Color image encryption method based on dynamic constraint holographic coding

Abstract

The invention discloses a color image encryption method based on dynamic constraint holographic coding, and the method comprises the encryption steps: firstly, coding a color plaintext image into a pure phase hologram based on dynamic constraint holographic coding, and then converting the pure phase hologram into a conversion amplitude through phase-to-amplitude conversion; finally, the converted amplitude is encrypted into a visible ciphertext image by using an iterative phase retrieval algorithm under structured light illumination, and a diffraction neural network is generated at the same time; and a decryption step: firstly, generating decryption structured light by using the decryption structured phase mask to illuminate the visible ciphertext image, carrying out forward diffraction propagation, generating a reconstruction amplitude after phase modulation of the diffraction neural network, and then converting the reconstruction amplitude into a conversion phase through amplitude-phase conversion, and finally, performing color holographic reconstruction decryption on the converted phase to obtain a color decrypted image. The color image encryption method provided by the invention has the advantages of large key space, high security and high concealment.

Description

Technical Field

[0001] The present invention relates to the field of information security technology, and in particular to a color image encryption method based on dynamic constraint holographic coding. Background Art

[0002] Since the dual random phase encoding technology was proposed, optical image encryption technology has developed rapidly. In recent years, cutting-edge technologies such as ghost imaging, metasurfaces, compressed sensing, and computational holography have been introduced into optical image encryption, greatly accelerating the practical application of optical image encryption technology. However, most of the current optical image encryption methods mainly solve the problem of grayscale image encryption protection. Compared with grayscale images, color images can show real color information, and thus can better reflect the content and details of the image. Therefore, how to encrypt and protect color images has become a research hotspot in the current field of optical image encryption.

[0003] At present, the research on optical color image encryption mainly focuses on double random phase coding, computational holography, digital holography, single pixel imaging, diffraction imaging, etc. For example, in the field of double random phase coding, Faragallah et al. proposed a block color image encryption based on double random phase coding in 2018. In 2021, Zhang et al. proposed a color image encryption method based on double random phase coding and multi-layer graphic coding. In 2024, Cui et al. proposed a color image encryption algorithm combining double random phase coding, 24-bit plane scrambling and two-dimensional quantum walk. In the field of computational holography, Hwang et al. proposed a color image encryption method based on Fresnel domain GS algorithm in 2012. In 2013, Liu et al. proposed a color image encryption method based on computational holography and chaos theory. In the field of digital holography, Wei et al. proposed a double color image encryption method based on off-axis digital holography and maximum length cellular automaton in 2017. In 2021, Su et al. proposed a color image encryption method based on phase-shifted digital holography and fingerprint key. In terms of single-pixel imaging, in 2021, Qu et al. proposed a color image encryption method based on single-pixel imaging and Arnold transform. In terms of diffraction imaging, in 2016, Qin et al. proposed a color image encryption method based on diffraction imaging and θ modulation. In 2018, He et al. proposed a color image encryption method based on wavelength multiplexing diffraction imaging. In 2023, Wang et al. proposed a color image encryption method based on diffraction imaging and chaotic fingerprint phase mask. However, all of the above-mentioned color image encryption methods directly encrypt the color plaintext image into a ciphertext image with a noise-like distribution, which results in poor encryption concealment, and the types and quantities of digital keys in the above-mentioned methods are relatively small, which will also lead to problems such as limited key space and insufficient security. In view of this situation, the present invention proposes a color image encryption method based on dynamic constrained holographic coding, aiming to achieve high-security and high-concealment color image encryption. Summary of the invention

[0004] The purpose of the present invention is to provide a color image encryption method based on dynamic constrained holographic coding. The present invention first encodes a color plaintext image into a pure phase hologram based on dynamic constrained holographic coding, then converts the pure phase hologram into a conversion amplitude through phase-amplitude conversion, and finally encrypts the conversion amplitude into a visible ciphertext image using an iterative phase recovery algorithm under structured light illumination, and simultaneously generates a diffraction neural network as a security key. The present invention realizes efficient and secure color image encryption, and has the advantages of large key space, high security, and good concealment.

[0005] To achieve the above-mentioned invention object, the technical solution provided by the present invention is as follows: a color image encryption method based on dynamic constrained holographic coding, characterized in that it includes encryption steps:

[0006] S1: Initial condition deployment: First, set the wavelengths of the three color channels of red (R), green (G), and blue (B); then, set four parallel planes H, B, G, and R in sequence along a straight line, denoted as Plane H, Plane B, Plane G, and Plane R respectively; then, set the distances between Plane B, Plane G, Plane R and Plane H to d B d G d R After that, the color plaintext image to be encrypted is decomposed into three components: R, G, and B. The amplitude distributions of these components are recorded as R component plaintext amplitude A and B respectively. R (x R ,y R ), G component plaintext amplitude A G (x G ,y G ), B component plaintext amplitude A B (x B ,y B ), which is used for the dynamic amplitude constraint of the corresponding plane. Then, the initial value of the dynamic constraint number i is set to 0. In addition, a complex amplitude U with unit amplitude and phase randomly distributed in [0,2π] is set on Plane H. H (x H ,y H ). Afterwards, the encryption step S2 is performed.

[0007] S2: Diffraction propagation under dynamic amplitude constraint of B component: R The collimated plane light wave is used as an encrypted light wave and is incident on Plane H. H (x H ,y H ) after phase modulation and encryption of the light wave U H (x H ,y H ) starts to propagate forward diffractively until Plane B, thereby obtaining the complex amplitude U of the encrypted light wave propagating forward to Plane B B (x B ,y B ). Then, the amplitude of the encrypted light wave transmitted forward to Plane B is extracted and saved, which is recorded as the B-plane reconstruction amplitude. Afterwards, calculate the B-plane reconstruction amplitude and B component plaintext amplitude A B (x B ,yB ) B Next, B (x B ,y B ) to constrain the dynamic amplitude of the B component, thereby obtaining the complex amplitude U′ of the encrypted light wave after the dynamic amplitude constraint of the B component B (x B ,y B ). After that, the encrypted light wave U′ B (x B ,y B ) starts to propagate in reverse diffraction until Plane H, thereby obtaining the complex amplitude U of the encrypted light wave transmitted in reverse to Plane H after the dynamic amplitude constraint of the B component BH (x H ,y H ). Then, BH (x H ,y H ) is used to constrain the unit amplitude, thereby obtaining the output complex amplitude U′ of the encrypted light wave after the dynamic amplitude constraint of the B component BH (x H ,y H ). Afterwards, the encryption step S3 is performed.

[0008] S3: Diffraction propagation under dynamic amplitude constraint of G component: Encrypted light wave U′ after encryption step S2 BH (x H ,y H ) starts to propagate forward diffractively until Plane G, thereby obtaining the complex amplitude U of the encrypted light wave propagating forward to Plane G G (x G ,y G ). Then, the amplitude of the encrypted light wave forward to Plane G is extracted and saved, which is recorded as the G plane reconstruction amplitude. Afterwards, calculate the G plane reconstruction amplitude and the G component plaintext amplitude A G (x G ,y G ) G Next, G (x G ,y G ) to constrain the dynamic amplitude of the G component, thereby obtaining the complex amplitude U′ of the encrypted light wave after the dynamic amplitude constraint of the G component G (x G ,y G ). After that, the encrypted light wave U′ G (x G ,y G) starts to propagate in reverse diffraction until Plane H, thereby obtaining the complex amplitude U of the encrypted light wave transmitted in reverse to Plane H after the dynamic amplitude constraint of the G component GH (x H ,y H ). Then, GH (x H ,y H ) is used to constrain the unit amplitude, thereby obtaining the output complex amplitude U′ of the encrypted light wave after the dynamic amplitude constraint of the G component GH (x H ,y H ). Afterwards, the encryption step S4 is performed.

[0009] S4: Diffraction propagation under dynamic amplitude constraint of R component: Encrypted light wave U′ after encryption step S3 GH (x H ,y H ) starts to propagate forward diffractively until Plane R, thereby obtaining the complex amplitude U of the encrypted light wave propagating forward to Plane R R (x R ,y R ). Then, the amplitude of the encrypted light wave transmitted forward to Plane R is extracted and saved, which is recorded as the R plane reconstruction amplitude. Afterwards, calculate the R plane reconstruction amplitude and the R component plaintext amplitude A R (x R ,y R ) R Next, R (x R ,y R ) to constrain the dynamic amplitude of the R component, thereby obtaining the complex amplitude U′ of the encrypted light wave after the dynamic amplitude constraint of the R component R (x R ,y R ). After that, the encrypted light wave U′ R (x R ,y R ) starts to propagate in reverse diffraction until Plane H, thereby obtaining the complex amplitude U of the encrypted light wave transmitted in reverse to Plane H after the dynamic amplitude constraint of the R component RH (x H ,y H ). Then, RH (x H ,y H ) is used to constrain the unit amplitude, thereby obtaining the output complex amplitude U′ of the encrypted light wave after the dynamic amplitude constraint of the R component RH (x H ,y H ). Afterwards, the encryption step S5 is performed.

[0010] S5: Phase output condition judgment: Calculate CC B 、CC G 、CC R The average CC of the three avg , when CC avg exceeds the preset threshold q, that is, the phase output condition is met, and the encryption step S7 is executed; when CC avg If the preset threshold q is not exceeded, that is, the convergence condition is not met, the encryption step S6 is executed.

[0011] S6: Phase update: using U′ obtained in encryption step S4 RH (x H ,y H )Update U H (x H ,y H ), that is: U H (x H ,y H )=U′ RH (x H ,y H ), and the number of dynamic constraints is also updated from i to i+1, that is, i=i+1. Then, the encryption step S2 is performed.

[0012] S7: Output of pure phase hologram and phase-to-amplitude conversion: U′ obtained in encryption step S4 RH (x H ,y H ) to perform phase extraction operations, thereby generating and outputting a pure phase hologram of a color plaintext image Afterwards, Perform phase-amplitude conversion to obtain the conversion amplitude A H (x H ,y H ). Afterwards, the encryption step S8 is performed.

[0013] S8: Generation and illumination of encrypted structured light: First, the encrypted structured phase mask is used to phase modulate the collimated plane light wave of unit amplitude, thereby generating phase-modulated encrypted structured light. Therefore, the complex amplitude distribution of the encrypted structured light is equal to the phase distribution ESPM(ξ,η) of the encrypted structured phase mask. Subsequently, the encrypted structured light generated after phase modulation by the encrypted structured phase mask begins to diffract and propagate forward until the preset visible ciphertext image is reached, thereby obtaining the complex amplitude U0(x0,y0) of the encrypted structured light transmitted forward to the front surface of the ciphertext image. After that, the encryption step S9 is executed.

[0014] S9: Unconstrained forward propagation: The encrypted structured light after amplitude modulation of the encrypted image continues to diffract and propagate forward, passing through the planes where the N pure phase masks to be restored are located in turn and then reaches the reconstructed image plane. The N pure phase masks to be restored are respectively denoted as pure phase mask 1, pure phase mask 2, ..., pure phase mask N, and the front surfaces of the N pure phase masks are respectively denoted as S forward 1, S forward 2, ..., S forward The rear surfaces of N,N pure phase masks are denoted as S backward 1, S backward 2, ..., S backward N, thus obtaining the encrypted structured light and transmitting it forward to S forward The complex amplitude U of n n (x n ,y n ), where n = 1, 2, ..., N + 1. Then, the encrypted structured light is extracted and saved and forwarded to S forward Amplitude A of n n (x n ,y n ) and phase Where n = 1, 2, ..., N + 1. Then, the encryption step S10 is performed.

[0015] S10: Convergence condition judgment: After obtaining the encrypted structured light, it is forwarded to the reconstructed image plane (S forward N+1) amplitude A N+1 (x N+1 ,y N+1 ), record it as the reconstruction amplitude, and then calculate the reconstruction amplitude A N+1 (x N+1 ,y N+1 ) and the conversion amplitude A H (x H ,y H ). When CC exceeds the preset threshold σ, that is, the convergence condition is met, the encryption step S13 is performed; when CC does not exceed the preset threshold σ, that is, the convergence condition is not met, the phase of the encrypted structured light forward to the reconstructed image plane is retained. unchanged, and using the conversion amplitude A H (x H ,y H ) instead of reconstructing the amplitude A N+1 (x N+1 ,y N+1 ) realizes the amplitude constraint, thereby generating a new complex amplitude on the reconstruction plane Afterwards, the encryption step S11 is performed.

[0016] S11: Backward propagation under phase constraints: The encrypted structured light forms a new complex amplitude after being constrained by amplitude on the reconstructed image plane The diffraction propagation starts to propagate backwards and reaches the back surfaces of N pure phase masks (S backward N,S backward N-1,......,S backward 1), and then the encrypted structured light is transmitted to S backward The complex amplitude U' of n n (x n ,y n ), where n = N, N-1, ..., 1. Afterwards, the encrypted structured light is extracted and saved and then transmitted to S backward The amplitude A' of n n (x n ,y n ) and phase Where n = N, N-1, ..., 1. Then, the encrypted structured light saved in the encryption step S11 is retained and transmitted back to S backward The amplitude A' of n n (x n ,y n ) remains unchanged, and the encrypted structured light saved in the encryption step S9 is forwarded to S forward The phase of n Instead of encrypting the encrypted structured light stored in step S11, it is transmitted back to S backward The phase of n Implement phase constraints to generate new complex amplitudes for the next segment of backward propagation Where n = N, N-1, ..., 1. It should be noted that the encrypted structured light is from S backward N back propagates until S backward 1. Each time it is transmitted to the next plane, the above process is repeated until the encrypted structured light is transmitted to S backward 1 ends. Afterwards, the encryption step S12 is performed.

[0017] S12: Forward propagation under phase constraint: retain the encrypted structured light saved in the encryption step S9 and forward it to S forward The amplitude A1(x1, y1) of 1 remains unchanged, and the encrypted structured light saved in the encryption step S11 is transmitted back to S backward Phase 1 Instead of encrypting the structured light in step S9, it is forwarded to S forward Phase 1 Phase constraint is achieved to generate a new complex amplitude U1″(x1,y1) for the next forward propagation. Then, the encrypted structured light begins to diffract forward and reaches S forward 2, S forward3, ..., S forward N and S forward N+1, thus updating the encrypted structured light and forwarding it to S forward The complex amplitude U of n n (x n ,y n ), where n = 2, 3, ..., N + 1. Afterwards, the encrypted structured light is extracted and saved and forwarded to S forward Amplitude A of n n (x n ,y n ) and phase Where n = 2, 3, ..., N + 1. Then, the encrypted structured light saved in the encryption step S12 is forwarded to S forward Amplitude A on n n (x n ,y n ) remains unchanged, and the encrypted structured light saved in the encryption step S11 is transmitted back to S backward The phase of n Instead of encrypting the encrypted structured light stored in step S12, it is forwarded to S forward The phase of n Implement phase constraints to generate a new complex amplitude U for the next forward propagation n ″(x n ,y n ), where n = 2, 3, ..., N. It should be noted that the encrypted structured light is from S forward 2 Forward propagation until S forward N+1, each time it is transmitted to the next plane, the above process is repeated once until the encrypted structured light is transmitted forward to S forward N+1 ends. After that, the encryption step S10 is performed.

[0018] S13: Generation and output of pure phase mask: On all planes where the pure phase mask to be restored is located, the encrypted structured light saved in the encryption step S11 is transmitted back to S backward The phase of n The encrypted structured light saved in the encryption step S12 is forwarded to S forward The phase of n Perform a phase subtraction operation to generate and output the phase distribution of all pure phase masks to be restored Where n = 1, 2, ..., N.

[0019] At this point, the encryption step is completed.

[0020] Decryption steps:

[0021] J1: Generation and illumination of decrypted structured light: First, the decrypted structured phase mask is used to phase modulate the collimated plane light wave to generate decrypted structured light. After that, the decrypted structured light generated after phase modulation by the decrypted structured phase mask begins to diffract forward to illuminate the preset ciphertext image, thereby obtaining the complex amplitude U of the decrypted structured light transmitted forward to the front surface of the ciphertext image. 0J (x0, y0). Afterwards, the decryption step J2 is performed.

[0022] J2: Forward propagation decryption: The decrypted structured light after amplitude modulation of the ciphertext image continues to diffract and propagate forward, thereby obtaining the decrypted structured light forward to S forward The complex amplitude U of 1 1J (x1, y1). After that, the decrypted structured light continues to diffract and propagate forward, reaching S forward 2. S forward 3.......,S forward N and S forward N+1 (reconstructed image plane), so that the decrypted structured light is transmitted forward to S forward The complex amplitude U of n nJ (x n ,y n ), where n = 2, 3, ..., N + 1. Then, the decrypted structured light is extracted and saved and forwarded to the reconstructed image plane (S forward N+1) amplitude A (N+1)J (x N+1 ,y N+1 ), recorded as the reconstruction amplitude. Then, for A (N+1)J (x N+1 ,y N+1 ) to perform amplitude-phase conversion operation, thereby obtaining the conversion phase Afterwards, the decryption step J3 is performed.

[0023] J3: Color holographic reconstruction decryption: converting phase Placed on Plane H, using unit amplitude and wavelength λ R A red collimated plane light wave with unit amplitude and wavelength λ G A green collimated plane light wave with unit amplitude and wavelength λ B The blue collimated plane light wave is incident on Plane H as the three-color decryption light wave at the same time. After phase modulation, the three-color decrypted light wave begins to propagate forward diffracted to Plane R, thereby obtaining the complex amplitude U of the three-color decrypted light wave forward to Plane R. RJ (x R ,y R ), U GJ (x R ,yR ), U BJ (x R ,y R ). After that, the amplitudes of the three-color decrypted light waves transmitted forward to Plane R are extracted and saved, and recorded as: R component decrypted amplitude A RJ (x R ,y R ), G component decryption amplitude A GJ (x R ,y R ), B component decryption amplitude A BJ (x R ,y R ). Then, the R component is decrypted to the amplitude A RJ (x R ,y R ), G component decryption amplitude A GJ (x R ,y R ), B component decryption amplitude A BJ (x R ,y R ) are synthesized into a color image, which is the final color decrypted image.

[0024] At this point, the decryption step is completed.

[0025] In the above-mentioned color image encryption method based on dynamic constrained holographic coding, the encryption step S1 is B ,d G ,d R The following relationship must be satisfied: B :d G :d R =λ R :λ G :λ B .

[0026] In the above-mentioned color image encryption method based on dynamic constrained holographic coding, the phase distribution design formula of the encrypted structured phase mask in the encryption step S8 includes at least one editable optical parameter used as a digital key.

[0027] In the above-mentioned color image encryption method based on dynamic constrained holographic coding, the phase distribution of the pure phase mask generated in the encryption step S13 is output as a grayscale phase map, which is used as a phase key.

[0028] In the above-mentioned color image encryption method based on dynamic constrained holographic coding, the decryption steps J1-J2 can be completed by digital means or by a combination of optical and digital means, wherein the optical decryption process in the decryption steps J1-J2 requires the use of the diffraction imaging system provided by the present invention, including a laser 1 for providing incident light, a polarization modulator 2 for modulating the polarization state of light, a microscope objective 3 for beam expansion, a pinhole 4 for filtering, a convex lens 5 for collimation, a phase modulator 60 for carrying the phase distribution of the decrypted structured phase mask, an amplitude modulator 7 for carrying the ciphertext image, and an amplitude modulator 8 for carrying the pure The phase modulation device 61-6N of the phase mask phase distribution is used to receive the image sensor device 8 of the reconstructed amplitude, characterized in that: the polarization modulation device 2 is a polarizer or a half-wave plate; the pinhole 4 is placed on the image focus of the microscope objective 3, and the image focus of the microscope objective 3 coincides with the object focus of the convex lens 5; the amplitude modulation device 7 is an amplitude mask or an amplitude-type spatial light modulator; the phase modulation device 61-6N is a phase mask or a phase-type spatial light modulator; the image sensor device 8 is a charge coupled device (CCD) or a complementary metal oxide semiconductor (CMOS), and the working mode is a grayscale mode.

[0029] In the above-mentioned color image encryption method based on dynamic constrained holographic coding, the decryption step J3 can be completed either digitally or optically, wherein the optical decryption process in the decryption step J3 requires the use of the color holographic reproduction system provided by the present invention, including a red laser 11, a green laser 12, and a blue laser 13 for providing three-color reproduction light, a polarization modulation device 21-23 for modulating the polarization state of light, a dichroic mirror 91, 92 for combining beams, a microscope objective 3 for expanding beams, and a needle for filtering. Hole 4, convex lens 5 for collimation, phase modulator 6 for carrying phase conversion, image sensor 8 for receiving color decrypted image, characterized in that: the polarization modulators 21-23 are polarizers or half-wave plates, respectively placed at the light outlets of the red laser 11, the green laser 12, and the blue laser 13, and perpendicular to the corresponding optical axes; the dichroism of the dichroic mirror 91 is high transmittance for red and high reflection for green, and the dichroism of the dichroic mirror 92 is high transmittance for both red and green and high reflection for blue; The optical axis of the red laser 11 is perpendicular to the optical axis of the green laser 12 and passes through the center of the dichroic mirror 91. The angles between the normal of the dichroic mirror 91 and the optical axes of the red laser 11 and the green laser 12 are 135° and 45° respectively. The dichroic mirror 92 is placed parallel to the dichroic mirror 91 and away from the red laser 11. The optical axis of the red laser 11 is perpendicular to the optical axis of the blue laser 13 and passes through the center of the dichroic mirror 92. The normal of the dichroic mirror 92 is 135° and 45° respectively. The angles included by the optical axes of 13 are 135° and 45° respectively; the microscope objective lens 3, pinhole 4, convex lens 5, phase modulation device 6, and image sensor device 8 are all located on the optical axis of the red light laser 11 and are perpendicular to the optical axis of the red light laser 11; the pinhole 4 is placed on the image focus of the microscope objective lens 3, and the image focus of the microscope objective lens 3 and the object focus of the convex lens 5 coincide with each other; the image sensor device 8 is a charge coupled device (CCD) or a complementary metal oxide semiconductor (CMOS), and the working mode is a color mode.

[0030] The beneficial effects of the present invention are as follows: (1) Different from a ciphertext image with a noise-like distribution, the present invention encrypts a color plaintext image into a ciphertext image with a visible image distribution, thereby effectively improving the concealment of color image encryption; (2) The present invention uses a dynamic constrained holographic coding method to calculate a hologram of a color plaintext image, effectively solving the problem of uneven quality levels of images reproduced by different color channels in traditional color holographic coding methods, thereby ensuring the high quality of the color decrypted image when correctly decrypted; (3) The present invention uses a structured phase mask in an iterative phase recovery algorithm to achieve structured light illumination, thereby greatly increasing the types and number of digital keys and effectively expanding the key space; (4) All pure phase masks output in the encryption step of the present invention are used as phase keys, thereby further expanding the key space and improving the security of color image encryption. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 The encryption flow chart of a color image encryption method based on dynamic constrained holographic coding.

[0032] Figure 2 Auxiliary coordinate system for dynamically constrained holographic encoding.

[0033] Figure 3 An iterative flow chart is provided to assist in describing the encryption steps, wherein ASD and IASD represent angular spectrum diffraction and inverse angular spectrum diffraction operations, respectively; CE and M represent correlation coefficient and average value operations, respectively; AC, PC, UAC, AE, PE, PS, and PAC represent amplitude constraint, phase constraint, unit amplitude constraint, amplitude extraction, phase extraction, phase subtraction, and phase-amplitude conversion operations, respectively; and POM represents a pure phase mask.

[0034] Figure 4 The encryption flow chart of a color image encryption method based on dynamic constrained holographic coding.

[0035] Figure 5 It is a diffraction imaging system, in which 1 represents a laser, 2 represents a polarization modulation device, 3 represents a microscope objective lens, 4 represents a pinhole, 5 represents a convex lens, 60-6N represents a phase modulation device, 7 represents an amplitude modulation device, and 8 represents an image sensor device.

[0036] Figure 6 It is a color holographic reproduction system, in which 11-13 represent red, green and blue lasers respectively; 21-23 represent polarization modulation devices; 3 represents microscope objective lens; 4 represents pinhole; 5 represents convex lens; 6 represents phase modulation device; 8 represents image sensor device; 91-92 represent dichroic mirrors.

[0037] Figure 7(a) is a color plaintext image ("Cat"), (b) is a pure phase hologram, (c) is a visible ciphertext image ("Peppers"), (d) is the phase distribution of the encrypted structured phase mask, (e) is the phase distribution of pure phase mask 1, (f) is the phase distribution of pure phase mask 2, and (g) is the phase distribution of pure phase mask 3.

[0038] Figure 8 (a) is the color decrypted image when the decryption digital key and the decryption phase key are correct; (b) is the color decrypted image when the decryption wavelength key λ deviates by 1nm and the other keys are correct; (c) is the color decrypted image when the decryption focal length key f deviates by 1mm and the other keys are correct; (d) is the color decrypted image when the decryption topological charge key P deviates by 1 and the other keys are correct; (e) is the color decrypted image when the decryption distance key Z deviates by 1mm and the other keys are correct; (f) is the color decrypted image when the decryption distance key z0 deviates by 1mm and the other keys are correct; (g) is the color decrypted image when the decryption distance (1) is the color decrypted image when the decryption distance of key z1 deviates by 1mm and other keys are correct; (2) is the color decrypted image when the decryption distance of key z2 deviates by 1mm and other keys are correct; (3) is the color decrypted image when the decryption distance of key z3 deviates by 1mm and other keys are correct; (4) is the color decrypted image when the decryption phase key (pure phase mask 1) is wrong and other keys are correct; (5) is the color decrypted image when the decryption phase key (pure phase mask 2) is wrong and other keys are correct; (6) is the color decrypted image when the decryption phase key (pure phase mask 3) is wrong and other keys are correct.

[0039] Fig. 9 (a) is the sensitivity curve of wavelength key λ; (b) is the sensitivity curve of focal length key f; (c) is the sensitivity curve of topological charge key P; (d) is the sensitivity curve of diffraction distance key Z; (e) is the sensitivity curve of diffraction distance key z0; (f) is the sensitivity curve of diffraction distance key z1; (g) is the sensitivity curve of diffraction distance key z2; (h) is the sensitivity curve of diffraction distance key z3. Specific implementation plan

[0040] The present invention is further described below in conjunction with the embodiments and drawings, but they are not intended to limit the present invention.

[0041] Embodiment: A color image encryption method based on dynamic constraint holographic coding, comprising: Figure 1 The encryption steps shown in FIG. Figure 2 Iterative flow chart shown):

[0042] S1: Initial condition deployment: First, set the wavelengths of the three color channels of red (R), green (G), and blue (B) to be λ R , G , B . Then, four parallel planes H, B, G, and R are set in sequence along a straight line, and are denoted as Plane H, Plane B, Plane G, and Plane R, respectively. Figure 3 Then, set the distances between Plane B, Plane G, Plane R and Plane H to d B ,d G ,d R , characterized in that: d B ,d G ,d R The following relationship must be satisfied:

[0043] d B :d G :d R =λ R :λ G :λ B (1)

[0044] After that, the color plaintext image to be encrypted is decomposed into three components: R, G, and B. The amplitude distributions of these components are recorded as R component plaintext amplitude A and B respectively. R (x R ,y R ), G component plaintext amplitude A G (x G ,y G ), B component plaintext amplitude A B (x B ,y B ), which is used for the dynamic amplitude constraint of the corresponding plane. Then, the initial value of the dynamic constraint number i is set to 0. In addition, a complex amplitude with unit amplitude and phase randomly distributed in [0,2π] is set on Plane H. in represents a phase randomly distributed in [0,2π]. Afterwards, the encryption step S2 is performed.

[0045] S2: Diffraction propagation under dynamic amplitude constraint of B component: R The collimated plane light wave is used as an encrypted light wave and is incident on Plane H. H (x H ,y H ) after phase modulation and encryption of the optical wave U H (x H ,y H) starts to propagate forward diffractively until Plane B, thereby obtaining the complex amplitude U of the encrypted light wave propagating forward to Plane B B (x B ,y B )for:

[0046]

[0047] in, Indicates wavelength as λ R , the distance is d B angular spectrum diffraction operation, FT(·) and IFT(·) represent Fourier transform and inverse Fourier transform, j is an imaginary unit, k = 2π / λ R is the wave number, and Represents the spatial frequency coordinate. Then, the amplitude of the encrypted light wave forward to Plane B is extracted and saved, recorded as the B-plane reconstruction amplitude Here, |·| represents the amplitude extraction operation. Then, the B-plane reconstruction amplitude is calculated. and B component plaintext amplitude A B (x B ,y B ) B Next, B (x B ,y B ) to constrain the dynamic amplitude of the B component, thereby obtaining the complex amplitude U′ of the encrypted light wave after the dynamic amplitude constraint of the B component B (x B ,y B )for:

[0048]

[0049] in, represents the B component amplitude constraint operation under the i-th dynamic constraint, arg(·) represents the phase extraction operation, represents the B component amplitude constraint factor under the i-th dynamic constraint, which can be expressed mathematically as:

[0050]

[0051] Afterwards, the encrypted light wave U′ B (x B ,y B ) starts to propagate in reverse diffraction until Plane H, thereby obtaining the complex amplitude U of the encrypted light wave transmitted in reverse to Plane H after the dynamic amplitude constraint of the B component BH (x H ,y H )for:

[0052]

[0053] in, Indicates wavelength as λ R , the diffraction distance is d B Then, U BH (x H ,y H ) is used to constrain the unit amplitude, thereby obtaining the output complex amplitude U′ of the encrypted light wave after the dynamic amplitude constraint of the B component BH (x H ,y H )=UAC[U BH (x H ,y H )]=exp{jarg[U BH (x H ,y H )]}, where UAC(·) represents the unit amplitude constraint operation. Then, the encryption step S3 is performed.

[0054] S3: Diffraction propagation under dynamic amplitude constraint of G component: Encrypted light wave U′ after encryption step S2 BH (x H ,y H ) starts to propagate forward diffractively until Plane G, thereby obtaining the complex amplitude of the encrypted light wave propagating forward to Plane G Then, the amplitude of the encrypted light wave transmitted forward to Plane G is extracted and saved, which is recorded as the G plane reconstruction amplitude. Afterwards, calculate the G plane reconstruction amplitude and the G component plaintext amplitude A G (x G ,y G ) G Next, G (x G ,y G ) to constrain the dynamic amplitude of the G component, thereby obtaining the complex amplitude U′ of the encrypted light wave after the dynamic amplitude constraint of the G component G (x G ,y G ). After that, the encrypted light wave U′ G (x G ,y G ) starts to propagate in reverse diffraction until Plane H, thereby obtaining the complex amplitude U of the encrypted light wave transmitted in reverse to Plane H after the dynamic amplitude constraint of the G component GH (x H ,y H ). Then, GH (x H,y H ) is used to constrain the unit amplitude, thereby obtaining the output complex amplitude U′ of the encrypted light wave after the dynamic amplitude constraint of the G component GH (x H ,y H )for:

[0055]

[0056] in, It represents the G component amplitude constraint operation under the i-th dynamic constraint. Afterwards, the encryption step S4 is performed.

[0057] S4: Diffraction propagation under dynamic amplitude constraint of R component: Encrypted light wave U′ after encryption step S3 GH (x H ,y H ) starts to propagate forward diffractively until Plane R, thereby obtaining the complex amplitude of the encrypted light wave propagating forward to Plane R Then, the amplitude of the encrypted light wave transmitted forward to Plane R is extracted and saved, which is recorded as the R plane reconstruction amplitude Afterwards, calculate the R plane reconstruction amplitude and the R component plaintext amplitude A R (x R ,y R ) R Next, R (x R ,y R ) to constrain the dynamic amplitude of the R component, thereby obtaining the complex amplitude U′ of the encrypted light wave after the dynamic amplitude constraint of the R component R (x R ,y R ). After that, the encrypted light wave U′ R (x R ,y R ) starts to propagate in reverse diffraction until Plane H, thereby obtaining the complex amplitude U of the encrypted light wave transmitted in reverse to Plane H after the dynamic amplitude constraint of the R component RH (x H ,y H ). Then, RH (x H ,y H ) is used to constrain the unit amplitude, thereby obtaining the output complex amplitude U′ of the encrypted light wave after the dynamic amplitude constraint of the R component RH (x H ,y H )for:

[0058]

[0059] in, It represents the R component amplitude constraint operation under the i-th dynamic constraint. Afterwards, the encryption step S5 is performed.

[0060] S5: Phase output condition judgment: Calculate CC B 、CC G 、CC R The average CC of the three avg , when CC avg exceeds the preset threshold q, that is, the phase output condition is met, and the encryption step S7 is executed; when CC avg If the preset threshold q is not exceeded, that is, the convergence condition is not met, the encryption step S6 is executed.

[0061] S6: Phase update: using U′ obtained in encryption step S4 RH (x H ,y H )Update U H (x H ,y H ), that is: U H (x H ,y H )=U′ RH (x H ,y H ), and the number of dynamic constraints is also updated from i to i+1, that is, i=i+1. Then, the encryption step S2 is performed.

[0062] S7: Output of pure phase hologram and phase-to-amplitude conversion: U′ obtained in encryption step S4 RH (x H ,y H ) to perform phase extraction operations, thereby generating and outputting a pure phase hologram of a color plaintext image Right now: Afterwards, Perform phase-amplitude conversion to obtain the conversion amplitude A H (x H ,y H )for:

[0063]

[0064] Wherein, PAC(·) represents a phase-amplitude conversion operation. Afterwards, the encryption step S8 is performed.

[0065] S8: Generation and illumination of encrypted structured light: First, the encrypted structured phase mask composed of the Fresnel zone plate and the radial Hilbert mask is used to phase modulate the collimated plane light wave of unit amplitude, thereby generating phase-modulated encrypted structured light. Therefore, the complex amplitude distribution of the encrypted structured light is equal to the phase distribution ESPM(ξ,η) of the encrypted structured phase mask, that is:

[0066]

[0067] Among them, λ is the wavelength of the encrypted incident light, f and r are the focal length and radius of the Fresnel zone plate, respectively, and P and θ are the topological charge and spatial azimuth of the radial Hilbert mask, respectively. Subsequently, the encrypted structured light generated after phase modulation by the encrypted structured phase mask begins to diffract and propagate forward until it reaches the preset visible ciphertext image. The complex amplitude of the encrypted structured light transmitted forward to the front surface of the ciphertext image is U0(x0,y0)=ASD λ,Z [ESPM(ξ,η)], where Z is the distance from the encrypted structured phase mask to the ciphertext image. Afterwards, the encryption step S9 is performed.

[0068] S9: Unconstrained forward propagation: The encrypted structured light after amplitude modulation of the encrypted image continues to diffract and propagate forward, passing through the planes where the N pure phase masks to be restored are located in turn and then reaches the reconstructed image plane. The N pure phase masks to be restored are respectively denoted as pure phase mask 1, pure phase mask 2, ..., pure phase mask N, and the front surfaces of the N pure phase masks are respectively denoted as S forward 1, S forward 2, ..., S forward The rear surfaces of N,N pure phase masks are denoted as S backward 1, S backward 2, ..., S backward N, the encrypted structured light is transmitted forward to S forward The complex amplitude U1(x1,y1) of 1 is:

[0069]

[0070] Among them, A S (x0, y0) is the amplitude of the preset visible ciphertext image, z0 is the amplitude of the ciphertext image to S forward 1. After that, the encrypted structured light continues to diffract and propagate forward, reaching S forward 2. S forward 3. ……, S forward N and S forward N+1 (reconstructed image plane), where the encrypted structured light is forwarded to S forward The complex amplitude U of n n (x n ,y n )for:

[0071]

[0072] Among them, z n-1 For S forward n-1 to S forwardn, n = 2:1:N+1 means n is incremented from 2 to N+1 with a step size of 1. Then, the encrypted structured light is extracted and saved and forwarded to S forward Amplitude A of n n (x n ,y n ) and phase They are:

[0073]

[0074] Wherein, n=1:1:N+1 means that n is incremented from 1 to N+1 with a step length of 1. Then, the encryption step S10 is performed.

[0075] S10: Convergence condition judgment: After obtaining the encrypted structured light, it is forwarded to the reconstructed image plane (S forward N+1) amplitude A N+1 (x N+1 ,y N+1 )=|U N+1 (x N+1 ,y N+1 )|, record it as the reconstruction amplitude, and then calculate the reconstruction amplitude A N+1 (x N+1 ,y N+1 ) and the conversion amplitude A H (x H ,y H ). When CC exceeds the preset threshold σ, that is, the convergence condition is met, the encryption step S13 is performed; when CC does not exceed the preset threshold σ, that is, the convergence condition is not met, the phase of the encrypted structured light forward to the reconstructed image plane is retained. unchanged, and using the conversion amplitude A H (x H ,y H ) instead of reconstructing the amplitude A N+1 (x N+1 ,y N+1 ) realizes the amplitude constraint, thereby generating a new complex amplitude on the reconstruction plane Right now: Afterwards, the encryption step S11 is performed.

[0076] S11: Backward propagation under phase constraints: The encrypted structured light forms a new complex amplitude after being constrained by amplitude on the reconstructed image plane The diffraction propagation starts to propagate backwards and reaches the back surfaces of N pure phase masks (S backward N,S backward N-1,......,S backward 1), where the encrypted structured light is transmitted backward to S backward The complex amplitude U' of n n (xn ,y n )for:

[0077]

[0078] Among them, z n For S backward n to S backward The distance of n+1, n=N:-1:1 means n is incremented from N to 1 with a step length of -1. After that, the encrypted structured light is extracted and saved and then transmitted to S backward The amplitude A' of n n (x n ,y n ) and phase They are:

[0079]

[0080] Wherein, n=N:-1:1 means that n is incremented from N to 1 with a step length of -1. Then, the encrypted structured light saved in the encryption step S11 is retained and transmitted to S backward The amplitude A' of n n (x n ,y n ) remains unchanged, and the encrypted structured light saved in the encryption step S9 is forwarded to S forward The phase of n Instead of encrypting the encrypted structured light stored in step S11, it is transmitted back to S backward The phase of n Implement phase constraints to generate new complex amplitudes for the next segment of backward propagation Right now:

[0081]

[0082] Among them, n = N:-1:1 means that n is incremented from N to 1 with a step length of -1. It should be noted that the encrypted structured light is backward N back propagates until S backward 1, each time it is transmitted to the next plane, formulas (13)-(15) are cyclically executed once until the encrypted structured light is transmitted backward to S backward 1 ends. Afterwards, the encryption step S12 is performed.

[0083] S12: Forward propagation under phase constraint: retain the encrypted structured light saved in the encryption step S9 and forward it to S forward The amplitude A1(x1, y1) of 1 remains unchanged, and the encrypted structured light saved in the encryption step S11 is transmitted back to S backward Phase 1 Instead of encrypting the structured light in step S9, it is forwarded to S forward Phase 1 Phase constraints are implemented to generate a new complex amplitude U1″(x1,y1) for the next forward propagation, namely: Then, the encrypted structured light begins to diffract and propagate forward, reaching S forward 2, S forward 3, ..., S forward N and S forward N+1, where the encrypted structured light is forwarded to S forward The complex amplitude U of n n (x n ,y n ) is updated to:

[0084]

[0085] Among them, n = 2:1:N+1 means that n is incremented by 1 from 2 to N+1. After that, the encrypted structured light is extracted and saved and forwarded to S forward Amplitude A of n n (x n ,y n ) and phase They are:

[0086]

[0087] Wherein, n=2:1:N+1 means that n is incremented from 2 to N+1 with a step length of 1. Then, the encrypted structured light saved in the encryption step S12 is forwarded to S forward Amplitude A on n n (x n ,y n ) remains unchanged, and the encrypted structured light saved in the encryption step S11 is transmitted back to S backward The phase of n Instead of encrypting the encrypted structured light stored in step S12, it is forwarded to S forward The phase of n Implement phase constraints to generate a new complex amplitude U for the next forward propagation n ″(x n ,y n ),Right now:

[0088]

[0089] Among them, n = 2:1:N means that n is incremented from 2 to N with a step size of 1. It should be noted that the encrypted structured light is forward 2 Forward propagation until S forward N+1, each time it is transmitted to the next plane, formulas (16)-(18) are cycled once until the encrypted structured light is transmitted forward to S forwardN+1 ends. After that, the encryption step S10 is performed.

[0090] S13: Generation and output of pure phase mask: On all planes where the pure phase mask to be restored is located, the encrypted structured light saved in the encryption step S11 is transmitted back to S backward The phase of n The encrypted structured light saved in the encryption step S12 is forwarded to S forward The phase of n Perform a phase subtraction operation to generate and output the phase distribution of all pure phase masks to be restored, where the phase distribution of pure phase mask n is for:

[0091]

[0092] Wherein, mod(·) represents a modulo operation, and n=1:1:N represents that n is incremented from 1 to N in steps of 1.

[0093] At this point, the encryption step is completed.

[0094] like Figure 4 Decryption steps shown:

[0095] J1: Generation and illumination of decrypted structured light: First, the decrypted structured phase mask is used to phase modulate the collimated plane light wave to generate decrypted structured light. After that, the decrypted structured light generated after phase modulation by the decrypted structured phase mask begins to diffract forward to illuminate the preset ciphertext image. The complex amplitude U of the decrypted structured light transmitted forward to the front surface of the ciphertext image is 0J (x0,y0), that is:

[0096]

[0097] Where DSPM(ξ,η) is the phase distribution of the decrypted structured phase mask, λ J To decipher the wavelength of the incident light, d J To decrypt the distance from the structured phase mask to the ciphertext image, the decryption step J2 is then performed.

[0098] J2: Forward propagation decryption: After the amplitude modulation of the ciphertext image, the decrypted structured light continues to diffract and propagate forward, and the decrypted structured light is forwarded to S forward The complex amplitude U of 1 1J (x1,y1) is:

[0099]

[0100] Among them, z 0J To decrypt the ciphertext image to S forward1. After that, the decrypted structured light continues to diffract and propagate forward, reaching S forward 2. S forward 3.......,S forward N and S forward N+1 (reconstructed image plane), where the decrypted structured light is forwarded to S forward The complex amplitude U of n nJ (x n ,y n )for:

[0101]

[0102] Among them, z (n-1)J S is the decryption time forward n-1 to S forward n, n = 2:1:N+1 means n is incremented from 2 to N+1 with a step size of 1. Then, the decrypted structured light is extracted and saved and forwarded to the reconstructed image plane (S forward N+1) amplitude A (N+1)J (x N+1 ,y N+1 ), that is: A (N+1)J (x N+1 ,y N+1 )=|U (N+1)J (x N+1 ,y N+1 )|, recorded as the reconstruction amplitude. Then, for A (N+1)J (x N+1 ,y N+1 ) to perform amplitude-phase conversion operation, thereby obtaining the conversion phase for:

[0103]

[0104] Wherein, APC(·) represents the amplitude-phase conversion operation. Afterwards, the decryption step J3 is performed.

[0105] J3: Color holographic reconstruction decryption: converting phase Placed on Plane H, using unit amplitude and wavelength λ R A red collimated plane light wave with unit amplitude and wavelength λ G A green collimated plane light wave with unit amplitude and wavelength λ B The blue collimated plane light wave is incident on Plane H as the three-color decryption light wave at the same time. After phase modulation, the three-color decrypted light wave begins to propagate forward diffracted to Plane R, thereby obtaining the complex amplitude U of the three-color decrypted light wave forward to Plane R. RJ (x R ,y R), U GJ (x R ,y R ), U BJ (x R ,y R ) are:

[0106]

[0107] Afterwards, the amplitudes of the three-color decrypted light waves transmitted forward to Plane R are extracted and saved, and recorded as: R component decrypted amplitude A RJ (x R ,y R )=|U RJ (x R ,y R )|、G component decryption amplitude A GJ (x R ,y R )=|U GJ (x R ,y R )|、B component decryption amplitude A BJ (x R ,y R )=|U BJ (x R ,y R )|. Then, the R component is decrypted to amplitude A RJ (x R ,y R ), G component decryption amplitude A GJ (x R ,y R ), B component decryption amplitude A BJ (x R ,y R ) are synthesized into a color image, which is the final color decrypted image.

[0108] At this point, the decryption step is completed. It should be noted that the above decryption step can be completed in a digital manner or in an optical-digital combination manner, wherein the optical decryption process in the decryption steps J1-J2 requires the use of the diffraction imaging system provided by the present invention, and the optical decryption process in the decryption step J3 requires the use of the color holographic reproduction system provided by the present invention.

[0109] The above-mentioned diffraction imaging system, such as Figure 5As shown, it includes a laser 1 for providing incident light; a polarization modulator 2 for modulating the polarization state of light, a microscope objective 3 for beam expansion, a pinhole 4 for filtering, a convex lens 5 for collimation, a phase modulator 60 for carrying the phase distribution of a decrypted structured phase mask, an amplitude modulator 7 for carrying a ciphertext image, phase modulators 61-6N for carrying the phase distribution of a pure phase mask, and an image sensor 8 for receiving the reconstructed amplitude, characterized in that: the polarization modulator 2 is a polarizer or a half-wave plate; the pinhole 4 is placed on the image focus of the microscope objective 3, and the image focus of the microscope objective 3 coincides with the object focus of the convex lens 5; the amplitude modulator 7 is an amplitude mask or an amplitude-type spatial light modulator; the phase modulators 61-6N are phase masks or phase-type spatial light modulators; the image sensor 8 is a charge coupled device (CCD) or a complementary metal oxide semiconductor (CMOS), and the working mode is a grayscale mode. The specific optical decryption process is as follows: the laser light emitted by the laser 1 first passes through the polarization modulator 2 to form polarized light, and then the polarized light passes through the beam expansion and collimation system composed of the microscope objective 3, the pinhole 4, and the convex lens 5 to form a collimated plane light wave, and then the plane light wave is phase-modulated by the phase modulator 60 that carries the phase distribution of the decrypted structured phase mask to generate the decrypted structured light, and then the decrypted structured light is diffracted and propagated forward to the amplitude modulator 7 used to carry the ciphertext image, and then the decrypted structured light after amplitude modulation by the amplitude modulator 7 continues to diffract and propagate forward to the diffraction neural network composed of the phase modulators 61-6N that carry the phase distribution of the pure phase mask, and then the decrypted structured light after phase modulation by the phase modulators 61-6N in the diffraction neural network continues to diffract and propagate forward to the image sensor 8, and at this time the image collected on the image sensor 8 is the reconstructed amplitude. At this point, the optical decryption process in the decryption steps J1-J2 is completed, and then the reconstructed amplitude collected by the image sensor device 8 is uploaded to the computer, and then the reconstructed amplitude is converted into phase using a computer program to obtain a conversion phase.

[0110] The above-mentioned color holographic reconstruction system, such as Figure 6As shown, it includes a red laser 11, a green laser 12, and a blue laser 13 for providing three-color reproduction light, a polarization modulator 21-23 for modulating the polarization state of light, dichroic mirrors 91, 92 for beam combining, a microscope objective 3 for beam expansion, a pinhole 4 for filtering, a convex lens 5 for collimation, a phase modulator 6 for carrying the conversion phase, and an image sensor 8 for receiving a color decrypted image, characterized in that: the polarization modulators 21-23 are polarizers or half-wave plates, which are respectively placed at the light outlets of the red laser 11, the green laser 12, and the blue laser 13, and are perpendicular to the corresponding optical axes; the dichroism of the dichroic mirror 91 is high transmittance for red and high reflection for green, and the dichroism of the dichroic mirror 92 is high transmittance for both red and green and high reflection for blue; the optical axis of the red laser 11 is perpendicular to the optical axis of the green laser 12 and passes through the center of the dichroic mirror 91, and the dichroic mirror The angles between the normal of the dichroic mirror 91 and the optical axes of the red laser 11 and the green laser 12 are 135° and 45° respectively; the dichroic mirror 92 is placed parallel to the dichroic mirror 91 and away from the red laser 11, the optical axis of the red laser 11 is perpendicular to the optical axis of the blue laser 13 and passes through the center of the dichroic mirror 92, and the angles between the normal of the dichroic mirror 92 and the optical axes of the red laser 11 and the blue laser 13 are 135° and 45° respectively; the microscope objective lens 3, the pinhole 4, the convex lens 5, the phase modulation device 6, and the image sensor device 8 are all located on the optical axis of the red laser 11 and perpendicular to the optical axis of the red laser 11; the pinhole 4 is placed on the image focus of the microscope objective lens 3, and the image focus of the microscope objective lens 3 coincides with the object focus of the convex lens 5; the image sensor device 8 is a charge coupled device (CCD) or a complementary metal oxide semiconductor (CMOS), and the working mode is a color mode. The specific optical decryption process is as follows: first, the laser light emitted by the red laser 11, the laser light emitted by the green laser 12, and the laser light emitted by the blue laser 13 pass through the polarization modulation devices 21-23 respectively to form polarized light, and then the red polarized light passes through the dichroic mirror 91, and the green polarized light passes through the dichroic mirror 92, and the reflected light is combined into a beam of red-green polarized light, and then the red-green polarized light passes through the dichroic mirror 92, and the blue polarized light passes through the dichroic mirror 92, and the reflected light is combined into a beam of red-green-blue polarized light, and then the red-green-blue polarized light passes through the beam expansion and collimation system composed of the microscope objective 3, the pinhole 4, and the convex lens 5 to form a collimated plane light wave, and then the plane light wave is phase modulated by the phase modulation device 6 that carries the conversion phase and begins to diffract and propagate forward until the image sensor device 8, and the image collected on the image sensor device 8 is the color decrypted image. At this point, the optical decryption process in the decryption step J3 is completed.

[0111] The content of the present invention is further explained below in conjunction with specific embodiments and drawings.

[0112] First, a color image (“Cat”) with a pixel count of 1024×1024 is selected as the original plaintext image, such as Figure 7 As shown in (a). The wavelengths of the three color channels R, G, and B are set to λ R =670nm,λ G =532nm,λ B =473nm, the distances between Plane B, Plane G, Plane R and Plane H are d B ,d G ,d R , the preset threshold q is 0.93. After the dynamic constrained holographic encoding process of encryption steps S1-S9, the generated pure phase hologram is as follows Figure 7 (b) is shown. After that, the pure phase hologram is subjected to a phase-to-amplitude conversion operation to obtain the conversion amplitude, which is then encrypted using an iterative phase recovery algorithm under structured light illumination. A grayscale image (“Peppers”) with a pixel count of 1024×1024 is selected as the preset visible ciphertext image, as shown in Figure 7 As shown in (c). It is assumed that the diffraction neural network to be restored includes three pure phase masks (pure phase mask 1, pure phase mask 2, pure phase mask 3), the wavelength λ of the light wave is 632.8nm, the distance Z from the encrypted structured phase mask to the ciphertext image is 40mm, the distance z0 from the ciphertext image to the pure phase mask 1 is 40mm, the distance z1 from the pure phase mask 1 to the pure phase mask 2 is 150mm, the distance z2 from the pure phase mask 2 to the pure phase mask 3 is 100mm, and the distance z3 from the pure phase mask 3 to the reconstructed image plane is 150mm. The preset threshold σ is 0.9999. The encrypted structured phase mask consists of a Fresnel zone plate with a focal length f of 20mm and a radial Hilbert mask with a topological charge number P of 6. Its phase distribution is shown in Figure 7 After the iterative phase recovery process of encryption steps S9-S13, the phase distributions of the three pure phase masks (pure phase mask 1, pure phase mask 2, and pure phase mask 3) are respectively as follows: Figure 7 (e)-(g) are shown. At this point, the encryption step is completed, the ciphertext is a preset visible image, and the key includes a digital key and a phase key, where the digital key includes the wavelength λ of the light wave used in the encryption process, the optical parameters (focal length f and topological charge number P) in the encrypted structured phase mask, and the diffraction distance (Z, z0, z1, z2, z3), and the phase key refers to the generated pure phase mask (pure phase mask 1, pure phase mask 2, pure phase mask 3).

[0113] Next, the validity and security of the key in the present invention are tested. When the decryption digital key and the decryption phase key are both correct, the obtained color decrypted image is as follows: Figure 8 (a); when the decryption wavelength key λ deviates by 1nm and other keys are correct, the obtained color decrypted image is as follows Figure 8 (b) When the decryption focal length key f deviates by 1 mm and other keys are correct, the obtained color decrypted image is as follows: Figure 8 (c) When the decryption topological charge key P deviates by 1 and the other keys are correct, the obtained color decrypted image is as follows: Figure 8 (d) When the decryption distance key Z deviates by 1 mm and other keys are correct, the obtained color decrypted image is as follows: Figure 8 (e) When the decryption distance key z0 deviates by 1 mm and other keys are correct, the obtained color decrypted image is as follows: Figure 8 (f) When the decryption distance key z1 deviates by 1 mm and other keys are correct, the obtained color decrypted image is as follows: Figure 8 (g) When the decryption distance key z2 deviates by 1 mm and other keys are correct, the obtained color decrypted image is as follows: Figure 8 (h) When the decryption distance key z3 deviates by 1 mm and other keys are correct, the obtained color decrypted image is as follows: Figure 8 (i) When the decrypted phase key (pure phase mask 1) is wrong and other keys are correct, the obtained color decrypted image is as follows: Figure 8 (j) When the decrypted phase key (pure phase mask 2) is wrong and other keys are correct, the obtained color decrypted image is as follows: Figure 8 (k) As shown; when the decryption phase key (pure phase mask 3) is wrong and other keys are correct, the obtained color decrypted image is as follows Figure 8 (l). Figure 8 It can be seen from the color decrypted image that when the digital key and the phase key are correct, the original color plaintext image can be reconstructed with high quality, but when any digital key or phase key is wrong, the correct original color plaintext image cannot be restored. At this time, the color decrypted image shows obvious noise distribution, which illustrates the effectiveness and security of the digital key and phase key in the present invention.

[0114] The sensitivity of the digital key in the present invention is examined below. Fig. 9 The correlation coefficients (CC) between the three color components of the color decrypted image and the three color components of the original plaintext image are given when the decryption phase key is correct. R 、CC G 、CC B ) and the deviation of each digital key, that is, the sensitivity curve of each digital key, where Fig. 9(a)-(h) represent the sensitivity curves of wavelength key λ, focal length key f, topological charge key P, diffraction distance key Z, diffraction distance key z0, diffraction distance key z1, diffraction distance key z2, and diffraction distance key z3, respectively. Fig. 9 The sensitivity curve in the figure shows that when any digital key has a slight deviation, CC R 、CC G 、CC B All of them drop sharply to near 0, at which point the original color plaintext image cannot be correctly restored, indicating that the digital key in the present invention has a high sensitivity.

[0115] In summary, the present invention discloses a color image encryption method based on dynamic constrained holographic coding. In the present invention, the encryption process first encodes the color plaintext image into a pure phase hologram based on dynamic constrained holographic coding, then converts the pure phase hologram into a conversion amplitude through phase-amplitude conversion, and finally uses the iterative phase recovery algorithm under structured light illumination to encrypt the conversion amplitude into a visible ciphertext image, and generates a diffraction neural network at the same time, wherein the ciphertext has a distribution of visible images rather than a noise-like distribution, thus showing extremely high imperceptibility, thereby effectively improving the concealment of color image encryption; in addition, the use of the dynamic constrained holographic coding method effectively balances the quality level of the reproduced images of different color channels, thereby ensuring the high quality of the color decrypted image when correctly decrypted; in addition, in the iterative phase recovery algorithm under structured light illumination, due to the introduction of the structured phase mask and the output of the diffraction neural network, the types and quantities of keys are greatly increased, the key space is effectively expanded, and the security of color image encryption is improved. The decryption process can be completed either digitally or through a combination of optical and digital methods. The diffraction imaging system and color holographic reproduction system used for optical decryption have a simple structure and are easy to build.

Claims

1. A color image encryption method based on dynamic constrained holographic coding, characterized in that: The encryption steps include: S1: Initial condition deployment: First, set the wavelengths of the three color channels of red (R), green (G), and blue (B); then, set four parallel planes H, B, G, and R in sequence along a straight line, denoted as Plane H, Plane B, Plane G, and Plane R respectively; then, set the distances between Plane B, Plane G, and Plane R and Plane H to be d B ,d G ,d R After that, the color plaintext image to be encrypted is decomposed into three components: R, G, and B. The amplitude distributions of these components are recorded as R component plaintext amplitude A and B respectively. R (x R ,y R ), G component plaintext amplitude A G (x G ,y G ), B component plaintext amplitude A B (x B ,y B ), which is used for the dynamic amplitude constraint of the corresponding plane. Then, the initial value of the dynamic constraint number i is set to 0. In addition, a complex amplitude U with unit amplitude and phase randomly distributed in [0,2π] is set on Plane H. H (x H ,y H ). Afterwards, the encryption step S2 is performed. S2: Diffraction propagation under dynamic amplitude constraint of B component: R The collimated plane light wave is used as an encrypted light wave and is incident on Plane H. H (x H ,y H ) after phase modulation and encryption of the optical wave U H (x H ,y H ) starts to propagate forward diffractively until Plane B, thereby obtaining the complex amplitude U of the encrypted light wave propagating forward to Plane B B (x B ,y B ). Then, the amplitude of the encrypted light wave transmitted forward to Plane B is extracted and saved, which is recorded as the B-plane reconstruction amplitude. Afterwards, calculate the B-plane reconstruction amplitude and B component plaintext amplitude A B (x B ,y B ) B Next, B (x B ,y B ) to constrain the dynamic amplitude of the B component, thereby obtaining the complex amplitude U′ of the encrypted light wave after the dynamic amplitude constraint of the B component B (x B ,y B ). After that, the encrypted light wave U′ B (x B ,y B ) starts to propagate in reverse diffraction until Plane H, thereby obtaining the complex amplitude U of the encrypted light wave transmitted in reverse to Plane H after the dynamic amplitude constraint of the B component BH (x H ,y H ). Then, BH (x H ,y H ) is used to constrain the unit amplitude, thereby obtaining the output complex amplitude U′ of the encrypted light wave after the dynamic amplitude constraint of the B component BH (x H ,y H ). Afterwards, the encryption step S3 is performed. S3: Diffraction propagation under dynamic amplitude constraint of G component: Encrypted light wave U′ after encryption step S2 BH (x H ,y H ) starts to propagate forward diffractively until Plane G, thereby obtaining the complex amplitude U of the encrypted light wave propagating forward to Plane G G (x G ,y G ). Then, the amplitude of the encrypted light wave forward to Plane G is extracted and saved, which is recorded as the G plane reconstruction amplitude. Afterwards, calculate the G plane reconstruction amplitude and the G component plaintext amplitude A G (x G ,y G ) G Next, G (x G ,y G ) to constrain the dynamic amplitude of the G component, thereby obtaining the complex amplitude U′ of the encrypted light wave after the dynamic amplitude constraint of the G component G (x G ,y G ). After that, the encrypted light wave U′ G (x G ,y G ) starts to propagate in reverse diffraction until Plane H, thereby obtaining the complex amplitude U of the encrypted light wave transmitted in reverse to Plane H after the dynamic amplitude constraint of the G component GH (x H ,y H ). Then, GH (x H ,y H ) is used to constrain the unit amplitude, thereby obtaining the output complex amplitude U′ of the encrypted light wave after the dynamic amplitude constraint of the G component GH (x H ,y H ). Afterwards, the encryption step S4 is performed. S4: Diffraction propagation under dynamic amplitude constraint of R component: Encrypted light wave U′ after encryption step S3 GH (x H ,y H ) starts to propagate forward diffractively until Plane R, thereby obtaining the complex amplitude U of the encrypted light wave propagating forward to Plane R R (x R ,y R ). Then, the amplitude of the encrypted light wave transmitted forward to Plane R is extracted and saved, which is recorded as the R plane reconstruction amplitude. Afterwards, calculate the R plane reconstruction amplitude and the R component plaintext amplitude A R (x R ,y R ) R Next, R (x R ,y R ) to constrain the dynamic amplitude of the R component, thereby obtaining the complex amplitude U′ of the encrypted light wave after the dynamic amplitude constraint of the R component R (x R ,y R ). After that, the encrypted light wave U′ R (x R ,y R ) starts to propagate in reverse diffraction until Plane H, thereby obtaining the complex amplitude U of the encrypted light wave transmitted in reverse to Plane H after the dynamic amplitude constraint of the R component RH (x H ,y H ). Then, RH (x H ,y H ) is used to constrain the unit amplitude, thereby obtaining the output complex amplitude U′ of the encrypted light wave after the dynamic amplitude constraint of the R component RH (x H ,y H ). Afterwards, the encryption step S5 is performed. S5: Phase output condition judgment: Calculate CC B 、CC G 、CC R The average CC of the three avg , when CC avg exceeds the preset threshold q, that is, the phase output condition is met, and the encryption step S7 is executed; when CC avg If the preset threshold q is not exceeded, that is, the convergence condition is not met, the encryption step S6 is executed. S6: Phase update: using U′ obtained in encryption step S4 RH (x H ,y H )Update U H (x H ,y H ), that is: U H (x H ,y H )=U′ RH (x H ,y H ), and the number of dynamic constraints is also updated from i to i+1, that is, i=i+1. Then, the encryption step S2 is performed. S7: Output of pure phase hologram and phase-to-amplitude conversion: U′ obtained in encryption step S4 RH (x H ,y H ) to perform phase extraction operations, thereby generating and outputting a pure phase hologram of a color plaintext image Afterwards, Perform phase-amplitude conversion to obtain the conversion amplitude A H (x H ,y H ). Afterwards, the encryption step S8 is performed. S8: Generation and illumination of encrypted structured light: First, the encrypted structured phase mask is used to phase modulate the collimated plane light wave of unit amplitude, thereby generating phase-modulated encrypted structured light. Therefore, the complex amplitude distribution of the encrypted structured light is equal to the phase distribution ESPM(ξ,η) of the encrypted structured phase mask. Subsequently, the encrypted structured light generated after phase modulation by the encrypted structured phase mask begins to diffract and propagate forward until the preset visible ciphertext image is reached, thereby obtaining the complex amplitude U0(x0,y0) of the encrypted structured light transmitted forward to the front surface of the ciphertext image. After that, the encryption step S9 is executed. S9: Unconstrained forward propagation: The encrypted structured light after amplitude modulation of the encrypted image continues to diffract and propagate forward, passing through the planes where the N pure phase masks to be restored are located in turn and then reaches the reconstructed image plane. The N pure phase masks to be restored are respectively denoted as pure phase mask 1, pure phase mask 2, ..., pure phase mask N, and the front surfaces of the N pure phase masks are respectively denoted as S forward 1, S forward 2, ..., S forward The rear surfaces of N,N pure phase masks are denoted as S backward 1, S backward 2, ..., S backward N, thus obtaining the encrypted structured light and transmitting it forward to S forward The complex amplitude U of n n (x n ,y n ), where n = 1, 2, ..., N + 1. Then, the encrypted structured light is extracted and saved and forwarded to S forward Amplitude A of n n (x n ,y n ) and phase Where n = 1, 2, ..., N + 1. Then, the encryption step S10 is performed. S10: Convergence condition judgment: After obtaining the encrypted structured light, it is forwarded to the reconstructed image plane (S forward N+1) amplitude A N+1 (x N+1 ,y N+1 ), record it as the reconstruction amplitude, and then calculate the reconstruction amplitude A N+1 (x N+1 ,y N+1 ) and the conversion amplitude A H (x H ,y H ) is a correlation coefficient CC. When CC exceeds the preset threshold σ, that is, the convergence condition is met, the encryption step S13 is performed; When CC does not exceed the preset threshold σ, that is, the convergence condition is not met, the phase of the encrypted structured light forward to the reconstructed image plane is retained. unchanged, and using the conversion amplitude A H (x H ,y H ) instead of reconstructing the amplitude A N+1 (x N+1 ,y N+1 ) realizes the amplitude constraint, thereby generating a new complex amplitude on the reconstruction plane Afterwards, the encryption step S11 is performed. S11: Backward propagation under phase constraints: The encrypted structured light forms a new complex amplitude after being constrained by amplitude on the reconstructed image plane The diffraction propagation starts to propagate backwards and reaches the back surfaces of N pure phase masks (S backward N,S backward N-1,......,S backward 1), and then the encrypted structured light is transmitted to S backward The complex amplitude U of n n ′(x n ,y n ), where n = N, N-1, ..., 1. Afterwards, the encrypted structured light is extracted and saved and then transmitted to S backward Amplitude A of n n ′(x n ,y n ) and phase Where n = N, N-1, ..., 1. Then, the encrypted structured light saved in the encryption step S11 is retained and transmitted back to S backward Amplitude A of n n ′(x n ,y n ) remains unchanged, and the encrypted structured light saved in the encryption step S9 is forwarded to S forward The phase of n Instead of encrypting the encrypted structured light stored in step S11, it is transmitted back to S backward The phase of n Implement phase constraints to generate new complex amplitudes for the next segment of backward propagation Where n = N, N-1, ..., 1. It should be noted that the encrypted structured light is from S backward N back propagates until S backward 1. Each time it is transmitted to the next plane, the above process is repeated until the encrypted structured light is transmitted to S backward 1 ends. Afterwards, the encryption step S12 is performed. S12: Forward propagation under phase constraint: retain the encrypted structured light saved in the encryption step S9 and forward it to S forward The amplitude A1(x1, y1) of 1 remains unchanged, and the encrypted structured light saved in the encryption step S11 is transmitted back to S backward Phase 1 Instead of encrypting the structured light in step S9, it is forwarded to S forward Phase 1 Phase constraint is achieved to generate a new complex amplitude U″1(x1,y1) for the next forward propagation. Then, the encrypted structured light begins to diffract forward and reaches S forward 2, S forward 3, ..., S forward N and S forward N+1, thus updating the encrypted structured light and forwarding it to S forward The complex amplitude U of n n (x n ,y n ), where n = 2, 3, ..., N + 1. Afterwards, the encrypted structured light is extracted and saved and forwarded to S forward Amplitude A of n n (x n ,y n ) and phase Where n = 2, 3, ..., N + 1. Then, the encrypted structured light saved in the encryption step S12 is forwarded to S forward Amplitude A on n n (x n ,y n ) remains unchanged, and the encrypted structured light saved in the encryption step S11 is transmitted back to S backward The phase of n Instead of encrypting the encrypted structured light stored in step S12, it is forwarded to S forward The phase of n Implement phase constraints to generate a new complex amplitude U for the next forward propagation n ″(x n ,y n ), where n = 2, 3, ..., N. It should be noted that the encrypted structured light is from S forward 2 Forward propagation until S forward N+1, each time it is transmitted to the next plane, the above process is repeated once until the encrypted structured light is transmitted forward to S forward N+1 ends. After that, the encryption step S10 is performed. S13: Generation and output of pure phase mask: On all planes where the pure phase mask to be restored is located, the encrypted structured light saved in the encryption step S11 is transmitted back to S backward The phase of n The encrypted structured light saved in the encryption step S12 is forwarded to S forward The phase of n Perform a phase subtraction operation to generate and output the phase distribution of all pure phase masks to be restored Where n = 1, 2, ..., N. At this point, the encryption step is completed. Decryption steps: J1: Generation and illumination of decrypted structured light: First, the decrypted structured phase mask is used to phase modulate the collimated plane light wave to generate decrypted structured light. After that, the decrypted structured light generated after phase modulation by the decrypted structured phase mask begins to diffract forward to illuminate the preset ciphertext image, thereby obtaining the complex amplitude U of the decrypted structured light transmitted forward to the front surface of the ciphertext image. 0J (x0, y0). Afterwards, the decryption step J2 is performed. J2: Forward propagation decryption: The decrypted structured light after amplitude modulation of the ciphertext image continues to diffract and propagate forward, thereby obtaining the decrypted structured light forward to S forward The complex amplitude U of 1 1J (x1, y1). After that, the decrypted structured light continues to diffract and propagate forward, reaching S forward 2. S forward 3.......,S forward N and S forward N+1 (reconstructed image plane), so that the decrypted structured light is transmitted forward to S forward The complex amplitude U of n nJ (x n ,y n ), where n = 2, 3, ..., N + 1. Then, the decrypted structured light is extracted and saved and forwarded to the reconstructed image plane (S forward N+1) amplitude A (N+1)J (x N+1 ,y N+1 ), recorded as the reconstruction amplitude. Then, for A (N+1)J (x N+1 ,y N+1 ) to perform amplitude-phase conversion operation, thereby obtaining the conversion phase Afterwards, the decryption step J3 is performed. J3: Color holographic reconstruction decryption: converting phase Placed on Plane H, using unit amplitude and wavelength λ R A red collimated plane light wave with unit amplitude and wavelength λ G A green collimated plane light wave with unit amplitude and wavelength λ B The blue collimated plane light wave is incident on Plane H as the three-color decryption light wave at the same time. After phase modulation, the three-color decrypted light wave begins to propagate forward diffracted to Plane R, thereby obtaining the complex amplitude U of the three-color decrypted light wave forward to Plane R. RJ (x R ,y R ), U GJ (x R ,y R ), U BJ (x R ,y R ). After that, the amplitudes of the three-color decrypted light waves transmitted forward to Plane R are extracted and saved, and recorded as: R component decrypted amplitude A RJ (x R ,y R ), G component decryption amplitude A GJ (x R ,y R ), B component decryption amplitude A BJ (x R ,y R ). Then, the R component is decrypted into amplitude A RJ (x R ,y R ), G component decryption amplitude A GJ (x R ,y R ), B component decryption amplitude A BJ (x R ,y R ) are synthesized into a color image, which is the final color decrypted image. At this point, the decryption step is completed.

2. According to claim 1, a color image encryption method based on dynamic constrained holographic coding is characterized in that: The encryption step S1 in d B ,d G ,d R The following relationship must be satisfied: B :d G :d R =λ R :λ G :λ B .

3. The color image encryption method based on dynamic constrained holographic coding according to claim 1 is characterized in that: The phase distribution design formula for encrypting the structured phase mask in the encryption step S8 includes at least one editable optical parameter, which is used as a digital key.

4. The color image encryption method based on dynamic constrained holographic coding according to claim 1 is characterized in that: The phase distribution of the pure phase mask generated in the encryption step S13 is output as a grayscale phase map, which is used as a phase key.

5. The color image encryption method based on dynamic constrained holographic coding according to claim 1 is characterized in that: The decryption steps J1-J2 can be completed either digitally or in an optical-digital combination manner.

6. A color image encryption method based on dynamic constrained holographic coding according to claim 1 and claim 5, characterized in that: The optical decryption process in the decryption steps J1-J2 requires the use of a diffraction imaging system, including a laser 1 for providing incident light, a polarization modulator 2 for modulating the polarization state of light, a microscope objective 3 for beam expansion, a pinhole 4 for filtering, a convex lens 5 for collimation, a phase modulator 60 for carrying the phase distribution of the decrypted structured phase mask, an amplitude modulator 7 for carrying the ciphertext image, a phase modulator 61-6N for carrying the phase distribution of the pure phase mask, and an image sensor 8 for receiving the reconstructed amplitude.

7. A color image encryption method based on dynamic constrained holographic coding according to claim 1 and claim 6, characterized in that: In the diffraction imaging system, the polarization modulation device 2 is a polarizer or a half-wave plate; the pinhole 4 is placed at the image focus of the microscope objective 3, and the image focus of the microscope objective 3 coincides with the object focus of the convex lens 5; The amplitude modulation device 7 is an amplitude mask or an amplitude type spatial light modulator; the phase modulation devices 61-6N are phase masks or phase type spatial light modulators; the image sensor device 8 is a charge coupled device (CCD) or a complementary metal oxide semiconductor (CMOS), and the working mode is a grayscale mode.

8. The color image encryption method based on dynamic constrained holographic coding according to claim 1 is characterized in that: The decryption step J3 can be completed either digitally or optically.

9. A color image encryption method based on dynamic constrained holographic coding according to claim 1 and claim 8, characterized in that: The optical decryption process in the decryption step J3 requires the use of a color holographic reproduction system, including a red laser 11, a green laser 12, and a blue laser 13 for providing three-color reproduction light, a polarization modulation device 21-23 for modulating the polarization state of light, a dichroic mirror 91, 92 for beam combining, a microscope objective 3 for beam expansion, a pinhole 4 for filtering, a convex lens 5 for collimation, a phase modulation device 6 for carrying the conversion phase, and an image sensor device 8 for receiving the color decrypted image.

10. A color image encryption method based on dynamic constrained holographic coding according to claim 1 and claim 9, characterized in that: In the color holographic reproduction system, the polarization modulation devices 21-23 are polarizers or half-wave plates, which are respectively placed at the light outlets of the red laser 11, the green laser 12, and the blue laser 13, and are perpendicular to the corresponding optical axes; the dichroism of the dichroic mirror 91 is characterized by high transmittance for red and high reflection for green, and the dichroism of the dichroic mirror 92 is characterized by high transmittance for both red and green and high reflection for blue; the optical axis of the red laser 11 is perpendicular to the optical axis of the green laser 12 and passes through the center of the dichroic mirror 91, and the angles between the normal of the dichroic mirror 91 and the optical axes of the red laser 11 and the green laser 12 are 135° and 45° respectively; the dichroic mirror 92 is placed parallel to the dichroic mirror 91 and away from the red laser 11. Laser 11, the optical axis of the red laser 11 is perpendicular to the optical axis of the blue laser 13 and passes through the center of the dichroic mirror 92, and the angles between the normal of the dichroic mirror 92 and the optical axes of the red laser 11 and the blue laser 13 are 135° and 45° respectively; the microscope objective 3, the pinhole 4, the convex lens 5, the phase modulation device 6, and the image sensor device 8 are all located on the optical axis of the red laser 11 and perpendicular to the optical axis of the red laser 11; the pinhole 4 is placed on the image focus of the microscope objective 3, and the image focus of the microscope objective 3 and the object focus of the convex lens 5 coincide with each other; the image sensor device 8 is a charge coupled device (CCD) or a complementary metal oxide semiconductor (CMOS), and the working mode is a color mode.

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