CN109918927B - Image encryption method and device - Google Patents
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Abstract
The present application relates to the field of image processing technologies, and in particular, to an image encryption method and apparatus. The image encryption method comprises the following steps: acquiring a quaternion matrix of an image to be encrypted; determining a parallel component matrix and a vertical component matrix of the image to be encrypted based on the quaternion matrix; determining a complex value mask of the image to be encrypted based on the parallel component matrix and the vertical component matrix; and generating an encrypted image corresponding to the image to be encrypted based on the complex value mask. By adopting the image encryption algorithm, the encryption information can be prevented from being concentrated, the problem of obvious outline highlighting is further solved, and the safety of the image in transmission can be improved.
Description
Technical Field
The present application relates to the field of image processing technologies, and in particular, to an image encryption method and apparatus.
Background
With the rapid development of computer networks and communication technologies, a large amount of multimedia data such as images, videos, etc. is generated every day, and the multimedia data may contain some important or private information. On one hand, the internet brings convenience to the transmission and use of the data; meanwhile, the openness and the sharing of the network also enable information to be subject to tampering or malicious use, and huge loss is brought to people. In order to protect the security of the image content, the image may be encrypted at the sending end.
At present, in a plurality of modes for encrypting images, a quaternion matrix method is widely used for encrypting the images, but the traditional quaternion matrix encryption method has the defects of limitation on the encryption complexity, concentrated encryption information and obvious outline.
Disclosure of Invention
In view of the above, an object of the embodiments of the present application is to provide an image encryption method and apparatus, which can avoid the encryption information from being concentrated, and further solve the problem of obvious outline.
Mainly comprises the following aspects:
in a first aspect, an embodiment of the present application provides an image encryption method, where the method includes:
acquiring a quaternion matrix of an image to be encrypted;
determining a parallel component matrix and a vertical component matrix of the image to be encrypted based on the quaternion matrix;
determining a complex value mask of the image to be encrypted based on the parallel component matrix and the vertical component matrix;
and generating an encrypted image corresponding to the image to be encrypted based on the complex value mask.
In some embodiments, the determining a complex-valued mask of the image to be encrypted based on the parallel component matrix and the vertical component matrix includes:
transforming the parallel component matrix to obtain a parallel derivation matrix corresponding to the parallel component matrix;
transforming the vertical component matrix to obtain a vertical derivation matrix corresponding to the vertical component matrix;
and determining the complex value mask of the image to be encrypted according to the parallel derivation array and the vertical derivation array.
In some embodiments, the determining a complex-valued mask of the image to be encrypted according to the parallel derivation array and the vertical derivation array includes:
performing equal-mode decomposition on the parallel derivation array to obtain a first complex value mask and a second complex value mask corresponding to the parallel derivation array;
and performing equal-mode decomposition on the vertical derivation array to obtain a third complex value mask and a fourth complex value mask corresponding to the vertical derivation array.
In some embodiments, the generating an encrypted image corresponding to the image to be encrypted based on the complex-value mask includes:
determining a first ciphertext of the image to be encrypted according to the first complex value mask and the third complex value mask;
determining a second ciphertext of the image to be encrypted according to the second complex value mask and the fourth complex value mask;
and generating an encrypted image corresponding to the image to be encrypted according to the first ciphertext and the second ciphertext.
In some embodiments, the parallel component matrix is determined by the following equation:
determining the vertical component matrix by:
wherein F (u, v) is the quaternion matrix, F||(u, v) is the parallel component matrix, F⊥(u, v) is the vertical component matrix and p is the pure quaternion.
In some embodiments, the parallel derived array is obtained by the following formula:
the vertical derived matrix is obtained by the following formula:
wherein M is||For the parallel derived arrays, M⊥For the vertical derivation of arrays, A1＝F||1(u,v)+jF||2(u,v)，A2＝F||3(u,v)+jF||4(u,v)，B1＝F⊥1(u,v)+jF⊥2(u,v)，B2＝F⊥3(u,v)+jF⊥4(u, v), j is an imaginary unit, the superscript "+" indicates taking the conjugate, F||1(u,v)、F||2(u,v)、F||3(u,v)、F||4(u, v) are the components of the parallel component matrix, F⊥1(u,v)、F⊥2(u,v)、F⊥3(u,v)、F⊥4(u, v) are the components of the vertical component matrix.
In some embodiments, the first complex-valued mask is derived by the following equation:
obtaining the second complex-valued mask by:
obtaining the third complex-valued mask by:
obtaining the fourth complex-valued mask by:
wherein, P11(u, v) is the first complex-valued mask, P12(u, v) is the second complex-valued mask, D||(u, v) is the amplitude of the parallel derived arrays,
for the phase of the parallel derived array, θ1(u, v) is a random matrix subject to uniform distribution, 0 ≦ θ1(u,v)≤1，P21(u, v) is the third complex-valued mask, P22(u, v) is the fourth complex-valued mask, D⊥(u, v) is the amplitude of the vertical derived matrix,
for the phase of the vertical derived array, θ2(u, v) is a random matrix subject to uniform distribution, 0 ≦ θ2(u, v) is less than or equal to 1, and i is an imaginary number unit.
In a second aspect, an embodiment of the present application provides an image encryption apparatus, including:
the acquisition module is used for acquiring a quaternion matrix of the image to be encrypted;
the first determining module is used for determining a parallel component matrix and a vertical component matrix of the image to be encrypted based on the quaternion matrix;
the second determination module is used for determining the complex value mask of the image to be encrypted based on the parallel component matrix and the vertical component matrix;
and the generating module is used for generating an encrypted image corresponding to the image to be encrypted based on the complex value mask.
In some embodiments, the second determination module comprises a transformation module and a third determination module;
the transformation module is used for transforming the parallel component matrix to obtain a parallel derivation matrix corresponding to the parallel component matrix;
the transformation module is further configured to transform the vertical component matrix to obtain a vertical derivation matrix corresponding to the vertical component matrix;
and the third determining module is used for determining the complex value mask of the image to be encrypted according to the parallel derivation array and the vertical derivation array.
In some embodiments, the third determining module is specifically configured to determine the complex-valued mask of the image to be encrypted according to the following steps:
performing equal-mode decomposition on the parallel derivation array to obtain a first complex value mask and a second complex value mask corresponding to the parallel derivation array;
and performing equal-mode decomposition on the vertical derivation array to obtain a third complex value mask and a fourth complex value mask corresponding to the vertical derivation array.
In some embodiments, the generating module is specifically configured to generate an encrypted image corresponding to the image to be encrypted according to the following steps:
determining a first ciphertext of the image to be encrypted according to the first complex value mask and the third complex value mask;
determining a second ciphertext of the image to be encrypted according to the second complex value mask and the fourth complex value mask;
and generating an encrypted image corresponding to the image to be encrypted according to the first ciphertext and the second ciphertext.
In some embodiments, the parallel component matrix is determined by the following equation:
determining the vertical component matrix by:
wherein F (u, v) is the quaternion matrix, F||(u, v) is the parallel component matrix, F⊥(u, v) is the vertical component matrix and p is the pure quaternion.
In some embodiments, the parallel derived array is obtained by the following formula:
the vertical derived matrix is obtained by the following formula:
wherein M is||For the parallel derived arrays, M⊥For the vertical derivation of arrays, A1＝F||1(u,v)+jF||2(u,v)，A2＝F||3(u,v)+jF||4(u,v)，B1＝F⊥1(u,v)+jF⊥2(u,v)，B2＝F⊥3(u,v)+jF⊥4(u, v), j is an imaginary unit, the superscript "+" indicates taking the conjugate, F||1(u,v)、F||2(u,v)、F||3(u,v)、F||4(u, v) are the components of the parallel component matrix, F⊥1(u,v)、F⊥2(u,v)、F⊥3(u,v)、F⊥4(u, v) are the components of the vertical component matrix.
In some embodiments, the first complex-valued mask is derived by the following equation:
obtaining the second complex-valued mask by:
obtaining the third complex-valued mask by:
obtaining the fourth complex-valued mask by:
wherein, P11(u, v) is the first complex-valued mask, P12(u, v) is the second complex-valued mask, D||(u, v) is the amplitude of the parallel derived arrays,
for the phase of the parallel derived array, θ1(u, v) are complianceUniformly distributed random matrix, 0 ≦ theta1(u,v)≤1，P21(u, v) is the third complex-valued mask, P22(u, v) is the fourth complex-valued mask, D⊥(u, v) is the amplitude of the vertical derived matrix,
for the phase of the vertical derived array, θ2(u, v) is a random matrix subject to uniform distribution, 0 ≦ θ2(u, v) is less than or equal to 1, and i is an imaginary number unit.
In a third aspect, an embodiment of the present application provides an electronic device, including: a processor, a memory and a bus, the memory storing machine-readable instructions executable by the processor, the processor and the memory communicating via the bus when the electronic device is running, the machine-readable instructions being executed by the processor to perform the steps of the image encryption method according to the first aspect or any one of the possible embodiments of the first aspect.
In a fourth aspect, this application further provides a computer-readable storage medium, on which a computer program is stored, where the computer program is executed by a processor to perform the steps of the image encryption method in the first aspect or any one of the possible implementation manners of the first aspect.
Based on any one of the above aspects, the image encryption method and apparatus provided in the embodiments of the present application determine, based on the quaternion matrix, a parallel component matrix and a vertical component matrix of the image to be encrypted; determining a complex value mask of the image to be encrypted based on the parallel component matrix and the vertical component matrix; and generating an encrypted image corresponding to the image to be encrypted based on the complex value mask. By adopting the image encryption algorithm, the encryption information can be prevented from being concentrated, the problem of obvious outline highlighting is further solved, and the safety of the image in transmission can be improved.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings that are required to be used in the embodiments will be briefly described below, it should be understood that the following drawings only illustrate some embodiments of the present application and therefore should not be considered as limiting the scope, and for those skilled in the art, other related drawings can be obtained from the drawings without inventive effort.
Fig. 1 is a flowchart illustrating an image encryption method according to a first embodiment of the present application;
FIG. 2 is a block diagram showing one of the functional blocks of an image encryption apparatus according to the second embodiment of the present application;
fig. 3 shows a second functional block diagram of an image encryption apparatus according to a second embodiment of the present application;
fig. 4 shows a schematic structural diagram of an electronic device provided in the third embodiment of the present application.
Icon: 200-image encryption means; 210-an obtaining module; 220-a first determination module; 230-a second determination module; 240-a generation module; 232-a transformation module; 234-a third determination module; 400-an electronic device; 410-a processor; 420-a memory; 430-bus.
Detailed Description
In order to make the purpose, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application, and it should be understood that the drawings in the present application are for illustrative and descriptive purposes only and are not used to limit the scope of protection of the present application. Additionally, it should be understood that the schematic drawings are not necessarily drawn to scale. The flowcharts used in this application illustrate operations implemented according to some embodiments of the present application. It should be understood that the operations of the flow diagrams may be performed out of order, and steps without logical context may be performed in reverse order or simultaneously. One skilled in the art, under the guidance of this application, may add one or more other operations to, or remove one or more operations from, the flowchart.
In addition, the described embodiments are only a part of the embodiments of the present application, and not all of the embodiments. The components of the embodiments of the present application, generally described and illustrated in the figures herein, can be arranged and designed in a wide variety of different configurations. Thus, the following detailed description of the embodiments of the present application, presented in the accompanying drawings, is not intended to limit the scope of the claimed application, but is merely representative of selected embodiments of the application. All other embodiments, which can be derived by a person skilled in the art from the embodiments of the present application without making any creative effort, shall fall within the protection scope of the present application.
In order to enable a person skilled in the art to use the present disclosure, the following embodiments are given in connection with the specific application scenario "image encryption". It will be apparent to those skilled in the art that the general principles defined herein may be applied to other embodiments and applications without departing from the spirit and scope of the application.
The method, apparatus, electronic device or computer storage medium described in the embodiments of the present application may be applied to any scenario that requires image encryption, and the embodiments of the present application do not limit specific application scenarios, and any scheme for using image encryption provided by the embodiments of the present application is within the scope of the present application.
With the rapid development of computer networks and communication technologies, a large amount of multimedia data such as images, videos, etc. is generated every day, and the multimedia data may contain some important or private information. On one hand, the internet brings convenience to the transmission and use of the data; on the other hand, the openness and the shareability of the network also make the data face to be tampered or used maliciously, which brings huge loss to people.
In order to protect the security of the image content, the image is usually encrypted at the sending end, that is, the image is encoded by a certain method to form an image similar to random noise, and the receiving end decrypts the image by using an authorized key, thereby effectively protecting the security of the image content.
Since 1995, the image encryption technology has gained wide attention based on the dual random phase encoding technology of the optical 4f system. On the one hand, in order to improve the security of the encryption system, some transformations containing parameters are introduced into the 4f encryption system; on the other hand, in order to improve the transmission efficiency of the system, a multi-image encryption method based on phase recovery is proposed one after another. Quaternion is used as the popularization of the traditional complex number and comprises 1 real part component and 3 imaginary part components, a plurality of single-channel images or color images can be coded into a whole for processing by adopting quaternion matrix representation, and the quaternion matrix representation is widely applied to the field of color image processing and analysis in recent years.
In order to solve the above problems, the image encryption method and apparatus provided in the embodiments of the present application obtain a quaternion matrix of an image to be encrypted; determining a parallel component matrix and a vertical component matrix of the image to be encrypted based on the quaternion matrix; determining a complex value mask of the image to be encrypted based on the parallel component matrix and the vertical component matrix; and generating an encrypted image corresponding to the image to be encrypted based on the complex value mask. By adopting the image encryption algorithm, the encryption information can be prevented from being concentrated, the problem of obvious outline highlighting is further solved, and the safety of the image in transmission can be improved.
For the convenience of understanding of the present application, the technical solutions provided in the present application will be described in detail below with reference to specific embodiments.
Example one
Referring to fig. 1, fig. 1 is a flowchart of an image encryption method according to an embodiment of the present application, where the method includes:
s101: and acquiring a quaternion matrix of the image to be encrypted.
In specific implementation, an image to be encrypted is obtained first, the image to be encrypted is represented as a first quaternion matrix, and further, the first quaternion matrix is subjected to fourier transform to obtain a second quaternion matrix.
Here, the formula representing the image to be encrypted as the first quaternion matrix may be f (x, y) to f1(x,y)+if2(x,y)+jf3(x,y)+kf4(x, y), wherein f (x, y) is a first quaternion matrix, f1(x,y)、f2(x,y)、f3(x,y)、f4(x, y) are the single-channel images corresponding to the image to be encrypted, wherein the imaginary units i, j, k satisfy ij-ji-k, jk-kj-i, ki-ik-j, i2＝j2＝k2＝-1。
Here, the image to be encrypted may have two forms:
the first form: the image to be encrypted can be N different single-channel gray-scale or color images, N is more than or equal to 1 and less than or equal to 4, namely the N images can be represented by a first quaternion matrix, and at the moment, f1(x,y)、f2(x,y)、f3(x,y)、f4(x, y) each represents a respective gray-scale or color image, and if N ≠ 4, then f exists1(x,y)、f2(x,y)、f3(x,y)、f4One or two or three of (x, y) are 0. Therefore, the image to be encrypted is represented by adopting the quaternion matrix, the N single-channel images can be encoded into a whole to be encrypted, and the transmission efficiency can be effectively improved.
The second form: the image to be encrypted may be an image.
An example is as follows: the image to be encrypted is a color image which is composed of three single-channel images of red R, green G and blue B, and at the moment, f1(x,y)、f2(x,y)、f3(x,y)、f4(x, y) respectively represent R, G, B single-channel images, in which f is present1(x,y)、f2(x,y)、f3(x,y)、f4One of the components (x, y) is 0.
Here, the formula for performing Fourier transform on the first quaternion matrix to obtain the second quaternion matrix is
Wherein, mu is pure four-element number, mu is i gamma1+jγ2+kγ3，γ1、γ2、γ3Is a real number, and γ1 2+γ2 2+γ3 2＝1。
In particular, the four-element can be arranged on the left sideCalculation formula of number Fourier transform
The second quaternion matrix is obtained, and of course, other types of quaternion fourier transform formulas can be used to transform the first quaternion matrix to obtain the second quaternion matrix, such as a right-side quaternion fourier transform and a double-side quaternion fourier transform.
S102: and determining a parallel component matrix and a vertical component matrix of the image to be encrypted based on the quaternion matrix.
Here, after the quaternion matrix of the image to be encrypted is obtained, the second quaternion matrix is obtained, the quaternion matrix is subjected to spectrum decomposition to obtain a parallel component matrix and a vertical component matrix, and the quaternion matrix is decomposed into the two matrices, so that the encryption information concentration can be avoided, the problem of obvious outline is further solved, and the attack resistance can be effectively improved.
S103: and determining a complex value mask of the image to be encrypted based on the parallel component matrix and the vertical component matrix.
In a specific implementation, after the parallel component matrix and the vertical component matrix are obtained, different complex value masks of the image to be encrypted can be determined based on the parallel component matrix and the vertical component matrix, respectively. By adopting the mode, the parallel component matrix and the vertical component matrix of the image to be encrypted can be obtained through the quaternion matrix of the image to be encrypted, and then different complex value masks of the image to be encrypted are determined. By adopting the embodiment, the ciphertext information can be put in different complex value masks, and the problem of outline appearance can be avoided.
S104: and generating an encrypted image corresponding to the image to be encrypted based on the complex value mask.
The different complex value masks of the image to be encrypted are respectively processed, so that the encrypted image corresponding to the image to be encrypted can be generated, and the encryption process of the image to be encrypted is completed. By adopting the mode, the safety of the encrypted image in the transmission process can be improved.
The image encryption method provided by the embodiment of the application obtains a quaternion matrix of an image to be encrypted; determining a parallel component matrix and a vertical component matrix of the image to be encrypted based on the quaternion matrix; determining a complex value mask of the image to be encrypted based on the parallel component matrix and the vertical component matrix; and generating an encrypted image corresponding to the image to be encrypted based on the complex value mask. By adopting the image encryption algorithm, the encryption information can be prevented from being concentrated, the problem of obvious outline highlighting is further solved, and the safety of the image in transmission can be improved.
In one possible implementation, the determining a complex-valued mask of the image to be encrypted based on the parallel component matrix and the vertical component matrix in step S103 includes the following steps:
the method comprises the following steps: and transforming the parallel component matrix to obtain a parallel derivation matrix corresponding to the parallel component matrix.
In a specific implementation, the parallel component matrix is converted to obtain a parallel derived matrix corresponding to the parallel component matrix expressed in a complex form.
Step two: and transforming the vertical component matrix to obtain a vertical derivation matrix corresponding to the vertical component matrix.
In a specific implementation, the vertical component matrix is converted to obtain a vertical derived matrix corresponding to the vertical component matrix expressed in a complex form.
Step three: and determining the complex value mask of the image to be encrypted according to the parallel derivation array and the vertical derivation array.
In specific implementation, after the parallel component matrix and the vertical component matrix are obtained, the corresponding parallel derivation array and the corresponding vertical derivation array can be obtained according to the parallel component matrix and the vertical component matrix, and then different complex value masks of the image to be encrypted are determined according to the parallel derivation array and the vertical derivation array. By adopting the above embodiment, the problem of outline appearance can be avoided by placing the ciphertext information in different complex value masks.
In a possible implementation manner, the determining a complex-valued mask of the image to be encrypted according to the parallel derivation array and the vertical derivation array in step three includes the following steps:
step (1): and performing equal-mode decomposition on the parallel derivation array to obtain a first complex value mask and a second complex value mask corresponding to the parallel derivation array.
In specific implementation, after the parallel derivation array is obtained, the parallel derivation array can be subjected to equal-modulus decomposition to obtain two complex value masks corresponding to the parallel derivation array, namely a first complex value mask and a second complex value mask.
Step (2): and performing equal-mode decomposition on the vertical derivation array to obtain a third complex value mask and a fourth complex value mask corresponding to the vertical derivation array.
In specific implementation, after a vertical derived array is obtained, the vertical derived array can be subjected to equal-modulus decomposition to obtain two complex value masks corresponding to the vertical derived array, namely a third complex value mask and a fourth complex value mask.
Here, the complex value masks of the image to be encrypted may include a first complex value mask, a second complex value mask, a third complex value mask, and a fourth complex value mask.
In one possible implementation, the step S104 of generating an encrypted image corresponding to the image to be encrypted based on the complex-valued mask includes the following steps:
step a: and determining a first ciphertext of the image to be encrypted according to the first complex value mask and the third complex value mask.
In a specific implementation, the first complex-valued mask and the third complex-valued mask may be subjected to weighted summation to determine a first ciphertext corresponding to the image to be encrypted, and a calculation formula of the first ciphertext may be C1(u,v)＝aP11(u,v)+bP21(u, v) wherein C1(u, v) is the first ciphertext, P11(u, v) is a first complex-valued mask, P21(u, v) is a third complex-valued mask, a, b are constants, 0<a<1，0<b<1。
Step b: and determining a second ciphertext of the image to be encrypted according to the second complex value mask and the fourth complex value mask.
In a specific implementation, the second complex-valued mask and the fourth complex-valued mask may be subjected to weighted summation to determine a second ciphertext corresponding to the image to be encrypted, where a calculation formula of the second ciphertext is C2(u,v)＝cP12(u,v)+dP22(u, v) wherein C2(u, v) is the second ciphertext, P12(u, v) is a second complex-valued mask, P22(u, v) is a fourth complex-valued mask, c, d are constants, 0<c<1，0<d<1。
Step c: and generating an encrypted image corresponding to the image to be encrypted according to the first ciphertext and the second ciphertext.
In a specific implementation, an encrypted image corresponding to an image to be encrypted may be generated according to the first ciphertext and the second ciphertext. Specifically, the amplitude of the first ciphertext, the phase of the first ciphertext, the amplitude of the second ciphertext, and the phase of the second ciphertext may be used as four single-channel images as the encrypted image.
Here, after processing the plurality of single-channel images corresponding to the image to be encrypted, an encrypted image after encryption can be obtained. Specifically, the image to be encrypted is represented by the quaternion matrix, a plurality of single-channel images can be represented as a whole to be processed, the transmission efficiency of the image can be effectively improved, meanwhile, the parallel component matrix and the vertical component matrix can prevent ciphertext information from being concentrated in the pure phase mask, and the attack resistance strength can be effectively improved. By adopting the mode, the image coding is carried out on the image to be encrypted, so that the encrypted image similar to random noise is obtained, the content of the original image to be encrypted can be effectively hidden, and the safety of the image in the transmission process is further improved.
In one possible embodiment, the parallel component matrix is determined by the following formula:
determining the vertical component matrix by:
wherein F (u, v) is the quaternion matrix, F||(u, v) is the parallel component matrix, F⊥(u, v) is the vertical component matrix and p is the pure quaternion.
In specific implementation, after the quaternion matrix is obtained, the quaternion matrix is subjected to spectrum decomposition to obtain a parallel component matrix and a vertical component matrix, so that the concentration of encrypted information can be avoided, and the problem of obvious outline can be further solved.
In addition, F (u, v) ═ F||(u,v)+F⊥(u,v)。
In one possible embodiment, the parallel derived array is obtained by the following formula:
in the specific implementation, the parallel component matrix F is firstly||(u, v) to obtain a parallel derived matrix M corresponding to the parallel component matrix expressed in complex form||So as to derive the matrix M according to the parallel||And obtaining two complex value masks corresponding to the image to be encrypted, namely a first complex value mask and a second complex value mask.
The vertical derived matrix is obtained by the following formula:
in one embodiment, the vertical component matrix F is first obtained⊥(u, v) are transformed to obtain a matrix F of complex and vertical components⊥(u, v) corresponding vertical derivation matrix M⊥So as to derive the matrix M from the vertical⊥And obtaining two complex value masks corresponding to the image to be encrypted, namely a third complex value mask and a fourth complex value mask.
Wherein M is||For the parallel derived arrays, M⊥For the vertical derivation of arrays, A1＝F||1(u,v)+jF||2(u,v)，A2＝F||3(u,v)+jF||4(u,v)，B1＝F⊥1(u,v)+jF⊥2(u,v)，B2＝F⊥3(u,v)+jF⊥4(u, v), j is an imaginary unit, the superscript "+" indicates taking the conjugate, F||1(u,v)、F||2(u,v)、F||3(u,v)、F||4(u, v) are the components of the parallel component matrix, F⊥1(u,v)、F⊥2(u,v)、F⊥3(u,v)、F⊥4(u, v) are the components of the vertical component matrix.
Here, the parallel component matrix F||(u, v) is a quaternion matrix, F||(u,v)＝F||1(u,v)+iF||2(u,v)+fF||3(u,v)+kF||4(u, v), vertical component matrix F⊥(u, v) is a quaternion matrix, F⊥(u,v)＝F⊥1(u,v)+iF⊥2(u,v)+fF⊥3(u,v)+kF⊥4(u, v) the imaginary units i, f, k satisfy if-fi-k, fk-kf-i, ki-ik-f, i2＝f2＝k2＝-1；A1 *Is A1Conjugation of (A)1 *＝F||1(u,v)-jF||2(u,v)；A2 *Is A2Conjugation of (A)2 *＝F||3(u,v)-jF||4(u,v)；B1 *Is B1Conjugation of (B)1 *＝F⊥1(u,v)-jF⊥2(u,v)；B2 *Is B2Conjugation of (B)2 *＝F⊥3(u,v)-jF⊥4(u,v)。
In one possible embodiment, the first complex-valued mask is obtained by the following formula:
in a specific implementation, the matrix M is derived by parallel representation in complex form||And performing equal-mode decomposition to obtain two complex value masks corresponding to the image to be encrypted, namely a first complex value mask and a second complex value mask, wherein the calculation formulas of the first complex value mask and the second complex value mask are different.
Obtaining the second complex-valued mask by:
in a specific implementation, the matrix M is derived by parallel representation in complex form||And performing equal-mode decomposition to obtain two complex value masks corresponding to the image to be encrypted, namely a first complex value mask and a second complex value mask, wherein the calculation formulas of the first complex value mask and the second complex value mask are different.
Obtaining the third complex-valued mask by:
in a specific implementation, the matrix M is derived by vertically expressing the matrix M in complex form⊥And performing equal-mode decomposition to obtain two complex value masks corresponding to the image to be encrypted, namely a third complex value mask and a fourth complex value mask, wherein the calculation formulas of the third complex value mask and the fourth complex value mask are different.
Obtaining the fourth complex-valued mask by:
in a specific implementation, the matrix M is derived by vertically expressing the matrix M in complex form⊥And performing equal-mode decomposition to obtain two complex value masks corresponding to the image to be encrypted, namely a third complex value mask and a fourth complex value mask, wherein the calculation formulas of the third complex value mask and the fourth complex value mask are different.
Wherein, P11(u, v) is the first complex-valued mask, P12(u, v) is the second complex-valued mask, D||(u, v) is the amplitude of the parallel derived arrays,
for the phase of the parallel derived array, θ1(u, v) is a random matrix subject to uniform distribution, 0 ≦ θ1(u,v)≤1，P21(u, v) is the third complex-valued mask, P22(u, v) is the fourth complex-valued mask, D⊥(u, v) is the amplitude of the vertical derived matrix,
for the phase of the vertical derived array, θ2(u, v) is a random matrix subject to uniform distribution, 0 ≦ θ2(u, v) is less than or equal to 1, and i is an imaginary number unit.
In the embodiment of the application, a quaternion matrix of an image to be encrypted is obtained; determining a parallel component matrix and a vertical component matrix of the image to be encrypted based on the quaternion matrix; determining a complex value mask of the image to be encrypted based on the parallel component matrix and the vertical component matrix; and generating an encrypted image corresponding to the image to be encrypted based on the complex value mask. By adopting the image encryption algorithm, the encryption information can be prevented from being concentrated, the problem of obvious outline highlighting is further solved, and the safety of the image in transmission can be improved.
Example two
Based on the same application concept, the second embodiment of the present application further provides an image encryption apparatus corresponding to the image encryption method provided in the first embodiment of the present application, and since the principle of the apparatus in the embodiment of the present application for solving the problem is similar to the image encryption method in the above embodiment of the present application, the implementation of the apparatus may refer to the implementation of the method, and repeated details are not repeated.
Referring to fig. 2, there is shown one of functional block diagrams of an image encryption apparatus 200 according to a second embodiment of the present application; referring to fig. 3, there is shown a second functional block diagram of an image encryption apparatus 200 according to a second embodiment of the present application; wherein the image encryption apparatus 200 comprises:
an obtaining module 210, configured to obtain a quaternion matrix of an image to be encrypted;
a first determining module 220, configured to determine a parallel component matrix and a vertical component matrix of the image to be encrypted based on the quaternion matrix;
a second determining module 230, configured to determine a complex-valued mask of the image to be encrypted based on the parallel component matrix and the vertical component matrix;
and a generating module 240 for generating an encrypted image corresponding to the image to be encrypted based on the complex value mask.
In one possible embodiment, referring to fig. 3, the second determining module 230 includes a transforming module 232 and a third determining module 234;
the transformation module 232 is configured to transform the parallel component matrix to obtain a parallel derivation matrix corresponding to the parallel component matrix;
the transformation module 232 is further configured to transform the vertical component matrix to obtain a vertical derivation array corresponding to the vertical component matrix;
the third determining module 234 is configured to determine a complex value mask of the image to be encrypted according to the parallel derivation array and the vertical derivation array.
In a possible implementation manner, referring to fig. 3, the third determining module 234 is specifically configured to determine the complex-valued mask of the image to be encrypted according to the following steps:
performing equal-mode decomposition on the parallel derivation array to obtain a first complex value mask and a second complex value mask corresponding to the parallel derivation array;
and performing equal-mode decomposition on the vertical derivation array to obtain a third complex value mask and a fourth complex value mask corresponding to the vertical derivation array.
In a possible implementation manner, referring to fig. 2 and 3, the generating module 240 is specifically configured to generate an encrypted image corresponding to the image to be encrypted according to the following steps:
determining a first ciphertext of the image to be encrypted according to the first complex value mask and the third complex value mask;
determining a second ciphertext of the image to be encrypted according to the second complex value mask and the fourth complex value mask;
and generating an encrypted image corresponding to the image to be encrypted according to the first ciphertext and the second ciphertext.
In one possible embodiment, the parallel component matrix is determined by the following formula:
determining the vertical component matrix by:
wherein F (u, v) is the quaternion matrix, F||(u, v) is the parallel component matrix, F⊥(u, v) is the vertical component matrix and p is the pure quaternion.
In one possible embodiment, the parallel derived array is obtained by the following formula:
the vertical derivation is obtained by the following formulaArraying:
wherein M is||For the parallel derived arrays, M⊥For the vertical derivation of arrays, A1＝F||1(u,v)+jF||2(u,v)，A2＝F||3(u,v)+jF||4(u,v)，B1＝F⊥1(u,v)+jF⊥2(u,v)，B2＝F⊥3(u,v)+jF⊥4(u, v), j is an imaginary unit, the superscript "+" indicates taking the conjugate, F||1(u,v)、F||2(u,v)、F||3(u,v)、F||4(u, v) are the components of the parallel component matrix, F⊥1(u,v)、F⊥2(u,v)、F⊥3(u,v)、F⊥4(u, v) are the components of the vertical component matrix.
In one possible embodiment, the first complex-valued mask is obtained by the following formula:
obtaining the second complex-valued mask by:
obtaining the third complex-valued mask by:
obtaining the fourth complex-valued mask by:
wherein, P11(u, v) is the same asA complex value mask, P12(u, v) is the second complex-valued mask, D||(u, v) is the amplitude of the parallel derived arrays,
for the phase of the parallel derived array, θ1(u, v) is a random matrix subject to uniform distribution, 0 ≦ θ1(u,v)≤1，P21(u, v) is the third complex-valued mask, P22(u, v) is the fourth complex-valued mask, D⊥(u, v) is the amplitude of the vertical derived matrix,
for the phase of the vertical derived array, θ2(u, v) is a random matrix subject to uniform distribution, 0 ≦ θ2(u, v) is less than or equal to 1, and i is an imaginary number unit.
The image encryption device 200 according to the second embodiment of the present application obtains a quaternion matrix of an image to be encrypted; determining a parallel component matrix and a vertical component matrix of the image to be encrypted based on the quaternion matrix; determining a complex value mask of the image to be encrypted based on the parallel component matrix and the vertical component matrix; and generating an encrypted image corresponding to the image to be encrypted based on the complex value mask. By adopting the image encryption algorithm, the encryption information can be prevented from being concentrated, the problem of obvious outline highlighting is further solved, and the safety of the image in transmission can be improved.
EXAMPLE III
Based on the same application concept, referring to fig. 4, a schematic structural diagram of an electronic device 400 provided in the third embodiment of the present application includes: the image encryption method includes a processor 410, a memory 420, and a bus 430, where the memory 420 stores machine-readable instructions executable by the processor 410, when the electronic device 400 runs, the processor 410 communicates with the memory 420 through the bus 430, and when the machine-readable instructions are run by the processor 410, the steps of the image encryption method in the first embodiment of the method shown in fig. 1 are performed.
In particular, the machine readable instructions, when executed by the processor 410, perform the steps of:
acquiring a quaternion matrix of an image to be encrypted;
determining a parallel component matrix and a vertical component matrix of the image to be encrypted based on the quaternion matrix;
determining a complex value mask of the image to be encrypted based on the parallel component matrix and the vertical component matrix;
and generating an encrypted image corresponding to the image to be encrypted based on the complex value mask.
Based on the same application concept, a third embodiment of the present application further provides a computer-readable storage medium, where a computer program is stored on the computer-readable storage medium, and when the computer program is executed by a processor, the step of the image encryption method in the first embodiment of the method shown in fig. 1 is executed.
Specifically, the storage medium can be a general-purpose storage medium, such as a removable disk, a hard disk, or the like, and when a computer program on the storage medium is executed, the image encryption method can be executed, so that not only can the transmission efficiency of the image be effectively improved, but also the problem of appearance of the contour can be avoided.
Based on the same application concept, a third embodiment of the present application further provides a computer program product, which includes a computer-readable storage medium storing a program code, where instructions included in the program code may be used to execute the steps of the image encryption method, and specific implementation may refer to the above method embodiments, and is not described herein again.
It can be clearly understood by those skilled in the art that, for convenience and brevity of description, the specific working processes of the system and the apparatus described above may refer to corresponding processes in the method embodiments, and are not described in detail in this application. In the several embodiments provided in the present application, it should be understood that the disclosed system, apparatus and method may be implemented in other ways. The above-described apparatus embodiments are merely illustrative, and for example, the division of the modules is merely a logical division, and there may be other divisions in actual implementation, and for example, a plurality of modules or components may be combined or integrated into another system, or some features may be omitted, or not executed. In addition, the shown or discussed mutual coupling or direct coupling or communication connection may be an indirect coupling or communication connection of devices or modules through some communication interfaces, and may be in an electrical, mechanical or other form.
The modules described as separate parts may or may not be physically separate, and parts displayed as modules may or may not be physical units, may be located in one place, or may be distributed on a plurality of network units. Some or all of the units can be selected according to actual needs to achieve the purpose of the solution of the embodiment.
In addition, functional units in the embodiments of the present application may be integrated into one processing unit, or each unit may exist alone physically, or two or more units are integrated into one unit.
The functions, if implemented in the form of software functional units and sold or used as a stand-alone product, may be stored in a non-volatile computer-readable storage medium executable by a processor.
Based on such understanding, the technical solutions of the present application may be embodied in the form of a software product, which is stored in a storage medium and includes several instructions for causing a computer device (which may be a personal computer, a server, or a network device) to execute all or part of the steps of the methods described in the embodiments of the present application. And the aforementioned storage medium includes: various media capable of storing program codes, such as a usb disk, a removable hard disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), a magnetic disk, or an optical disk.
The above description is only for the specific embodiments of the present application, but the scope of the present application is not limited thereto, and any person skilled in the art can easily conceive of the changes or substitutions within the technical scope of the present application, and shall be covered by the scope of the present application. Therefore, the protection scope of the present application shall be subject to the protection scope of the claims.
Claims (7)
1. An image encryption method, characterized in that the method comprises:
acquiring a quaternion matrix of an image to be encrypted;
determining a parallel component matrix and a vertical component matrix of the image to be encrypted based on the quaternion matrix;
determining a complex value mask of the image to be encrypted based on the parallel component matrix and the vertical component matrix;
generating an encrypted image corresponding to the image to be encrypted based on the complex value mask;
the determining a complex value mask of the image to be encrypted based on the parallel component matrix and the vertical component matrix includes:
transforming the parallel component matrix to obtain a parallel derivation matrix corresponding to the parallel component matrix;
transforming the vertical component matrix to obtain a vertical derivation matrix corresponding to the vertical component matrix;
determining a complex value mask of the image to be encrypted according to the parallel derivation array and the vertical derivation array;
the parallel derived array is obtained by the following formula:
the vertical derived matrix is obtained by the following formula:
wherein M is||For the parallel derived arrays, M⊥For the vertical derivation of arrays, A1＝F||1(u,v)+jF||2(u,v)，A2＝F||3(u,v)+jF||4(u,v)，B1＝F⊥1(u,v)+jF⊥2(u,v)，B2＝F⊥3(u,v)+jF⊥4(u, v), j is an imaginary unit, the superscript "+" indicates taking the conjugate, F||1(u,v)、F||2(u,v)、F||3(u,v)、F||4(u, v) are the components of the parallel component matrix, F⊥1(u,v)、F⊥2(u,v)、F⊥3(u,v)、F⊥4(u, v) are the components of the vertical component matrix.
2. The method according to claim 1, wherein the determining a complex-valued mask of the image to be encrypted according to the parallel derivation array and the vertical derivation array comprises:
performing equal-mode decomposition on the parallel derivation array to obtain a first complex value mask and a second complex value mask corresponding to the parallel derivation array;
and performing equal-mode decomposition on the vertical derivation array to obtain a third complex value mask and a fourth complex value mask corresponding to the vertical derivation array.
3. The method according to claim 2, wherein the generating an encrypted image corresponding to the image to be encrypted based on the complex-valued mask comprises:
determining a first ciphertext of the image to be encrypted according to the first complex value mask and the third complex value mask;
determining a second ciphertext of the image to be encrypted according to the second complex value mask and the fourth complex value mask;
and generating an encrypted image corresponding to the image to be encrypted according to the first ciphertext and the second ciphertext.
4. The method of claim 1, wherein the parallel component matrix is determined by the formula:
determining the vertical component matrix by:
wherein F (u, v) is the quaternion matrix, F||(u, v) is the parallel component matrix, F⊥(u, v) is the vertical component matrix and p is the pure quaternion.
5. The method of claim 2, wherein the first complex-valued mask is derived by the following equation:
obtaining the second complex-valued mask by:
obtaining the third complex-valued mask by:
obtaining the fourth complex-valued mask by:
wherein, P11(u, v) is the first complex-valued mask, P12(u, v) is the second complex-valued mask, D||(u, v) is the amplitude of the parallel derived arrays,
for the phase of the parallel derived array, θ1(u, v) is a random matrix subject to uniform distribution, 0 ≦ θ1(u,v)≤1，P21(u, v) is the third complex-valued mask, P22(u, v) is the fourth complex-valued mask, D⊥(u, v) is the amplitude of the vertical derived matrix,
for the phase of the vertical derived array, θ2(u, v) is a random matrix subject to uniform distribution, 0 ≦ θ2(u, v) is less than or equal to 1, and i is an imaginary number unit.
6. An image encryption apparatus, characterized in that the apparatus comprises:
the acquisition module is used for acquiring a quaternion matrix of the image to be encrypted;
the first determining module is used for determining a parallel component matrix and a vertical component matrix of the image to be encrypted based on the quaternion matrix;
the second determination module is used for determining the complex value mask of the image to be encrypted based on the parallel component matrix and the vertical component matrix;
the generating module generates an encrypted image corresponding to the image to be encrypted based on the complex value mask;
the second determination module comprises a transformation module and a third determination module;
the transformation module is used for transforming the parallel component matrix to obtain a parallel derivation matrix corresponding to the parallel component matrix;
the transformation module is further configured to transform the vertical component matrix to obtain a vertical derivation matrix corresponding to the vertical component matrix;
the third determining module is configured to determine a complex value mask of the image to be encrypted according to the parallel derivation array and the vertical derivation array;
the conversion dieThe block obtains the parallel derived arrays by the following formula:
the transformation module obtains the vertical derivation array by the following formula:
wherein M is||For the parallel derived arrays, M⊥For the vertical derivation of arrays, A1＝F||1(u,v)+jF||2(u,v)，A2＝F||3(u,v)+jF||4(u,v)，B1＝F⊥1(u,v)+jF⊥2(u,v)，B2＝F⊥3(u,v)+jF⊥4(u, v), j is an imaginary unit, the superscript "+" indicates taking the conjugate, F||1(u,v)、F||2(u,v)、F||3(u,v)、F||4(u, v) are the components of the parallel component matrix, F⊥1(u,v)、F⊥2(u,v)、F⊥3(u,v)、F⊥4(u, v) are the components of the vertical component matrix.
7. The apparatus according to claim 6, wherein the third determining module is specifically configured to determine the complex-valued mask of the image to be encrypted according to the following steps:
performing equal-mode decomposition on the parallel derivation array to obtain a first complex value mask and a second complex value mask corresponding to the parallel derivation array;
and performing equal-mode decomposition on the vertical derivation array to obtain a third complex value mask and a fourth complex value mask corresponding to the vertical derivation array.
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