Method for encrypting and decrypting multiple three-dimensional objects by using computer holography and phase-truncated asymmetric encryption

Abstract

This invention discloses a method for encrypting and decrypting multiple three-dimensional objects using computational holography and phase-truncated asymmetric encryption. The method includes: extracting the spectral components of the original image or conjugate image, and then processing them to obtain a digital hologram; generating a ciphertext digital hologram from the digital hologram using a phase-truncated nonlinear encryption system; encoding the ciphertext digital hologram as a phase template; obtaining a sum signal containing information about multiple three-dimensional objects, and then superimposing it with a complex random signal to form a sum signal in the form of complex noise; processing the complex noise sum signal to obtain an amplitude-type digital hologram ciphertext containing information about multiple three-dimensional objects, and then binarizing and encoding it to form the ciphertext for public transmission; constructing a decrypted digital hologram using corresponding interference suppression and compensation signals; obtaining a ciphertext digital hologram of a single three-dimensional object by spectral processing of the superimposed public ciphertext and decrypted digital hologram, and then decrypting it to obtain a plaintext digital hologram; reconstructing the original three-dimensional object from the spectral components of the original image or conjugate image of the plaintext digital hologram. This invention improves the noise resistance of the ciphertext.

Description

Technical Field

[0001] This invention relates to three-dimensional object encryption technology, and more particularly to a multi-three-dimensional object encryption and decryption method using computational holography and phase truncation asymmetric encryption. Background Technology

[0002] In today's information society, information security is becoming increasingly important. Digital carriers containing three-dimensional information of objects are an important component of multimedia information. Encrypting three-dimensional digital carriers is of great significance for improving information security and preventing information leakage and tampering. Summary of the Invention

[0003] The purpose of this invention is to solve the security problem of three-dimensional information digital carriers and to provide a multi-three-dimensional object encryption and decryption method using computational holography and phase truncation asymmetric encryption, which can improve the security of digital carriers containing three-dimensional information and enhance the anti-interference ability of public ciphertext.

[0004] The technical solution adopted in this invention is:

[0005] A computational holographic and phase-truncation asymmetric encryption and decryption method for multi-3D objects, comprising an encryption part and a decryption part;

[0006] Encryption steps:

[0007] S11, First, the spectral components of the original image or conjugate image are extracted from the off-axis digital hologram of the Fresnel diffraction light wave of the recorded object by Fourier transform and window function filtering.

[0008] S12, the filtered spectral components are processed by a computational holographic coding method involving horizontal conjugate symmetry and inverse Fourier transform to obtain a digital hologram with zero-order images removed;

[0009] S13, the obtained digital hologram is used to generate a ciphertext digital hologram through a phase-truncation nonlinear encryption system;

[0010] S14, use a phase recovery algorithm to encode the encrypted digital hologram into a phase template;

[0011] S15, the phase templates from the encrypted digital holograms of each three-dimensional object are superimposed to obtain a sum signal containing information of multiple three-dimensional objects, and then a complex random signal is superimposed to form a complex noise form sum signal;

[0012] S16, the complex noise form and signal are subjected to vertical conjugate symmetric arrangement and inverse Fourier transform computational holographic encoding to obtain amplitude-type digital hologram ciphertext containing information of multiple three-dimensional objects; the amplitude-type digital hologram ciphertext is binarized and encoded to form ciphertext for public transmission;

[0013] S17, using interference suppression signals corresponding to each three-dimensional object and public encrypted digital holography. Figure 2 The compensation signal for the quantization error caused by value-based quantization is used to construct the decrypted digital hologram;

[0014] Decryption steps:

[0015] S21, the spectrum of the overlay of the public ciphertext and the decrypted digital hologram is filtered by a window function and calculated by Fresnel diffraction to obtain the ciphertext digital hologram corresponding to a single three-dimensional object;

[0016] S22, obtain the plaintext digital hologram using the ciphertext digital hologram corresponding to a single three-dimensional object and the two private keys generated in the phase-truncation nonlinear encryption;

[0017] S23, extract the spectral components of the original image or conjugate image of the plaintext digital hologram, and reconstruct the original three-dimensional object by inverse Fourier transform and Fresnel diffraction of the spectral components.

[0018] Furthermore, the specific steps of S11 are as follows:

[0019] S11-1, Calculate and obtain the Fresnel diffraction light wave of the three-dimensional object U0(x0,y0;z) on the holographic recording plane, with the following expression:

[0020]

[0021] Where Δ represents the depth of the object along the z-axis, d is the distance between the object plane and the holographic recording plane, and λ is the wavelength of light.

[0022] S11-2, the intensity distribution of the off-axis digital hologram of the Fresnel diffracted light wave is represented as follows:

[0023] I = |U H | 2 +|R| 2 +U H Rexp[-j2π(f x x+f y y)]+U H * Rexp[j2π(f x x+f y y)] (1)

[0024] Among them, U H and Rexp[j2π(f x x+f y y)] represent the complex amplitude distributions of the object wave and the reference wave on the recording plane, respectively, and R represents the amplitude of the reference wave; |U H | 2 +|R| 2The self-interference term and the DC term are considered as background noise, and both are collectively referred to as the zero-order image component; U H Rexp[-j2π(f x x+f y y)] and U H * Rexp[j2π(f x x+f y y)] represents the original image and the conjugate image components, respectively, with * indicating conjugation; f x and f y f represents the spatial carrier frequency components along the x and y directions in the spatial frequency coordinate system. x and f y The value depends on the off-axis interference angle; x and y are the spatial coordinates of the recording plane.

[0025] S11-3, Perform a Fourier transform on the off-axis digital hologram to convert the hologram in the spatial domain into the Fourier transform domain, obtaining the spatial spectrum distribution of the hologram; the specific expression is as follows:

[0026] F{I}=F{|U H | 2}+F{|R| 2}+F{U H Rexp[-j2π(f x x+f y y)}+F{U H * Rexp[j2π(f x x+f y y)]} (3)

[0027] Wherein, the symbol F represents the Fourier transform;

[0028] S11-4, After Fourier transform, a window function is used to extract the spectral components of the original image or conjugate image. The specific expression is as follows:

[0029] ψ(u,v)=F[I(x,y)]W(u,v) (4)

[0030] Where F represents the Fourier transform, and W(u,v) is a window function that filters out the spectral components of the original or conjugate image of a 3D object.

[0031] Furthermore, either the original image or the conjugate image component can be used to reconstruct the complex amplitude distribution of the object light wave.

[0032] Furthermore, the specific expression for the real-valued digital hologram with the zero-order image removed in step S12 is as follows:

[0033] X(m,n)=F -1 [ξ(u,v)] (5)

[0034] Among them, F -1 This represents the inverse Fourier transform; ξ(u,v) is a spatial complex-valued signal, formed by rotating the complex-valued spectral component ψ(u,v) of the three-dimensional object and its conjugate by 180 degrees to obtain the complex-valued component R. 180° [ψ * [u,v] are arranged in a horizontal direction.

[0035] Specifically, let the size of ψ(u,v) be Mpixel×Mpixel, and the shaded areas represent the first row, first column and N+2 column with the value 0 respectively. The size of the signal after conjugate symmetry arrangement is (M+1)pixel*(2N+2)pixel.

[0036] Furthermore, the specific steps of step S13 are as follows:

[0037] S13-1, Asymmetric encryption system acquires the input digital hologram.

[0038] S13-2, Digital hologram multiplied by random phase template e jR1 Then, the phase and amplitude of the fractional Fourier transform are calculated, and the phase of the fractional Fourier transform is used as the first private key.

[0039] S13-3, multiply the amplitude of the fractional Fourier transform by the random phase template e. jR2 Then, the inverse fractional Fourier transform (IFFT) is calculated to obtain its phase and amplitude. The amplitude of the IFFT is used as the ciphertext C, and the phase of the IFFT is used as the second private key. The specific expression for obtaining ciphertext C through asymmetric encryption is as follows:

[0040]

[0041] Where X represents a digital hologram; F p This represents the p-th order fractional Fourier transform, where p is the fractional order of the fractional Fourier transform, and abs() represents the modulo operation; F -p This represents the p-th order fractional Fourier inverse transform.

[0042] The first private key A1 and the second private key A2 are represented as follows:

[0043]

[0044] Among them, F p This represents the p-th order fractional Fourier transform, where abs() represents the modulo operation and arg() represents the phase operation; F -p This represents the p-th order fractional Fourier inverse transform.

[0045] Furthermore, in S14, a phase template is generated using a phase retrieval algorithm. It includes the following steps:

[0046] S14-1, phase template The phase signal of the plane P1 is initially set to a random phase signal;

[0047] S14-2, calculate the Fresnel diffraction forward transform with wavelength λ and distance z to obtain the complex signal of the diffracted light wave at observation surface P2;

[0048] S14-3, the amplitude of the complex signal of the diffracted light wave from the observation surface P2 is represented by the encrypted image C corresponding to the i-th three-dimensional object. i The phase is replaced, and the diffracted light wave signal is obtained after amplitude constraint;

[0049] S14-4, calculate the complex amplitude signal of plane P1 by Fresnel inverse diffraction at a distance of z for the amplitude-constrained signal;

[0050] S14-5, constrain the amplitude of the diffracted light wave signal of plane P1 to 1 while preserving the phase, to obtain the complex signal of the object plane after amplitude constraint;

[0051] S14-6, the complex signal of the object plane after amplitude constraint is used as the initial object wavefunction for the next iteration, until the algorithm converges or the number of iterations is reached; the obtained optical wave signal of plane P1 is used as the phase template.

[0052] The encrypted image C of the three-dimensional object i i For example, at the end of the iteration, the generated phase template Satisfying the relation:

[0053]

[0054] Where, the symbol |.| represents the modulo operation, FrT represents the Fresnel diffraction operation, λ is the wavelength, and z represents the diffraction distance; C i This represents the encrypted image corresponding to the i-th 3D object.

[0055] Furthermore, the specific expression for the complex noise form of the signal in S15 is as follows:

[0056]

[0057] in, Representing the encrypted images C1, C2, ..., C respectively. N The corresponding phase template signal; R η η represents the random amplitude, and η represents the random phase.

[0058] Furthermore, the specific expression for the ciphertext in the form of a digital hologram in step S16 is as follows:

[0059] E1 = F -1 [ζ(x,y)] (11)

[0060] Where E1 represents ciphertext in the form of a digital hologram; F -1 Represents the first-order fractional Fourier inverse transform; ζ(x,y) is the complex-valued component R formed by rotating the complex noise form of the three-dimensional object and the signal S(x,y) and the conjugate component of the signal S(x,y) by 180 degrees. 180° [S * [x,y] are arranged vertically; S(x,y) is the specific expression of S;

[0061] Furthermore, the ciphertext E1 is binarized to form a binary digital hologram ciphertext E. B The specific expression is as follows:

[0062] E B =Bin(E1) (12)

[0063] Bin() represents the binarization operation.

[0064] Furthermore, the specific steps of S17 are as follows:

[0065] S17-1, based on interference suppression signal D and quantization error compensation signal E q The three-dimensional object decryption signal K1 is calculated; where the phase template signal corresponding to the current ciphertext image is subtracted from the complex noise form of the sum signal to obtain the interference suppression signal D of the current ciphertext image;

[0066] Specifically, taking the decryption of three-dimensional object 1 as an example, interference suppression signals and public encrypted digital holograms are used. Figure 2 The compensation signal for quantization error caused by value-based conversion is used to construct and decrypt the Fourier digital hologram.

[0067] Among them, interference suppression signal

[0068] Quantization error compensation signal E q =E1-E B (14)

[0069] The decryption signal K1 = D + E for 3D object 1 q (15)

[0070] S17-2, the three-dimensional object decryption signal K1 is arranged in a conjugate symmetric manner in the vertical direction to obtain Key1(x,y); Key1(x,y) is transformed by inverse Fourier transform to obtain the digital holographic key B1 for decryption;

[0071] Decryption using digital hologram key: B1 = F -1 (Key1(x,y)) (16)

[0072] Furthermore, the calculation expression for the encrypted digital hologram of a single three-dimensional object in S21 is as follows:

[0073]

[0074] Where C1 represents the current ciphertext signal; B1 represents the digital hologram key used to decrypt the current 3D object; E B The ciphertext represents the binary digital hologram; W represents the window function, F represents the Fourier transform, FrT represents the Fresnel diffraction operation, λ is the wavelength, and z represents the diffraction distance of the current 3D object.

[0075] Furthermore, the ciphertext C1 in S22 is sent to the decryption system to obtain the plaintext digital hologram. Figure X 1. The specific calculation process is as follows:

[0076] X1=|F -p [f p (C1×A2))×A1]| (18)

[0077] Where A1 and A2 are two private keys generated in the phase-truncated asymmetric encryption system; F p and F -p They represent the p-order fractional Fourier forward transform and the p-order fractional Fourier inverse transform, respectively.

[0078] Furthermore, the calculation expression for the 3D object reconstruction signal RO in S23 is as follows:

[0079]

[0080] Where F represents Fourier transform, W represents the window function used to filter out the spectral components of a three-dimensional object, FrT represents Fresnel diffraction operation, λ is the wavelength, and d1 represents the diffraction distance.

[0081] Furthermore, the correlation coefficient (NC) is used to evaluate the quality of the reconstructed 3D object.

[0082]

[0083] Where O represents the three-dimensional object reconstructed from the off-axis digital hologram, RO is the three-dimensional object decrypted using the decryption digital hologram key B1 and the private keys A1 and A2 generated in the phase-truncated asymmetric encryption system and the public encrypted digital hologram E; E represents the mathematical expectation.

[0084] This invention employs the above technical solution, extracting the spectral components of the original or conjugate image from an off-axis digital hologram recording Fresnel diffraction light waves of a recording object through Fourier transform and window function filtering; the filtered spectral components are then processed using a computational holographic encoding method involving horizontal conjugate symmetry and inverse Fourier transform to obtain a digital hologram with zero-order images removed; the obtained digital hologram is then processed through a phase-truncation nonlinear encryption system to generate a ciphertext digital hologram; the ciphertext digital hologram is encoded into a phase template using a phase recovery algorithm; the phase templates from the ciphertext digital holograms of various three-dimensional objects are superimposed to obtain a sum signal containing information about multiple three-dimensional objects; this sum signal is then superimposed with a complex random signal to form a sum signal in the form of complex noise. The complex noise sum signal is then processed using computational holographic encoding involving vertical conjugate symmetry and inverse Fourier transform to obtain an amplitude-type digital hologram ciphertext containing information about multiple three-dimensional objects. This amplitude-type digital hologram ciphertext is binarized to form ciphertext for public transmission. Interference suppression signals corresponding to each three-dimensional object and public ciphertext digital holograms are used. Figure 2 The compensation signal for quantization errors introduced by value-based quantization is used to construct the decrypted digital hologram. The spectrum of the superimposed public ciphertext and decrypted digital hologram is filtered by a window function and calculated using Fresnel diffraction to obtain the ciphertext digital hologram corresponding to a single three-dimensional object. The plaintext digital hologram is obtained using this ciphertext digital hologram and two private keys generated in phase-truncated nonlinear encryption. The spectral components of the original image or conjugate image of the plaintext digital hologram are extracted, and these spectral components are then subjected to inverse Fourier transform and Fresnel diffraction to reconstruct the original three-dimensional object.

[0085] This invention offers excellent security and noise resistance. The loss of any decryption key will cause the reconstruction of the 3D object to fail. Using computational holography to generate public ciphertext allows for the extraction of a ciphertext digital hologram corresponding to a single 3D object from the public ciphertext using only a single decrypted digital hologram, reducing the burden of key management. Furthermore, the binarization of the public ciphertext further enhances its noise resistance. Attached Figure Description

[0086] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments;

[0087] Figure 1 This is a flowchart of the encryption algorithm of the present invention;

[0088] Figure 2 This is a flowchart of the decryption algorithm of the present invention;

[0089] Figure 3 This is the off-axis holographic recording optical path of the present invention;

[0090] Figure 4 This is a schematic diagram of the horizontally conjugate symmetrical arrangement of the spectral components of the present invention;

[0091] Figure 5This is a block diagram illustrating the phase-truncation asymmetric encryption principle of the present invention.

[0092] Figure 6 This is a block diagram illustrating the principle of the phase recovery algorithm of the present invention;

[0093] Figure 7 This is the virtual optical path diagram used in the phase retrieval algorithm of this invention;

[0094] Figure 8 This is a schematic diagram of the vertically conjugate symmetrical arrangement of complex signals according to the present invention;

[0095] Figure 9 This is a schematic diagram of the vertically conjugate symmetrical arrangement of the decryption signals of the present invention;

[0096] Figure 10 The present invention provides a decryption system for decrypting ciphertext C into plaintext X.

[0097] Figure 11 The original three-dimensional object, the off-axis Fresnel digital hologram, and the reconstructed three-dimensional object of this invention;

[0098] Figure 12 The ciphertext generated by the Fourier digital hologram and phase-truncated asymmetric encryption system (PTFT) that records the spectral information of each three-dimensional object in this invention;

[0099] Figure 13 This is the common binary encrypted digital hologram of the present invention;

[0100] Figure 14 The present invention reconstructs a three-dimensional object image using a decrypted digital hologram and two private keys.

[0101] Figure 15 The reconstruction images of the three-dimensional object 1 under different combinations of decryption keys in this invention and their similarity to the three-dimensional object reconstructed from off-axis digital holograms;

[0102] Figure 16 The decryption results and similarity of the binary encrypted digital holograms under various noise conditions are presented in this invention.

[0103] Figure 17 This invention provides the decryption results and similarity of non-binary encrypted digital holograms under various noise conditions. Implementation

[0104] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings.

[0105] like Figures 1 to 17As shown in one example, the present invention discloses a method for encrypting and decrypting multiple three-dimensional objects using computational holography and phase truncation asymmetric encryption, which includes an encryption part and a decryption part;

[0106] like Figure 1 As shown, the encryption steps are as follows:

[0107] S11, First, the spectral components of the original image or conjugate image are extracted from the off-axis digital hologram of the Fresnel diffraction light wave of the recorded object by Fourier transform and window function filtering.

[0108] S12, the filtered spectral components are processed by a computational holographic coding method involving horizontal conjugate symmetry and inverse Fourier transform to obtain a digital hologram with zero-order images removed;

[0109] S13, the obtained digital hologram is used to generate a ciphertext digital hologram through a phase-truncation nonlinear encryption system;

[0110] S14, use a phase recovery algorithm to encode the encrypted digital hologram into a phase template;

[0111] S15, the phase templates from the encrypted digital holograms of each three-dimensional object are superimposed to obtain a sum signal containing information of multiple three-dimensional objects, and then a complex random signal is superimposed to form a complex noise form sum signal;

[0112] S16, the complex noise form and signal are subjected to vertical conjugate symmetric arrangement and inverse Fourier transform computational holographic encoding to obtain amplitude-type digital hologram ciphertext containing information of multiple three-dimensional objects; the amplitude-type digital hologram ciphertext is binarized and encoded to form ciphertext for public transmission;

[0113] S17, using interference suppression signals corresponding to each three-dimensional object and public encrypted digital holography. Figure 2 The compensation signal for the quantization error caused by value-based quantization is used to construct the decrypted digital hologram;

[0114] like Figure 2 As shown, the decryption steps are as follows:

[0115] S21, the spectrum of the overlay of the public ciphertext and the decrypted digital hologram is filtered by a window function and calculated by Fresnel diffraction to obtain the ciphertext digital hologram corresponding to a single three-dimensional object;

[0116] S22, obtain the plaintext digital hologram using the ciphertext digital hologram corresponding to a single three-dimensional object and the two private keys generated in the phase-truncation nonlinear encryption;

[0117] S23, extract the spectral components of the original image or conjugate image of the plaintext digital hologram, and reconstruct the original three-dimensional object by inverse Fourier transform and Fresnel diffraction of the spectral components.

[0118] Furthermore, the intensity distribution of the off-axis digital hologram of the Fresnel diffracted light wave in S11 is represented as follows:

[0119] I = |U H | 2 +|R| 2 +U H Rexp[-j2π(f x x+f y y)]+U H * Rexp[j2π(f x x+f y y)] (1)

[0120] Among them, U H and Rexp[j2π(f x x+f y y)] represent the complex amplitude distributions of the object wave and the reference wave on the recording plane, respectively, and R represents the amplitude of the reference wave; |U H | 2 +|R| 2 The self-interference term and the DC term are considered as background noise, and both are collectively referred to as the zero-order image component; U H Rexp[-j2π(f x x+f y y)] and U H * Rexp[j2π(f x x+f y [y)] represents the original image and the conjugate image components, respectively. Either the original image or the conjugate image component can be used to reconstruct the complex amplitude distribution of the object light wave; f x and f y f represents the spatial carrier frequency components along the x and y directions in the spatial frequency coordinate system. x and f y The value depends on the off-axis interference angle, where x and y are the spatial coordinates of the recording plane.

[0121] Please see Figure 3 Let the distance between the object plane and the holographic recording plane be d, and the wavelength of light be λ. The Fresnel diffracted light wave of the three-dimensional object U0(x0,y0;z) on the holographic recording plane can be represented by formula (2).

[0122]

[0123] Where Δ represents the depth of the object along the z-axis.

[0124] The Fourier transform of a hologram can be expressed as:

[0125] F{I}=F{|U H |2}+F{|R| 2}+F{U H Rexp[-j2π(f x x+f y y)}+F{U H * Rexp[j2π(f x x+f y y)]}(3)

[0126] Here, the symbol F represents the Fourier transform. Using the operation of F{I}, the hologram in the spatial domain is transformed into the Fourier transform domain, and the spatial spectrum distribution of the hologram is obtained.

[0127] The spatial spectral distribution of a hologram contains original image and conjugate image components, either of which can be used to reconstruct the complex amplitude distribution of the object light wave. To reduce the size of the off-axis digital hologram, the original image or conjugate image spectral components are extracted using a rectangular window function after Fourier transform of I(x,y), which can be expressed by formula (4).

[0128] ψ(u,v)=F[I(x,y)]W(u,v) (4)

[0129] Where F represents the Fourier transform, and W(u,v) is a window function that filters out the spectral components of the original or conjugate image of a 3D object.

[0130] The filtered spectral components are first arranged in a conjugate symmetric pattern in the horizontal direction, and then subjected to an inverse Fourier transform to obtain a real-valued Fourier digital hologram. The conjugate symmetric arrangement is as follows: Figure 4 As shown. Figure 4 In this context, ψ(u,v) represents the complex-valued spectral signal of a three-dimensional object, and R... 1800 [ψ * [u,v] represents the complex-valued component formed by rotating the conjugate component of the complex-valued spectral signal by 180 degrees. Let ψ(u,v) be M pixels × N pixels, and the shaded areas represent the first row, first column, and N+2th column with values ​​of 0, respectively. The signal size after conjugate symmetry arrangement is (M+1) pixels * (2N+2) pixels.

[0131] Then, the inverse Fourier transform of the signal after conjugate symmetry is calculated to obtain a real-valued digital hologram corresponding to the three-dimensional object with the zero-order image removed.

[0132] X(m,n)=F -1 [ξ(u,v)] (5)

[0133] Among them, F -1This represents the inverse Fourier transform; ξ(u,v) is a spatial complex-valued signal, formed by rotating the complex-valued spectral component ψ(u,v) of the three-dimensional object and its conjugate by 180 degrees to obtain the complex-valued component R. 1800 [ψ(u,v)] are arranged in a horizontal direction.

[0134] Digital holography using phase-truncation nonlinear encryption (PTFT) method Figure X Encrypted as ciphertext C.

[0135] Please see Figure 5 , Figure 5 This is a block diagram illustrating the principle of using a phase-truncation asymmetric encrypted digital hologram.

[0136] The input to the asymmetric encryption system is a digital hologram. Figure X The digital hologram is multiplied by a random phase template e jR1 The fractional Fourier transform is then calculated, and the resulting phase is used as private key 1. The magnitude of the calculated fractional Fourier transform is then multiplied by the random phase template e. jR2 Then, the fractional Fourier inverse transform is calculated, and the obtained amplitude is used as the ciphertext C, and the obtained phase is used as the private key 2.

[0137] The asymmetric encryption process can be expressed by the following formula:

[0138]

[0139] Where F p This represents the p-th order fractional Fourier transform, and abs() represents the modulo operation. -p This represents the p-th order fractional Fourier inverse transform.

[0140] Private keys A1 and A2 are as follows:

[0141]

[0142] Where F p This represents the p-th order fractional Fourier transform, where abs() represents the modulo operation and arg() represents the phase operation. -p This represents the p-th order fractional Fourier inverse transform.

[0143] The encrypted image C is encoded using a phase retrieval algorithm and used as a phase template. The principle block diagram of the phase retrieval algorithm is as follows: Figure 6 As shown.

[0144] Please see Figure 6 and Figure 7 Phase templates are generated using a phase retrieval algorithm. It includes the following steps:

[0145] (1) The phase signal of the P1 plane where the phase template is located is initially set to a random phase signal;

[0146] (2) Calculate the Fresnel diffraction forward transform with wavelength λ and distance z to obtain the complex signal of the diffracted light wave at the observation surface P2;

[0147] (3) The amplitude of the complex signal of the diffracted light wave at the observation surface P2 is represented by the encrypted image C corresponding to the i-th three-dimensional object. i The phase is replaced, and the diffracted light wave signal is obtained after amplitude constraint;

[0148] (4) Calculate the complex amplitude signal of the observation surface P1 by Fresnel inverse diffraction at a distance of z for the signal after amplitude constraint;

[0149] (5) The amplitude of the diffracted light wave signal in plane P1 is constrained to 1, and the phase is preserved to obtain the complex signal of the object plane after amplitude constraint.

[0150] (6) The complex signal is used as the initial object wave function for the next iteration until the algorithm converges or the number of iterations is reached; the obtained optical wave signal of the P1 plane is used as the phase template.

[0151] The encrypted image C of the three-dimensional object i i For example, at the end of the iteration, the generated phase template Satisfying the relation:

[0152]

[0153] Where the symbol |.| represents the modulo operation, FrT represents the Fresnel diffraction operation, λ is the wavelength, and z represents the diffraction distance. C i This represents the encrypted image corresponding to the i-th 3D object.

[0154] The phase templates from each three-dimensional object are superimposed to obtain a sum signal containing the spectral information of multiple three-dimensional objects. This sum signal is then superimposed with a complex random signal to form a sum signal in the form of complex noise. The sum signal in the form of complex noise is represented by formula (10).

[0155]

[0156] in It is related to the encrypted images C1, C2, C N The corresponding phase template signal. R η η represents the random amplitude, and η represents the random phase.

[0157] To form a public ciphertext in real-valued form, the complex signal S is processed according to... Figure 8The method shown performs a conjugate symmetric arrangement, where the shaded area represents the first row, first column, and M+2 rows with values ​​of 0. Let the size of the complex signal S be M*N pixels. The size of the signal ζ(x,y) after vertical conjugate symmetry arrangement is (2M+2)*(N+1) pixels.

[0158] The inverse Fourier transform of the complex signal after conjugate symmetry arrangement is calculated to obtain the ciphertext E1 in the form of a digital hologram.

[0159] E1 = F -1 [ζ(u,v)] (11)

[0160] To improve the anti-interference performance of the ciphertext, the ciphertext E1 is binarized to form a binary digital hologram ciphertext E. B This encrypted text will be transmitted publicly as public encrypted text.

[0161] E B =Bin(E1) (12)

[0162] Bin() represents the binary operation.

[0163] Taking the decryption of a three-dimensional object 1 as an example, interference suppression signals and public encrypted digital holograms are used. Figure 2 The compensation signal for the quantization error caused by quantization is used to construct the decrypted Fourier digital hologram. The interference suppression signal D and the quantization error compensation signal Eq are shown in formulas (13) and (14) respectively, and formula (15) is the decryption signal of the three-dimensional object 1.

[0164] Interference suppression signal

[0165] Quantization error compensation signal E q =E1-E B (14)

[0166] The decryption signal K1 = D + E for 3D object 1 q (15)

[0167] The decryption complex signal K1 of the three-dimensional object 1 is... Figure 9 The Key1(x,y) is obtained by arranging the elements in a conjugate symmetric manner in the vertical direction. The shaded areas represent the first row, first column, and M+2 row, where each element takes a value of 0. After inverse Fourier transform, Key1(x,y) yields the digital holographic key B1 used for decryption.

[0168] Calculate the inverse Fourier transform of Key1 to obtain the digital holographic key B1 required to decrypt 3D object 1.

[0169] B1 = F -1 (Key1(x,y)) (16)

[0170] Taking the decryption process of three-dimensional object 1 as an example, the encrypted digital hologram E is first calculated. B The Fourier transform of the sum signal and the decryption key B1 of the digital hologram is then used to extract the spectral components of the sum signal using a window function. Quantity, The ciphertext signal C1 corresponding to the plaintext image X1 is then obtained by Fresnel diffraction. The decryption process is shown in formula (17).

[0171]

[0172] Where E B For the encrypted digital hologram, B1 is the key for decrypting the digital hologram corresponding to the three-dimensional object 1, W represents the window function, F represents the Fourier transform, FrT represents the Fresnel diffraction operation, λ is the wavelength, and z represents the diffraction distance.

[0173] Send the ciphertext C1 into the following... Figure 10 The decryption system shown obtains the plaintext image X1.

[0174] The process of calculating the plaintext image X1 by sending the ciphertext C1 into the decryption system is as follows:

[0175] X1=|F -p [F p (C1×A2))×A1]| (18)

[0176] A1 and A2 are two private keys generated in the phase-truncated asymmetric encryption system. p and F -p They represent the p-order fractional Fourier forward transform and the p-order fractional Fourier inverse transform, respectively.

[0177] Calculate the Fourier transform for X1, then use a window function to extract the spectral components of the original image or conjugate image. Calculate the inverse Fourier transform for the extracted spectral components to obtain the Fresnel diffracted light wave of the three-dimensional object. The original three-dimensional object can be reconstructed by Fresnel diffraction of the diffracted light wave.

[0178] The 3D object reconstruction signal RO in the CCD plane is represented by formula (19).

[0179]

[0180] Where F represents the Fourier transform, W represents the window function used to filter out the spectral components of the three-dimensional object, FrT represents the Fresnel diffraction operation, λ is the wavelength, and d i Indicates the diffraction distance.

[0181] The quality of the reconstructed 3D object is evaluated using the correlation coefficient NC shown in formula (20).

[0182]

[0183] Where O represents the three-dimensional object reconstructed from the off-axis digital hologram, and RO is the three-dimensional object decrypted using the decryption digital hologram key B1, the private keys A1 and A2 generated in the phase-truncation asymmetric encryption system, and the public encrypted digital hologram E.

[0184] Please see Figure 11 , Figure 11 (a) represents three three-dimensional objects, each 128*128 pixels in size; (b) represents an off-axis Fresnel digital hologram recording the three-dimensional objects, each 512*512 pixels in size; (c) represents three three-dimensional objects reconstructed from the off-axis hologram. The recording parameters for the off-axis digital hologram recording the three-dimensional objects are set as follows: (1) Three-dimensional object 1: wavelength λ = 532nm, distance between the object and the holographic recording plane 1000mm; (2) Three-dimensional object 2: wavelength λ = 532nm, distance between the object and the holographic recording plane 1100mm; (3) Three-dimensional object 3: wavelength λ = 532nm, distance between the object and the holographic recording plane 1200mm.

[0185] Fourier digital holograms recording the spectral information of each three-dimensional object and ciphertext generated by a phase-truncated asymmetric encryption system (PTFT) are as follows: Figure 12 As shown.

[0186] Please see Figure 13 , Figure 13 It is a public binary encrypted digital image, with a size of 260*259 pixels.

[0187] Please see Figure 14 , Figure 14 It is a hologram with 256 grayscale levels for decryption calculation corresponding to three-dimensional object 1, three-dimensional object 2 and three-dimensional object 3.

[0188] Please see Figure 15 , Figure 15 This represents the reconstructed image of 3D object 1 under different key combinations and its similarity to the 3D object reconstructed from the off-axis digital hologram. Here, E represents the common binary digital hologram; B1 is the digital hologram used for decryption; and A1 and A2 represent the two private keys in the asymmetric encryption system. The decryption results show that when private key A1 or A2 is missing, the useful information of the 3D object cannot be decrypted, while the absence of private key B1 only allows for the decryption of the fuzzy outline of the 3D object.

[0189] Please see Figure 16 First, various types of noise are superimposed on the binary encrypted digital hologram, and then the noisy digital hologram is processed. Figure 2After value processing, the reconstructed image of the 3D object 1 obtained by combining the key is used to calculate the similarity between the obtained reconstructed image and the 3D object reconstructed from the off-axis digital hologram. It can be seen that the binary encrypted digital hologram has strong robustness to Gaussian noise, multiplicative interference, and Poisson noise.

[0190] Please see Figure 17 First, various types of noise are superimposed on the unbindified encrypted digital hologram. After filtering the noisy digital hologram, the reconstructed image of the 3D object 1 is obtained by combining it with the key. Then, the similarity between the obtained reconstructed image and the 3D object reconstructed from the off-axis digital hologram is calculated. Figure 16 In comparison, it can be seen that under the same intensity of noise superimposed, the unbindified ciphertext digital hologram can only decipher the blurry outline of a three-dimensional object. Therefore, binarization of the encrypted digital hologram improves the anti-interference capability of the public ciphertext.

[0191] This invention employs the above technical solution, extracting the spectral components of the original or conjugate image from an off-axis digital hologram recording Fresnel diffraction light waves of an object using Fourier transform and window function filtering; the filtered spectral components are then processed using a computational holographic encoding method involving horizontal conjugate symmetry and inverse Fourier transform to obtain a digital hologram with zero-order images removed; the obtained digital hologram is then processed using a phase-truncation nonlinear encryption system to generate a ciphertext digital hologram; the ciphertext digital hologram is encoded into a phase template using a phase recovery algorithm; the phase templates from the ciphertext digital holograms of various three-dimensional objects are superimposed to obtain a sum signal containing information about multiple three-dimensional objects; this sum signal is then superimposed with a complex random signal to form a sum signal in the form of complex noise. The complex noise sum signal is then processed using computational holographic encoding involving vertical conjugate symmetry and inverse Fourier transform to obtain an amplitude-type digital hologram ciphertext containing information about multiple three-dimensional objects. This amplitude-type digital hologram ciphertext is binarized to form ciphertext for public transmission. Interference suppression signals corresponding to each three-dimensional object and public ciphertext digital holograms are used. Figure 2 The compensation signal for quantization errors introduced by value-based quantization is used to construct the decrypted digital hologram. The spectrum of the superimposed public ciphertext and decrypted digital hologram is filtered by a window function and calculated using Fresnel diffraction to obtain the ciphertext digital hologram corresponding to a single three-dimensional object. The plaintext digital hologram is obtained using this ciphertext digital hologram and two private keys generated in phase-truncated nonlinear encryption. The spectral components of the original image or conjugate image of the plaintext digital hologram are extracted, and these spectral components are then subjected to inverse Fourier transform and Fresnel diffraction to reconstruct the original three-dimensional object.

[0192] This invention offers excellent security and noise resistance. The loss of any decryption key will cause the reconstruction of the 3D object to fail. Using computational holography to generate public ciphertext allows for the extraction of a ciphertext digital hologram corresponding to a single 3D object from the public ciphertext using only a single decrypted digital hologram, reducing the burden of key management. Furthermore, the binarization of the public ciphertext further enhances its noise resistance.

[0193] Obviously, the described embodiments are only a part of the embodiments of this application, not all of them. Without conflict, the embodiments and features in the embodiments of this application can be combined with each other. The components of the embodiments of this application described and illustrated herein can generally be arranged and designed in various different configurations. Therefore, the detailed description of the embodiments of this application is not intended to limit the scope of the claimed application, but merely to illustrate selected embodiments of this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without inventive effort are within the scope of protection of this application.

Claims

1. A method for encrypting and decrypting multi-3D objects using computational holography and phase truncation asymmetric encryption, characterized by: It includes an encryption part and a decryption part; The encryption steps are as follows: S11, First, the spectral components of the original image or conjugate image are extracted from the off-axis digital hologram of the Fresnel diffraction light wave of the recorded object by Fourier transform and window function filtering. S12, the filtered spectral components are processed by a computational holographic coding method involving horizontal conjugate symmetry and inverse Fourier transform to obtain a digital hologram with zero-order images removed; S13, the obtained digital hologram is used to generate a ciphertext digital hologram through a phase-truncation nonlinear encryption system; the specific steps of step S13 are as follows: S13-1, Asymmetric encryption system acquires the input digital hologram. S13-2, Digital hologram multiplied by random phase template Then, the fractional Fourier transform is calculated to obtain the phase and amplitude of the fractional Fourier transform, and the phase of the fractional Fourier transform is used as the first private key. S13-3, multiply the amplitude of the fractional Fourier transform by the random phase template. Then, the inverse fractional Fourier transform (IFFT) is calculated to obtain its phase and amplitude. The amplitude of the IFFT is used as the ciphertext C, and the phase of the IFFT is used as the second private key. Specifically, the specific expression for obtaining ciphertext C through asymmetric encryption is as follows: Where X represents a digital hologram; F p This represents the p-th order fractional Fourier transform, where p is the fractional order of the fractional Fourier transform, and abs() represents the modulo operation; F -p This represents the p-th order fractional inverse Fourier transform; The first private key A1 and the second private key A2 are represented as follows: Among them, F p This represents the p-th order fractional Fourier transform, where abs() represents the modulo operation and arg() represents the phase operation; F -p This represents the p-th order fractional inverse Fourier transform; S14, use a phase recovery algorithm to encode the encrypted digital hologram into a phase template; S15, the phase templates from the encrypted digital holograms of each three-dimensional object are superimposed to obtain a sum signal containing information of multiple three-dimensional objects, and then a complex random signal is superimposed to form a complex noise form sum signal; S16, the complex noise form and signal are subjected to vertical conjugate symmetric arrangement and inverse Fourier transform computational holographic encoding to obtain amplitude-type digital hologram ciphertext containing information of multiple three-dimensional objects; the amplitude-type digital hologram ciphertext is binarized and encoded to form ciphertext for public transmission; S17, construct the decrypted digital hologram using the interference suppression signal corresponding to each three-dimensional object and the compensation signal for the quantization error caused by the binarization of the public ciphertext digital hologram; The decryption steps are as follows: S21, the spectrum of the overlay of the public ciphertext and the decrypted digital hologram is filtered by a window function and calculated by Fresnel diffraction to obtain the ciphertext digital hologram corresponding to a single three-dimensional object; S22, obtain the plaintext digital hologram using the ciphertext digital hologram corresponding to a single three-dimensional object and the two private keys generated in the phase-truncation nonlinear encryption; S23, extract the spectral components of the original image or conjugate image of the plaintext digital hologram, and reconstruct the original three-dimensional object by inverse Fourier transform and Fresnel diffraction of the spectral components.

2. The multi-dimensional object encryption and decryption method based on computational holography and phase truncation asymmetric encryption according to claim 1, characterized in that: The specific steps of S11 are as follows: S11-1, Calculate and obtain the Fresnel diffraction light wave of the three-dimensional object U0(x0,y0;z) on the holographic recording plane. The specific expression is as follows: Where Δ represents the depth of the object along the z-axis, d is the distance between the object plane and the holographic recording plane, and λ is the wavelength of light. S11-2, the intensity distribution of the off-axis digital hologram of Fresnel diffracted light waves is represented as: I=|U H | 2 +|R| 2 +U H Rexp[-j2π(f x x+f y y)]+U H * Rexp[j2π(f x x+f y y)] (1) Among them, U H and Rexp[j2π(f x x+f y y)] represent the complex amplitude distributions of the object wave and the reference wave on the recording plane, respectively, and R represents the amplitude of the reference wave; |U H | 2 +|R| 2 The self-interference term and the DC term are considered as background noise, and both are collectively referred to as the zero-order image component; U H Rexp[-j2π(f x x+f y y)] and U H * Rexp[j2π(f x x+f y y)] represents the original image and the conjugate image components, respectively, with * indicating conjugation; f x and f y f represents the spatial carrier frequency components along the x and y directions in the spatial frequency coordinate system. x and f y The value depends on the off-axis interference angle; x and y are the spatial coordinates of the recording plane. S11-3, Perform a Fourier transform on the off-axis digital hologram to convert the hologram in the spatial domain into the Fourier transform domain, obtaining the spatial spectrum distribution of the hologram; the specific expression is as follows: F{I}=F{|U H | 2 }+F{|R| 2 }+F{U H Rexp[-j2π(f x x+f y y)}+F{U H *Rexp[j2π(f x x+f y y)]} (3) Wherein, the symbol F represents the Fourier transform; S11-4, After Fourier transform, a window function is used to extract the spectral components of the original or conjugate image of the 3D object. The specific expression is as follows: ψ(u,v)=F[I(x,y)]W(u,v) (4) Where F represents the Fourier transform, and W(u,v) is a window function that filters out the spectral components of the original or conjugate image of a 3D object.

3. The multi-dimensional object encryption and decryption method based on computational holography and phase truncation asymmetric encryption according to claim 1, characterized in that: The specific expression for the real-valued digital hologram with the zero-order image removed in step S12 is as follows: X(m,n)=F -1 [ξ(u,v)] (5) Among them, F -1 The expression represents the inverse Fourier transform; ξ(u,v) is a spatial complex-valued signal, which is the complex-valued component R formed by rotating the original or conjugate image spectral component ψ(u,v) of the three-dimensional object and its conjugate by 180 degrees. 1800 [ψ * [u,v] are arranged in a horizontal direction.

4. The multi-dimensional object encryption and decryption method based on computational holography and phase truncation asymmetric encryption according to claim 1, characterized in that: In S14, a phase template is generated using a phase retrieval algorithm. It includes the following steps: S14-1, phase template The phase signal of the plane P1 is initially set to a random phase signal; S14-2, calculate the Fresnel diffraction forward transform with wavelength λ and distance z′ to obtain the complex signal of the diffracted light wave at observation surface P2; S14-3, the amplitude of the complex signal of the diffracted light wave from the observation surface P2 is represented by the encrypted image C corresponding to the i-th three-dimensional object. i The phase is replaced, and the diffracted light wave signal is obtained after amplitude constraint; S14-4, calculate the complex amplitude signal of plane P1 by Fresnel inverse diffraction at a distance of z′ on the amplitude-constrained signal; S14-5, constrain the amplitude of the diffracted light wave signal of plane P1 to 1 while preserving the phase, to obtain the complex signal of the object plane after amplitude constraint; S14-6, the complex signal of the object plane after amplitude constraint is used as the initial object wavefunction for the next iteration, until the algorithm converges or the number of iterations is reached; the obtained optical wave signal of plane P1 is used as the phase template. Specifically, the encrypted image C of any three-dimensional object i i The generated phase template Satisfying the relation: Where, the symbol |.| represents the modulo operation, FrT represents the Fresnel diffraction operation, λ is the wavelength, and z′ represents the diffraction distance; C i This represents the encrypted image corresponding to the i-th 3D object.

5. The multi-dimensional object encryption and decryption method based on computational holography and phase truncation asymmetric encryption according to claim 1, characterized in that: The specific expressions for the complex noise form and the signal in S15 are as follows: in, Representing the encrypted images C1, C2, ..., c respectively. N The corresponding phase template signal; R η η represents the random amplitude, and η represents the random phase.

6. The multi-dimensional object encryption and decryption method based on computational holography and phase truncation asymmetric encryption according to claim 1, characterized in that: The specific expression for the ciphertext in the form of a digital hologram in step S16 is as follows: E1=F -1 [ζ(x,y)] (11) Where E1 represents ciphertext in the form of a digital hologram; F -1 Represents the inverse Fourier transform; ζ(x,y) is the complex-valued component R formed by rotating the complex noise form of the three-dimensional object and the signal S(x,y) and the conjugate component of the signal S(x,y) by 180 degrees. 1800 [S * [x,y] are arranged vertically; S(x,y) is the specific expression of S; Binarize the ciphertext E1 to form a binary digital hologram ciphertext E B The specific expression is as follows: E B =Go(E1) (12) Bin() represents the binarization operation.

7. The multi-dimensional object encryption and decryption method based on computational holography and phase truncation asymmetric encryption according to claim 1, characterized in that: The specific steps for S17 are as follows: S17-1, based on interference suppression signal D and quantization error compensation signal E q The current 3D object decryption signal K1 is calculated. The interference suppression signal D of the current ciphertext image is obtained by subtracting the complex noise form of the phase template signal corresponding to the current ciphertext image. The quantization error compensation signal is: E q =E1-E B (14) The decryption signal for 3D object 1 is: K1 = D + E q (15) S17-2, the decryption signal K1 of the three-dimensional object is arranged in a conjugate symmetric manner in the vertical direction to obtain Key1(x,y); Key1(x,y) is then subjected to an inverse Fourier transform to obtain the digital holographic key B1 for decryption, and the specific expression is as follows: B1=F -1 (Key1(x,y)) (16)。 8. The multi-dimensional object encryption and decryption method based on computational holography and phase truncation asymmetric encryption according to claim 1, characterized in that: The calculation expression for the encrypted digital hologram of a single three-dimensional object in S21 is as follows: Where C1 represents the encrypted image; B1 represents the digital holographic key used to decrypt the current 3D object; E B This represents the ciphertext of a binary digital hologram; W represents the window function, F represents the Fourier transform, FrT represents the Fresnel diffraction operation, λ is the wavelength, z′ represents the diffraction distance of the current 3D object, and the symbol |.| represents the modulus operation; The encrypted image C1 in S22 is sent to the decryption system to obtain the plaintext digital hologram X1. The specific calculation process is as follows: X1=|F -p [F p (C1×A2)×A1]| (18) Where A1 and A2 are two private keys generated in the phase-truncated asymmetric encryption system; F p and F -p They represent the p-order fractional Fourier forward transform and the p-order fractional Fourier inverse transform, respectively.

9. The multi-dimensional object encryption and decryption method based on computational holography and phase truncation asymmetric encryption according to claim 1, characterized in that: The calculation expression for the 3D object reconstruction signal RO in S23 is as follows: Where F represents Fourier transform, W represents the window function used to filter out the spectral components of a three-dimensional object, FrT represents Fresnel diffraction operation, λ is the wavelength, and d1 represents the diffraction distance; Furthermore, the quality of the reconstructed 3D object is evaluated using the correlation coefficient (NC). Where O represents the 3D object reconstructed from the off-axis digital hologram, and RO is the result of the private keys A1 and a2 generated using the decryption digital hologram key B1 and the phase-truncated asymmetric encryption system, along with the public encrypted digital hologram E. B The deciphered 3D object; E represents the expected value.

Images