CN110312053A

CN110312053A - Optical encryption method based on hierarchical Fourier spectrum decomposition and mixed random mask

Info

Publication number: CN110312053A
Application number: CN201910392392.3A
Authority: CN
Inventors: 潘良; 温建峰; 赵艳春
Original assignee: NANTONG INSTITUTE OF TECHNOLOGY
Current assignee: NANTONG INSTITUTE OF TECHNOLOGY
Priority date: 2019-05-10
Filing date: 2019-05-10
Publication date: 2019-10-08
Anticipated expiration: 2039-05-10
Also published as: CN110312053B

Abstract

The invention discloses an optical encryption method based on hierarchical Fourier spectrum decomposition and mixed random mask, which comprises the following steps: constructing a mixed random mask; performing optical modulation on the initial plaintext according to fractional order Fourier transform and a mixed random mask to obtain a Fourier spectrum; and (4) dividing the Fourier spectrum by an equal-film decomposition method to obtain and output a ciphertext and a private key. The invention realizes the encryption of the optical image by fusing the Fresnel wave band, the Hilbert phase and the chaotic mask, has more ideal anti-interference capability and safety, and has more ideal decryption quality under the attacks of noise, shearing and the like.

Description

Optical encryption method based on hierarchical Fourier spectrum decomposition and mixed random mask

Technical Field

The invention relates to the field of optical image encryption, in particular to an optical encryption method based on hierarchical Fourier spectrum decomposition and mixed random mask.

Background

With the development of globalization trend, cross-country and cross-region communication is more common, and meanwhile, the problem of information security is serious, especially the phenomena of stealing and leakage of user information are more prominent due to the popularization and application of the internet [1 ]. The image has rich visual content and is a common medium for communication in various fields, such as medicine, security protection, industrial engineering and the like [2 ]. However, when the image is used across areas, the image is often realized by means of a network, and at the moment, the image is vulnerable to unknown attacks, so that related information is subjected to random attacks, and the authenticity identification of the content is difficult [3 ]. In order to ensure the authenticity of the image information at the receiving end, domestic and foreign scholars design corresponding image encryption technologies, and the encryption schemes widely studied at present mainly include 2 directions: chaotic encryption and optical encryption [4 ]. For example, Zhang et al [5] propose a plaintext related image encryption method based on chaos in order to enhance the plaintext attack resistance of an encryption system, perform one scrambling on a plaintext by iterating a key obtained by piecewise linear mapping by using characteristics of the plaintext, perform two diffusions on a scrambling result by designing a diffusion function, and highly change a pixel value. Liu 6 provides an image encryption method based on a bit plane and improved Logistic mapping for optimizing the security of an encrypted ciphertext, a plaintext is scrambled by utilizing a chaotic sequence output by iterative Logistic mapping, the scrambled ciphertext is decomposed into a high 4-bit matrix and a low 4-bit matrix, the Logistic mapping is iterated by utilizing low 4-bit matrix information, a group of key streams closely related to the plaintext is output, an XOR operator is combined, the high 4-bit matrix information is diffused, and an encrypted result is obtained by combining the encrypted high 4-bit matrix and the initial low 4-bit matrix. Li et al [7] propose a hyperchaotic image encryption method based on pixel-level and bit-level replacement in order to enhance the anti-attack capability of the encryption system, utilize the output sequence of the iterative 5D hyperchaotic system as the key stream, and construct the pixel-level and bit-level replacement method, highly disturb the pixel position of the plaintext, at the same time, define the diffusion scheme, implement encryption on the confusion result.

The methods all belong to the category of chaotic encryption, and the scheme effectively utilizes the complex phase space and randomness of the chaotic system, and can improve the transmission security of the image in an open network to a certain extent, however, the chaotic system has poincare restorability, and the image is encrypted by utilizing the output sequence of the chaotic system, so that the security of the ciphertext is not ideal [3-4 ]. In recent years, optical encryption is researched by broad scholars due to the characteristics of parallelism, high speed and the like, for example, Zhangbo et al [3] designs an optical image encryption method based on coherent superposition and modular equal vector decomposition, generates a chaotic phase mask by utilizing plaintext and Logistic mapping, completes modulation on an initial image through Fourier transformation to obtain a corresponding Fourier spectrum, designs a one-way coding mechanism by combining an equal modular decomposition mechanism and a phase-amplitude truncation coding technology, outputs a coded ciphertext and amplitude information through the correlated superposition of laser beams, and verifies the attack resistance of the encryption technology through experimental results. Wang et al [8] proposed a new asymmetric optical image encryption scheme based on a phase retrieval method, constructed two phase masks through a random sequence of an iterative chaotic system, and encrypted a plaintext through a retrieval technique to obtain a real-valued function, and test data verified the reliability and encryption speed of the scheme. Muhammad et al [97] propose an optical image encryption technology of Hartley transform coupling Gyrator transform in order to improve the external attack resistance of a ciphertext, introduce Hartley transform to preprocess an image, obtain a first ciphertext through a phase-amplitude truncation mechanism, combine a random mask, perform Gyrator transform processing on the ciphertext, output a corresponding Gyrator frequency spectrum, and complete decomposition by using a phase-amplitude truncation method to obtain an encrypted ciphertext.

The optical encryption scheme can enhance the anti-attack capability of a ciphertext, but in the process of modulating the plaintext, a common chaotic phase mask is adopted, and the mask has high randomness.

Reference documents:

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Disclosure of Invention

In order to solve the technical problems, the invention provides an optical encryption method based on hierarchical Fourier spectrum decomposition and mixed random mask, which has more ideal anti-interference capability and safety and has more ideal decryption quality under attacks such as noise, shearing and the like.

In order to achieve the purpose, the technical scheme of the invention is as follows:

an optical encryption method based on hierarchical Fourier spectrum decomposition and mixed random mask comprises the following steps:

the method comprises the following steps: constructing a mixed random mask;

step two: performing optical modulation on the initial plaintext according to fractional order Fourier transform and a mixed random mask to obtain a Fourier spectrum;

step three: and (4) dividing the Fourier spectrum by an equal-film decomposition method to obtain and output a ciphertext and a private key.

Further, the first step specifically comprises:

step 101: according to SHA-256 Hash method, a 256-bit external key K is formed and divided into 32 sub-keys K_i；

Step 102: introducing a two-dimensional Ushiki mapping by said subkey k_iCalculating initial conditions of two-dimensional Ushiki mapping, and then outputting a group of random sequences through iteration to obtain a chaotic phase mask CRM;

step 103: introducing an amplitude of a Fresnel wave band and a Hilbert phase function, and fusing the amplitude of the Fresnel wave band and the Hilbert phase function with the chaotic phase mask to obtain a mixed random mask.

Further, the step 102 specifically includes:

step 102-1: introducing a two-dimensional Ushiki mapping to generate a set of random sequences, the two-dimensional Ushiki mapping being a function of:

wherein, y_n、x_nIs a system variable; a. b and c are chaotic control parameters, b is 0.1, c is 0.2, a belongs to [2.5,3.8 ]]；

Step 102-2: computing an initial value x of a two-dimensional Ushiki mapping from a child key ki₀And y₀The calculation formula is as follows:

step 102-3: according to the initial value x₀And y₀And performing M multiplied by N iterations on the function of the two-dimensional Ushiki mapping by the chaotic control parameters a, b and c to obtain two random sequences: x ═ X₁，x₂.....x_M×N}、Y＝{y₁，y₂.....y_M×N}；

Step 102-4: according to the sequence { x_iAnd { y }_iAnd constructing a chaotic phase mask CRM, wherein the calculation formula is as follows:

wherein Z is x_nAnd y_mA two-dimensional sequence of constructs.

Further, the step 103 specifically includes:

calculating a Fresnel zone function F (r) according to the formula:

wherein r is the radius of the focus ring; f is the focal length; λ is the wavelength of the light wave; j is an imaginary number;

and calculating a Hilbert phase function, wherein the calculation formula is as follows:

H(ρ，θ)＝exp(jρθ)

where (ρ, θ) is the polar coordinate, the calculation function is:

ρ＝x²+y²，θ＝tan^-1(y/x)

calculating a hybrid random mask C (x, y) by the formula:

C(x，y)＝exp{j{arg[CRM(x，y)]}×{arg[F(r)]}×{arg[H(ρ，θ)]}}

wherein arg () is an argument function.

Further, the fractional order Fourier transform is:

wherein F (u, v) represents a fractional order Fourier transform;is an angle; (x, less) is the spatial domain coordinate; (u, v) are Fourier transform domain coordinates; a is the order of the Fourier transform; a. the_aIs a phase factor, depending on the value of a.

Further, the medium membrane decomposition method in the third step specifically comprises the following steps:

step 301: acquiring amplitude A (u, v) and phase information psi (u, v) of a modulation result;

wherein,in order to round the symbol down,

step 302: calculating a function of the rotation angle theta (u, v), wherein the calculation formula is as follows:

θ(u，v)＝2πr×rand(u，v)

wherein rand (u, v) is a random function satisfying a uniform distribution;

step 302: performing equimodular decomposition on I (u, v), and outputting two independent components, namely ciphertext P₁(u, v) with the private key P₂(u, v) the calculation formula is:

P₁(u，v)＝{0.5A(u，v)/cos[ψ(u，v)-θ(u，v)]}×exp{iθ(u，v)} (15)

P₂(u，v)＝{0.5A(u，v)/cos[ψ(u，v)-θ(u，v)]}×exp{i[2ψ(u，v)-θ(u，v)]}。

the invention has the beneficial effects that:

the optical encryption method based on the hierarchical Fourier spectrum decomposition and the mixed random mask realizes the encryption of an optical image by fusing a Fresnel wave band, a Hilbert phase and a chaotic mask, and firstly, a 256-bit external key is formed according to an SHA-256 Hash method and is divided into 32 sub-keys; introducing two-dimensional Ushiki mapping, calculating initial conditions of the two-dimensional Ushiki mapping by using a sub-key, and outputting a group of random sequences through iteration so as to construct a chaotic phase mask; then, introducing a Fresnel wave band amplitude and a Hilbert phase function, and fusing the Fresnel wave band amplitude and the Hilbert phase function with the chaotic phase mask to form a mixed mask, wherein the randomness and the optical axis calibration precision are considered; based on fractional order Fourier transform, combining with a mixed mask to complete optical modulation on an initial plaintext, and acquiring a Fourier spectrum; and finally, the Fourier spectrum is divided by an equimode decomposition method, and a ciphertext and a private key are output, so that the method has more ideal anti-interference capability and safety, and has more ideal decryption quality under attacks such as noise, shearing and the like.

Drawings

FIG. 1 is a flow chart of an encryption method of the present invention; .

FIG. 2 is a diagram of an opto-electric hybrid for the encryption process of the present invention;

FIG. 3 is a schematic diagram of a chaotic attractor in accordance with the present invention;

FIG. 4 is a schematic diagram of hybrid random mask generation of the present invention, wherein (a) is the original plaintext, (b) is the chaotic phase mask, (c) is the Fresnel band mask, (d) is the Hilbert phase mask, and (e) is the hybrid random phase mask;

FIG. 5 is a diagram illustrating the results of the optical encryption of the present invention, wherein (a) is the result of the optical modulation, (b) is the output ciphertext, and (c) is the private key;

FIG. 6 is a schematic diagram of an equi-modal decomposition process of the present invention;

FIG. 7 is a schematic diagram of the decrypting optoelectronic device of the present invention;

FIG. 8 shows the results of different schemes of encryption, where (a) is the original plaintext, (b) is the output ciphertext of the present invention, (c) is the first ciphertext of document [3], (d) is the second ciphertext of document [3], and (e) is the ciphertext of document [9 ];

FIG. 9 is a diagram illustrating the results of the key sensitivity test according to the present invention, wherein (a) is the ciphertext of the wrong key, (b) is the difference between the ciphertexts, and (c) is the histogram corresponding to the difference between the ciphertexts;

FIG. 10 is a schematic diagram of the shear attack resistance test of the present invention, in which (a) is the shear destruction and decryption result of the ciphertext, (b) is the shear destruction and decryption result of the first and second ciphertexts of document [3], and (c) is the shear destruction and decryption result of the ciphertext of document [9 ];

fig. 11 is a schematic diagram of the test of the noise attack resistance capability of the present invention.

Detailed Description

Preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

As shown in fig. 1 and fig. 2, the optical encryption method based on hierarchical Fourier spectrum decomposition and mixed random mask provided in this embodiment includes 3 stages: (1) constructing a mixed random mask; (2) initial image modulation by means of fractional order Fourier transform; (3) and outputting the ciphertext based on the equimodular decomposition.

The phase mask is an important element in the optical encryption process, and has a great influence on the security of a ciphertext. Therefore, the problem of randomness and optical axis calibration is considered, and a chaotic phase mask is fused with Fresnel wave band and Hilbert phase functions to construct a mixed mask. First, a two-dimensional Ushiki mapping is introduced to generate a set of random sequences, whose function is:

wherein, y_n、x_nIs a system variable; a. b and c are control variables of the chaotic system according to the literature [10 ]]It is understood that when b is 0.1, c is 0.2, a is e [2.5,3.8 ]]When the chaotic attractor is used, the expression (1) is in a chaotic state, and a typical chaotic attractor is shown in fig. 3.

The initial condition of the set (1) cannot be improved by simply relying on empirical values, and for this reason, the SHA-256 hashing method is introduced to generate a group of keys K related to the plaintext and decompose the keys K into 32 sub-keys K_i：

K＝k₁，k₂····k₃₂ (2)

Then, according to the sub-key k_iTo calculate an initial value x of the Ushiki mapping₀And y₀：

Then according to x₀And y₀And chaotic control parameters a, b and c, and performing iteration on the formula (1) M times by N times to form two random sequences

X＝{x₁，x₂.....x_M×N}、Y＝{y₁，y₂.....y_M×N}. Then according to the sequence { x_iAnd { y }_iConstructing a chaotic Phase mask CRM (chaotic Phase mask):

wherein Z is x_nAnd y_mA two-dimensional sequence of constructs.

Taking fig. 4(a) as an example, the random mask formed according to equations (1) to (4) is shown in fig. 4(b), where b is 0.1, c is 0.2, and a is 3.72. However, in the optical encryption process, if such a completeness is used alone. The Fresnel wave band [12] and Hilbert phase function [13] are introduced to solve. Wherein the Fresnel axis is aligned, the calculation function is:

wherein r represents the radius of the focus ring; f is the focal length; λ is the wavelength of the light wave; j is an imaginary number; f (r) is a function of the Fresnel bands.

In addition, the opposite halves of any radial line of the Hilbert phase function have a relative bit error of P π radians (where P represents the Hilbert order), which helps align the axis of the optical device, and its function H (ρ, θ) is:

H(ρ，θ)＝exp(jρθ) (6)

where (ρ, θ) is the polar coordinate, the calculation function is:

ρ＝x²+y²，θ＝tan^-1{y/x) (7)

according to CRM (x, y), F (r) and H (rho, theta) output by the process, fusing the CRM (x, y), the F (r) and the H (rho, theta) to establish a mixed random mask:

C(x，y)＝exp{j{arg[CRM(x，y)]}×{arg[F(r)]}×{arg[H(ρ，θ)]}} (8)

wherein arg () represents the argument function; c (x, y) is a mixed random mask.

Similarly, taking fig. 4(a) as an example, the output 3 masks are shown in fig. 4(c) to 4(e) according to equations (5) to (8), respectively. The graph shows that the mixed random phase mask effectively combines the characteristics of CRM (x, y), F (r) and H (rho, theta) masks, so that the mixed random phase mask not only has good randomness, but also can fully solve the problem of optical axis calibration in a photoelectric mixing device.

The fractional order Fourier transform is an extended version of the classical Fourier transform, and for a digital image f (x, y), its corresponding fractional order Fourier transform:

wherein F (u, v) represents a fractional order Fourier transform;is an angle; cot is the cotangent function; cos is the cosine function; sin is a sine function; (x, y) are spatial coordinates; (u, v) are Fourier transform domain coordinates; a is the order of the Fourier transform; a. the_aIs a phase factor, depending on the value of a. Order toThe inverse transform of equation (9)^[14]：

From document [14], it is known that the optical implementation of the fractional Fourier transform is relatively simple and can be done with a single or two lenses. Optical modulation is applied to the plaintext based on equation (9) using a hybrid random phase mask:

I(u，v)＝F^α[f(x，y)exp[i2πC(x，y)] (12)

wherein, F^aRepresenting a Fourier transform.

Taking fig. 4(a) as an example, taking a to 0.84, the output modulation result according to the above transformation process is shown in fig. 5 (a).

In order to destroy the linear relation of an encryption system and enhance the security of a ciphertext, an equimode decomposition method is introduced to process a Fourier modulation result of a plaintext. The equimodular decomposition is an asymmetric cryptosystem based on coherent superposition, and can divide an image into two independent components, and the process is shown in fig. 6. Let the modulation result be I (u, v), then the amplitude and phase information is:

wherein A (u, v) is amplitude information; ψ (u, v) is phase information;

is a round-down operation; and | is an absolute value arithmetic sign.

In addition, the rotation angle θ (u, v) function in fig. 6 is^[15]：

θ(u，v)＝2π×rand(u，v) (14)

Where rand (u, v) is a random function that satisfies a uniform distribution.

Then according to fig. 6, I (u, v) is subjected to an equi-modal decomposition, outputting two independent components P₁(u, v) and P₂(u, v) are:

P₁(u，v)＝{0.5A(u，v)/cos[ψ(u，v)-θ(u，v)]}×exp{iθ(u，v)} (15)

P₂(u，v)＝{0.5A(u，v)/cos[ψ(u，v)-θ(u，v)]}×exp{i[2ψ(u，v)-θ(u，v)]} (16)

calculating by the formula (15) and the formula (16), and converting P into₁(u, v) treating as ciphertext; and P is₂(u, v) is then used as the private key for decryption. The results of the equi-modal decomposition of the sample shown in FIG. 5(a) are shown in FIG. 5(b) and FIG. 5 (c).

For ciphertext P₁The decryption process of (u, v) is simple and mainly depends on the private key P₂(u, v) the image is restored by corresponding electro-optical means, the process of which is shown in fig. 7. Using two spatial light modulator pairs P₁(u，v)、P₂(u, v) modulating, and the two beams interfere with each other in the beam splitter; the beam is then transformed in a fractional Fourier inverse transform. Finally, on the output plane of the optical transform system, the decrypted image can be recorded by an intensity detector. Taking fig. 5(b) as an example, the restored image is output by the decryption apparatus of fig. 7 based on the private key of fig. 5 (c). Discovery from the graphThe decryption quality is ideal, the details are clear and complete, and the distortion degree is low.

In order to verify the effectiveness and the attack resistance of the proposed algorithm, a matlab6.5 platform is adopted for implementation. In addition, reference [3] and reference [9] are used as control groups in the present experiment to reflect the advantages of the proposed protocol. The experimental parameters are set as follows: the chaos control variable b is 0.1, c is 0.2, a is 3.39; the wavelength λ of light wave is 632.8mm, the radius r of the focusing ring is 0.003m, and the focal length f is 40 mm; the order P of Hilbert is 2; the order of the fractional Fourier transform is 0.84.

And (3) encryption effect testing:

taking FIG. 8(a) as an example, with the help of the proposed method, document [3]]And document [9]]The three schemes perform encryption processing on the data, and the output results are shown in fig. 8(b) to 7 (e). It is found from the figure that after the initial plaintext is modulated by three different optical encryption methods, the content information is sufficiently concealed, an attacker can not easily learn any useful clue from the content information, and the original plaintext has ideal visual concealment. However, the three ciphertext output forms are really different, wherein the proposed algorithm is the same as the document [9]]In agreement, both produce a ciphertext, but document [3]]2 ciphertexts are generated. Meanwhile, in order to objectively measure the safety of the three schemes, the test depends on the entropy value^[1]The evaluation and the calculation data are shown in Table 1. From the data, it was found that the three schemes all produced ciphertext entropy close to theoretical "8", but the proposed scheme has the largest entropy, about 7.997, as compared to document [3]]Corresponding two ciphertext entropy values are 7.984, 7.981, respectively [9]Has an entropy value of about 7.969. This is explained with respect to document [3]]And document [9]]The encryption security of the proposed scheme has certain advantages. The two-dimensional Ushiki mapping is iterated by the algorithm by using the key acquired by the SHA-256 Hash method, so that the constructed chaotic phase mask gives consideration to randomness and sensitivity, a Fresnel wave band and a Hilbert phase function are fused to form a new mixed mask, the problem of optical axis calibration is effectively solved, the security of a ciphertext can be enhanced, and meanwhile, the ciphertext is acquired by combining fractional order Fourier transform and an equimodular decomposition method, the nonlinearity of the ciphertext is optimized, and the encryption security of the ciphertext is highest. Document [3]Then vector division is equalized by coherent superposition and modulusThe decoding method generates a ciphertext by utilizing Fourier transform and phase-amplitude truncation coding technologies with different orders, and although the technology adopts an equal modulus decomposition and phase-amplitude truncation coding technology, the linear characteristic of the ciphertext can be obviously reduced, and the plaintext attack resistance of the ciphertext is improved, the optical encryption method only utilizes a common chaotic mask during optical encryption, and cannot solve the problem of optical axis calibration in a photoelectric mixing device, so that the safety of the photoelectric mixing device needs to be further improved. Document [9]]The Hartley transform and the phase-amplitude truncation mechanism are utilized to output the ciphertext through the Gyrator transform, the technology can destroy the linear relation of an encryption system, but the plaintext is ignored in the whole optical modulation process, the sensitivity of the ciphertext to the plaintext is reduced, and when the Gyrator transform is carried out, a single chaotic mask is adopted, the defect of optical axis calibration cannot be overcome, and the safety of the ciphertext is not ideal.

As shown in table 1 below:

table 1 test of entropy data

Table 1Entropy data test

Name (R)	FIG. 8(b)	FIG. 8(c)	FIG. 8(d)	FIG. 8(e)
					Entropy value	7.997	7.984	7.981	7.969

And (3) sensitivity test:

key sensitivity is a common analytical indicator for measuring encryption algorithms, and generally needs to meet the avalanche effect, and when the encryption key is slightly modified, the obtained ciphertext is distinct^[16]. To this end, the sensitivity of the chaotic variable a ═ 3.39 was tested herein. First, the deviation Δ is introduced as 10^-16To establish an error key a₁＝3.39+10^-16. The remaining keys are unchanged. Using fig. 8(a) as a sample, the set of error keys is used to encrypt the sample, and the result is shown in fig. 9(a) -9 (c). It can be seen from the figure that even if key a occurs 10^-16The corresponding ciphertext thereof is visually greatly different from that of fig. 8(b), see fig. 9(b), and the histogram thereof greatly fluctuates in the diagonal direction, see fig. 9 (c). This indicates that the proposed optical encryption scheme satisfies the strict "avalanche effect".

And (3) testing the anti-attack capability:

(1) and (3) testing the anti-chosen plaintext attack capacity:

security analysis model in which plaintext attack is commonly selected^[3]. To this end, three protocols were analyzed for their ability to resist such attacks by means of the NPCR (number of Pixel Change Rate) and UACI (unified Average Change intensity) curves as a function of:

wherein, WXH is the size of the plaintext; di printing is binarization operation; i and I' respectively represent corresponding ciphertexts after two different plaintexts are encrypted.

Tampering the pixel value 76 at (201, 87) in fig. 7(a) with 101, thereby generating a new plaintext; then, the two different plaintexts are optically encrypted by means of the proposed scheme, the document [3] and the document [9] to obtain 2 ciphertexts; NPCR and UACI curves corresponding to different algorithms were obtained based on equations (17) to (19), and the data are shown in fig. 9. The graph shows that the algorithm and the document [3] have higher capability of resisting attack of the chosen plaintext, while the document [9] has weaker capability of resisting the attack, and the stable NPCR values of the three are respectively 99.87%, 99.69% and 98.13%. Similarly, the stable UACI values were 35.72%, 35.06%, and 34.61%, respectively. The main reason is that the proposed scheme and the optical encryption process of the document [3] are both related to plaintext, so that the scheme is very sensitive to the change of the initial image content, and the chosen plaintext attack resistance of the scheme and the document [3] is effectively improved, but the proposed scheme considers the Fresnel zone and the Hilbert phase function, so that the optical axis calibration problem in the optical-electrical hybrid device can be solved, and the attack resistance of the scheme is slightly higher than that of the document [3 ]. While the optical encryption process of document [9] ignores the plaintext, making it less resistant to chosen plaintext attacks.

(2) And (3) cutting attack capability test:

the shearing attack is an important index for objectively measuring the security of the encryption method. Therefore, fig. 8(b) to 8(e) are taken as examples, and the same degree of cutting damage is applied to them, as shown in fig. 10(a), 10(b), and 10 (c); the truncated ciphertext is then restored by the proposed scheme, the decryption process of documents [3] and [9], and the result is shown in fig. 10(b), fig. 10(e) and fig. 10 (c). The decryption quality of the proposed scheme is found to be the highest according to the recovered data, and the details are clear and complete, see fig. 10 (a); the decryption quality of document [3] is acceptable, but some details are lost, see fig. 10 (b); the visual effect of decryption of document [9] is poor, see fig. 10 (c).

The image is interfered by noise in network transmission and subsequent processing, so that the encryption scheme can be sufficiently resistant to noise attack^[1]. Therefore, in this document, gaussian noise with different intensities is applied to fig. 8(b) to 8(e), and the formed noise image is:

E′＝E(1+kN) (20)

wherein E' is the noise-added image; k represents a noise intensity coefficient; n is gaussian noise.

Fig. 11 shows the ciphertext recovery quality of the three algorithms under different strength attacks. The graph shows that when the value of the intensity coefficient k is gradually increased, the value of the MSE (Mean-Square Error) of the restoration result is also increased, and the three optical encryption technologies all present more robust anti-noise capability; however, the noise immunity of the proposed technique is higher, and when the intensity coefficient k is equal to 1, the MSE value of the restored image is about 666, which is smaller than documents [3] and [9], and the MSE of the restored image respectively reaches 857 and 1049. This illustrates that the proposed optical encryption scheme is more robust to noise.

In order to enhance the security of the ciphertext, the embodiment designs an optical image encryption algorithm of a hierarchical Fourier spectrum decomposition and a mixed random mask. Constructing a chaotic mask by combining a plaintext content and an SHA-256 method through two-dimensional Ushiki mapping; in order to solve the problem of optical axis calibration, the characteristics of a focusing ring introduced into a Fresnel wave band, relative error between the focusing ring and a Hilbert phase function and the like are fully utilized, and masks of the focusing ring and the Hilbert phase function are fused with a chaotic mask to form a new phase mask; and then, the fractional Fourier transform is utilized to complete optical modulation on the plaintext. And finally, segmenting the Fourier spectrum by means of an equimode decomposition method to obtain a corresponding ciphertext. The values of various external attack experiments indicate the safety and robustness of the optical encryption scheme.

With respect to the preferred embodiments of the present invention, it should be noted that, for those skilled in the art, various changes and modifications can be made without departing from the inventive concept of the present invention, and these changes and modifications are within the scope of the present invention.

Claims

1. An optical encryption method based on hierarchical Fourier spectrum decomposition and mixed random mask is characterized by comprising the following steps:

the method comprises the following steps: constructing a mixed random mask;

2. The method for optical encryption based on hierarchical Fourier spectrum decomposition and mixed random mask as claimed in claim 1, wherein the first step is specifically:

3. The method for optical encryption based on hierarchical Fourier spectrum decomposition and mixed random mask as claimed in claim 2, wherein the step 102 specifically comprises:

Step 102-2: according to the subkey k_iCalculating an initial value x of a two-dimensional Ushiki mapping₀And y₀The calculation formula is as follows:

step 102-3: according to the initial value x₀And y₀Mixing ofChaos control parameters a, b, c perform M × N iterations on the two-dimensional Ushiki mapped function to obtain two random sequences: x ═ X₁,x₂…..x_M×N}、Y＝{y₁,y₂…..y_M×N}；

wherein Z is x_nAnd y_mA two-dimensional sequence of constructs.

4. The method for optical encryption based on hierarchical Fourier spectrum decomposition and mixed random mask as claimed in claim 2, wherein the step 103 specifically comprises:

calculating a Fresnel zone function F (r) according to the formula:

H(ρ,θ)＝exp(jρθ)

where (ρ, θ) is the polar coordinate, the calculation function is:

ρ＝x²+y²,θ＝tan^-1(y/x)

calculating a hybrid random mask C (x, y) by the formula:

C(x,y)＝exp{j{arg[CRM(x,y)]}×{arg[F(r)]}×{arg[H(ρ,θ)]}}

wherein arg () is an argument function.

5. The method of claim 1, wherein the fractional Fourier transform is to:

wherein F (u, v) represents a fractional order Fourier transform;is an angle; (x, y) are spatial coordinates; (u, v) are Fourier transform domain coordinates; a is the order of the Fourier transform; a. the_aIs a phase factor, depending on the value of a.

6. The method for optical encryption based on hierarchical Fourier spectrum decomposition and mixed random mask as claimed in claim 1 or 4, wherein the third-step medium film decomposition method specifically comprises:

wherein,in order to round the symbol down,

θ(u,v)＝2π×rand(u,v)

wherein rand (u, v) is a random function satisfying a uniform distribution;

P₁(u,v)＝{0.5A(u,v)/cos[ψ(u,v)-θ(u,v)]}×exp{iθ(u,v)}(15)

P₂(u,v)＝{0.5A(u,v)/cos[ψ(u,v)-θ(u,v)]}×exp{i[2ψ(u,v)-θ(u,v)]}。