WO2017004790A1 - Cryptographic decoding method of image coding system based on double random phase and device utilizing same - Google Patents

Abstract

The present invention discloses a cryptographic decoding method of an image coding system based on a double random phase and a device utilizing the same. The cryptographic decoding method employs a hybrid adaptive iterative phase recovery algorithm, and comprises: recovering, via the phase recovery algorithm, an amplitude (i.e., a plaintext) and phase (i.e., a spatial domain key) of an input plane, provided that a frequency domain magnitude of the input plane is known; and calculating a frequency domain key. The decoding process requires no other a priori information but only an encrypted text which requires image decoding, effectively reducing a difficulty of implementing decoding.

Description

Cryptographic cracking method and device based on double random phase image coding system Technical field

The present invention relates to the field of optical information processing, and in particular to a cryptographic cracking method and apparatus based on a dual random phase image encoding system.

Background technique

Data encryption and information hiding based on optical theory and method are a new generation of information security technology that has begun to develop in the world in recent years. Parallel data processing is an inherent capability of an optical system, as each pixel in a two-dimensional image in an optical system can be propagated and processed simultaneously. When a large amount of information processing is performed, the parallel processing capability of the optical system clearly has an absolute advantage. Moreover, the more complex the processed image, the greater the amount of information, the more obvious this advantage. At the same time, the optical encryption device has more degrees of freedom than the electronic encryption device. Information can be hidden in multiple degrees of freedom space. In the process of data encryption or information hiding, the wavelength, focal length, amplitude, light intensity, phase, polarization state and parameters of the optical components can be calculated by calculating the interference, diffraction, filtering, imaging, holography, etc. of the light. Perform multidimensional coding. Compared with traditional mathematics-based computer cryptography and information security technology, it has many advantages such as multi-dimensional, large capacity, high degree of freedom, high robustness, and natural parallelism.

Among the many optical encryption schemes, the research results of B.Javidi in the United States are the most representative. In 1995, Javidi et al. first proposed a dual random phase image encoding and encryption scheme that can be implemented by optical devices, and successfully encrypted a plaintext image into a noise image. This technology has been protected by US patents. Thereafter, other encryption schemes based on dual random phase image coding systems have been proposed.

The dual random phase encoding encryption scheme is implemented by a standard 4-F system. The plaintext image is placed on the input surface of the 4-F system, and two independent (ie, statistically independent) random phase plates (as the key of the 4-F system) ) respectively placed on the input plane and the spectrum plane (also called the Fourier plane) of the 4-F system, so that the plaintext information is randomly disturbed in the spatial domain and the frequency domain, respectively, thereby whitening the spectral density distribution to reach For the purpose of encrypting the image, finally, a stationary white noise encrypted image whose statistical characteristics are shifted with time is obtained on the output surface of the 4-F system. The entire encryption process can be expressed by:

ψ(x,y)=FT ^-1 {FT{f(x,y)exp[i2πn(x,y)]}·exp[i2πb(u,v)]}

Where f(x, y) is the plaintext image to be encrypted, ψ(x, y) is the encrypted ciphertext, exp[i2πn(x, y)] is the spatial domain key, exp[i2πb(u, v )] is the frequency domain key, FT{·} represents the Fourier transform, and FT ^-1 {·} represents the inverse Fourier transform.

When decrypting, ciphertext ψ(x, y) is placed on the input side of the 4-F system. After Fourier transform, the conjugate exp[-i2πb(x,y)] of the frequency domain key is used on the spectrum plane. (decryption key) filtering, the decryption process is the inverse transformation of the encryption process, which can be expressed as:

Where f(x, y) represents the plaintext obtained after decryption.

In the field of cryptanalysis, which is opposite and mutually reinforcing in the field of cryptography, Spain's A. Carnicer et al. first discovered that the spectrum plane density of the double random phase image coding system can be analyzed by the method of "choose ciphertext attack". Key, however, the above method requires the attacker to select a large number of well-designed ciphertexts on the one hand, which is difficult and complicated to implement, and on the other hand, there are many resources to be acquired, such as obtaining ciphertext (x, y) in advance and The corresponding plaintext f(x, y), that is, the plaintext-ciphertext pair needs to be obtained in advance.

technical problem

The embodiment of the invention provides a cryptographic cracking method and a cryptographic cracking device based on a double random phase image encoding system, which are used for cracking only by using ciphertext, and reducing the difficulty of cracking implementation.

Technical solution

An embodiment of the present invention provides a cryptographic cracking method based on a dual random phase image encoding system, where the method includes:

Initializing a random number as an input function for each pixel in the image to be decrypted;

Performing support recovery processing on the basis of the input function;

Performing plaintext recovery processing on the basis of the support recovery processing;

Performing accurate recovery processing on the basis of the plaintext recovery processing;

Determining a plaintext, a spatial domain key, and a frequency domain key on the basis of the exact recovery process;

Wherein, the supporting recovery processing is performed on the basis of the input function, including:

Iterative processing of the input function g(x, y), wherein each iterative processing includes:

Performing a Fourier transform on g(x, y) to obtain G(u, v), where g(x, y) represents the pixel value of the pixel of the xth row and the yth column in the image to be decrypted. ;

Substituting the amplitude value of G(u,v) with the amplitude of the ciphertext of the image to be decrypted in the frequency domain |ψ(u,v)|, and performing an inverse Fourier transform to obtain an intermediate function g'(x,y) );

The K pixel position at which the amplitude value of the intermediate function is the largest is taken as the support S of the current iteration, and the pixel value of each pixel is updated according to the first formula, and then returned to the pair g in the process of performing the support recovery process ( x, y) performing a Fourier transform step and subsequent steps until a preset support recovery iteration stop condition is satisfied, the initial value of K being a preset value greater than 2;

The first formula is

In the above first formula, β is a preset coefficient;

The clear text recovery process is performed on the basis of the support recovery process, including:

Performing the iterative process of step S1, step S2, and step S3 on the basis of S and g(x, y) obtained when the support resumes the iteration stop, until the preset plaintext recovery iteration stop condition is satisfied, wherein Step S1 is a Fourier transform on g(x, y) to obtain G(u, v), and step S2 is to replace the amplitude value of G(u, v) with the ciphertext of the image to be decrypted. The amplitude of the frequency domain |ψ(u,v)| Performing an inverse Fourier transform to obtain g'(x, y); the step S3 is to update the input function according to the first formula;

The accurate recovery processing is performed on the basis of the plaintext recovery processing, including:

On the basis of S and g(x, y) obtained when the plaintext recovery processing is stopped, iteratively performs steps S1, S2, and S3 of T1 times, and then iteratively performs steps S4, S5, and S6 of T2, alternately until the said The cumulative number of iterations in the exact recovery process reaches T3, wherein the T1, T2, and T3 are preset values greater than 2, and the T3 is greater than the sum of the T1 and the T2;

When the cumulative number of iterations in the precise recovery process reaches the T3, the mean square error NMSE is calculated according to the third formula;

If the NMSE reaches the preset precision, performing the step of determining the plaintext, the spatial domain key, and the frequency domain key on the basis of the accurate recovery process, if the NMSE does not reach the preset precision, Clearing the cumulative number of iterations in the exact recovery process, and returning to perform the iterative processing of the step S1, the step S2, and the step S3 based on the S and g(x, y) obtained at the time. Until the plaintext recovery iteration stop condition is satisfied;

Wherein, the step S4 is performing Fourier transform on g(x, y) to obtain G(u, v), and the step S5 is to replace the amplitude value of G(u, v) with the image to be decrypted. The ciphertext is subjected to inverse Fourier transform after the amplitude |ψ(u,v)| in the frequency domain to obtain an intermediate function g'(x, y), and the step S6 is K which maximizes the amplitude value of the intermediate function. The pixel position is used as the support S of the current iteration, and the input function is updated according to the second formula;

The second formula is:

所述第三公式中的M和N分别为所述待解密图像中像素点的总行数和总列数； The third formula is:

M and N in the third formula are respectively the total number of rows and the total number of columns of pixels in the image to be decrypted;

The determining the plaintext, the spatial domain key, and the frequency domain key on the basis of the accurate recovery process, including:

Determining an amplitude value of g(x, y) obtained by the accurate restoration processing as a plaintext of the image to be decrypted, and determining a phase portion of g(x, y) obtained by the accurate restoration processing as the The spatial domain key of the image to be decrypted;

Determining a frequency domain key exp[i2πb(u,v)] of the image to be decrypted according to a fourth formula,

Wherein the fourth formula is:

或

or

Another aspect of the embodiments of the present invention provides a cryptographic cracking apparatus based on a dual random phase image encoding system, including:

An initialization unit, configured to initialize a random number as an input function for each pixel in the image to be decrypted;

Supporting a recovery processing unit for performing support recovery processing on the basis of the input function;

a plaintext recovery processing unit, configured to perform plaintext recovery processing on the basis of the support recovery processing;

An accurate recovery processing unit, configured to perform an accurate recovery process on the basis of the plaintext recovery process;

a determining unit, configured to determine a plaintext, a spatial domain key, and a frequency domain key on the basis of the accurate recovery process;

The support recovery processing unit is specifically configured to:

An iterative process is performed on an input function of each pixel, wherein an iterative process for any pixel (x, y) in the image to be decrypted includes:

Performing a Fourier transform on g(x, y) to obtain G(u, v), where g(x, y) represents the The pixel value of the pixel of the xth row and the yth column in the image to be decrypted;

Substituting the amplitude value of G(u,v) with the amplitude of the ciphertext of the image to be decrypted in the frequency domain |ψ(u,v)|, and performing an inverse Fourier transform to obtain an intermediate function g'(x,y) );

The K pixel position where the amplitude value of the intermediate function is the largest is taken as the support S of the current iteration, and the input function is updated according to the first formula, and then returns to the pair g(x, y) in the process of performing the support recovery process. Performing a Fourier transform step and a subsequent step until a preset support recovery iteration stop condition is satisfied, and the initial value of the K is a preset value greater than 2;

The first formula is

In the above first formula, β is a preset coefficient;

The plaintext recovery processing unit is specifically configured to:

On the basis of S and g(x, y) obtained when the support recovery is iteratively stopped, the iterative process of step S1, step S2 and step S3 is performed until the preset plaintext recovery iteration stop condition is satisfied, wherein Step S1 is a Fourier transform on g(x, y) to obtain G(u, v), and step S2 is to replace the amplitude value of G(u, v) with the ciphertext of the image to be decrypted. Performing an inverse Fourier transform on the amplitude |ψ(u,v)| of the frequency domain to obtain g'(x, y); the step S3 is to update the input function according to the first formula;

The precision recovery processing unit is specifically configured to:

On the basis of S and g(x, y) obtained when the plaintext recovery iteration is stopped, iteratively performs steps S1, S2 and S3 of T1 times, and then iteratively performs steps T4, S5 and S6 of T2, and alternates until The cumulative number of iterations in the exact recovery process reaches T3, wherein the T1, T2, and T3 are preset values greater than 2, and the T3 is greater than the sum of the T1 and the T2;

When the cumulative number of iterations in the precise recovery process reaches the T3, the mean square error NMSE is calculated according to the third formula;

If the NMSE reaches a preset accuracy, performing the accurate recovery process Determining a plaintext, a spatial domain key, and a frequency domain key, if the NMSE does not reach the preset precision, clearing the cumulative number of iterations in the exact recovery process, and obtaining the S obtained at the time And returning to perform the iterative process of step S1, step S2, and step S3 on the basis of g(x, y) until the plaintext recovery iteration stop condition is satisfied;

Wherein, the step S4 is performing Fourier transform on g(x, y) to obtain G(u, v), and the step S5 is to replace the amplitude value of G(u, v) with the image to be decrypted. The ciphertext is subjected to inverse Fourier transform after the amplitude |ψ(u,v)| in the frequency domain to obtain an intermediate function g'(x, y), and the step S6 is K which maximizes the amplitude value of the intermediate function. The pixel position is used as the support S of the current iteration, and the input function is updated according to the second formula;

The second formula is:

所述第三公式中的M和N分别为所述待解密图像中像素点的总行数和总列数；The third formula is:

M and N in the third formula are respectively the total number of rows and the total number of columns of pixels in the image to be decrypted;

Wherein, the determining unit is specifically configured to:

Determining an amplitude value of g(x, y) obtained by the accurate restoration processing as a plaintext of the image to be decrypted, and determining a phase portion of g(x, y) obtained by the accurate restoration processing as the The spatial domain key of the image to be decrypted;

Determining a frequency domain key exp[i2πb(u,v)] of the image to be decrypted according to a fourth formula,

Wherein the fourth formula is:

或

or

Beneficial effect

It can be seen from the above technical solution that the ciphertext attack problem in which the ciphertext recovers only the plaintext, the spatial domain key and the frequency domain key is converted into a standard phase recovery problem, that is, When the input surface frequency domain strength is known, the amplitude of the input surface (ie, plaintext) and phase (ie, spatial domain key) can be recovered by the phase recovery algorithm, and then the frequency domain key can be calculated. In this scheme, a hybrid adaptive iterative phase recovery algorithm is used. In addition to the ciphertext of the image to be decrypted, no other prior information is needed in the cracking process, thereby effectively reducing the difficulty of cracking.

DRAWINGS

In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the embodiments or the description of the prior art will be briefly described below. Obviously, the drawings in the following description are only It is a certain embodiment of the present invention, and other drawings can be obtained from those skilled in the art without any inventive labor.

1 is a schematic diagram of a principle of a dual random phase image coding system;

2 is a schematic flowchart of an embodiment of a cryptography cracking method based on a dual random phase image encoding system according to an embodiment of the present invention;

3a and 3b are schematic diagrams illustrating a specific application scenario for determining S and δ by K according to an embodiment of the present invention;

4 is a schematic flowchart of a hybrid adaptive iterative algorithm in an application scenario according to an embodiment of the present invention;

FIG. 5-a is an original image to be encrypted (8-bit grayscale image) according to an embodiment of the present invention;

Figure 5-b is a result of encrypting the original image to be encrypted shown in Figure 5-a by a dual random phase image encoding system;

FIG. 5-c is a support recovered by the support recovery process of FIG. 5-c by using the cryptographic cracking method in the embodiment of the present invention;

FIG. 5-d is an original image obtained by recovering FIG. 5-c by using a cryptographic cracking method in the embodiment of the present invention;

6-a is an original image to be encrypted (binary graph) according to an embodiment of the present invention;

6-b is a result of encrypting the original image to be encrypted shown in FIG. 6-a by a dual random phase image encoding system;

Figure 6-c is a support recovered by the support recovery process of Figure 6-c by using the cryptographic cracking method in the embodiment of the present invention;

FIG. 6-d is an original image obtained by recovering FIG. 6-c by using a cryptographic cracking method in the embodiment of the present invention;

FIG. 7 is a schematic structural diagram of an embodiment of a cryptography cracking apparatus based on a dual random phase image encoding system according to an embodiment of the present invention.

detailed description

The technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the drawings in the embodiments of the present invention. It is a partial embodiment of the invention, and not all of the embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative efforts are within the scope of the present invention.

First, the inventive concept of the cryptographic cracking method in the embodiment of the present invention is explained. FIG. 1 is a schematic diagram of the principle of the dual random phase image encoding system. The dual random phase image coding system is implemented using a standard 4-F system, 103, 104 are two Fourier lenses, and two statistically independent random phase plates 102 and 105 are placed in the input plane and spectrum of the 4-F system, respectively. On the plane, the spatial information and the spectral information of the original image 101 (represented by f(x, y)) are randomly disturbed, thereby whitening the spectral density distribution to achieve the purpose of encrypting the image, and the statistical characteristics are obtained on the output plane. A constant stationary white noise image 106 (represented by ψ(u,v)).

The entire encryption process can be expressed by:

ψ(x,y)=FT ^-1 {FT{f(x,y)exp[i2πn(x,y)]}·exp[i2πb(u,v)]};

f(x, y) is the plaintext image to be encrypted, ψ(x, y) is the encrypted ciphertext, exp[i2πn(x, y)] is the spatial domain key, exp[i2πb(u,v)] For the frequency domain key, FT{·} represents the Fourier transform, and FT ^-1 {·} represents the inverse Fourier transform.

When decrypting, ciphertext x(x, y) is placed on the input side of the 4-F system. After Fourier transform, the conjugate exp[-i2πb(x,y)] of the frequency domain key is used on the spectrum surface. (decryption key) filtering, the decryption process is the inverse transformation of the encryption process, which can be expressed as:

代表解密的明文。

Represents the plaintext of decryption.

If the cracker can obtain the ciphertext (x, y), it will be Fourier transformed to get Ψ(u,v),

Ψ(u,v)=FT{ψ(x,y)}

Let the 4-F system input plane signal be g(x,y) (ie g(x,y)=f(x,y)·exp[i2πn(x,y)]), then the encryption equation can be written as

ψ(x,y)=FT ^-1 {FT{g(x,y)}·exp[i2πb(u,v)]};

Rewrite the above equation to get:

FT{ψ(x,y)}=FT{g(x,y)}·exp[i2πb(u,v)]

Ψ(u,v)=FT{g(x,y)}·exp[i2πb(u,v)];

If the Fourier transform of g(x, y) is written as G(u,v), that is, G(u,v)=FT{g(x,y)};

From the above:

Ψ(u,v)=G(u,v)·exp[i2πb(u,v)];

For the two ends of the above formula, Ψ(u,v)|=|G(u,v)|;

It can be seen that if the cracker can obtain the ciphertext ψ(x, y) corresponding to the plaintext f(x, y), the input plane (that is, the plaintext f(x, y)·exp[ with the phase key] can be obtained. I2πn(x, y)]) The intensity in the frequency domain. At this point, the ciphertext attack problem that only restores the corresponding plaintext and system keys from ciphertext is converted into a standard. The phase recovery problem, that is, in the case of the known input plane frequency domain strength, the phase recovery algorithm can recover the amplitude (ie, plaintext) and phase (ie, spatial domain key) of the input plane, and then calculate the frequency domain. Key. Because the resources available for ciphertext attacks are extremely limited (only ciphertext information is known), we design a hybrid adaptive iterative phase recovery algorithm. The advantages of this algorithm are: (1) no priors are needed. Information, the difficulty of cracking is greatly reduced; (2) By effectively combining various phase recovery algorithms, the recovery effect is very satisfactory, and the correlation coefficient between the recovery result and the original image can usually be above 0.9.

The cryptographic cracking method based on the dual random phase image encoding system in the embodiment of the present invention is described below. Referring to FIG. 2, the cryptographic cracking method in the embodiment of the present invention includes:

201. Initialize a random number as an input function for each pixel in the image to be decrypted;

In the embodiment of the present invention, the cryptographic cracking device initializes a random number as an input function for each pixel in the image to be decrypted, and the random number initialized by each pixel corresponds to a random value in the gray range, for example, gray. The degree range is 0 to 255, and the value of the random number initialized at each pixel (ie, the pixel value) is a value randomly selected from 0 to 255.

202. Perform support recovery processing on the basis of the above input function;

In the embodiment of the present invention, the cryptographic cracking device iteratively processes the input function g(x, y) in the support recovery processing phase, wherein each iterative processing includes:

Performing a Fourier transform on g(x, y) to obtain G(u, v), where g(x, y) represents the pixel value of the pixel of the xth row and the yth column in the image to be decrypted. ;

Substituting the amplitude value of G(u,v) with the amplitude of the ciphertext of the image to be decrypted in the frequency domain |ψ(u,v)|, and performing an inverse Fourier transform to obtain an intermediate function g'(x,y) );

The K pixel position where the amplitude value of the intermediate function is the largest is taken as the support S of the current iteration, and the input function is updated according to the first formula, and then returns to the pair g(x, y) in the process of performing the support recovery process. Perform the Fourier transform step and subsequent steps until the preset support is restored The initial value of the K is a preset value greater than 2, and optionally, the initial value of K may take 1% of the total number of pixels in the image to be decrypted;

The first formula is

In the above first formula, β is a preset coefficient, and generally, β is 0.9, or β can be summarized according to actual conditions or experience, and is not limited herein. The first formula above indicates that if the pixel point is in the S range, the input function (ie, the pixel value) of the pixel point remains unchanged. If the pixel point is outside the S range, the new input function of the pixel point is this time. An iterative linear combination of input and output. This algorithm can be called the Dynamic Hybrid Input-Output (DH) algorithm.

Optionally, the K pixel points with the largest amplitude value of the intermediate function are used as the support S of the current iteration, and the input function is updated according to the first formula, and then includes:

The cryptographic cracking device determines whether the cumulative number of iterations in the support recovery process reaches T4, wherein the T4 is a preset value greater than 2, and specifically, T4 may take 200.

If the number of accumulated iterations in the support recovery process does not reach T4, returning to performing the Fourier transform on the g(x, y) in the support recovery process and subsequent steps;

If the cumulative number of iterations in the support recovery process reaches T4, it is determined whether the threshold determined by K is less than a preset threshold, wherein the threshold determined by K is equal to the current g'(x, y). The amplitude value of the Kth g'(x, y) whose amplitude value is arranged from large to small;

If the threshold determined by K is less than the preset threshold, determining that the preset support recovery iteration stop condition is satisfied;

If the threshold determined by K is not less than the preset threshold, the cryptographic cracking device clears the cumulative number of iterations in the support recovery process, and makes K=K+a%*M*N, Returning to the step of performing Fourier transform on g(x, y) in performing the support recovery process and a subsequent step, wherein M and N are respectively a total number of rows and a total number of columns of pixels in the image to be decrypted, and a is a preset value not less than 1, for example, a is equal to 1.

Taking T4 equal to 200 as an example, step 202 is specifically performed as follows: 200 times per iteration in the support recovery process, and observing a threshold determined by K (for convenience of description, the threshold value determined by K is described as δ) δ is not less than the preset threshold (for convenience of description, the threshold value determined by δ is described as c ₁ ), indicating that the black background area should still have a value, and the support area is not large enough, then the K value is increased to be decrypted. The a% of the total pixel in the image, and the output g(x, y) of this iteration is taken as the input of the next iteration, and the iteration is continued until the next 200 times; if δ is smaller than c ₁ , the plain text object and the background are It has been possible to distinguish between the support recovery process and the support of the last iteration as the support for recovery to the next stage (ie, step 203).

The following examples illustrate the support S and δ determined by K. Assume that the size of the picture to be decrypted is 5*5 pixels as shown in Figure 3-a. The pixel value of each pixel is marked on Figure 3-a. When the value of K of the iteration is 6, then the 6 pixel points whose amplitude value of the intermediate function (that is, the pixel value of the sub-pixel point) is the largest is taken as the support S of the current iteration, and the support determined according to the K value is supported. S is the pixel portion of the white bottom in Figure 3-b. The amplitude value of the sixth g'(x, y) when the amplitude value of the secondary function is arranged from large to small is the threshold value determined by K, δ. That is 20 in Figure 3-b. The actual situation is similar, except that the picture is larger, the number of pixels is more, and each pixel value is a complex number. You need to take the modulo (or take the amplitude part) and compare the size to determine S and δ.

203. Perform plaintext recovery processing on the basis of the foregoing support recovery processing;

In the embodiment of the present invention, the plaintext recovery processing process is similar to the above-described support recovery processing process, and the only difference is that the S obtained when the support recovery iteration stops is kept unchanged during the plaintext recovery processing, that is, the standard mixed input-output is used ( HIO, Hybrid Input-Output algorithm.

Specifically, the cryptographic cracking device performs plaintext recovery processing on the basis of the foregoing support recovery processing, including:

On the basis of S and g(x, y) obtained when the support recovery is iteratively stopped, the iterative process of step S1, step S2 and step S3 is performed until the preset plaintext recovery iteration stop condition is satisfied, wherein the step S1 is a Fourier transform on g(x, y) to obtain G(u, v), and step S2 is to replace the amplitude value of G(u, v) with the ciphertext of the image to be decrypted at the frequency. The amplitude of the domain |ψ(u,v)| is then inverse Fourier transformed to obtain g'(x, y); the step S3 is to update the input function according to the first formula;

Optionally, in the foregoing plaintext recovery process, after the step S3, the following includes:

Determining whether the cumulative number of iterations in the plaintext recovery process reaches a preset number of iterations;

If the cumulative number of iterations in the plaintext recovery process reaches a preset number of iterations, it is determined that the preset plaintext recovery iteration stop condition is satisfied;

If the cumulative number of iterations in the plaintext recovery process does not reach the preset number of iterations, then the step S1 is performed (ie, a new iteration is performed). Specifically, for an image to be decrypted of 256*256 pixels, the number of iterations may be preset to a value of about 600 or 600. Of course, for other sizes of images to be decrypted, the number of iterations may be increased or decreased as appropriate.

204. Perform accurate recovery processing on the basis of the above plaintext recovery processing;

In the embodiment of the present invention, a CF (English full name Change Flipping) algorithm is introduced in the process of accurate recovery, which is similar to the DHIO algorithm except that the first formula in the DHIO algorithm is replaced with the second formula:

The main function of the CF algorithm is to further accurately support the boundary, and can effectively improve the pixel distribution inside and outside, thereby reducing the error in the frequency domain. In step 204, the HIO algorithm and the CF algorithm are alternately used. The specific process is as follows:

On the basis of S and g(x, y) obtained when the plaintext recovery processing is stopped, iteratively performs steps S1, S2, and S3 of T1 times, and then iteratively performs steps S4, S5, and S6 of T2, alternately until the said The cumulative number of iterations during the exact recovery process reaches T3, wherein the T1, T2, and T3 Is a preset value greater than 2, and the T3 is greater than a sum of the T1 and the T2;

When the cumulative number of iterations in the accurate recovery process reaches the T3, a mean squared error (NMSE) is calculated according to the third formula;

If the NMSE reaches the preset precision, performing the step of determining the plaintext, the spatial domain key, and the frequency domain key on the basis of the accurate recovery process, if the NMSE does not reach the preset precision, Clearing the cumulative number of iterations in the exact recovery process, and returning to perform the iterative processing of the step S1, the step S2, and the step S3 based on the S and g(x, y) obtained at the time. (ie, returning to the plaintext recovery process based on the S and g(x, y) obtained at the time) until the plaintext recovery iteration stop condition is satisfied.

Wherein, the step S4 is performing Fourier transform on g(x, y) to obtain G(u, v), and the step S5 is to replace the amplitude value of G(u, v) with the image to be decrypted. The ciphertext is subjected to inverse Fourier transform after the amplitude |ψ(u,v)| in the frequency domain to obtain an intermediate function g'(x, y), and the step S6 is K which maximizes the amplitude value of the intermediate function. The pixel is used as the support S of the current iteration, and the input function is updated according to the second formula described above;

所述第三公式中的M和N分别为所述待解密图像中像素点的总行数和总列数。The third formula is:

M and N in the third formula are the total number of rows and the total number of columns of pixels in the image to be decrypted, respectively.

Specifically, the above T1 is equal to 10, the above T2 is equal to 10, and the above T3 is equal to 200.

205. Determine a plaintext, a spatial domain key, and a frequency domain key on the basis of the foregoing accurate recovery processing;

In the embodiment of the present invention, when the accurate recovery phase ends (that is, the NMSE reaches the preset precision), the cryptographic cracking device determines the amplitude value of g(x, y) obtained after the accurate recovery process as the to-be-decrypted a plaintext of the image, the phase portion of g(x, y) obtained after the accurate restoration processing is determined as a spatial domain key of the image to be decrypted;

Determining a frequency domain key exp[i2πb(u,v)] of the image to be decrypted according to a fourth formula,

Wherein the fourth formula is:

或

or

和

求解出两种频域密钥，用这两种频域密钥分别解密后续密文，能够解密出有意义图像的频域密钥则是正确的频域密钥。* represents the complex conjugate of the original function. Since the original plaintext is not known in the actual situation, it cannot be judged whether the restored plaintext is inverted, so it can be passed separately.

with

Two frequency domain keys are solved, and the subsequent ciphertexts are respectively decrypted by using the two frequency domain keys, and the frequency domain key capable of decrypting the meaningful image is the correct frequency domain key.

It should be noted that the recovered plaintext may be shifted or flipped compared with the original plaintext. This is unavoidable, but it does not affect the cracker's understanding of the plaintext information, so it can be regarded as a successful recovery.

T4 is set above 200, the number of iterations of step 203 to restore the plaintext pre-processing 600, T3 is above 200, in step 204 the predetermined accuracy of C _2, the embodiment of the present invention hybrid adaptive iterative algorithm implemented The flow diagram can be as shown in Figure 4.

It should be noted that g(x, y) in the embodiment of the present invention is a binary function, and the physical meaning representation is an image. For a specific x, y value, g(x, y) corresponds to a coordinate (x). , pixel value at y).

The effect of cracking the ciphertext using the cryptographic cracking method in the embodiment of the present invention is further illustrated by the result of the computer simulation. As shown in FIG. 5-a, the original image to be encrypted (8-bit grayscale image) is shown in FIG. 5. -b is the result of encrypting the original image to be encrypted shown in FIG. 5-a by the dual random phase image encoding system, as shown in FIG. 5-c, the cryptographic cracking method in the embodiment of the present invention is used to perform FIG. 5-c. The support recovered by the support recovery process, as shown in FIG. 5-d, is an original image obtained by restoring FIG. 5-c by using the cryptographic cracking method in the embodiment of the present invention. As shown in Figure 6-a, the original image to be encrypted (binary image) is shown. Figure 6-b shows the original image to be encrypted shown in Figure 6-a encrypted by the dual random phase image encoding system. As shown in FIG. 6-c, the support recovered by the support recovery process of FIG. 6-c is performed by using the cryptographic cracking method in the embodiment of the present invention, and FIG. 6-d is a cryptographic crack in the embodiment of the present invention. Method The original image obtained by restoring Fig. 6-c is performed.

It can be seen from the above technical solution that the solution of the present invention converts the ciphertext attack problem of only the plaintext, the spatial domain key and the frequency domain key from the ciphertext into a standard phase recovery problem, that is, the known input. In the case of the surface frequency domain strength, the amplitude of the input surface (ie, plaintext) and phase (ie, the spatial domain key) can be recovered by the phase recovery algorithm, and then the frequency domain key can be calculated. In this scheme, a hybrid adaptive iterative phase recovery algorithm is used. In addition to the ciphertext of the image to be decrypted, no other prior information is needed in the cracking process, thereby effectively reducing the difficulty of cracking.

The embodiment of the present invention further provides a cryptographic cracking apparatus based on a dual random phase image encoding system. As shown in FIG. 7, the cryptographic cracking apparatus 700 in the embodiment of the present invention includes:

The initializing unit 701 is configured to initialize a random number as an input function for each pixel in the image to be decrypted;

Support recovery processing unit 702, configured to perform support recovery processing on the basis of the input function;

The plaintext recovery processing unit 703 is configured to perform plaintext recovery processing on the basis of the support recovery process;

The accurate recovery processing unit 704 is configured to perform an accurate recovery process on the basis of the plaintext recovery process;

a determining unit 705, configured to determine a plaintext, a spatial domain key, and a frequency domain key on the basis of the exact recovery process;

The support recovery processing unit 702 is specifically configured to:

Iterative processing of the input function g(x, y), wherein each iterative processing includes:

Performing a Fourier transform on g(x, y) to obtain G(u, v), where g(x, y) represents the pixel value of the pixel of the xth row and the yth column in the image to be decrypted. ;

Substituting the amplitude value of G(u,v) with the amplitude of the ciphertext of the image to be decrypted in the frequency domain |ψ(u,v)|, and performing an inverse Fourier transform to obtain an intermediate function g'(x,y) );

The K pixel position where the amplitude value of the intermediate function is the largest is taken as the support S of the current iteration, and the input function is updated according to the first formula, and then returns to the pair g(x, y) in the process of performing the support recovery process. Performing a Fourier transform step and a subsequent step until a preset support recovery iteration stop condition is satisfied, and the initial value of the K is a preset value greater than 2;

The first formula is

In the above first formula, β is a preset coefficient;

The plaintext recovery processing unit 703 is specifically configured to:

On the basis of S and g(x, y) obtained when the support recovery is iteratively stopped, the iterative process of step S1, step S2 and step S3 is performed until the preset plaintext recovery iteration stop condition is satisfied, wherein Step S1 is a Fourier transform on g(x, y) to obtain G(u, v), and step S2 is to replace the amplitude value of G(u, v) with the ciphertext of the image to be decrypted. Performing an inverse Fourier transform on the amplitude |ψ(u,v)| of the frequency domain to obtain g'(x, y); the step S3 is to update the input function according to the first formula;

The exact recovery processing unit 704 is specifically configured to:

On the basis of S and g(x, y) obtained when the plaintext recovery iteration is stopped, iteratively performs steps S1, S2 and S3 of T1 times, and then iteratively performs steps T4, S5 and S6 of T2, and alternates until The cumulative number of iterations in the exact recovery process reaches T3, wherein the T1, T2, and T3 are preset values greater than 2, and the T3 is greater than the sum of the T1 and the T2;

When the cumulative number of iterations in the precise recovery process reaches the T3, the mean square error NMSE is calculated according to the third formula;

If the NMSE reaches the preset precision, performing the step of determining the plaintext, the spatial domain key, and the frequency domain key on the basis of the accurate recovery process, if the NMSE does not reach the preset precision, Clearing the cumulative number of iterations in the exact recovery process, and returning to perform the iterative processing of the step S1, the step S2, and the step S3 based on the S and g(x, y) obtained at the time. Until the plaintext recovery iteration stop condition is satisfied;

Wherein, the step S4 is performing Fourier transform on g(x, y) to obtain G(u, v), and the step S5 is to replace the amplitude value of G(u, v) with the image to be decrypted. The ciphertext is subjected to inverse Fourier transform after the amplitude |ψ(u,v)| in the frequency domain to obtain an intermediate function g'(x, y), and the step S6 is K which maximizes the amplitude value of the intermediate function. The pixel is used as the support S of the current iteration, and the input function is updated according to the second formula;

The second formula is:

所述第三公式中的M和N分别为所述待解密图像中像素点的总行数和总列数；The third formula is:

M and N in the third formula are respectively the total number of rows and the total number of columns of pixels in the image to be decrypted;

The determining unit 705 is specifically configured to:

Determining an amplitude value of g(x, y) obtained by the accurate restoration processing as a plaintext of the image to be decrypted, and determining a phase portion of g(x, y) obtained by the accurate restoration processing as the The spatial domain key of the image to be decrypted;

Determining a frequency domain key exp[i2πb(u,v)] of the image to be decrypted according to a fourth formula,

Wherein the fourth formula is:

或

or

Optionally, the support recovery processing unit 702 is specifically configured to:

The K pixel points having the largest amplitude value of the intermediate function are used as the support S of the current iteration, and After updating the input function according to the first formula, determining whether the cumulative number of iterations in the support recovery process reaches T4, wherein the T4 is a preset value greater than 2;

If the number of accumulated iterations in the support recovery process does not reach T4, returning to performing the Fourier transform on the g(x, y) in the support recovery process and subsequent steps;

If the cumulative number of iterations in the support recovery process reaches T4, it is determined whether the threshold determined by K is less than a preset threshold, wherein the threshold determined by K is equal to the current g'(x, y). The amplitude value of the Kth g'(x, y) whose amplitude value is arranged from large to small;

If the threshold determined by K is less than the preset threshold, determining that the preset support recovery iteration stop condition is satisfied;

If the threshold determined by K is not less than the preset threshold, the cumulative number of iterations in the support recovery process is cleared, and K=K+a%*M*N is returned, and then returned to the execution center. The step of performing Fourier transform on g(x, y) in the support recovery process and the subsequent steps, wherein a is a preset value not less than 1.

Optionally, the plaintext recovery processing unit 703 is specifically configured to:

After updating the input function according to the first formula, determining whether the cumulative number of iterations in the plaintext recovery process reaches a preset number of iterations;

If the cumulative number of iterations in the plaintext recovery process reaches a preset number of iterations, it is determined that the preset plaintext recovery iteration stop condition is satisfied;

If the cumulative number of iterations in the plaintext recovery process does not reach the preset number of iterations, the process returns to step S1.

It should be understood that the cryptographic cracking device in the embodiment of the present invention may be used as the cryptographic cracking device mentioned in the foregoing method embodiments, and may be used to implement all the technical solutions in the foregoing method embodiments, each of which is The function of the function module may be specifically implemented according to the method in the foregoing method embodiment. For the specific implementation process, refer to the related description in the foregoing embodiment, and details are not described herein again.

It can be seen from the above technical solution that the solution of the present invention converts the ciphertext attack problem of only the plaintext, the spatial domain key and the frequency domain key from the ciphertext into a standard phase recovery problem, that is, the known input. In the case of the surface frequency domain strength, the amplitude of the input surface (ie, plaintext) and phase (ie, the spatial domain key) can be recovered by the phase recovery algorithm, and then the frequency domain key can be calculated. In this scheme, a hybrid adaptive iterative phase recovery algorithm is used. In addition to the ciphertext of the image to be decrypted, no other prior information is needed in the cracking process, thereby effectively reducing the difficulty of cracking.

In the several embodiments provided by the present application, it should be understood that the disclosed apparatus and method may be implemented in other manners. For example, the device embodiments described above are merely illustrative. For example, the division of the above units is only a logical function division. In actual implementation, there may be another division manner, for example, multiple units or components may be combined or may be Integrate into another system, or some features can be ignored or not executed. In addition, the mutual coupling or direct coupling or communication connection shown or discussed may be an indirect coupling or communication connection through some interface, device or unit, and may be in an electrical, mechanical or other form.

The units described as separate components may or may not be physically separated, and the components displayed as units may or may not be physical units, that is, may be located in one place, or may be distributed to multiple network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the solution of the embodiment.

In addition, each functional unit in each embodiment of the present invention may be integrated into one processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit. The above integrated unit can be implemented in the form of hardware or in the form of a software functional unit.

The integrated unit, if implemented in the form of a software functional unit and sold or used as a standalone product, may be stored in a computer readable storage medium. Based on such understanding, the technical solution of the present invention, which is essential or contributes to the prior art, or all or part of the technical solution, may be embodied in the form of a software product stored in a storage medium. A number of instructions are included to cause a computer device (which may be a personal computer, server, or network device, etc.) to perform all or part of the steps of the methods described in various embodiments of the present invention. The foregoing storage medium includes: a U disk, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk, and the like. .

It should be noted that, for the foregoing method embodiments, for the sake of brevity, they are all described as a series of action combinations, but those skilled in the art should understand that the present invention is not limited by the described action sequence. Because certain steps may be performed in other sequences or concurrently in accordance with the present invention. In the following, those skilled in the art should also understand that the embodiments described in the specification are all preferred embodiments, and the actions and modules involved are not necessarily required by the present invention.

In the above embodiments, the descriptions of the various embodiments are all focused, and the parts that are not detailed in a certain embodiment can be referred to the related descriptions of other embodiments.

The above is a description of a cryptographic cracking method and apparatus based on the dual random phase image encoding system provided by the present invention. For those skilled in the art, according to the idea of the embodiment of the present invention, in the specific implementation manner and application scope There are variations, and in summary, the description should not be construed as limiting the invention.

Claims (9)

A cryptographic cracking method based on a double random phase image coding system, comprising: Initializing a random number as an input function for each pixel in the image to be decrypted; Performing support recovery processing on the basis of the input function; Performing plaintext recovery processing on the basis of the support recovery processing; Performing accurate recovery processing on the basis of the plaintext recovery processing; Determining a plaintext, a spatial domain key, and a frequency domain key on the basis of the exact recovery process; Wherein, the supporting recovery processing is performed on the basis of the input function, including: Iterative processing of the input function g(x, y), wherein each iterative processing includes: Performing a Fourier transform on g(x, y) to obtain G(u, v), where g(x, y) represents the pixel value of the pixel of the xth row and the yth column in the image to be decrypted. ; Substituting the amplitude value of G(u,v) with the amplitude of the ciphertext of the image to be decrypted in the frequency domain |ψ(u,v)|, and performing an inverse Fourier transform to obtain an intermediate function g'(x,y) ); The K pixel position where the amplitude value of the intermediate function is the largest is taken as the support S of the current iteration, and the input function is updated according to the first formula, and then returns to the pair g(x, y) in the process of performing the support recovery process. Performing a Fourier transform step and a subsequent step until a preset support recovery iteration stop condition is satisfied, and the initial value of the K is a preset value greater than 2; The first formula is

In the above first formula, β is a preset coefficient; The clear text recovery process is performed on the basis of the support recovery process, including: Performing the iterative process of step S1, step S2, and step S3 on the basis of S and g(x, y) obtained when the support resumes the iteration stop, until the preset plaintext recovery iteration stop condition is satisfied, wherein Step S1 is a Fourier transform on g(x, y) to obtain G(u, v), and the step S2 is Substituting the amplitude value of G(u,v) with the amplitude of the ciphertext of the image to be decrypted in the frequency domain |ψ(u,v)|, and performing inverse Fourier transform to obtain g'(x, y); The step S3 is to update the input function according to the first formula; The accurate recovery processing is performed on the basis of the plaintext recovery processing, including: On the basis of S and g(x, y) obtained when the plaintext recovery processing is stopped, iteratively performs steps S1, S2, and S3 of T1 times, and then iteratively performs steps S4, S5, and S6 of T2, alternately until the said The cumulative number of iterations in the exact recovery process reaches T3, wherein the T1, T2, and T3 are preset values greater than 2, and the T3 is greater than the sum of the T1 and the T2; When the cumulative number of iterations in the precise recovery process reaches the T3, the mean square error NMSE is calculated according to the third formula; If the NMSE reaches the preset precision, performing the step of determining the plaintext, the spatial domain key, and the frequency domain key on the basis of the accurate recovery process, if the NMSE does not reach the preset precision, Clearing the cumulative number of iterations in the exact recovery process, and returning to perform the iterative processing of the step S1, the step S2, and the step S3 based on the S and g(x, y) obtained at the time. Until the plaintext recovery iteration stop condition is satisfied; Wherein, the step S4 is performing Fourier transform on g(x, y) to obtain G(u, v), and the step S5 is to replace the amplitude value of G(u, v) with the image to be decrypted. The ciphertext is subjected to inverse Fourier transform after the amplitude |ψ(u,v)| in the frequency domain to obtain an intermediate function g'(x, y), and the step S6 is K which maximizes the amplitude value of the intermediate function. The pixel position is used as the support S of the current iteration, and the input function is updated according to the second formula; The second formula is:

The third formula is:

M and N in the third formula are respectively the total number of rows and the total number of columns of pixels in the image to be decrypted; The determining the plaintext, the spatial domain key, and the frequency domain key on the basis of the accurate recovery process, including: Determining an amplitude value of g(x, y) obtained by the accurate restoration processing as a plaintext of the image to be decrypted, and determining a phase portion of g(x, y) obtained by the accurate restoration processing as the The spatial domain key of the image to be decrypted; Determining a frequency domain key exp[i2πb(u,v)] of the image to be decrypted according to a fourth formula, Wherein the fourth formula is:

or

The cryptographic cracking method according to claim 1, wherein the K pixel position at which the amplitude value of the intermediate function is the largest is taken as the support S of the current iteration, and the input function is updated according to the first formula, and then includes : Determining whether the cumulative number of iterations in the support recovery process reaches T4, wherein the T4 is a preset value greater than 2; If the number of accumulated iterations in the support recovery process does not reach T4, returning to performing the Fourier transform on the g(x, y) in the support recovery process and subsequent steps; If the cumulative number of iterations in the support recovery process reaches T4, it is determined whether the threshold determined by K is less than a preset threshold, wherein the threshold determined by K is equal to the current g'(x, y). The amplitude value of the Kth g'(x, y) whose amplitude value is arranged from large to small; If the threshold determined by K is less than the preset threshold, determining that the preset support recovery iteration stop condition is satisfied; If the threshold determined by K is not less than the preset threshold, the cumulative number of iterations in the support recovery process is cleared, and K=K+a%*M*N is returned, and then returned to the execution center. Support recovery The step of performing Fourier transform on g(x, y) and the subsequent steps in the complex processing, wherein a is a preset value not less than 1. The cryptographic cracking method according to claim 2, wherein the initial value of K takes 1% of the total number of pixels in the image to be decrypted; The a is equal to 1. The cryptographic cracking method according to any one of claims 1 to 3, wherein in the plaintext restoring process, the step S3 includes: Determining whether the cumulative number of iterations in the plaintext recovery process reaches a preset number of iterations; If the cumulative number of iterations in the plaintext recovery process reaches a preset number of iterations, it is determined that the preset plaintext recovery iteration stop condition is satisfied; If the cumulative number of iterations in the plaintext recovery process does not reach the preset number of iterations, the process returns to step S1. The cryptographic cracking method according to any one of claims 1 to 3, wherein the T1 is equal to 10, the T2 is equal to 10, and the T3 is equal to 200. The cryptographic cracking method according to any one of claims 1 to 3, characterized in that the β is equal to 0.9. A cryptographic cracking device based on a double random phase image encoding system, comprising: An initialization unit, configured to initialize a random number as an input function for each pixel in the image to be decrypted; Supporting a recovery processing unit for performing support recovery processing on the basis of the input function; a plaintext recovery processing unit, configured to perform plaintext recovery processing on the basis of the support recovery processing; An accurate recovery processing unit for performing an exact recovery on the basis of the plaintext recovery process Reason a determining unit, configured to determine a plaintext, a spatial domain key, and a frequency domain key on the basis of the accurate recovery process; The support recovery processing unit is specifically configured to: Iterative processing of the input function g(x, y), wherein each iterative processing includes: Performing a Fourier transform on g(x, y) to obtain G(u, v), where g(x, y) represents the pixel value of the pixel of the xth row and the yth column in the image to be decrypted. ; Substituting the amplitude value of G(u,v) with the amplitude of the ciphertext of the image to be decrypted in the frequency domain |ψ(u,v)|, and performing an inverse Fourier transform to obtain an intermediate function g'(x,y) ); The K pixel position where the amplitude value of the intermediate function is the largest is taken as the support S of the current iteration, and the input function is updated according to the first formula, and then returns to the pair g(x, y) in the process of performing the support recovery process. Performing a Fourier transform step and a subsequent step until a preset support recovery iteration stop condition is satisfied, and the initial value of the K is a preset value greater than 2; The first formula is

In the above first formula, β is a preset coefficient; The plaintext recovery processing unit is specifically configured to: On the basis of S and g(x, y) obtained when the support recovery is iteratively stopped, the iterative process of step S1, step S2 and step S3 is performed until the preset plaintext recovery iteration stop condition is satisfied, wherein Step S1 is a Fourier transform on g(x, y) to obtain G(u, v), and step S2 is to replace the amplitude value of G(u, v) with the ciphertext of the image to be decrypted. Performing an inverse Fourier transform on the amplitude |ψ(u,v)| of the frequency domain to obtain g'(x, y); the step S3 is to update the input function according to the first formula; The precision recovery processing unit is specifically configured to: Iteratively executes T1 based on S and g(x, y) obtained when the plaintext recovery iteration stops. Subsequent steps S1, S2 and S3, then iteratively performing T2 times steps S4, S5 and S6, alternately until the cumulative number of iterations in the exact recovery process reaches T3, wherein T1, T2 and T3 are greater than a preset value of 2, and the T3 is greater than a sum of the T1 and the T2; When the cumulative number of iterations in the precise recovery process reaches the T3, the mean square error NMSE is calculated according to the third formula; If the NMSE reaches the preset precision, performing the step of determining the plaintext, the spatial domain key, and the frequency domain key on the basis of the accurate recovery process, if the NMSE does not reach the preset precision, Clearing the cumulative number of iterations in the exact recovery process, and returning to perform the iterative processing of the step S1, the step S2, and the step S3 based on the S and g(x, y) obtained at the time. Until the plaintext recovery iteration stop condition is satisfied; Wherein, the step S4 is performing Fourier transform on g(x, y) to obtain G(u, v), and the step S5 is to replace the amplitude value of G(u, v) with the image to be decrypted. The ciphertext is subjected to inverse Fourier transform after the amplitude |ψ(u,v)| in the frequency domain to obtain an intermediate function g'(x, y), and the step S6 is K which maximizes the amplitude value of the intermediate function. The pixel is used as the support S of the current iteration, and the input function is updated according to the second formula; The second formula is:

The third formula is:

M and N in the third formula are respectively the total number of rows and the total number of columns of pixels in the image to be decrypted; Wherein, the determining unit is specifically configured to: Determining an amplitude value of g(x, y) obtained by the accurate restoration processing as a plaintext of the image to be decrypted, and determining a phase portion of g(x, y) obtained by the accurate restoration processing as the The spatial domain key of the image to be decrypted; Determining a frequency domain key exp[i2πb(u,v)] of the image to be decrypted according to a fourth formula, Wherein the fourth formula is:

or

The cryptographic cracking device according to claim 7, wherein the support recovery processing unit is specifically configured to: After the K pixel points having the largest amplitude value of the intermediate function are used as the support S of the current iteration, and after updating the input function according to the first formula, it is determined whether the cumulative number of iterations in the support recovery process reaches T4, Wherein, the T4 is a preset value greater than 2; If the number of accumulated iterations in the support recovery process does not reach T4, returning to performing the Fourier transform on the g(x, y) in the support recovery process and subsequent steps; If the cumulative number of iterations in the support recovery process reaches T4, it is determined whether the threshold determined by K is less than a preset threshold, wherein the threshold determined by K is equal to the current g'(x, y). The amplitude value of the Kth g'(x, y) whose amplitude value is arranged from large to small; If the threshold determined by K is less than the preset threshold, determining that the preset support recovery iteration stop condition is satisfied; If the threshold determined by K is not less than the preset threshold, the cumulative number of iterations in the support recovery process is cleared, and K=K+a%*M*N is returned, and then returned to the execution center. The step of performing Fourier transform on g(x, y) in the support recovery process and the subsequent steps, wherein a is a preset value not less than 1. The cryptographic cracking apparatus according to claim 7 or 8, wherein the plaintext recovery processing unit is specifically configured to: After the input function of each pixel point is updated according to the first formula, it is determined whether the cumulative number of iterations in the plaintext recovery process reaches a preset number of iterations; If the cumulative number of iterations in the plaintext recovery process reaches a preset number of iterations, it is determined that the preset plaintext recovery iteration stop condition is satisfied; If the cumulative number of iterations in the plaintext recovery process does not reach the preset number of iterations, the process returns to step S1.

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