CN117793264B - JPEG (joint photographic experts group) encryption domain reversible information hiding algorithm for separating and extracting sensitive information - Google Patents
JPEG (joint photographic experts group) encryption domain reversible information hiding algorithm for separating and extracting sensitive information Download PDFInfo
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Abstract
The invention relates to the technical field of data storage security, in particular to a JPEG (joint photographic experts group) encryption domain reversible information hiding algorithm for separating and extracting sensitive information. The method comprises the steps of partitioning and quantizing a JPEG original image to obtain quantized DCT coefficients, and dividing an image matrix into 64X 64 DCT coefficient blocks with the size of 8X 8; counting the number of coefficients with the median value of 0 in the AC coefficient in each 8 multiplied by 8 DCT coefficient block, and sorting from large to small and embedding according to the sorting according to the counting result; DC coefficient in each 8 multiplied by 8 DCT coefficient block is encrypted by one-dimensional tangent chaos, AC coefficient is encrypted by Paillier homomorphic, ciphertext image is generated, ciphertext image is decrypted, embedded sensitive information is separated and extracted to obtain JPEG original image, encryption safety and image quality stability are improved by Paillier homomorphic encryption technology, capacity of embedding additional information on compressed image is improved, separable sensitive information extraction is realized, and decryption result is not affected.
Description
Technical Field
The invention relates to the technical field of data storage security, in particular to a JPEG (joint photographic experts group) encryption domain reversible information hiding algorithm for separating and extracting sensitive information.
Background
With the development of cloud computing, cloud storage is a main mode of data storage, the public does not need to purchase special storage equipment to store a large amount of personal data, but selects the mode of cloud storage to store the large amount of personal data, so that the cost caused by data storage is greatly saved, and at the same time, immeasurable risks such as leakage, tampering and propagation of personal privacy data exist in the cloud-stored data. To solve such problems, encryption domain reversible information hiding has been developed. The encryption domain reversible information hiding means that in order to store a data file more safely, a content owner encrypts file data before uploading the multimedia file to make the data invisible, and a cloud platform manager embeds some additional sensitive information in the encrypted multimedia data to facilitate management and storage of the encrypted multimedia data, so that cloud platform storage resources are managed more conveniently.
Most of encryption domain reversible information hiding methods are applied to uncompressed images, and the uncompressed images have more embedding space, larger embedding capacity and good performance of embedding additional data. But today more popular is a joint photographic experts group (Joint Photographic Experts Group, JPEG) image that compresses the image in such a way that the additional information embedded in the JPEG image is less. When the content owner encrypts the uploaded multimedia file, most of the encryption methods adopt a symmetrical encryption or stream encryption mode, the encryption mode is too simple and is easy to crack the encrypted content by an attacker, so that the privacy data uploaded by the user is obtained, and meanwhile, the traditional encryption methods cannot modify the ciphertext data after encryption and embed additional information.
Disclosure of Invention
In view of this, the present invention provides a reversible information hiding algorithm in the JPEG encryption domain for separating and extracting sensitive information, which is used to improve the security of encryption and the stability of image quality, and to increase the capacity of embedding additional information on a compressed image, so as to realize separable and extractable sensitive information, and to operate the encrypted ciphertext without affecting the decryption result.
In a first aspect, the present invention provides a JPEG encryption domain reversible information hiding algorithm for separating and extracting sensitive information, the algorithm comprising:
Step one, processing a JPEG original image, blocking and quantizing the JPEG original image by adopting 512 multiplied by 512 to obtain quantized Discrete Cosine Transform (DCT) coefficients, and dividing an image matrix into 64 multiplied by 64 DCT coefficient blocks with 8 multiplied by 8, wherein each DCT coefficient block with 8 multiplied by 8 comprises a Direct Current (DC) coefficient and an Alternating Current (AC) coefficient;
Counting the number of coefficients with the median value of 0 of the AC coefficients in each 8X 8 DCT coefficient block according to 64X 64 8 DCT coefficient blocks in the first step, and sorting from large to small and embedding according to the sorting;
Thirdly, according to the embedding in the second step, adopting one-dimensional tangent chaotic encryption to DC coefficients in each 8 multiplied by 8 DCT coefficient block, and adopting Paillier homomorphic encryption to AC coefficients to generate a ciphertext image;
And step four, decrypting the ciphertext image according to the encryption in the step three, and separating and extracting the embedded sensitive information to obtain the JPEG original image.
Optionally, the AC coefficient using Paillier homomorphic encryption includes: selecting a coefficient with the median value of the AC coefficient of 1 or-1, adopting Paillier homomorphic encryption and simultaneously embedding sensitive information; the positive coefficients with the values of 1 or minus 1 are encrypted in the same state by Paillier; and for negative coefficients other than 1 or-1, using modified Paillier homomorphic encryption.
Optionally, the selecting a coefficient with the median of AC coefficient of 1 or-1, adopts Paillier homomorphic encryption and simultaneously embeds sensitive information, and includes:
S1, comparing the coefficient with the number of other coefficients with non-zero values according to the coefficient with the AC coefficient value of 1 or-1 in each 8X 8 DCT coefficient block to allocate the ciphertext value distribution range;
And S2, selecting binary data 0 or 1 to embed according to the distribution range of the ciphertext value in the step S1, and respectively carrying out Paillier homomorphic encryption on the 0 and the 1.
Optionally, after step S2, the method further includes: selecting and recording ciphertext after encrypting 0 and 1, and respectively marking asAnd/>Will/>And/>As a key for extracting sensitive information.
Optionally, the decrypting the ciphertext image, separating and extracting the embedded sensitive information to obtain the JPEG original image, includes:
step V1, calculating a key according to the extended Euclidean And/>Modulo multiplication inversion element/>And/>；
Step V2, according to the modular multiplication inverse element in step V1And/>Multiplying the image with the ciphertext value, calculating embedded sensitive information, and recovering the JPEG original image.
Optionally, the decrypting the ciphertext image, separating and extracting the embedded sensitive information to obtain the JPEG original image, includes:
Step W1, decrypting the ciphertext image according to the Paillier homomorphic encryption private key to generate a decrypted plaintext value;
and step W2, calculating embedded sensitive information according to the plaintext value in the step W1 and through the property of Paillier homomorphic encryption, and recovering the JPEG original image.
Optionally, the generating process of the private key includes:
a. randomly generating two prime numbers p and q, wherein p and q satisfy And/>The greatest common divisor of (2) is 1, and the formula is:
；
b. Generating private key coefficients Coefficient/>The formula of (2) is:
；
wherein lcm is the calculated least common multiple;
c. Constructing an L function, wherein the formula is as follows:
；
d. calculating private key coefficients Coefficient/>The formula of (2) is:
；
Wherein mod is a modulo operation, and the remainder is calculated;
e. According to the private key coefficient And/>Generating a private key as/>。
Optionally, the formula for ciphertext value c is:
；
M is a plaintext value to be encrypted, and the public key received from the user at the cloud is (n, g); n is the product of p and q, and the integer g is randomly selected, and g meets the following requirements The value range is/>And the greatest common divisorG and/>Mutual quality; taking g=n+1, then the public key is (n, g); r is a random number randomly generated by a data encryption party, and r meets the/>And/>I.e. r and n are mutually prime.
In a third aspect, the present invention provides a computer readable storage medium, where the computer readable storage medium includes a stored program, where when the program runs, the program controls a device where the computer readable storage medium is located to execute the JPEG encrypted domain reversible information hiding algorithm for separating and extracting sensitive information in the first aspect or any possible implementation manner of the first aspect.
In a fourth aspect, the present invention provides an electronic device comprising: one or more processors; a memory; and one or more computer programs, wherein the one or more computer programs are stored in the memory, the one or more computer programs comprising instructions that, when executed by the device, cause the device to perform the JPEG encrypted domain reversible information hiding algorithm for separate extraction of sensitive information in the first aspect or any possible implementation of the first aspect.
In the technical scheme provided by the invention, the algorithm comprises the steps of processing a JPEG original image, adopting 512 multiplied by 512 to divide and quantize the JPEG original image to obtain quantized DCT coefficients, and dividing an image matrix into 64 multiplied by 8 DCT coefficient blocks, wherein each multiplied by 8 DCT coefficient block comprises a DC coefficient and an AC coefficient; counting the number of coefficients with the median value of 0 in the AC coefficient in each 8 multiplied by 8 DCT coefficient block, and sorting from large to small and embedding according to the sorting according to the counting result; DC coefficient in each 8 x 8 DCT coefficient block is encrypted by one-dimensional tangent chaos, AC coefficient is encrypted by Paillier homomorphic, ciphertext image is generated, ciphertext image is decrypted, embedded sensitive information is separated and extracted to obtain JPEG original image.
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In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings that are needed in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and that other drawings can be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flowchart of a method for generating a ciphertext image according to an embodiment of the present invention;
FIG. 2 is a block diagram of discrete cosine transform coefficients according to an embodiment of the present invention;
FIG. 3 is a block diagram of another DCT coefficient block according to one embodiment of the present invention;
Fig. 4 is a bifurcation diagram of the unimodal chaotic map provided by the embodiment of the invention;
FIG. 5 is a bifurcation diagram of a Chebyshev mapping provided by an embodiment of the present invention;
fig. 6 is a bifurcation diagram of a one-dimensional tangent chaotic map provided by an embodiment of the present invention;
fig. 7 is a schematic diagram of LE comparison of three chaotic mappings provided in an embodiment of the present invention;
fig. 8 is a schematic diagram of LE of a one-dimensional tangent chaotic map provided by an embodiment of the present invention;
FIG. 9 is a schematic diagram of SE comparison for three chaotic mappings provided by an embodiment of the present invention;
FIG. 10 is a flowchart of a method for decrypting ciphertext images according to an embodiment of the invention;
FIG. 11 is a schematic diagram illustrating encryption of plaintext data 10 according to an embodiment of the present invention;
FIG. 12 is a schematic diagram of encrypting plaintext data 50 according to an embodiment of the present invention;
fig. 13 is a schematic diagram of encrypting plaintext data 1 according to an embodiment of the present invention;
fig. 14 is a schematic diagram of another encryption of plaintext data 1 according to an embodiment of the present invention;
FIG. 15 is a diagram illustrating screening 10000-45000 ciphertext values according to an embodiment of the present invention;
Fig. 16 is a schematic diagram of an electronic device according to an embodiment of the present invention.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments of the present invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
It should be understood that the described embodiments are merely some, but not all, embodiments of the invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The terminology used in the embodiments of the invention is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. As used in this embodiment of the invention, the singular forms "a," "an," and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise.
It should be understood that the term "and/or" as used herein is merely one way of describing an association of associated objects, meaning that there may be three relationships, e.g., a and/or b, which may represent: the first and second cases exist separately, and the first and second cases exist separately. In addition, the character "/" herein generally indicates that the front and rear associated objects are an "or" relationship.
Depending on the context, the word "if" as used herein may be interpreted as "at … …" or "at … …" or "in response to a determination" or "in response to a detection". Similarly, the phrase "if determined" or "if detected (stated condition or event)" may be interpreted as "when determined" or "in response to determination" or "when detected (stated condition or event)" or "in response to detection (stated condition or event), depending on the context.
In order to ensure the safety of media data of the super-computing cloud platform and ensure the safe and reliable storage and forwarding of information, before uploading image data, a user firstly encrypts the image so as not to enable other people to see the uploaded data, and in order to facilitate management of data information on the cloud platform, a super-computing cloud platform manager additionally embeds sensitive information into the image data encrypted by the user, and when the user needs to download an original image, the system extracts the embedded sensitive information and recovers the original image data, so that safe and reliable storage and forwarding of information are realized. The method and the device are used for processing the most popular JPEG image format uploaded to the cloud platform by the user, so that the safety of the image data stored by the cloud platform is ensured.
The JPEG image is processed, sensitive information is embedded into the JPEG image, and three modes of reversible information hiding are realized, namely reversible information hiding (Reversible DATA HIDING, RDH) based on quantized DCT coefficient operation, RDH based on modified quantization table and RDH based on modified Huffman coding. The invention adopts RDH method based on quantized discrete cosine transform (Discrete Cosine Transform, DCT) coefficient operation to realize JPEG image reversible information hiding under encryption domain.
The invention adopts the Paillier homomorphic encryption technology to realize reversible information hiding in the JPEG image, and utilizes the property of Paillier homomorphic encryption: ciphertext multiplication is equal to plaintext addition, and sensitive information is embedded while encryption by using an RDH method for quantizing DCT coefficients in a JPEG image. Meanwhile, when alternating current components in DCT coefficients are encrypted, the distribution range of generated ciphertext values is controlled, the size of the ciphertext values is controlled, meanwhile, ciphertext is overflowed to form ciphertext images, and the ciphertext images are stored in a cloud platform.
In the embodiment of the invention, paillier homomorphic encryption is invented based on the difficult problem of composite residual class, and the encryption algorithm satisfies addition and multiplication homomorphic, so the Paillier homomorphic encryption is named Paillier name.
Fig. 1 is a flowchart of a method for generating a ciphertext image according to an embodiment of the present invention, as shown in fig. 1, the method includes:
Step one, processing a JPEG original image, adopting 512 multiplied by 512 to divide and quantize the JPEG original image to obtain quantized discrete cosine transform DCT coefficients, and dividing an image matrix into 64 multiplied by 64 DCT coefficient blocks with 8 multiplied by 8, wherein each DCT coefficient block with 8 multiplied by 8 comprises a direct current DC coefficient and an alternating current AC coefficient.
In the embodiment of the present invention, as shown in fig. 2, each DCT coefficient block includes 1 DC coefficient at the top left corner and 63 AC coefficients left, where the DC coefficients are referred to as DC coefficients, which represent average brightness values of an image, and have a large influence on image quality, and modifications thereof may cause loss and irreversible changes to the image, so that in the process of reversible information hiding, values of the DC coefficients are not modified as much as possible, and only encryption operation is performed on the DC coefficients; whereas AC coefficients are called AC coefficients, which have less impact on image quality and a greater range of variation, more information can be embedded, including most zeros and other data that tends to be zeros. As shown in fig. 3, a randomly selected 8 x 8 block of DCT coefficients, where-58 is the DC coefficient, and the remaining data (e.g., -4, 0,3, 1, 17, 6, -5, -1, -16, 11, -8, 5, 10, -3, 4, 2) are AC coefficients, which contain most of the data0 and 1 and-1.
And step two, counting the number of coefficients with the value of 0 in the AC coefficient in each 8X 8 DCT coefficient block according to 64X 64 8 DCT coefficient blocks in the step one, and sequencing from large to small and embedding according to the sequencing according to the counting result.
In the embodiment of the present invention, for a randomly selected 8×8 DCT coefficient block, as shown in fig. 3, it is found by statistics that the more DCT coefficient blocks with 0 coefficients are included in the AC coefficients, the more numbers 1 and-1 are included in the AC coefficients. The number of the 0-value AC coefficients in each 8 multiplied by 8 block is counted, the 0-value AC coefficients are ordered from large to small, the 0-value AC coefficients are selected to be embedded, and the embedding capacity is improved.
And thirdly, according to the embedding in the second step, adopting one-dimensional tangent chaotic encryption to DC coefficients in each 8 multiplied by 8 DCT coefficient block, and adopting Paillier homomorphic encryption to AC coefficients to generate a ciphertext image.
In the embodiment of the invention, when the DC coefficient is subjected to chaotic encryption, the DC coefficient is encrypted into a chaotic sequence with good chaotic performance by adopting one-dimensional tangent chaotic encryption; embedding ciphertext obtained by homomorphic encryption of binary data 0 or 1 while homomorphic encryption of AC coefficient PaillierAnd/>Forming ciphertext DCT coefficient, adopting a method for controlling the ciphertext value range of the AC coefficient in the homomorphic encryption process, and controlling the ciphertext value range of the AC coefficient containing embedded sensitive information to beOther AC coefficients control the ciphertext value range to/>A ciphertext image is formed.
In the embodiment of the invention, a mode of encrypting and embedding information is adopted, one-dimensional tangent chaotic encryption is firstly carried out on DC coefficients in each 8 multiplied by 8 DCT coefficient block, the safety of data is ensured, then 1 and-1 in AC coefficients are selected to carry out Paillier homomorphic encryption and simultaneously embed sensitive information, and the rest AC coefficients only carry out Paillier homomorphic encryption.
In the embodiment of the invention, the method for encrypting the AC coefficient by adopting the Paillier homomorphic encryption comprises the following steps: selecting a coefficient with the median value of the AC coefficient of 1 or-1, adopting Paillier homomorphic encryption and simultaneously embedding sensitive information; the positive coefficients with the values of 1 or minus 1 are encrypted in the same state by Paillier; and for negative coefficients other than 1 or-1, using modified Paillier homomorphic encryption.
In the embodiment of the invention, selecting the coefficient with the median value of the AC coefficient of 1 or-1, adopting Paillier homomorphic encryption and simultaneously embedding sensitive information, and comprising the following steps:
Step S1, comparing the coefficient with the other coefficient number of which the value is non-zero according to the coefficient with the value of the AC coefficient of 1 or-1 in each 8X 8 DCT coefficient block to allocate the range of ciphertext value distribution.
In the embodiment of the invention, in the encryption process of 1 and-1 in the AC coefficient, according to the comparison of the duty ratio of the AC coefficient value of 1 and-1 in each 8 multiplied by 8 DCT coefficient block to the data size of other non-zero values, the distribution range of the ciphertext value is distributed, so that the histogram distribution of the encrypted ciphertext-containing data value of the image is more uniform, the encrypted ciphertext image is not easy to be detected by an attacker to change, and the information safety is ensured.
And S2, selecting binary data 0 or 1 to embed according to the distribution range of the ciphertext value in the step S1, and respectively carrying out Paillier homomorphic encryption on the 0 and the 1.
In the embodiment of the present invention, after step S2, the method further includes: selecting and recording ciphertext after encrypting 0 and 1, and respectively marking asAnd/>Will/>And/>As a key for extracting sensitive information.
It should be noted that a modified Paillier homomorphic encryption algorithm is employed for encryption of negative coefficients, thereby enabling proper decryption of negative data.
In the embodiment of the invention, a new one-dimensional tangent chaotic map (Logtan) is adopted to carry out chaotic encryption on the DC coefficient, and compared with two types of traditional chaotic maps, the one-dimensional tangent chaotic map adopted by the invention can generate better chaotic sequences, has better chaotic performance, is safer for ciphertext after chaotic encryption on the DC coefficient, is not easy to be cracked by an attacker, and enhances the safety of stored data.
Classical one-dimensional chaotic mapping has a single-peak (Logistic) chaotic mapping and Chebyshev (Chebyshev) mapping, and the following calculation formulas are given:
as can be seen from an analysis of the bifurcation diagrams of these two conventional mappings, as shown in FIG. 4, the abscissa To control parameters, ordinate/>For the nth unimodal chaotic map value, the/>, in the unimodal (Logistic) chaotic map，/>When the system enters a chaotic state, as shown in figure 5, the abscissa/>For controlling parameters,/>For the nth Chebyshev chaotic map value,/>, in the Chebyshev map，/>And when the system enters a chaotic state. It can be seen that the two chaotic maps have smaller parameter ranges when entering the chaotic state, and have certain limitations.
In the embodiment of the invention, as shown in fig. 6, a new one-dimensional tangent chaotic map is adopted to carry out chaotic encryption on a DC coefficient, compared with the former two traditional chaotic mapping systems, the chaotic system has good chaotic performance, and the chaotic sequences of the chaotic systems are uniformly distributed in a pseudo-random form, so that the problem that the range of parameters of the former two chaotic maps entering into the chaotic state is smaller, and the chaotic system has a larger parameter interval, and the formula is as follows:
In the middle of ，/>For controlling parameters,/>And/>And the one-dimensional tangent chaotic map has better chaotic performance.
In the embodiment of the invention, the encryption test of the chaotic system is compared with that of the chaotic system:
According to the invention, a Lyapunov (Lyapunov) index and Shannon (Shannon) entropy are adopted to carry out chaotic system test comparison, and one-dimensional tangent (Logtan) chaotic mapping adopted in the chaotic system test comparison analysis is compared with a unimodal (Logistic) chaotic mapping and Chebyshev (Chebyshev) mapping.
Wherein the Lyapunov exponent and Shannon entropy are calculated as follows:
Lyapunov index Negative values indicate that the system is contracting in that direction, when/>When the value is positive, the system enters a chaotic state. As shown in fig. 7 and 8, the LE (Lyapunov index) of three chaotic mappings are compared when/>The system enters a chaotic state, and the one-dimensional tangent (Logtan) chaotic mapping is larger in positive value range than the single-peak (logic) chaotic mapping and Chebyshev (Chebyshev) chaotic mapping, so that the chaotic performance is better.
Entropy value in Shannon entropyThe larger the chaotic sequence generated by the chaotic system, the more disordered the chaotic sequence is, and the better the chaotic performance is. As shown in fig. 9, SE (Shannon entropy) comparison of three chaotic maps, entropy value/>, of one-dimensional tangent (Logtan) chaotic mapThe maximum and stable chaos sequence is the best, and the chaos performance is the best.
By comparing the one-dimensional tangent chaotic map with the LE and SE of the two traditional chaotic maps, the chaotic sequence of the one-dimensional tangent chaotic map is most disordered, the chaotic performance is best, and the encrypted ciphertext is the safest. Therefore, the invention adopts the one-dimensional tangent chaotic mapping to encrypt the DC coefficient of the JPEG image, thereby guaranteeing the safety of ciphertext data.
And step four, decrypting the ciphertext image according to the encryption in the step three, and separating and extracting the embedded sensitive information to obtain the JPEG original image.
When an administrator of the super-computing cloud platform manages the ciphertext image data, the administrator needs to check the sensitive information which is previously embedded into the ciphertext image so as to be used for classifying and managing the ciphertext image data, and the administrator of the super-computing cloud platform can directly extract the sensitive information from the ciphertext image without decrypting the ciphertext image. After the user obtains the ciphertext image uploaded by the user from the super computing cloud platform, the user can perform decryption operation, recover the original image and analyze out sensitive information.
The method is characterized in that the method comprises the steps of firstly, directly decrypting the ciphertext image, then extracting the embedded sensitive information, and secondly, firstly, extracting the sensitive information from the ciphertext image, then, decrypting the ciphertext image and recovering the original image. For both of these approaches, embedded sensitive information can be extracted and the original ciphertext image restored.
Fig. 10 is a flowchart of a method for decrypting a ciphertext image according to an embodiment of the present invention, as shown in fig. 10, the present invention proposes a separable reversible information hiding algorithm, that is, the extraction of sensitive information and decryption of an original image can be performed separately, and the original image can be completely restored, so as to realize true homomorphic reversibility. The cloud platform manager can utilize the embedded key on the premise of unknown decryption keyAnd/>And extracting the embedded sensitive information, calculating the modular multiplication inverse element of the embedded key, multiplying the modular multiplication inverse element with the ciphertext value, calculating and analyzing the embedded sensitive information, and recovering the original image. The user can directly decrypt the ciphertext image homomorphically into the original image containing the embedded information by using the decryption key, and extract the sensitive information in the embedded image according to the special property of homomorphic encryption, and restore the original image.
In the embodiment of the present invention, according to the encryption in the third step, the ciphertext image is decrypted, and the embedded sensitive information is separated and extracted to obtain the JPEG original image, which includes:
step V1, calculating a key according to the extended Euclidean And/>Modulo multiplication inversion element/>And/>。
In the embodiment of the invention, the Paillier homomorphic encryption algorithm relates to a modular multiplication inverse element and an extended Euclidean algorithm, and plays a key role in encryption, decryption and operation.
Modulo multiplication inversion element: two prime integers x and n, one of which is presentThe method meets the following conditions:
；
From the formula, it can be seen that The remainder of division by n is 1, and the sufficient requirement for the existence of a multiplicative inverse is/>Is mutually compatible with n. Namely: maximum common divisor/>Wherein x is called/>Can be described as/>. And/>Can be found using an extended euclidean algorithm.
Extended euclidean algorithm: euclidean algorithm is also known as rolling phase division, i.e. solving for the greatest common divisor of x and y. The extended euclidean algorithm is to give a linear equation based on the euclidean algorithm:
；
given the values of a, b and m, the values of x and y are solved. Only is provided with When, namely: the linear equation is solved if and only if m is a multiple of the greatest common divisor of both a and b. And when m is 1, only a and b are mutually exclusive.
Step V2, according to the modular multiplication inverse element in step V1And/>Multiplying the image with the ciphertext value, calculating embedded sensitive information, and recovering the JPEG original image.
In the embodiment of the invention, sensitive information is directly extracted from the ciphertext image:
From the image encryption and embedding process, it is known that, for the ciphertext after the analysis of the AC coefficient encryption and embedding information, according to the range of ciphertext values, it can be clearly known that the ciphertext between 1.0x 4-2×104 is necessarily embedded with sensitive information, and the ciphertext between 2 x 10 4-4.5×104 is only Paillier homomorphic encryption. Only based on the key formed after encrypting the sensitive information And/>And calculate the modular multiplication inverse element/>, of the twoAnd/>(Obtained by using Euclidean algorithm expanded by modular multiplication inverse element calculation) and ciphertext/>, formed by homomorphic encryptionOr/>The embedded sensitive information can be calculated and analyzed by multiplication.
Namely:
Wherein the method comprises the steps of And/>Is the result of the addition homomorphism of 1 and-1 in the AC coefficient and 0 or 1 of the sensitive information, and the formula is as follows:
While the key And/>The result of the multiplication with the respective modular multiplication inverses is as follows:
Therefore, it is known from the formula that only Or/>Ciphertext capable of encrypting AC coefficient is restored to the original ciphertext value range of 1.0X10 4-2×104, namely/>, calculated by the formulaOr/>The value of (1) is between 1.0X10 4-2×104, according to the key/>Or/>It can be confirmed that 0 or 1 is embedded. If use/>Or/>The result calculated according to the above formula ranges between 2.0X10 4-4.5×104, and it is considered that no embedded information operation is performed and only Paillier homomorphic encryption is performed. After the embedded sensitive information is extracted, the original ciphertext image is restored, when the user needs to download, the original ciphertext image is transmitted to the user, and the user can decrypt the ciphertext image by using the private key and restore the original image.
In the embodiment of the present invention, according to the encryption in the third step, the ciphertext image is decrypted, and the embedded sensitive information is separated and extracted to obtain the JPEG original image, which includes:
Step W1, decrypting the ciphertext image according to the Paillier homomorphic encryption private key to generate a decrypted plaintext value;
in the embodiment of the invention, the generation process of the private key comprises the following steps:
a. randomly generating two prime numbers p and q, wherein p and q satisfy And/>The greatest common divisor of (2) is 1, and the formula is:
；
b. Generating private key coefficients Coefficient/>The formula of (2) is:
；
wherein lcm is the calculated least common multiple;
c. Constructing an L function, wherein the formula is as follows:
；
d. calculating private key coefficients Coefficient/>The formula of (2) is:
；
Wherein mod is a modulo operation, and the remainder is calculated;
e. According to the private key coefficient And/>Generating a private key as/>。
In the embodiment of the present invention, the formula of the ciphertext value c is:
；
M is a plaintext value to be encrypted, and the public key received from the user at the cloud is (n, g); n is the product of p and q, and the integer g is randomly selected, and g meets the following requirements The value range is/>And the greatest common divisorG and/>Mutual quality; taking g=n+1, then the public key is (n, g); r is a random number randomly generated by a data encryption party, and r meets the/>And/>I.e. r and n are mutually prime.
And step W2, calculating embedded sensitive information according to the plaintext value in the step W1 and through the property of Paillier homomorphic encryption, and recovering the JPEG original image.
In the embodiment of the invention, according to the ciphertext value c obtained from the cloud and the private keyAnd (5) performing ciphertext decryption. The plaintext value m is obtained according to the following formula:
。
in the embodiment of the invention, firstly, ciphertext of two data is generated by encryption, which are respectively And/>. Wherein the method comprises the steps of，/>。
According to the formula:
；
wherein Paillier addition homomorphic encryption properties: for the two ciphertexts c 1 and c 2, multiplying in the ciphertext domain equals adding in the plaintext domain. Namely:
Wherein, Equivalent to/>M in (c), i.e., the plaintext result from decrypting c is/>。
In the embodiment of the invention, sensitive information is extracted after the image is decrypted:
After the ciphertext image is embedded with the information, if the ciphertext image has the Paillier homomorphic encryption private key, the ciphertext image can be decrypted, the decrypted image contains the embedded information, the image containing the embedded sensitive information can be processed by utilizing the property of homomorphic encryption algorithm, the embedded sensitive information is extracted, and the original image is restored.
Firstly, utilizing homomorphic encryption algorithm according to private keyThe original ciphertext image is decrypted.
According to the nature of homomorphic encryption: ciphertext multiplication is equal to plaintext addition, i.e., has the following formula:
the D function is a decryption function, and the ciphertext multiplied by the two homomorphic encryptions is decrypted, so that the two plaintext are added.
If the ciphertext generated by homomorphic encryption of 1 is 12972, the keyIs 29533,/>21487. /(I)
When N is 209, g is 210, and r is 48, then there are:
if the ciphertext generated by homomorphic encryption of-1 is 17481, the key Is 29533,/>21487.
When N is 209, g is 210, and r is 48, then there are:
According to the above formula, according to homomorphic encryption property, ciphertext multiplication is equal to plaintext addition, embedded information and original AC coefficient can be judged according to decrypted value, if embedded sensitive information is 0 and AC coefficient value is 1, decrypted value is 1, embedded data and original AC coefficient can be deduced according to decrypted value because the added values of embedded information and selected AC coefficient are inconsistent, and embedded information and original image can be completely extracted.
In the embodiment of the invention, for the processing of the negative coefficient:
In the case where m is a negative number, the above-mentioned Paillier homomorphic encryption algorithm cannot be used to decrypt the original plaintext after encryption. Therefore, the encrypted part in the Paillier homomorphic encryption algorithm needs to be improved, and the encryption formula is that: Instead of:
Operation to replace negative numbers, i.e. first find the multiplicative inverse of g According to the simplified residual series/>The euler theorem is:
Thus the extended Euclidean algorithm can be utilized to calculate the multiplicative inverse Thus, the encryption of the negative number can be supported, and the Paillier homomorphic encryption algorithm can be utilized to operate on the negative number data.
When homomorphic addition encryption is carried out on two negative numbers, the steps can be utilized firstAnd/>Conversion to ciphertextAnd/>According to/>And (5) carrying out addition homomorphic encryption. But note that if/>And (2) andIf the calculated result (answer) is negative, the plaintext result decrypted after the homomorphic encryption is added is not negative but the value of answer (mod n).
In the embodiment of the invention, the first mode in the method for decrypting the ciphertext image is to find the ciphertext value range of the embedded sensitive information according to the distribution range of the previous homomorphic encryption control ciphertext value and to obtain the embedded keyAnd/>And calculating a modular multiplication inverse element, multiplying the modular multiplication inverse element with the ciphertext value, analyzing and extracting embedded sensitive information, decrypting the ciphertext image according to the encryption key, and then recovering the original image. The second way is to obtain homomorphic encryption key to decrypt the ciphertext image to form plaintext, and utilize homomorphic encryption property: and the ciphertext multiplication is equal to the plaintext addition, the plaintext data is analyzed, the embedded sensitive information is extracted, and the original image is restored.
In the embodiment of the invention, the ciphertext value meeting the conditions can be screened, the ciphertext value range is controlled, the uniform distribution of the histogram of the ciphertext value after encrypting the plaintext data is ensured, the safety of the data is ensured, and the ciphertext value is not easy to be found by a monitored person.
From the Paillier homomorphic encryption algorithm described above, it is known that the parameters related to ciphertext generation are p, q, g, r, n,Parameters p, q and r are used for controlling the generation size of ciphertext data according to a homomorphic encryption formula, and other parameters are related to the parameters. Where r is randomly generated data, r satisfies/>And/>I.e. r and n are mutually exclusive. While large primes p and q are the most dominant parameters that control the size range of ciphertext values. As can be seen from fig. 11 and 12, r is randomly generated from 10000, and after the values of p and q are fixed, the range of values of ciphertext after encrypting plaintext is determined regardless of whether r values are randomly generated. For example, p=11 and q=19 in fig. 11 and 12, the range of ciphertext values does not exceed 4.5×10 4.
Influence of parameters p and q on ciphertext value range in homomorphic encryption: the parameters in the encryption process are determined to be related to large prime numbers p and q according to the Paillier homomorphic encryption formula, and the influence of p and q on the size of the ciphertext value range is studied by fixing other parameters. As can be seen from fig. 13 and 14, r is randomly generated from 10000, and the plaintext data 1 is Paillier homomorphic encrypted, and in fig. 13, when p=17 and q=19, the ciphertext value range is up to 1.05×10 5, and in fig. 14, when p=23 and q=29, the ciphertext value range is up to 4.5×10 4. Meanwhile, when the values of the parameters p and q are larger and larger, the generated ciphertext value range is larger and larger, so that the p and q can be controlled in a certain data range, the ciphertext value range is not too large, the data quantity is too large, and the storage space is saved.
The flow for controlling the size of the ciphertext range is selected as follows:
First, as shown in fig. 15, r is randomly generated from 10000, and the range of ciphertext values is controlled to be 1.0×10 4-4.5×104, so that the encrypted ciphertext value data is ensured to be 5 bits.
And encrypting 1 and-1 in the AC coefficient and embedding sensitive information, and controlling ciphertext value data after encrypting 1 and-1 and embedding the sensitive information (binary 0 or 1) to be in a range of 1.0 multiplied by 10 4-2.0×104.
For other data in the AC coefficients, the ciphertext data is controlled to be between 2.0 x 10 4-4.5×104.
Paillier homomorphic encryption is carried out on the embedded sensitive information 0 and 1, and the encrypted ciphertext value is recorded asAnd。
If the ciphertext data values after 1 encryption are respectivelyAnd/>Wherein/>And/>The range of ciphertext value data is satisfied, and for 1 embedded binary data 0, the following are included according to Paillier homomorphic encryption: /(I)
For 1 embedded binary data 1, the homomorphic encryption according to Paillier is:
。
In the embodiment of the invention, after the homomorphic encryption of the AC coefficient, a ciphertext data value with a certain range and five digits is formed, the range of the AC coefficient is limited to be between [ -1024,1024], and for the ciphertext data value range of the AC coefficient after the homomorphic encryption of Paillier is between 1.0x10 4 and 4.5x10 4, the limitation of the range value of the AC coefficient is obviously far exceeded, and the DCT coefficient cannot be inversely quantized to form a ciphertext image. Therefore, the homomorphic encrypted ciphertext data value needs to be overflowed to meet the requirement of the AC coefficient range, so that a ciphertext image can be formed. The specific steps of the overflow treatment are as follows:
Assume that the ciphertext value formed by encrypting the AC coefficient is Where the subscript n is the number of AC coefficients to be encrypted,To meet range-required values after overflow processing,/>The remainder of the ciphertext value divided by 5. The following formula is provided:
Because a plurality of 0 coefficients exist in the quantized AC coefficients, the encrypted ciphertext values are processed to be close to the 0 coefficients, so that the encrypted ciphertext values have no large data fluctuation, and the safety of image data is better ensured. Ciphertext value after homomorphic encryption The modulo-5 operation is performed so that it contains only numbers between 0 and 4 and fits into the range of AC coefficients, will/>Written into the AC coefficients and forms a ciphertext image by dequantization. By recording remainder/>To decrypt the ciphertext image. Meanwhile, the overflow processing operation greatly reduces the influence of too large ciphertext data caused by homomorphic encryption on the increment of the image file, and can ensure that the increment of the image file is kept in a smaller range.
In the embodiment of the invention, each step can be executed by the electronic equipment. For example, electronic devices include, but are not limited to, tablet computers, portable PCs, desktop PCs, and the like.
Compared with the prior art, the invention has the beneficial effects that:
(1) It is proposed to encrypt the JPEG image using the Paillier homomorphic encryption algorithm and embed sensitive data during the encryption process. Specifically, only proper quantized AC coefficients in the JPEG image are homomorphic encrypted, so that sensitive data is embedded.
(2) The method for generating the ciphertext value range by controlling the Paillier homomorphic encryption is provided, so that the ciphertext value is prevented from being too large to occupy too much storage space. The method ensures that homomorphic encryption ciphertext values fall within a certain range, and avoids the over-wide numerical range of the ciphertext values. The uniform distribution of ciphertext after homomorphic encryption is realized, and the safety of data is enhanced.
(3) In encrypting the JPEG image, a separate data encryption algorithm is used for the DCT coefficients. When sensitive data is embedded, the direct current coefficient adopts one-dimensional tangent chaotic encryption, and the alternating current coefficient adopts homomorphic encryption. Therefore, the scheme not only enhances the encryption security, but also can realize more sensitive data embedding and increases the data embedding capacity.
In the technical scheme provided by the invention, the algorithm comprises the steps of processing a JPEG original image, adopting 512 multiplied by 512 to divide and quantize the JPEG original image to obtain quantized DCT coefficients, and dividing an image matrix into 64 multiplied by 8 DCT coefficient blocks, wherein each multiplied by 8 DCT coefficient block comprises a DC coefficient and an AC coefficient; counting the number of coefficients with the median value of 0 in the AC coefficient in each 8 multiplied by 8 DCT coefficient block, and sorting from large to small and embedding according to the sorting according to the counting result; DC coefficient in each 8 x 8 DCT coefficient block is encrypted by one-dimensional tangent chaos, AC coefficient is encrypted by Paillier homomorphic, ciphertext image is generated, ciphertext image is decrypted, embedded sensitive information is separated and extracted to obtain JPEG original image.
The embodiment of the invention provides a computer readable storage medium, which comprises a stored program, wherein when the program runs, an electronic device in which the computer readable storage medium is arranged is controlled to execute the JPEG encryption domain reversible information hiding algorithm for separating and extracting sensitive information.
Fig. 16 is a schematic diagram of an electronic device according to an embodiment of the present invention, and as shown in fig. 16, an electronic device 21 includes: the processor 211, the memory 212, and the computer program 213 stored in the memory 212 and executable on the processor 211, the computer program 213, when executed by the processor 211, implements the JPEG encryption domain reversible information hiding algorithm for separating and extracting sensitive information in the embodiment, and is not described herein in detail for avoiding repetition.
The electronic device 21 includes, but is not limited to, a processor 211, a memory 212. It will be appreciated by those skilled in the art that fig. 5 is merely an example of the electronic device 21 and is not meant to be limiting of the electronic device 21, and may include more or fewer components than shown, or may combine certain components, or different components, e.g., the electronic device may further include an input-output device, a network access device, a bus, etc.
The Processor 211 may be a central processing unit (Central Processing Unit, CPU), other general purpose Processor, digital signal Processor (DIGITAL SIGNAL Processor, DSP), application specific integrated circuit (ApplicationSpecific Integrated Circuit, ASIC), field-Programmable gate array (Field-Programmable GATE ARRAY, FPGA) or other Programmable logic device, discrete gate or transistor logic device, discrete hardware components, or the like. A general purpose processor may be a microprocessor or the processor may be any conventional processor or the like.
The memory 212 may be an internal storage unit of the electronic device 21, such as a hard disk or a memory of the electronic device 21. The memory 212 may also be an external storage device of the electronic device 21, such as a plug-in hard disk provided on the electronic device 21, a smart memory card (SMART MEDIA CARD, SMC), a Secure Digital (SD) card, a flash memory card (FLASH CARD), or the like. Further, the memory 212 may also include both internal storage units and external storage devices of the electronic device 21. The memory 212 is used to store computer programs and other programs and data required by the network device. The memory 212 may also be used to temporarily store data that has been output or is to be output.
It will be clear to those skilled in the art that, for convenience and brevity of description, specific working procedures of the above-described systems, apparatuses and units may refer to corresponding procedures in the foregoing method embodiments, which are not repeated herein.
The foregoing description of the preferred embodiments of the invention is not intended to be limiting, but rather to enable any modification, equivalent replacement, improvement or the like to be made within the spirit and principles of the invention.
Claims (8)
1. A JPEG encryption domain reversible information hiding algorithm for separating and extracting sensitive information, the algorithm comprising:
Step one, processing a JPEG original image, blocking and quantizing the JPEG original image by adopting 512 multiplied by 512 to obtain quantized Discrete Cosine Transform (DCT) coefficients, and dividing an image matrix into 64 multiplied by 64 DCT coefficient blocks with 8 multiplied by 8, wherein each DCT coefficient block with 8 multiplied by 8 comprises a Direct Current (DC) coefficient and an Alternating Current (AC) coefficient;
Counting the number of coefficients with the median value of 0 of the AC coefficients in each 8X 8 DCT coefficient block according to 64X 64 8 DCT coefficient blocks in the first step, and sorting from large to small and embedding according to the sorting;
Thirdly, according to the embedding in the second step, adopting one-dimensional tangent chaotic encryption to DC coefficients in each 8 multiplied by 8 DCT coefficient block, and adopting Paillier homomorphic encryption to AC coefficients to generate a ciphertext image;
step four, decrypting the ciphertext image according to the encryption in the step three, and separating and extracting the embedded sensitive information to obtain a JPEG original image;
the AC coefficient adopts Paillier homomorphic encryption comprising: selecting a coefficient with the median value of the AC coefficient of 1 or-1, adopting Paillier homomorphic encryption and simultaneously embedding sensitive information; the positive coefficients with the values of 1 or minus 1 are encrypted in the same state by Paillier; and for negative coefficients other than 1 or-1, employing improved Paillier homomorphic encryption;
the selecting the coefficient with the median value of 1 or-1 of the AC coefficient, adopting Paillier homomorphic encryption and simultaneously embedding sensitive information, and comprises the following steps:
S1, comparing the coefficient with the number of other coefficients with non-zero values according to the coefficient with the AC coefficient value of 1 or-1 in each 8X 8 DCT coefficient block to allocate the ciphertext value distribution range;
And S2, selecting binary data 0 or 1 to embed according to the distribution range of the ciphertext value in the step S1, and respectively carrying out Paillier homomorphic encryption on the 0 and the 1.
2. The algorithm according to claim 1, further comprising, after step S2: selecting and recording ciphertext after encrypting 0 and 1, and respectively marking asAnd/>Will/>And/>As a key for extracting sensitive information.
3. The algorithm according to claim 1, wherein the decrypting the ciphertext image according to the encrypting in the third step, and separating and extracting the embedded sensitive information to obtain the JPEG original image, comprises:
step V1, calculating a key according to the extended Euclidean And/>Modulo multiplication inversion element/>And/>；
Step V2, according to the modular multiplication inverse element in step V1And/>Multiplying the image with the ciphertext value, calculating embedded sensitive information, and recovering the JPEG original image.
4. The algorithm according to claim 1, wherein the decrypting the ciphertext image according to the encrypting in the third step, and separating and extracting the embedded sensitive information to obtain the JPEG original image, comprises:
Step W1, decrypting the ciphertext image according to the Paillier homomorphic encryption private key to generate a decrypted plaintext value;
and step W2, calculating embedded sensitive information according to the plaintext value in the step W1 and through the property of Paillier homomorphic encryption, and recovering the JPEG original image.
5. The algorithm of claim 4, wherein the generation of the private key comprises:
a. randomly generating two prime numbers p and q, wherein p and q satisfy And/>The greatest common divisor of (2) is 1, and the formula is:
；
b. Generating private key coefficients Coefficient/>The formula of (2) is:
；
wherein lcm is the calculated least common multiple;
c. Constructing an L function, wherein the formula is as follows:
；
d. calculating private key coefficients Coefficient/>The formula of (2) is:
；
Wherein mod is a modulo operation, and the remainder is calculated;
e. According to the private key coefficient And/>Generating a private key as/>。
6. An algorithm according to claim 3, wherein the formula for ciphertext value c is:
；
M is a plaintext value to be encrypted, and the public key received from the user at the cloud is (n, g); n is the product of p and q, and the integer g is randomly selected, and g meets the following requirements The value range is/>And greatest common divisor/>G and/>Mutual quality; taking g=n+1, then the public key is (n, g); r is a random number randomly generated by a data encryption party, and r satisfies the following conditionsAnd/>I.e. r and n are mutually prime.
7. A computer readable storage medium, characterized in that the computer readable storage medium comprises a stored program, wherein the program when run controls a device in which the computer readable storage medium is located to execute the JPEG encrypted domain reversible information hiding algorithm for separating and extracting sensitive information according to any one of claims 1 to 6.
8. An electronic device, comprising: one or more processors; a memory; and one or more computer programs, wherein the one or more computer programs are stored in the memory, the one or more computer programs comprising instructions that, when executed by the device, cause the device to perform the JPEG encrypted domain reversible information hiding algorithm for separating and extracting sensitive information of any one of claims 1 to 6.
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