlapping 8 x 8 blocks, sorts the quantized DCT blocks by the number of 0 coefficients, has a DC component and an AC component in each block, and for JPEG images the low frequency DC component contains most of the information of the image and we embed the information into the AC component. As shown in fig. 2.

Firstly, pre-operation is carried out, after the to-be-embedded bit KEY is selected from the DCT alternating current coefficient, the coefficient with the absolute value larger than the embedded bit is moved for one bit in the direction of increasing the numerical value, and a space is left for embedding, so that separable extraction can be ensured when the embedded information is extracted. In the algorithm, data is embedded by utilizing homomorphism, and the embedded secret information can be converted into a form capable of being embedded by utilizing homomorphism based on a formula.

c＝E[m,r]＝g ^m r ^N mod N ²

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

Let A be an initial image sequence with size N x N, embedding matrix with extracted DC coefficient by using homomorphic encryption characteristic, performing zigzag scanning, and embedding when meeting AC coefficient position

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

Wherein m is ₁ 、m ₂ Representing two different ciphertexts, r ₁ 、r ₂ Their parameters, (N, g) represent the public key in the cryptosystem, E.]Representing an encryption operation, D.]Representing a decryption operation.

The AC coefficient on the embedding bit and the encrypted secret information are embedded by utilizing the homomorphic characteristic of multiplication and are brought into a formula of multiplication of two numbers.

In order to enable the image in the ciphertext domain to be directly decrypted, when paillier encryption is carried out, a threshold value T and a parameter r can be used for carrying out the range (-1024, 1024) which accords with the quantized DCT coefficient on the encrypted data, when paillier multiplication is used for carrying out homomorphic embedding, the size of an embedded number cannot be controlled, and the embedded AC coefficient is controlled to be (-128, 128) in the algorithm.

As shown in the above equation. Thus, the embedded data is subjected to the operation of the encrypted coefficient range according to the threshold T and the parameter r.

Therefore, the embedded encrypted data can be in a certain range, and the separation can be realized when the receiver extracts the information, namely the information can be extracted from the ciphertext, and the information can also be extracted from the decrypted plaintext.

2. Control of parameter r to encrypted value in homomorphic encryption

2.1 plain text to cipher text mapping characteristics in homomorphic encryption

In the process of encryption, the processes of generating the public key and the private key are fixed, but for image pixels, the ciphertext generated by the encryption method generates the same waveform as the pixel histogram statistic of the plaintext. And, for a JPEG image, the range size of the coefficients in the quantized DCT coefficients is [ -1024,1024]. Under the condition that the key parameters are the same, the plaintext and the ciphertext after homomorphic encryption are mapped one by one.

When the parameter r is fixed: for example, when the key is N = p × q =11 × 13=143,g =8400, that is, when the public key of the cryptosystem is (143,8400) and the encrypted digital text is m =11,m =12,m =13, when r =3, the value after encryption is c _m＝11 ＝13180，c _m＝12 ＝1114，c _m＝13 ＝12407。

Random parameters g and r are selected in the paillier homomorphic encryption process, the order of the parameter g is a nonzero multiple of n, and the parameter g participates in the encryption and decryption processes of data, so that the algorithm fixes the value of g and operates the encrypted parameter r. In order to solve the problem of consistent image waveforms and make encrypted images more meaningful, different parameter r values are selected for encryption, and when r takes different parameters, the encrypted values are different.

Each encryption is performed by generating random r, and the parameter r is a prime number with n in the range of 2 to n, namely r belongs to [2, n ]. The encryption is performed from 2 to n at the encryption end r in a circulating mode, and the size of the encrypted alternating current coefficient can be controlled through different parameters r.

When the parameter r varies: such as a keyN = p × q =11 × 13=143,g =8400, and when the encrypted numerical value is 10, when r =2,3,4, the value after encryption is c _r＝2 ＝5101，c _r＝3 ＝19915，c _r＝4 ＝20029。

2.2 controlling ciphertext size with parameter r

The parameter r exists only in the encryption formula, and the value of the parameter r is no longer needed in the decryption formula. If the parameter r is a fixed value, the histogram of the encrypted image is similar to the waveform of the histogram of the plaintext image before encryption. The encrypted coefficient histogram is easy to identify and attack as the unencrypted histogram waveform. Therefore, in order to keep the encrypted ciphertext within the maximum range of the DCT coefficient and have good ciphertext property, the encryption is carried out in r epsilon [2, n ] in the encryption process.

As shown in FIG. 3, where m ₁ 、m ₂ 、m ₃ 、m ₄ 、m ₅ Are all plain text, marked by asterisks ₃ Just waiting to embed into the position, the size range of the ciphertext is adjusted through the operation of the parameter r, m ₃ Different parameters r can be selected _c 、r _d 、r _e Then different encrypted ciphertexts are generated to determine the ciphered ciphertext c _3rc 、c _3rd 、c _3re Such that the range of the ciphertext can be controlled to be between (-128,128) by the portion of the overflow operation in this embodiment. Where m represents the plaintext coefficients, the quantities are represented by black curves, and E (m) represents the encrypted numerical curve. D (E (m)) represents a numerical curve obtained by decrypting the encrypted water-tight text data.

3. Multi-number encryption model

In fig. 4, the quantized DCT coefficients are obtained from the original plaintext image, which is divided into 8 × 8 blocks as can be seen. And performing demonstration operation on one block, wherein in the 8 multiplied by 8DCT demonstration block, the dark color part is a direct current coefficient and is subjected to chaotic encryption, the light color part is an alternating current coefficient of secret information to be embedded, and other white parts are other alternating current coefficients. Wherein, paillier encryption is carried out in the alternating current coefficient. The method comprises the steps that a pentagram mark is marked in an alternating current coefficient distribution diagram to be embedded with a tributary coefficient, the part is subjected to paillier encryption and embedded with secret information, other green parts are non-embedded direct current coefficients, and the part is only subjected to paillier encryption.

4. RDH-EI framework

The JPEG homomorphic encryption reversible information hiding algorithm proposed in this embodiment is as shown in fig. 1, and first reads the DCT coefficients after JPEG image quantization, and encrypts the DC and AC coefficients respectively. Chaotic encryption is performed on the DC coefficient, homomorphic encryption is performed on the AC coefficient, and embedding is performed by utilizing the multiplication characteristic of the AC coefficient, and the detailed steps are pointed out in the following.

5. Can be separated and extracted

In fig. 5, the extraction of the secret information and the recovery of the original image are briefly described, and the algorithm may separate the extracted information (a) from the ciphertext image containing the secret information, first extract the private information to generate (b) the ciphertext image, and then decrypt the ciphertext image to obtain the plaintext image. (a) If the image is decrypted, the (d) plaintext image containing the secret information is generated, and the privacy information can be extracted from the plaintext image. The specific steps are described in the following two subsections.

5.1 extract first and decrypt later

As with the embedding process, the receiver first 8 × 8 blocks the quantized DCT coefficients of the ciphertext image containing the secret information, sorts by how many 0 coefficients of each block, and decrypts according to the range of coefficients by the embedded information. The following is the derivation procedure:

is provided with

Then the

At this time

Thus is that

This is the encryption of a new message, m ₁ +m ₂ Having a random element r ₁ ·r ₂ . Decryption of c ₁ And c ₂ First (c) ₁ ·c ₂ ) Power λ (n):

known from the theorem of Kamichael (r) ₁ ·r ₂ ) ^nλ(n) ≡1mod n ² ：

g ^λ(n) ＝(1+n) ^{λ(n)[g](1+n)} mod n ²

(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

Thus, 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 { λ (n) [ g ]](1 + n) so the decryption process is done by multiplying by μ, resulting in m ₁ +m ₂ mod n。

Example (c): it is assumed that a public key (n, g) = (11 × 13, 20049) = (143, 20449), λ (n) =60, μ =114 has been proposed. If someone encrypts two messages, say (m) ₁ ，r ₁ ) = (2, 4) and (m) ₁ ，r ₂ ) = (3,7), the resulting ciphertext will be E (m) ₁ ) =19460 and E (m) ₂ )＝12170。

Product E (m) of these ciphertexts ₁ )·E(m ₂ ) Is composed of

E(m ₁ )·E(m ₂ )＝19460×12170＝236828200＝8331mod 20449

The decryption process proceeds from computing L ([ E (m) ] ₁ )·E(m ₂ )] ^λ(n) mod n ² ) Beginning:

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

finally, multiplying the result by μ =114 completes the decryption process:

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

the algorithm can thus extract the secret information in the ciphertext domain in the above-described operations without destroying the ciphertext.

5.2 decryption before extraction

The ciphertext image with the private information is decrypted first. Firstly, chaotic decryption is carried out on the DC coefficient in the quantized DCT coefficient, and high-frequency information in the image can be restored to the original position, wherein the high-frequency information contains a large amount of important information of the image. And secondly, directly carrying out paillier decryption on the AC coefficient:

and then, extracting the information according to the embedded KEY KEY, and recovering the image while extracting the information, thereby completely hiding the reversible information.

6. Overflow handling

When the quantized DCT coefficients are encrypted, an image must maintain the same cryptographic scheme. The AC coefficients in the quantized DCT coefficients are encrypted after the key is selected. For natural images, the value of the pixel AC coefficient ranges 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 according to the difference of the values of the r, the encrypted AC coefficient is subjected to complementation, and if the complemented coefficient is between-128 and 128, the encrypted AC coefficient can be written into a JPEG image. The remainder is T for the encrypted number, so that the decryption can be performed according to the remainder T during decryption.

c＝e mod 128

Wherein e is the encrypted AC coefficient, c represents the encrypted AC coefficient after being subjected to residue extraction, and T represents the remainder of the encrypted AC coefficient.

TABLE 1 encrypted coefficients corresponding to the range (-128,128) obtained for different parameters r

For example, the public key cryptosystem is (n, g) = (143, 9622), and when the peak values in the DCT coefficients are 1 and-1, we perform an embedding operation thereon. Assuming that the embedded secret information is '1', for the peak value of '1' in the AC coefficient, we need to encrypt the AC coefficient and the embedded secret information separately, and then embed the secret information by using the multiplication characteristic of homomorphic encryption. While the encrypted value must also conform to the overflow handling operation, e.g. when the encrypted AC coefficient is c ₁ =12884, overflow handling is satisfied at this time, and the encrypted embedded information is c at this time ₂ =12884, perform embedding:

c _e ＝c ₁ c ₂ ＝12884×12884mod n ² ＝12923mod n ²

c _e '＝c _e mod128＝12923mod128＝123

upon decryption, traversal to the extent of [ -128,128,128]With embedded secret information, exemplified by the above value, the value c with secret information _e ' =123, and at the extraction end, the value is restored to the value before the control coefficient size according to the threshold value T.

7. Ciphertext collision avoidance processing

In the Paillier homomorphic encryption system, for a certain numerical value in the same encryption system, the parameter r is determined to ensure the one-to-one mapping between the plaintext and the ciphertext. However, for an image, it is necessary to operate on a plurality of coefficients, for example, the coefficient with the highest peak value in an image is determined as KEY, and assuming that the embedded coefficient is '1', the security of the image can be ensured by one-to-one mapping between plaintext and ciphertext in the same encryption system, but at this time, the waveform of the statistical histogram of the plaintext image is the same as that of the ciphertext image, which is not beneficial for secure transmission, so the transformation of the waveform is adjusted by adjusting a plurality of parameters r. Because Paillier encryption is also performed on other non-embedded AC coefficients, ciphertext collision may occur when r =39, for example, n =11 × 13=143, g =9927, λ =60, and AC coefficient AC =4, and the generated ciphertext is 9633 but the value after decryption is 101, which indicates that the encrypted ciphertext with plaintext value "4" collides with the encrypted ciphertext with plaintext value "101", because the encrypted ciphertext needs to be controlled within a certain range, so that the range after encryption by Paillier becomes smaller, and ciphertext collision occurs.

TABLE 2 demonstration table for collision control of different parameters r to partial number ciphertext

From Table 2, the different quantized DCT coefficients-5, -4, -3, -2, -1, 2,3,4, 5; in order to control the size of the encrypted coefficient, a threshold value T =75 is adopted, and values of the parameter r are respectively determined to be 98, 64, 38, 36, 136, 95, 136, 36, 38, 64 and 98 through the value range after screening; obtaining the values of the encrypted coefficients-9701, -9619, -9641, -9629, -9635, -9604, 9635, 9629, 9641, 9619, 9701; the encrypted value is left with 128: -101, -19, -41, -29, -35, -4, 35, 29, 41, 19, 101.

3. Experiment and analysis of results

In the experiments of the examples, we downloaded some commonly used 512 by 512 images, including Baboon, couple, boat, lena, from the USC-SIPI image database. Meanwhile, 337 images are randomly extracted from the BOSS image library to analyze the feasibility of the algorithm.

1. Feasibility of algorithm

1.1 Algorithm verification on Single Picture

The experiment firstly selects an image lena diagram to verify the feasibility of the algorithm, an 8-bit gray image (shown as a diagram a) with the image size of 512 × 512 is respectively processed on a direct current coefficient and an alternating current coefficient which are subjected to quantized DCT transformation, chaotic encryption is carried out after the direct current coefficient is independently extracted, information embedding is carried out while Paillier encryption is carried out after the alternating current coefficient is extracted, parameters p =13 and q =17 of a Paillier encryption system are adopted, the upper limit value N = p × q =221.R belongs to [2, N ] content owner of a plaintext which can be encrypted hides secret information in the alternating current coefficient, and the specific experiment result is as follows in a diagram 6 (a) -a diagram 6 (c):

first, fig. 6 (a) is divided into 8 × 8 blocks, and the quantized AC coefficients are homomorphically encrypted by paillier while embedding information. The method implements a ciphertext image of RDH, and fig. 6 (c) is a decrypted encrypted image.

Fig. 7 (a) -7 (c) are diagrams showing the effect of chaotically encrypting the dc coefficients in the algorithm, fig. 7 (a) is a plaintext image to be operated, fig. 7 (b) is an image obtained by extracting the dc coefficients from the plaintext image, and the image retains the basic contour of the plaintext image, and the image is still well recognized, and fig. 7 (c) is a dc coefficient after chaotically encrypting, and the PSNR of the dc coefficient is 22.8.

In order to further evaluate the performance of the algorithm, 4 8-bit grayscale images with a size of 512 × 512 as shown in fig. 8 (a) -8 (d) were selected for testing. In the experiment, 4 carrier images are subjected to 8 × 8 blocking, and under the condition that the QF quality factor is 50, the embedded secret information is a comparison graph of a pseudo-random series with 2500 bits.

The PSNR values of the airplan in fig. 8 (a) when 2500 bits are embedded are 9.73, the PSNR values of the Baboon in fig. 8 (b) when 2500 bits are embedded are 6.606, the PSNR values of the Lena in fig. 8 (c) when 2500 bits are embedded are 6.102, and the PSNR values of the Peppers in fig. 8 (d) when 2500 bits are embedded are 5.749. Fig. 8 (e) -fig. 8 (h) correspond to the four images of fig. 8 (a) -fig. 8 (d), respectively, after the four images are subjected to the algorithm.

1.2 Algorithm validation in BOSS database

In fig. 9 (a) to 9 (d), 337 grayscale images of 512 × 512 were randomly selected from the BOSS gallery, and their embedding capacities after compression into JPEG images were counted, and the quality factors were QualityFactor (QF) =50, 60, 70, and 80, and the maximum embedding capacity for each image was calculated. Fig. 9 (a) shows the embedding capacity distribution when QF =50, the minimum embedding capacity indicated by a straight line is 6912 bits, fig. 9 (b) shows the embedding capacity distribution when QF =60, the minimum embedding capacity indicated by a straight line is 7697 bits, fig. 9 (c) shows the embedding capacity distribution when QF =70, the minimum embedding capacity indicated by a straight line is 8473 bits, fig. 9 (d) shows the embedding capacity distribution when QF =80, and the minimum embedding capacity indicated by a straight line is 9610 bits.

2. Analysis of experiments

The performance of the algorithm of this embodiment in terms of embedding capacity, file increment, PSNR value, etc. is analyzed as follows:

2.1 embedding Capacity

In the scheme of this embodiment, the size of the encrypted key determines the block that cannot be embedded, but in the quantized DCT coefficients, the coefficient must be less than N to ensure the plaintext to be decrypted accurately, and we perform statistics of maximum ac coefficients of different quality factors on four graphs. As shown in table 3:

TABLE 3 values of the maximum AC coefficient for the four images at different quality factors

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

As can be seen from table 3, when the maximum value of the ac coefficient is the quality factor QF =80, and when QF =80 in the lena diagram is 159, that is, when the value of the key N is greater than 159, it can be guaranteed that the ciphertext can be completely decrypted without error, which is also an important reason that the embedding capacity of the algorithm is larger than that of other methods.

A comparison of how many embedded blocks are for different algorithms, with a quality factor of 80, is shown in table 4:

TABLE 4 comparison of how many different algorithms embed blocks

Analysis of the table above can result in the blocks of DCT coefficients after being divided into 8 by 8 blocks, which are divided into three forms: rule blocks, singular blocks, non-embeddable blocks. The rule block is a block that can be used completely, the singular block is a block that can be embedded under certain conditions, and the non-embedded block is a block that cannot be embedded with any data. For the present algorithm, a 512 by 512 image is divided into 4096 blocks of DCT coefficients. The present algorithm can fully utilize these blocks so the embedding capacity is better than other algorithms.

Fig. 10 (a) -10 (d) show the comparison of the proposed algorithm of this embodiment with other algorithm frameworks in terms of embedding capacity. When the mass coefficients are QF =50, QF =60, QF =70, and QF =80, they are compared with fig. 10 (a) babon, fig. 10 (b) Boat, fig. 10 (c) Couple, and fig. 10 (d) Lena. As can be seen from the implementation results, the baboons with more complex textures had the largest overall embedding capacity. As the quality factor increases, the embedding capacity also increases. In addition, the embedding capacity of the three images also increases along with the increase of the quality factor, and the embedding capacity of the algorithm provided by the embodiment is superior to that of other algorithms. In the algorithm of the present embodiment, no embedding failure occurs regardless of the embedding capacity. This can secure the effect of high embedding capacity, but the cost of the file is significantly increased in order to obtain higher embedding capacity.

The embodiment provides a JPEG image paillier homomorphic encryption domain reversible information hiding algorithm based on a quantized DCT coefficient. Experimental results and analysis show that the performance of the scheme is better than that of other schemes. The main contributions of the method are as follows:

1. the method proposes that the quantized DCT coefficient is subjected to double encryption, the direct current coefficient (DC coefficient) is subjected to safer chaotic encryption, the AC coefficient is subjected to addition homomorphic encryption, and the data is processed by adopting the characteristic of paillier homomorphic encryption (multiplication operation of multiplication characteristics in a ciphertext domain is equivalent to addition operation in a plaintext domain).

2. The proposed encryption JPEG quantization DCT coefficient RDH scheme orders the number of AC 0 coefficients in each 8 x 8 quantized DCT block, firstly selects a smooth block for embedding, and performs histogram shifting in the embedded block, so that other invalid histogram shifting which is not embedded in the block can be performed.

3. During encryption, reverse thinking is carried out, and a ciphertext meeting the range of DCT is generated according to the threshold T and the parameter r, so that the condition of Paillier homomorphic encryption can be met, and the size range of DCT can also be met. According to the Paillier homomorphic encryption multiplication characteristic, information can be embedded during encryption, and a more optimized scheme can be selected from embedding schemes for Paillier homomorphic encryption in the future to realize balance between file increment and embedding capacity.

Example two

The embodiment provides a JPEG image reversible information hiding system based on Paillier homomorphic encryption.

It should be noted here that the encryption module and the decryption module are the same as the example and the application scenario realized by the steps in the first embodiment, but are not limited to the disclosure of the first embodiment. It should be noted that the modules described above as part of a system may be implemented in a computer system such as a set of computer-executable instructions.

EXAMPLE III

The embodiment provides a JPEG image reversible information hiding method based on Paillier homomorphic encryption.

A JPEG image reversible information hiding method based on Paillier homomorphic encryption is applied to a receiving party and comprises the following steps:

receiving a ciphertext image containing the secret information, and performing separable extraction on the ciphertext image containing the secret information to obtain the secret information;

the ciphertext image containing the secret information is obtained by embedding the secret information into an AC coefficient, the AC coefficient is subjected to secret information embedding by utilizing multiplication characteristics of paillier encryption and paillier homomorphic encryption, a DC coefficient is subjected to chaotic encryption 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 JPEG original image and quantizing.

The specific implementation steps of the technical solution in this embodiment are the same as those in the first embodiment, and are not described herein again.

Example four

a decryption module configured to: receiving a ciphertext image containing secret information, and performing separable extraction on the ciphertext image containing the secret information to obtain the secret information;

an encryption module configured to: the ciphertext image containing the secret information is obtained by embedding the secret information into an AC coefficient, the AC coefficient is subjected to secret information embedding by utilizing multiplication characteristics of paillier encryption and paillier homomorphic encryption, a DC coefficient is subjected to chaotic encryption 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 JPEG original image and quantizing.

EXAMPLE five

The present embodiment provides a computer-readable storage medium, on which a computer program is stored, 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 or third embodiment.

EXAMPLE six

The embodiment provides a computer device, which includes a memory, a processor and a computer program stored in the memory and capable of running on the processor, wherein the processor executes the program to implement the steps in the JPEG image reversible information hiding method based on Paillier homomorphic encryption as described in the first embodiment or the third embodiment.

These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.

The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A JPEG image reversible information hiding method based on Paillier homomorphic encryption is characterized in that the method is applied to a sender and comprises the following steps:

2. The method for hiding the reversible information of the JPEG image based on Paillier homomorphic encryption according to claim 1, wherein the AC coefficient is embedded by utilizing the multiplication characteristics of the Paillier encryption and the Paillier homomorphic encryption, and the method comprises the following steps: the number of AC coefficients "0" is calculated in each DCT block to generate the embedded sequence in descending order.

3. The JPEG image reversible information hiding method based on Paillier homomorphic encryption according to claim 1, wherein the enabling of a receiver to decrypt the ciphertext image containing the secret information comprises: so that the receiver extracts the private information to generate a ciphertext image, and the ciphertext image is decrypted to obtain a plaintext image; or, the receiving party decrypts the image to generate a plaintext image containing the secret information, and the privacy information is extracted from the plaintext image.

4. A JPEG image reversible information hiding system based on Paillier homomorphic encryption is characterized in that the system is applied to a sender and comprises the following components:

5. A JPEG image reversible information hiding method based on Paillier homomorphic encryption is characterized in that the method is applied to a receiving party and comprises the following steps:

6. The JPEG image invertible information hiding method based on Paillier homomorphic encryption according to claim 5, wherein embedding the AC coefficients by utilizing multiplication characteristics of the Paillier encryption and the Paillier homomorphic encryption comprises: the number of AC coefficients "0" is calculated in each DCT block to generate the embedded sequence in descending order.

7. The JPEG image reversible information hiding method based on Paillier homomorphic encryption according to claim 5, wherein the decrypting the ciphertext image containing the secret information comprises: extracting the private information to generate a ciphertext image, and decrypting the ciphertext image to obtain a plaintext image; or, the clear text image containing the secret information is generated by decryption, and the privacy information is extracted from the clear text image.

8. A JPEG image reversible information hiding system based on Paillier homomorphic encryption is characterized by comprising:

9. A computer-readable storage medium, on which a computer program is stored, which, when being executed by a processor, carries out the steps of the method for reversible information hiding in JPEG images based on Paillier homomorphic encryption according to any of the claims 1-3 or 5-7.

10. Computer device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, characterized in that the processor implements the steps in the method for reversible information hiding in JPEG images based on Paillier homomorphic encryption according to any of the claims 1-3 or 5-7 when executing said program.