CN112801845A - Watermark embedding method and extraction method based on quantum image and quantum circuit - Google Patents

Watermark embedding method and extraction method based on quantum image and quantum circuit Download PDF

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CN112801845A
CN112801845A CN202110142897.1A CN202110142897A CN112801845A CN 112801845 A CN112801845 A CN 112801845A CN 202110142897 A CN202110142897 A CN 202110142897A CN 112801845 A CN112801845 A CN 112801845A
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watermark
quantum
embedding
image
operator
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魏战红
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Beijing Institute of Petrochemical Technology
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T1/00—General purpose image data processing
    • G06T1/0021—Image watermarking
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
    • H04L9/0816—Key establishment, i.e. cryptographic processes or cryptographic protocols whereby a shared secret becomes available to two or more parties, for subsequent use
    • H04L9/0852—Quantum cryptography

Abstract

The application relates to a watermark embedding method, an extraction method and a quantum circuit based on a quantum image, belonging to the technical field of quantum cryptography, wherein the embedding method comprises the following steps: respectively preparing a carrier quantum image and a watermark quantum image; constructing an overflow operator, a rotation operator and a key for controlling the watermark embedding position according to the watermark quantum image, and further establishing an embedding operator required for embedding the whole image; and operating the carrier quantum image by using the embedding operator to obtain the watermark-embedded quantum image. According to the method, the watermark embedding and extracting process strictly follows the quantum mechanics principle, auxiliary quantum entanglement resources are not needed, more watermark information can be embedded, and watermark embedding based on quantum images is effectively achieved.

Description

Watermark embedding method and extraction method based on quantum image and quantum circuit
Technical Field
The application belongs to the field of quantum cryptography, relates to a quantum information hiding technology, and particularly relates to a watermark embedding and extracting method based on a quantum image and a quantum circuit.
Background
The development of internet technology has promoted the development of multimedia communication, and images become an important multimedia form in network communication due to the intuitive image. Quantum computing and quantum computers are currently the research focus of all countries, and once a quantum computer becomes a practical computer, a quantum image becomes an important multimedia form.
In quantum computing, the basic unit of information is a qubit (bits), typically a computation basis |0>And |1>As the ground state. One quantum state may be a superposition of two ground statesCan be recorded as
Figure BDA0002929934070000011
Where a and b are both complex numbers, the quantum states need to satisfy the normalization constraint, satisfy | a2+|b|21. The image is an important information form in the communication process, the information of the image can be stored in a quantum system, and an image is represented in a quantum superposition state as follows:
Figure BDA0002929934070000012
here, the
Figure BDA0002929934070000013
|I>Satisfying the normalized constraint of the quantum state, where>Information of pixels, P, representing an image>It represents its corresponding position information and the qubit representation of such an image is referred to hereinafter as a quantum image. The evolution of a closed quantum system is characterized by a unitary transformation, that is to say the evolution of the quantum system between states at different times is described by a unitary operator. The unitary operator can be characterized by a quantum logic gate, a single quantum bit gate and a controlled not gate are important general gates, and a general quantum logic gate can be formed by the single quantum bit gate and the controlled not gate. The names, coincidences and corresponding unitary matrix representations of the commonly used single-quantum bit gates and controlled not gates are shown in fig. 4. The quantum computer is a physical device which can be used for carrying out high-speed mathematical and logical operations, storing and processing quantum information according to the law of quantum mechanics, and is realized by a quantum circuit consisting of quantum logic gates.
The quantum computer has the capability of parallel computing, can solve the data problem which cannot be solved by the classical computer, such as the problem of prime factor decomposition, and brings threat to the classical cryptosystem. At present, the problem of classical digital watermarking is considered by using a quantum mechanics principle, and the method has certain research value. Watermarking on quantum images (hereinafter referred to as quantum watermarking) research combines two new different interdisciplines of quantum images and quantum cryptography. In recent years, researchers have started research on quantum watermarks, and some research results have been obtained. However, the current research results have problems in the implementation and performance of the method.
The above is only for the purpose of assisting understanding of the technical aspects of the present invention, and does not represent an admission that the above is prior art.
Disclosure of Invention
In order to overcome the problems in the related art at least to a certain extent, the application provides a watermark embedding method, an extracting method and a quantum circuit based on quantum images, which can improve the watermark embedding and extracting efficiency by utilizing the parallelism of quantum computation, thereby improving the performance of the watermark technology.
In order to achieve the purpose, the following technical scheme is adopted in the application:
in a first aspect,
the application provides a watermark embedding method based on a quantum image, which comprises the following steps:
respectively preparing a carrier quantum image and a watermark quantum image;
constructing an overflow operator, a rotation operator and a key for controlling the watermark embedding position according to the watermark quantum image, and further establishing an embedding operator required for embedding the whole image;
and operating the carrier quantum image by using the embedding operator to obtain the watermark-embedded quantum image.
Optionally, the carrier quantum image is 2n×2nPixel size, the watermark quantum image is 2m×2mThe pixel size, the carrier quantum image and the watermark quantum image are respectively expressed by the following expressions:
Figure BDA0002929934070000021
wherein, | C>Representing a quantum image of the support, | W>Representing a quantum image of the watermark,
Figure BDA0002929934070000022
representing the pixel values of the pixels on the carrier quantum image,
Figure BDA0002929934070000023
and (4) representing the pixel value of each pixel point on the watermark quantum image, wherein m is less than or equal to n.
Optionally, the constructing an overflow operator, a rotation operator and a key for controlling the watermark embedding position according to the watermark quantum image specifically includes:
constructing an obtained overflow operator C according to the pixel value of each pixel point on the watermark quantum imagekRotation operator RkWhich are respectively represented as:
Figure BDA0002929934070000031
and constructing a sequence Key for describing the position coordinates of each embedded point as a Key according to the pixel number of the watermark quantum image, wherein the element number in the sequence Key is the pixel number of the watermark quantum image.
Optionally, an embedding operator corresponding to an embedding point k on the carrier quantum image is defined as Pk＝CkRk(ii) a The obtained embedding operator U required for embedding the whole imageeThe method specifically comprises the following steps:
Figure BDA0002929934070000032
in a second aspect of the present invention,
the application provides a watermark extraction method based on a quantum image, aiming at the quantum image embedded with the watermark obtained in the embedding method, the extraction method comprises the following steps:
and performing inverse operation by using an embedding operator constructed during watermark embedding according to the quantum image embedded with the watermark and the carrier quantum image to obtain an embedded watermark quantum image.
Optionally, the carrier quantum image is 2n×2nPixel size, the watermark quantum image is 2m×2mA pixel size; the carrier quantum image and the watermark quantum image are respectively expressed by the following expressions:
Figure BDA0002929934070000033
wherein, | C>Representing a quantum image of the support, | W>Representing a quantum image of the watermark,
Figure BDA0002929934070000034
representing the pixel values of the pixels on the carrier quantum image,
Figure BDA0002929934070000035
and (4) representing the pixel value of each pixel point on the watermark quantum image, wherein m is less than or equal to n.
Optionally, the embedding operator used when embedding the whole image is UeThe method specifically comprises the following steps:
Figure BDA0002929934070000036
wherein, PkAnd representing an embedding operator corresponding to the embedding point k, wherein the coordinate value of the point k is determined by a Key constructed during embedding.
Optionally, an embedding operator P corresponding to the embedding point kkAs defined by the following expression,
Figure BDA0002929934070000041
wherein, CkIndicating an overflow operator, RkRepresenting a rotation operator.
In a third aspect,
the application provides a quantum circuit, wherein the quantum circuit comprises a control NOT gate and a plurality of control gates; the quantum wires are used to implement the operations involved in the watermark embedding process in the embedding method described above,
and the method is used for realizing the inverse operation involved in the watermark extraction process in the extraction method.
Optionally, the multi-control gate consists of a basic quantum gate.
This application adopts above technical scheme, possesses following beneficial effect at least:
according to the technical scheme, the quantum mechanical principle is strictly followed in the watermark embedding and extracting process, auxiliary quantum entanglement resources are not needed, more watermark information can be embedded by the method, and watermark embedding and extracting based on quantum images are effectively achieved.
Additional advantages, objects, and features of the invention will be set forth in part in the description which follows and in part will become apparent to those having ordinary skill in the art upon examination of the following or may be learned from practice of the invention. The objectives and other advantages of the invention will be realized and attained by the structure particularly pointed out in the written description and claims hereof as well as the appended drawings.
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The accompanying drawings are included to provide a further understanding of the technology or prior art of the present application and are incorporated in and constitute a part of this specification. The drawings expressing the embodiments of the present application are used for explaining the technical solutions of the present application, and should not be construed as limiting the technical solutions of the present application.
Fig. 1 is a schematic flowchart of a quantum image-based watermark embedding method according to an embodiment of the present application;
fig. 2 is a frame diagram of an implementation of a quantum image-based watermark embedding method in the present application;
fig. 3 is a frame diagram of an implementation of a quantum image-based watermark extraction method in the present application;
FIG. 4 is a diagram illustrating a single qubit gate and a control NOT gate commonly used in quantum information technology;
fig. 5 is a diagram of quantum wires for watermark embedding and extraction in the present application;
FIG. 6 is an image of a support used in a simulation experiment of the present application;
FIG. 7 is a diagram of a watermark image used in a simulation experiment of the present application;
FIG. 8 is a schematic diagram of simulation effect in a simulation experiment of the present application;
fig. 9 is a graph showing a variation of a relation between watermark embedding capacity and PSNR according to the present embodiment.
Detailed Description
In order to make the objects, technical solutions and advantages of the present application more apparent, the technical solutions of the present application will be described in detail below. It is to be understood that the embodiments described are only a few embodiments of the present application and not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the examples given herein without making any creative effort, shall fall within the protection scope of the present application.
In order to solve the problems of method implementation and performance in quantum watermark research, the invention provides a quantum watermark embedding and extracting method in combination with the existing research results. The method strictly obeys the quantum mechanics principle in the implementation process, and the watermark embedding utilizes a quantum computing mode. A unitary operator for realizing watermark embedding is designed, and a quantum circuit diagram of specific realization is given. In addition, the problems existing in watermark embedding and extraction are also considered, and an overflow operator for preventing angle overflow is provided. The method utilizes the parallelism of quantum computation, improves the watermark embedding and extracting efficiency, and simultaneously ensures the safety of the method.
In one embodiment, the present application provides a quantum image-based watermark embedding method, including the following steps:
step S110, respectively preparing a carrier quantum image and a watermark quantum image;
specifically, in step S110, a frame 2 is preparedn×2nPixel-sized carrier image and a 2-framem×2mThe quantum representation forms (or carrier quantum image and watermark quantum image) of the pixel-size watermark image and the pixel-size watermark image are respectively as follows:
Figure BDA0002929934070000051
Figure BDA0002929934070000052
in the expressions (1) and (2), | C>Representing a quantum image of the support, | W>Representing a quantum image of the watermark,
Figure BDA0002929934070000053
representing the pixel values of the pixels on the carrier quantum image,
Figure BDA0002929934070000054
and (4) representing the pixel value of each pixel point on the watermark quantum image, wherein m is less than or equal to n.
And then, performing step S120, constructing an overflow operator, a rotation operator and a key for controlling the watermark embedding position according to the watermark quantum image, and further establishing an embedding operator required for embedding the whole image.
In the watermark embedding process, only the pixel information of the image is modified, the corresponding position information is not changed, and based on the characteristic represented by the quantum image, the watermark can be embedded by using a unitary operator;
specifically, in step S120, a correct overflow operator and a correct rotation operator are designed and constructed according to the size of the pixel value of each pixel point on the watermark image. Constructing an obtained overflow operator C according to the pixel value of each pixel point on the watermark quantum imagekRotation operator RkWhich are respectively represented as:
Figure BDA0002929934070000061
it is easily understood that in the expression (3)
Figure BDA0002929934070000062
Representing k points on the watermark imageThe pixel value.
The overflow operator is to prevent the overflow of the angle when the watermark is embedded, for example, when the angle and the rotation angle of the carrier image satisfy
Figure BDA0002929934070000063
In time, the overflow process is required to indicate that the angle of the image pixel overflows.
In step S120, a key for watermark embedding is generated according to the size of the watermark image, and the key is used to control the embedding position of the watermark. Specifically, a sequence Key describing the position coordinates of each embedded point is constructed as a Key according to the number of pixels of the watermark quantum image, wherein the number of elements in the sequence Key is the number of pixels of the watermark quantum image.
In step S120, according to the constructed rotation operator, overflow operator and key, an embedding operator corresponding to an embedding point k on the carrier quantum image may be defined as Pk＝CkRkThen the embedding operator U needed for embedding the whole image is obtainedeThe method specifically comprises the following steps:
Figure BDA0002929934070000064
in the expression (4), I represents an identity matrix.
And finally, performing step S130, and performing operation on the carrier quantum image by using the embedding operator in step S120 to obtain the watermark-embedded quantum image.
It should be noted that, when performing the operation, the flag array flag [2 ] is needed for the overflow operator in the embedded operator to participate in the operationn][2n]Control is carried out, in particular, if the pixel value at the position (a, b) of the quantum image of the carrier is thetaiThen flag [ a ]][b]The value is 1 and the other positions are assigned a position of 0. The implementation architecture of the embedding operation can be represented by fig. 2.
The present application also provides a quantum circuit for implementing the operations involved in the watermark embedding process in the embedding method, where the quantum circuit includes a control not gate and a multi-control gate, specifically, the multi-control gate here is composed of a basic quantum gate, the quantum circuit is specifically shown in fig. 5, and the number of gates in the quantum circuit is determined by the size of the watermark image and the size of the carrier image.
Corresponding to the embedding method, the present application also provides a watermark extraction method based on a quantum image, which aims at the quantum image embedded with the watermark obtained in the embedding method, and the extraction method includes:
and performing inverse operation by using an embedding operator constructed during watermark embedding according to the quantum image embedded with the watermark and the carrier quantum image to obtain the embedded watermark quantum image.
In the extraction method, the related contents of the embedding operator, the carrier quantum image, the watermark-embedded quantum image, and the like have been described in the foregoing embodiment of the embedding method, and are not described herein again. The architecture for implementing the inverse operation involved in the extraction in this extraction method can be represented by fig. 3.
Furthermore, it is easy to understand that since the quantum computation process implemented by the quantum logic gate is reversible, the extraction of the watermark can be implemented by using the same quantum circuit, i.e. the quantum circuit shown in fig. 5 is also used to implement the inverse operation involved in the watermark extraction process in the above extraction method.
According to the technical scheme, the quantum mechanical principle is strictly followed in the watermark embedding and extracting process, auxiliary quantum entanglement resources are not needed, more watermark information can be embedded by the method, and watermark embedding and extracting based on quantum images are effectively achieved.
The method and the quantum circuit are used for verifying the method and the quantum circuit, and measuring three performance indexes of invisibility, safety and embedding capacity of watermark performance. The present application also performs a relevant verification experiment, and further proves the implementability and technical effects of the present application by using the experimental results, which are specifically described below.
Because quantum computers are not yet put into practical use, the simulation verification experiment related to the quantum computers is carried out in a classical calculation set. The experimental environment is as follows:
Figure BDA0002929934070000071
Dual-Core CPU E66003.06GHz, 2.00GB memory, MATLAB R2012 a.
Fig. 6 shows all carrier images used in the simulation experiment, and fig. 7 shows the watermark images used. In classical digital watermarking, the invisibility of a watermark image is measured by Peak Signal-Noise-Ratio (PSNR), which can measure the similarity of two images, wherein the larger the PSNR, the smaller the influence of the watermark image on a carrier image is, and the less the watermark image is easily perceived. The PSNR is calculated as:
Figure BDA0002929934070000081
wherein f and f0For two images of size m × n, max (f) is the maximum pixel value on image f.
The specific simulation experiment process is as follows:
firstly, in the experimental process, an image piracy.GIF in fig. 6 is selected as a carrier image, and an image camera.GIF in fig. 7 is selected as a watermark image. In the program implementation process, a zero matrix U is firstly generatedEThe generated zero matrix is then modified from the quantum wire diagram in fig. 5 to a matrix that enables the computation process of fig. 5. And finally, embedding the mark array and the Key as control conditions to finish embedding and extracting the watermark and finish the simulation experiment. The simulation result is shown in fig. 8, where PSNR is 43.1720 dB.
Step two: selecting all carrier images in fig. 6, and taking the bupt.GIF in fig. 7 as watermark images, respectively executing the step one, wherein the simulation experiment results are shown in table 1:
TABLE 1 PSNR values of different carrier images after embedding watermarks
Carrier image PSNR(dB)
cameraman 41.3296
pirate 41.0990
womenblonde 42.1053
womandarkhair 42.1754
lena 42.3885
From the simulation experiment results of the first step and the second step, the PSNR is more than or equal to 41(dB), the requirement of the watermark on invisibility is met, and the watermark embedding method and the quantum line for completing embedding are feasible and effective, so that the method is safe.
And step three, in order to verify the advantages of the watermark embedding and extracting method provided by the invention on the embedding capacity, multiple simulation experiments are carried out. In the experiment, a carrier image len.GIF with the size of 512 × 512 in fig. 6 is selected, then a camera image tif in fig. 7 is selected as a watermark image, the size of the watermark image is changed, and multiple simulation experiments are carried out to obtain the embedding capacity and the corresponding PSNR value. Fig. 9 is a graph showing PSNR variation with embedded capacity. As can be seen from the graph, the size of the embedded watermark image can reach 300 × 300 under the premise that the PSNR value requirement is satisfied by the watermark embedding method.
The above description is only a preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims (10)

1. A watermark embedding method based on quantum images is characterized by comprising the following steps:
respectively preparing a carrier quantum image and a watermark quantum image;
constructing an overflow operator, a rotation operator and a key for controlling the watermark embedding position according to the watermark quantum image, and further establishing an embedding operator required for embedding the whole image;
and operating the carrier quantum image by using the embedding operator to obtain the watermark-embedded quantum image.
2. The watermark embedding method according to claim 1, wherein the carrier quantum image is 2n×2nPixel size, the watermark quantum image is 2m×2mThe pixel size, the carrier quantum image and the watermark quantum image are respectively expressed by the following expressions:
Figure FDA0002929934060000011
wherein, | C>Representing a quantum image of the support, | W>Representing a quantum image of the watermark,
Figure FDA0002929934060000012
representing the pixel values of the pixels on the carrier quantum image,
Figure FDA0002929934060000013
and (4) representing the pixel value of each pixel point on the watermark quantum image, wherein m is less than or equal to n.
3. The watermark embedding method according to claim 2, wherein the constructing of the overflow operator, the rotation operator and the key for controlling the watermark embedding position according to the watermark quantum image specifically includes:
constructing an obtained overflow operator C according to the pixel value of each pixel point on the watermark quantum imagekRotation operator RkWhich are respectively represented as:
Figure FDA0002929934060000014
and constructing a sequence Key for describing the position coordinates of each embedded point as a Key according to the pixel number of the watermark quantum image, wherein the element number in the sequence Key is the pixel number of the watermark quantum image.
4. The watermark embedding method according to claim 3, wherein an embedding operator corresponding to an embedding point k on the carrier quantum image is defined as Pk＝CkRk(ii) a The obtained embedding operator U required for embedding the whole imageeThe method specifically comprises the following steps:
Figure FDA0002929934060000015
5. a watermark extraction method based on a quantum image, the extraction method being directed to the watermark-embedded quantum image obtained in claim 1, and comprising:
and carrying out inverse operation by utilizing an embedding operator constructed during watermark embedding according to the quantum image embedded with the watermark and the carrier quantum image so as to obtain the embedded watermark quantum image.
6. The watermark extraction method according to claim 5, wherein the carrier quantum image is 2n×2nPixel size, the watermark quantum image is 2m×2mA pixel size;the carrier quantum image and the watermark quantum image are respectively expressed by the following expressions:
Figure FDA0002929934060000021
wherein, | C>Representing a quantum image of the support, | W>Representing a quantum image of the watermark,
Figure FDA0002929934060000022
representing the pixel values of the pixels on the carrier quantum image,
Figure FDA0002929934060000023
and (4) representing the pixel value of each pixel point on the watermark quantum image, wherein m is less than or equal to n.
7. The watermark extraction method according to claim 6, wherein the embedding operator used for embedding the whole image is UeThe method specifically comprises the following steps:
Figure FDA0002929934060000024
wherein, PkAnd representing an embedding operator corresponding to the embedding point k, wherein the coordinate value of the point k is determined by a Key constructed during embedding.
8. The watermark extraction method according to claim 7, wherein the embedding operator P corresponding to the embedding point kkAs defined by the following expression,
Pk＝CkRk，
Figure FDA0002929934060000025
wherein, CkIndicating an overflow operator, RkRepresenting a rotation operator.
9. A quantum circuit is characterized in that the quantum circuit comprises a control NOT gate and a multi-control gate; the quantum wires are used to implement the operations involved in the watermark embedding process in any of claims 1 to 4,
and for implementing the inverse operations involved in the watermark extraction process in any of claims 5 to 8.
10. A quantum wire as claimed in claim 9, wherein the multi-control gate is composed of a basic quantum gate.
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