Three-dimensional multi-image encryption method based on multi-dimensional multiplexing hologram

Abstract

The invention discloses a three-dimensional multi-image encryption method based on a multi-dimensional multiplexing hologram. Comprising the following steps: an encryption step: encrypting a plurality of three-dimensional plaintexts and corresponding OAM information into a phase type holographic ciphertext by using a chaotic radial Hilbert mask generation technology, a multi-dimensional parameter selection hologram generation technology and a multi-dimensional multiplexing encryption hologram generation technology; in the decryption step, a decryption user firstly needs to input a group of correct digital keys corresponding to the original plaintext image so as to construct a chaotic radial Hilbert mask required by decryption, and then a correct decryption result is generated by using a Fresnel diffraction-based hologram decryption technology. The decryption step can be completed by using a decryption device consisting of a laser light source, a polarization modulator, a microscope objective, a pinhole, a collimating lens, two lenses and two spatial light modulators. The method provided by the invention has the advantages of large key space, high key sensitivity, no crosstalk in decryption and simple structure of an optical decryption device.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of information security technology, and particularly relates to a three-dimensional multi-image encryption method based on multi-dimensional multiplexed hologram. BACKGROUND

[0002] In recent years, with the rapid development of information technology, three-dimensional digital images can effectively represent the real information such as depth, position and spatial structure of target objects due to their characteristics of large information capacity and rich content, and play an important role in many fields such as military, medical, education and business. Therefore, in order to protect the sensitive information in three-dimensional digital images from being stolen and tampered by illegal attackers, encryption technology for three-dimensional images has gradually become a research hotspot of domestic and foreign researchers. Among many encryption technologies, optical three-dimensional image encryption technology has attracted widespread attention of domestic and foreign research groups due to its characteristics of high encryption speed, strong security, large key space, high parallelism and ability to process large capacity images. Among them, the most representative is the random phase encoding technology (DRPE) based on 4f optical system proposed by Refregier and Javidi in 1995, and then advanced optical technologies such as integrated imaging, diffraction imaging, computer holography and orbital angular momentum (OAM) are gradually introduced into the optical three-dimensional image encryption method. Among them, the OAM technology has attracted widespread attention of domestic and foreign researchers due to its unique properties of synchronously transmitting multiple orthogonal independent mode information through the same frequency channel without increasing the bandwidth, and the channels carrying different OAM are mutually orthogonal and do not interfere with each other. The OAM technology is tried to be introduced into the three-dimensional image encryption method. For example, Jia et al. proposed a three-dimensional image encryption method based on OAM, phase holography technology and Fresnel zone plate (FZP). Later, Su et al. proposed a three-dimensional image encryption method based on OAM and spatial multiplexing technology. Recently, Shen et al. also proposed a three-dimensional image encryption method based on OAM and nonlinear holography technology.

[0003] However, the above encryption methods are all focused on the encryption protection of a single three-dimensional image, cannot encrypt multiple three-dimensional images at the same time, and cannot meet the demand for dynamic scene reconstruction and interaction in the current development of modern communication technology. In view of this problem, Kong et al. proposed a three-dimensional multi-image encryption technology based on OAM and super surface coding technology in 2025, which can encode multiple three-dimensional images into a super surface, and the effectiveness is verified through simulation and experiment. However, the current three-dimensional image encryption method based on OAM technology generally has the problem of insufficient key space, that is, only the topological charge number is used as the only key, which seriously threatens the security of the encryption system, and further limits the practicability of the three-dimensional image encryption method based on OAM technology. Therefore, in view of the limitations of the prior art, the present application discloses a three-dimensional multi-image encryption method based on multi-dimensional multiplexed hologram, which aims to realize three-dimensional multi-image encryption with large digital key space, high sensitivity and no crosstalk in decryption. SUMMARY

[0004] The present application aims to provide a three-dimensional multi-image encryption method based on multi-dimensional multiplexed hologram. The present application can encrypt multiple three-dimensional plaintexts and their corresponding OAM information into a phase-type holographic ciphertext by using chaotic radial Hilbert mask generation technology, multi-dimensional parameter selection hologram generation technology and multi-dimensional multiplexed encryption hologram generation technology. It has the advantages of high digital key sensitivity, large key space and no crosstalk in decryption. In order to achieve the above application purpose, the technical scheme provided by the present application is as follows: a three-dimensional multi-image encryption method based on multi-dimensional multiplexed hologram, characterized by comprising an encryption step:

[0005] S1: multi-dimensional parameter selection hologram generation: first, the nth(n=1, 2,..., N) three-dimensional plaintext image P n (x, y, z) in the multiple three-dimensional plaintext images to be encrypted is divided into m(m=1, 2,..., M) layers by using image layering algorithm, and the corresponding Dirac comb function is set for spatial sampling; second, the phase hologram generation technology based on Fresnel diffraction domain iterative phase recovery algorithm is used to encode all layer information in the spatial sampling result of P n (x, y, z) into a discrete phase hologram DPH n ; then, the encryption user needs to set a set of simple digital keys for P n (x, y, z), and generate the chaotic radial Hilbert mask CRHM n (n=1, 2,..., N) required in the encryption process by using chaotic radial Hilbert mask generation technology; finally, CRHM n (n=1, 2,..., N) and DPH n are multiplied to generate a holographic ciphertext carrying P nMultidimensional parameter selection hologram of (x,y,z) information and corresponding orbital angular momentum information MPH n .

[0006] S2: Multidimensional Multiplexing Encrypted Hologram Generation: First, all three-dimensional images are encrypted using step S1 to generate P. n (x,y,z).P2(x,y,z),...,P N The MPH1, MPH2, ..., MPH corresponding to (x,y,z) N ; then for MPH1, MPH2, ..., MPH N Perform an overlay operation to generate a multidimensional multiplexed encrypted hologram (MMH):

[0007] This concludes the encryption process.

[0008] Decryption steps:

[0009] J1: Decrypting Phase Group Generation: First, decrypting the nth (n = 1, 2, ..., N) 3D image P in the 3D image cluster if the user wants to... n To perform a decryption operation on (x,y,z), a set of conditions for P must be input. n The correct decryption key for (x,y,z) is obtained, and the chaotic radial Hilbert mask (CRHM) required for decryption is generated using the same chaotic matrix generation procedure and radial Hilbert mask generation technique as in encryption step S1. n Subsequently, a conjugation operation is performed on the chaotic radial Hilbert mask to generate a mask specific to P. n The decryption phase key for (x,y,z)

[0010] J2: Decrypting Multidimensional Multiplexed Holograms: First, the multidimensional multiplexed encrypted hologram MMH and... The product is multiplied, and then decoded using a Fresnel diffraction-based phase hologram decoding technique. Subsequently, a 3D image reconstruction technique is used to reconstruct the decoded result, thereby generating the decryption result of the nth (n = 1, 2, ..., N) 3D image in the 3D image cluster.

[0011] This concludes the decryption process.

[0012] The aforementioned three-dimensional multi-image encryption method based on multidimensional multiplexed holograms, wherein the encryption step S1, multidimensional parameter selection hologram generation, includes the following steps:

[0013] (i) 3D image preprocessing: First, the nth (n=1,2,...,N) 3D plaintext image P is processed using an image layering algorithm.n (x, y, z) is divided into m (m = 1, 2,..., M) layers and placed in different diffraction planes. Then the corresponding Dirac comb function pair P n (x, y, z) is spatially sampled, where P n (x, y, z) is the result of the m-th layer information of (x, y, z) after spatial sampling by the Dirac comb function. (x, y, z) can be expressed as:

[0014]

[0015] where Dira n (x, y, z) is expressed as the Dirac comb function corresponding to P n (x, y, z).

[0016] (ii) Convergence condition determination: first, an initial phase distribution element value interval [0, 2π] is generated by computer and is updated in the subsequent iteration process, then forward diffraction propagation, in turn to the image plane where is located, where the complex amplitude G n,m (u, v) arriving at the plane where

[0017]

[0018] where FrT λ，Z (g) is the Fresnel diffraction with wavelength λ and diffraction distance Z; Z m is the distance from to the plane where is located. Second, the amplitude extraction and phase extraction techniques are used to extract the amplitude A n,m (x, y) and phase n,m of G (u, v), respectively. The mathematical expression of this process is:

[0019] A n,m (x, y) = AE(G n,m (u, v))

[0020]

[0021] where AE(·) and PE(·) represent amplitude extraction and phase extraction operations, respectively. Then, the correlation coefficient (CC) is used to calculate the correlation of with A n,m (x, y), which can be expressed as:

[0022]

[0023] in and A respectively n,m (x,y) and The average pixel grayscale value is denoted by X, and X and Y represent the horizontal and vertical pixel counts of the image, respectively. After calculating the correlation coefficients for all layers, the minimum value min{CC} among all correlation coefficients is used. n,m Perform a convergence check; if min{CC} n,m If the value is greater than the preset threshold δ, it is considered convergent, and the system will output P during this iteration. n Discrete-phase hologram DPH of (x,y,z) n Conversely, if convergence fails, then G is retained. n,m Phase of (u,v) And using amplitude constraint technology to G n,m The amplitude A of (u,v) n,m (x,y) is replaced with Thus in A new complex amplitude is generated on the plane in which it is located.

[0024]

[0025] Where exp(g) is the exponentiation operation, j is the imaginary unit, n = 1, 2, ..., N, m = 1, 2, ..., M.

[0026] (iii) Inverse diffraction propagation: First, in A new complex amplitude is generated on the plane in which it is located. By applying Fresnel inverse diffraction to the back surface of the discrete-phase hologram ciphertext, the complex amplitude reaching the back surface of the discrete-phase hologram is obtained.

[0027]

[0028] Among them, IFRT λ，Z (g) represents the Fresnel inverse diffraction with wavelength λ and diffraction distance Z. Subsequently, for... Perform a phase extraction operation to obtain the updated phase. Finally Replace with Repeat sub-steps (ii)-(iii) until the convergence condition is met.

[0029] (iv) Single-channel multidimensional parameter selection hologram generation: First, the encrypted user needs to input two 3D images P from the 3D image cluster, specifically the nth (n = 1, 2, ..., N)th 3D image P. n Two chaotic initial values ​​α are encrypted from (x, y, z).n and β n where the general term of chaotic sequence α n+1 is:

[0030]

[0031] where α n ∈(0,1) and β n ∈(3.8,4). Then the chaotic sequence is arranged as a two-dimensional matrix to generate a chaotic matrix CM n . Next, the encryption user needs to input a set of optical parameters to generate a radial Hilbert mask RHM n (x,y,z) encrypted for P n . Next, the RHM n and CM n perform phase modulation operation to generate a chaotic radial Hilbert mask CRHM n carrying P n (x,y,z) encryption:

[0032] where ρ n is the topological charge number of the radial Hilbert mask, is the spatial azimuth angle of the radial Hilbert mask, n = 1, 2,..., N. Finally, CRHM n and DPH n generated in sub-step (iii) perform multiplication operation to generate a multi-dimensional parameter selection hologram MPH n carrying P n (x,y,z) information and corresponding orbital angular momentum information:

[0033] MPH n = DPH n × CRHM n

[0034] The above-mentioned three-dimensional multi-image encryption method based on multi-dimensional multiplexing hologram, the decryption step J2: multi-dimensional multiplexing hologram decryption, comprising the following steps:

[0035] (i) phase hologram decoding based on Fresnel diffraction: first, the multi-dimensional multiplexing encryption hologram MMH and perform multiplication operation, and then the multiplication result performs phase hologram decoding operation based on Fresnel diffraction, to obtain the decryption result of the nth(n = 1, 2,..., N) three-dimensional image on the m(m = 1, 2,..., M) layer

[0036]

[0037] (ii) three-dimensional image reconstruction: after the decryption result of all layers of the n th (n = 1, 2,..., N) three-dimensional image in the three-dimensional image cluster is obtained by the user, the decryption result of the three-dimensional image is decrypted by the user The spatial superposition technology is used for weighted fusion, and then P n The decryption result of (x, y, z)

[0038]

[0039] Wherein, γ(z) is a spatial weight function.

[0040] The present application has the following advantages: (1) the present application uses a chaotic matrix generation program, a radial Hilbert mask generation technology, and a phase modulation technology to generate a chaotic radial Hilbert mask used in the encryption step, wherein the chaotic matrix generation program can provide multiple high-sensitivity digital keys, which can effectively increase the key space; (2) the present application uses a multi-dimensional parameter selection hologram and a multi-dimensional multiplexing encryption hologram generation technology to encrypt multiple three-dimensional images into a phase-type holographic ciphertext, and the decryption has no crosstalk and high quality; (3) the encryption step in the present application is completed by a computer program, and the decryption step can be realized by a computer program or an optical method, wherein the optical path of the holographic imaging device used for optical decryption is simple and easy to build, and the decrypted three-dimensional image can be directly observed by the human eye or recorded by a camera. BRIEF DESCRIPTION OF DRAWINGS

[0041] Figure 1 It is a flowchart of the encryption step in a three-dimensional multi-image encryption method based on a multi-dimensional multiplexing hologram.

[0042] Figure 2 It is a generation flowchart of the multi-dimensional multiplexing encryption hologram in the encryption step in a three-dimensional multi-image encryption method based on a multi-dimensional multiplexing hologram.

[0043] Figure 3 It is a flowchart of the decryption step in a three-dimensional multi-image encryption method based on a multi-dimensional multiplexing hologram.

[0044] Figure 4 It is a three-dimensional multi-image reconstruction flowchart in a three-dimensional multi-image encryption method based on a multi-dimensional multiplexing hologram.

[0045] Figure 5Figure of optical decryption device for assisting description of decryption step, wherein 1 represents laser light source; 2 represents polarization modulation device; 3 represents microscopic objective; 4 represents pinhole; 5 represents collimating lens; 6 is spatial light modulator for carrying phase distribution of multi-dimensional multiplexed encrypted hologram; 71 and 72 are respectively first lens and second lens in 4f optical system, 8 is spatial light modulator for carrying phase distribution of decrypted chaotic radial Hilbert mask, 9 is CCD camera.

[0046] Figure 6 (a1)-(a4) are respectively three-dimensional plaintext images (‘cone’, ‘cuboid’, ‘cylinder’, ‘prism’); (b1)-(b4) are respectively depth maps corresponding to (a1)-(a4); (c1)-(c4) are respectively Dirac comb functions Dira1, Dira2, Dira3, Dira4 corresponding to (a1)-(a4); (d1)-(d4) are respectively discrete phase holograms DPH1, DPH2, DPH3, DPH4 corresponding to (a1)-(a4); (e1)-(e4) are respectively chaotic radial Hilbert masks CRHM1, CRHM2, CRHM3, CRHM4; (f1)-(f4) are respectively single-path multi-dimensional parameter selection holograms MPH1, MPH2, MPH3, MPH4 corresponding to (a1)-(a4); (g) is multi-dimensional multiplexed encrypted hologram, i.e. final ciphertext image MMH.

[0047] Figure 7 (a1)-(a2) are respectively decrypted results of original three-dimensional image ‘cone’ at distances of 400 mm and 410 mm from MMH when topological charge number key ρ ≠ 1, 2, 3, 4 and chaotic parameter keys are all correct; (a1)-(a2) are respectively decrypted results of original three-dimensional image ‘cone’ at distances of 400 mm and 410 mm from MMH when topological charge number key ρ ≠ 1, 2, 3, 4 and chaotic parameter keys are all correct; (a1)-(a2) are respectively decrypted results of original three-dimensional image ‘cone’ at distances of 400 mm and 410 mm from MMH when topological charge number key ρ ≠ 1, 2, 3, 4 and chaotic parameter keys are all correct; (a1)-(a2) are respectively decrypted results of original three-dimensional image ‘cone’ at distances of 400 mm and 410 mm from MMH when topological charge number key ρ ≠ 1, 2, 3, 4 and chaotic parameter keys are all correct; (a1)-(a2) are respectively decrypted results of original three-dimensional image ‘cone’ at distances of 400 mm and 410 mm from MMH when topological charge number key ρ ≠ 1, 2, 3, 4 and chaotic parameter keys are all correct.

[0048] Figure 8 (a1)-(a2) are respectively decrypted results of original three-dimensional image ‘cone’ at distances of 400 mm and 410 mm from MMH when topological charge number key ρ ≠ 1, 2, 3, 4 and chaotic parameter keys are all correct; -3 (a1)-(a2) are respectively decrypted results of original three-dimensional image ‘cone’ at distances of 400 mm and 410 mm from MMH when topological charge number key ρ ≠ 1, 2, 3, 4 and chaotic parameter keys are all correct;-3 Decryption results of the original three-dimensional image "cone" at the time distances of MMH 400 mm and 410 mm.

[0049] Figure 9 (a)-(c) are the key sensitivity curves of the topological charge key p, the first chaotic parameter key a, and the second chaotic parameter key b, respectively. DETAILED DESCRIPTION

[0050] The application will be further described below in conjunction with the embodiments and the accompanying drawings, but it is not as the basis for limiting the application.

[0051] Embodiment: A three-dimensional multi-image encryption method based on multi-dimensional multiplexed hologram, including the encryption steps as shown in Figure 1 The generation flowchart of the multi-dimensional multiplexed encryption hologram is shown in Figure 2 : First, the image layering algorithm is used to divide the nth(n = 1, 2,..., N) three-dimensional plaintext image P n (x, y, z) in the plurality of three-dimensional plaintext images to be encrypted into m (m = 1, 2,..., M) layers, and set the corresponding Dirac comb function for spatial sampling; second, the phase hologram generation technology based on the Fresnel diffraction domain iterative phase recovery algorithm is used to encode all layer information in the spatial sampling result of P n (x, y, z) into a discrete phase hologram DPH n ; then, the encryption user needs to set a group of simple digital keys for P n (x, y, z), and generate the chaotic radial Hilbert mask CRHM n (n = 1, 2,..., N) required in the encryption process by using the chaotic radial Hilbert mask generation technology; n (n = 1, 2,..., N) and DPH n are subjected to multiplication operation to generate a multi-dimensional parameter selection hologram MPH n carrying P n (x, y, z) information and corresponding orbital angular momentum information, including the following steps:

[0052] (i) three-dimensional image preprocessing: first, the image layering algorithm is used to divide the nth(n = 1, 2,..., N) three-dimensional plaintext image P n (x, y, z) into m (m = 1, 2,..., M) layers, and place them on different diffraction planes. Then set the corresponding Dirac comb function to spatially sample all layer information of P n (x, y, z), wherein the result of the mth layer information of P n (x, y, z) after spatial sampling by the Dirac comb function may be expressed as:

[0053]

[0054] where Dira n is expressed as the Dirac comb function corresponding to P n (x,y,z).

[0055] (ii) Convergence condition determination: Firstly, an initial phase distribution with an element value interval of [0, 2π] is generated by computer, and is updated constantly in the subsequent iteration process, and then forward-diffraction propagation, in turn, reaches the image plane where is located, wherein the complex amplitude G n,m (u,v) at the plane where is located can be expressed as:

[0056]

[0057] where FrT λ，Z (g) is expressed as the Fresnel diffraction with a wavelength λ and a diffraction distance Z; Z m is the distance from to the plane where is located. Secondly, the amplitude A n,m (x,y) and the phase of G n,m (u,v) are extracted by using the amplitude extraction and phase extraction techniques, respectively. The mathematical expression of this process is:

[0058] A n,m (x,y) = AE(G n,m (u,v))

[0059]

[0060] where AE(·) and PE(·) represent the amplitude extraction and phase extraction operations, respectively. Subsequently, the correlation coefficient (CC) is used to calculate the correlation of with A n,m (x,y), which can be expressed as:

[0061]

[0062] where and are the average pixel gray values of A n,m (x,y) and , respectively, and X and Y represent the horizontal pixel number and the vertical pixel number of the image, respectively. After the correlation coefficients of all layers are calculated, the minimum value min{CCn,m} is greater than a preset threshold δ, then the convergence is determined, and the system will output the P n,m} in this iteration process. n (x,y,z) of the discrete phase hologram DPH n . Otherwise, the convergence fails, and the G n,m (u,v) of the phase is retained. n,m (u,v) of the amplitude A n,m (x,y) is replaced by , thereby generating a new complex amplitude on the plane where

[0063]

[0064] where exp(g) is an exponential operation, j is an imaginary unit, n = 1, 2,..., N, and m = 1, 2,..., M.

[0065] (iii) inverse diffraction propagation: first, a new complex amplitude is generated on the plane where is propagated by a Fresnel inverse diffraction to the back surface of the bit-discrete phase hologram ciphertext, thereby obtaining a complex amplitude

[0066]

[0067] where IFrT λ，Z (g) represents a Fresnel inverse diffraction with a wavelength λ and a diffraction distance Z. Subsequently, a phase extraction operation is performed on to obtain an updated phase Finally, the is replaced by , and the sub-steps (ii)-(iii) are repeated until the convergence condition is met.

[0068] (iv) single-path multi-dimensional parameter selection hologram generation: first, the encryption user needs to input two chaotic initial values α n and β n for the encryption of the nth(n = 1, 2,..., N) three-dimensional image P n (x,y,z) in the three-dimensional image cluster, where the general term α n+1 of the chaotic sequence is:

[0069]

[0070] where α n∈(0,1) and β n ∈(3.8,4). This chaotic sequence is then arranged into a two-dimensional matrix to generate the chaotic matrix CM. n Next, the encrypted user needs to input a set of optical parameters to generate a P-value. n (x,y,z) encrypted radial Hilbert mask RHM n Next, regarding RHM n and CM n Perform phase modulation operation to generate a signal for P n (x,y,z) Encrypted Chaotic Radial Hilbert Mask CRHM n :

[0071]

[0072] Where, ρ n Let the topological charge number be the radial Hilbert mask. Let n be the spatial azimuth angle of the radial Hilbert mask, where n = 1, 2, ..., N. Finally, CRHM... n The DPH generated in sub-step (iii) n Perform a multiplication operation to generate a product carrying P n Multidimensional parameter selection hologram of (x,y,z) information and corresponding orbital angular momentum information MPH n :

[0073] MPH n =DPH n ×CRHM n

[0074] S2: Multidimensional Multiplexing Encrypted Hologram Generation: First, encryption step S1 is performed on all three-dimensional images in the three-dimensional image cluster to generate P. n (x,y,z).P2(x,y,z),...,P N The MPH1, MPH2, ..., MPH corresponding to (x,y,z) N ; then for MPH1, MPH2, ..., MPH N Perform an overlay operation to generate a multidimensional multiplexed encrypted hologram (MMH):

[0075]

[0076] This concludes the encryption process.

[0077] A three-dimensional multi-image encryption method based on multidimensional multiplexed holograms, including as follows Figure 3 The decryption steps shown are appended to aid in describing the encryption steps. Figure 4 The flowchart shown illustrates the generation process of the multidimensional multiplexed encrypted hologram.Figure 5 Decryption device) : J1 : Decryption phase set generation: First, the decryption user wants to decrypt the n-th (n = 1, 2,..., N) three-dimensional image P n (x, y, z) in the three-dimensional image cluster, he must input a set of correct decryption digital keys for P n (x, y, z) and generate the chaotic radial Hilbert mask CRHM needed for decryption using the same chaotic matrix generation program and radial Hilbert mask generation technique as in the encryption step S1 n , and then perform a conjugation operation on the chaotic radial Hilbert mask to generate the decryption phase mask for P n (x, y, z) only

[0078] J2 : Multi-dimensional multiplexed hologram decryption: First, the multi-dimensional multiplexed encryption hologram MMH and perform a multiplication operation, and then perform a decoding operation on the multiplication result using the phase hologram decoding technique based on Fresnel diffraction. Subsequently, perform a reconstruction operation on the decoding result using the three-dimensional image reconstruction technique to generate the decryption result of the n-th (n = 1, 2,..., N) three-dimensional image in the three-dimensional image cluster where the decryption flowchart of the n-th (n = 1, 2,..., N) three-dimensional plaintext image is shown in Figure 6 , including the following steps:

[0079] (i) Phase hologram decoding based on Fresnel diffraction: First, the multi-dimensional multiplexed encryption hologram MMH and perform a multiplication operation, and then perform a phase hologram decoding operation based on Fresnel diffraction on the multiplication result to obtain the decryption result of the n-th (n = 1, 2,..., N) three-dimensional image on the m-th (m = 1, 2,..., M) layer

[0080]

[0081] (ii) Three-dimensional image reconstruction: After obtaining the decryption results of all layers of the n-th (n = 1, 2,..., N) three-dimensional image in the three-dimensional image cluster, the decryption user performs a weighted fusion on using the spatial superposition technique to generate the decryption result of P n (x, y, z)

[0082]

[0083] where γ(z) is a spatial weight function.

[0084] The optical decryption used in the present application is described in detail below, and the optical decryption requires the use of an optical decryption device as shown in Figure 5 , which includes a laser light source 1 for providing incident light, a polarization modulation device 2 for modulating the polarization state of the incident light, a microscope objective 3 for converging the light beam, a pinhole 4 for spatial filtering, a collimating lens 5 for collimating the light beam, a spatial light modulator 6 for carrying the phase distribution of a multi-dimensional multiplexed encrypted hologram, a first lens 71 and a second lens 72 for building a 4f optical system, a spatial light modulator 8 for carrying the phase distribution of a decrypted chaotic radial Hilbert mask, and a CCD camera 9 for receiving a decrypted three-dimensional image. The characteristic is that the polarization modulation device 2 is a polarizer or a half-wave plate; the pinhole 4 is placed at the focal point of the microscope objective 3, and the focal point of the microscope objective 3 and the object focal point of the collimating lens 5 coincide; the spatial light modulator 6 for carrying the phase distribution of a multi-dimensional multiplexed encrypted hologram is placed at the object focal point of the first lens 71; the object focal point of the second lens 72 coincides with the image focal point of the first lens 71, and the object focal length of the second lens 72 is equal to the image focal length of the first lens 71; the spatial light modulator 8 for carrying the phase distribution of a decrypted chaotic radial Hilbert mask is placed at the image focal point of the second lens 72.

[0085] The specific optical decryption process is as follows: the laser emitted by the laser light source 1 first forms polarized light after passing through the polarization modulation device 2, and then the polarized light is incident to the microscope objective 3, which converges the incident light to the focal point. The pinhole 4 at the focal point position performs spatial filtering on the converging spherical light wave formed by the microscope objective 3, and then the diverging spherical light wave after spatial filtering by the pinhole 4 is incident to the collimating lens 5. Since the pinhole 4 is placed at the object focal point of the collimating lens 5, the diverging spherical light wave is modulated into collimated plane light wave after passing through the collimating lens 5, and then the collimated plane light wave is phase-modulated by the 4f optical system composed of the light modulator 6, the light modulator 8, and the first lens 71 and the second lens 72 to generate a decrypted light wave, and then the decrypted light wave continues to diffract and propagate forward and forms a decrypted three-dimensional image in space, at which time the CCD camera 9 performs shooting and capturing. The characteristic is that the decrypted three-dimensional image can be directly observed by the human eye or recorded by the camera.

[0086] The content of the present application is further explained below in conjunction with the drawings:

[0087] First, four three-dimensional models with a maximum depth of 10 mm ("cone", "cuboid", "cylinder", and "prism") as shown in Figure 6 (a1)-(a4) are modeled using computer graphics software as three-dimensional images P n (x,y,z) to be encrypted, where n = 1, 2, 3, 4, and in additionFigure 6 The depth information corresponding to (a1)-(a4) are respectively as follows: Figure 8 As shown in (b1)-(b4). Then, for P... n Perform a 3D image layering operation on (x, y, z), and set the shortest and longest distances from the layered results to the MMH to 400mm and 410mm, respectively. Then, set as follows... Figure 8 The Dirac comb functions shown in (c1)-(c4) are Dirac comb functions. n (n = 1, 2, 3, 4) for P n Spatial sampling is performed on all layer information of (x,y,z) to obtain the sampling result. Where n = 1, 2, 3, 4 and m = 1, 2. Next, the wavelength of the light wave is set to λ = 632.8 nm, and a phase hologram generation technique based on an iterative phase retrieval algorithm in the Fresnel diffraction domain is used to generate the hologram. Encoding as follows Figure 6 Discrete phase holograms DPH shown in (d1)-(d4) n Then, the topological charge number key ρ of the radial Hilbert mask is... n Let the chaotic initial values ​​α be 1, 2, 3, and 4 respectively. n and β n Both were set to 0.5 and 3.9, and the chaotic radial Hilbert mask generation technique was used to generate... Figure 6 The chaotic radial Hilbert mask CRHM shown in (e1)-(e4) n (n = 1, 2, 3, 4), then DPH n With CRHM n Perform product operations to generate, respectively, such as Figure 6 (f1)-(f4) show the carriers Figure 6 Multidimensional parameter selection hologram of track angle momentum information corresponding to (a1)-(a4) information MPH n (n = 1, 2, 3, 4). Finally, MPH n (n = 1, 2, 3, 4) are subjected to holographic overlay operation, and then... Figure 6 The multidimensional multiplexed encrypted hologram (MMH) shown in (g) is the final ciphertext image. The encryption process is now complete.

[0088] Next, according to Figure 3 The decryption steps shown perform a decryption operation, where the decryption key includes the payload key ρ. n and the chaotic initial value key α n and β n When the initial chaotic keys are all correct and the topological charge key ρ1 = 1, the decryption results at 400 mm and 410 mm from the multidimensional multiplexed encrypted hologram are as follows: Figure 7As shown in (a1)-(a2), when the initial chaotic key is correct and the topological charge key ρ2 = 2, the decryption results at 400 mm and 410 mm from the multidimensional multiplexed encrypted hologram are respectively as follows. Figure 7 As shown in (b1)-(b2), when the initial chaotic key is correct and the topological charge key ρ3 = 3, the decryption results at 400 mm and 410 mm from the bit-multiplexed encrypted hologram are respectively as follows. Figure 7 As shown in (c1)-(c2), when the initial chaotic key is correct and the topological charge key ρ4 = 4, the decryption results at 400 mm and 410 mm from the bit-multiplexed encrypted hologram are respectively as follows. Figure 7 As shown in (d1)-(d2). From Figure 7 The decryption results show that when all keys are correct, all three-dimensional plaintext images can be accurately reconstructed without crosstalk.

[0089] The validity and security of the key in this invention will now be examined. Here, the applicant only presents the key validity analysis results for the three-dimensional plaintext image "cone", but the analysis results for other three-dimensional plaintext images are similar. Figure 8 (a1)-(a2) respectively give the decryption results of the multidimensional multiplexing encrypted holograms at distances of 400mm and 410mm when the chaotic parameter keys are all correct, but the topological charge key ρ≠1,2,3,4; Figure 8 (b1)-(b2) respectively give the first chaotic parameter key α when the topological charge key ρ = 1. 1 When correct, but the second chaotic parameter key deviation Δβ 1 =1×10 -3 The decryption result at that time; Figure 8 c1)-(c2) respectively give the second chaotic parameter key β when the topological charge key ρ=1. 1 When correct, but the first chaotic parameter key deviation Δα 1 =1×10 -3 The decryption result at that time. According to Figure 8 The analysis clearly shows that when any key is incorrect, the system cannot correctly reconstruct the original 3D plaintext image. In this case, the correlation coefficient (CC) between the decryption result and the original image approaches 0, and the decryption result exhibits obvious noise distribution characteristics. This experimental result fully verifies the effectiveness and security of the key system in this invention.

[0090] Finally, the key sensitivity in this invention is examined. Figure 9 The relationship between the average correlation coefficient (Average CC) between the decryption result of the 3D image "cone" and the original plaintext image and the deviation of each key is given, which is the sensitivity curve of each key. The analysis results of other 3D plaintext images are similar. Figure 9(a)-(c) respectively show the sensitivity curves of the topological charge number key deviation Δρ, the first chaotic parameter key deviation Δα, and the second chaotic parameter key deviation Δβ. It can be seen from Figure 9 that when any key has a slight deviation, the average correlation coefficient between the decryption result and the original three-dimensional image sharply decreases to close to 0, and the decryption result shows obvious noise distribution. Only when all the digital key deviations are 0, the original three-dimensional plaintext image can be correctly recovered, thereby proving that the digital key in the application has high sensitivity.

[0091] The above is a specific implementation of the application, but not a limitation of the application. Those skilled in the art can make various equivalent technical solutions without departing from the scope of the application, and all equivalent technical solutions should be included in the patent protection scope of the application.

Claims

1. A three-dimensional multi-image encryption method based on multidimensional multiplexed holograms, characterized in that: Including encryption steps: S1: Multidimensional parameter selection hologram generation: First, an image layering algorithm is used to generate the nth (n=1,2,...,N) 3D plaintext image P from multiple images to be encrypted. n (x,y,z) is divided into m (m=1,2,...,M) layers, and corresponding Dirac comb functions are set for spatial sampling; then, a phase hologram generation technique based on the Fresnel diffraction domain iterative phase retrieval algorithm is used to generate P n All layer information in the spatial sampling results of (x,y,z) is encoded into a discrete phase hologram DPH. n Subsequently, the encrypted user needs to set a set of rules for P. n A simple digital key of (x,y,z) is used, and the chaotic radial Hilbert mask (CRHM) required for the encryption process is generated using the chaotic radial Hilbert mask generation technique. n (n = 1, 2, ..., N); finally, CRHM n (n = 1, 2, ..., N) and DPH n The multiplication operation is performed to generate a product carrying P n Multidimensional parameter selection hologram MPH of (x,y,z) information and corresponding orbital angular momentum information n ; S2: Multidimensional Multiplexing Encrypted Hologram Generation: First, all three-dimensional images are encrypted using step S1 to generate P. n (x,y,z).P2(x,y,z),...,P N The MPH1, MPH2, ..., MPH corresponding to (x,y,z) N ; then for MPH1, MPH2, ..., MPH N Perform an overlay operation to generate a multidimensional multiplexed encrypted hologram (MMH): The encryption process is now complete. Decryption steps: J1: Decrypting Phase Group Generation: First, decrypting the nth (n = 1, 2, ..., N) 3D image P in the 3D image cluster if the user wants to... n To perform a decryption operation on (x,y,z), a set of conditions for P must be input. n The correct decryption key for (x,y,z) is obtained, and the chaotic radial Hilbert mask (CRHM) required for decryption is generated using the same chaotic matrix generation procedure and radial Hilbert mask generation technique as in encryption step S1. n Subsequently, a conjugation operation is performed on the chaotic radial Hilbert mask to generate a mask specific to P. n The decryption phase key for (x,y,z) J2: Decrypting Multidimensional Multiplexed Holograms: First, the multidimensional multiplexed encrypted hologram MMH and... The product is multiplied, and then decoded using a Fresnel diffraction-based phase hologram decoding technique. Subsequently, a 3D image reconstruction technique is used to reconstruct the decoded result, thereby generating the decryption result of the nth (n = 1, 2, ..., N) 3D image in the 3D image cluster. This concludes the decryption process.

2. The three-dimensional multi-image encryption method based on multidimensional multiplexed holograms according to claim 1, characterized in that: The specific process of encryption step S1 is as follows: (i) 3D image preprocessing: First, the nth (n=1,2,...,N) 3D plaintext image P is processed using an image layering algorithm. n (x,y,z) is divided into m layers (m=1,2,...,M) and placed on different diffraction planes; then, the corresponding Dirac comb functions are set to P. n Spatial sampling is performed on all layer information (x, y, z), where P n The result of sampling the m-th layer information of (x,y,z) through the Dirac comb function space. It can be represented as: Among them, Dira n Represented as P n The Dirac comb function corresponding to (x,y,z); (ii) Convergence condition determination: First, use a computer to generate an initial phase with an element value distribution interval of [0, 2π]. And it was continuously updated in subsequent iterations, and then Propagation forward by diffraction, arriving in sequence The image plane in which it is located, and the image plane in which it reaches Complex amplitude G in the plane n,m (u,v) can be represented as: Among them, FrT λ，z (g) represents Fresnel diffraction with wavelength λ and diffraction distance Z; Z m for arrive The distance to the plane in which it is located; secondly, G is extracted using amplitude extraction and phase extraction techniques respectively. n,m The amplitude A of (u,v) n,m (x,y) and phase The mathematical expression for this process is: A n,m (x,y)=AE(G n,m (u,v)) Where AE(·) and PE(·) represent amplitude extraction and phase extraction operations, respectively; subsequently, the correlation coefficient (CC) is used to calculate... With A n,m The correlation between (x, y) can be represented as: in and A respectively n,m (x,y) and The average pixel grayscale value is denoted by X, and X and Y represent the horizontal and vertical pixel counts of the image, respectively. After calculating the correlation coefficients of all layers, the minimum value min{CC} among all correlation coefficients is used. n,m Perform a convergence check; if min{CC} n,m If the value is greater than the preset threshold δ, it is considered convergent, and the system will output P during this iteration. n Discrete-phase hologram DPH of (x,y,z) n Conversely, if convergence fails, then G is retained. n,m Phase of (u,v) And using amplitude constraint technology to G n,m The amplitude A of (u,v) n,m (x,y) is replaced with Thus in A new complex amplitude is generated on the plane in which it is located. Where exp(g) is the exponentiation operation, j is the imaginary unit, n = 1, 2, ..., N, m = 1, 2, ..., M; (iii) Inverse diffraction propagation: First, in A new complex amplitude is generated on the plane in which it is located. By applying Fresnel inverse diffraction to the back surface of the discrete-phase hologram ciphertext, the complex amplitude reaching the back surface of the discrete-phase hologram is obtained. Among them, IFRT λ，z (g) represents the Fresnel inverse diffraction with wavelength λ and diffraction distance Z; subsequently, for Perform a phase extraction operation to obtain the updated phase. Finally Replace with And repeat sub-steps (ii)-(iii) until the convergence condition is met; (iv) Single-channel multidimensional parameter selection hologram generation: First, the encrypted user needs to input two 3D images P from the 3D image cluster, specifically the nth (n = 1, 2, ..., N)th 3D image P. n Two chaotic initial values ​​α are encrypted from (x, y, z). n and β n The general term α of the chaotic sequence n+1 for: in α n ∈(0,1) and β n ∈(3.8,4); then the chaotic sequence is arranged into a two-dimensional matrix to generate the chaotic matrix CM. n Next, the encrypted user needs to input a set of optical parameters to generate a P-value. n (x,y,z) encrypted radial Hilbert mask RHM n Next, regarding RHM n and CM n Perform a phase modulation operation to generate a P-carrying... n (x,y,z) Encrypted Chaotic Radial Hilbert Mask CRHM n : Where, ρ n Let the topological charge number be the radial Hilbert mask. The spatial azimuth angle of the radial Hilbert mask, n = 1, 2, ..., N; finally, CRHM n The DPH generated in sub-step (iii) n Perform a multiplication operation to generate a product carrying P n Multidimensional parameter selection hologram MPH of (x,y,z) information and corresponding orbital angular momentum information n : MPH n =DPH n ×CRHM n 。 3. The three-dimensional multi-image encryption method based on multidimensional multiplexed holograms according to claim 1, characterized in that: The specific process of decryption step J2 is as follows: (i) Fresnel diffraction-based phase hologram decoding: First, multidimensional multiplexing of the encrypted hologram MMH and Perform a multiplication operation, and then perform a phase holographic decoding operation based on Fresnel diffraction on the multiplication result to obtain the decryption result of the nth (n=1,2,...,N) 3D image on the m (m=1,2,...,M) layer. (ii) 3D Image Reconstruction: After obtaining the decryption results of all layers of the nth (n = 1, 2, ..., N) 3D image in the 3D image cluster, the user then... Weighted fusion is performed using spatial overlay technology to generate P. n Decryption result of (x,y,z) Where γ(z) is the spatial weighting function.

4. The three-dimensional multi-image encryption method based on multidimensional multiplexed holograms according to claim 1, characterized in that: The device for optical decryption is a three-dimensional multi-image optical decryption device based on a multidimensional multiplexed hologram, comprising a laser source (1) for providing incident light, a polarization modulation device (2) for modulating the polarization state of the incident light, a microscope objective (3) for converging the beam, a pinhole (4) for spatial filtering, a collimating lens (5) for collimating the beam, a spatial light modulator (6) for carrying the phase distribution of the multidimensional multiplexed encrypted hologram, a first lens (71) and a second lens (72) for constructing a 4f optical system, a spatial light modulator (8) for carrying the phase distribution of the decrypted chaotic radial Hilbert mask, and a CCD camera (9) for receiving the decrypted three-dimensional image; wherein, the polarization... The modulation device (2) is a polarizer or a half-wave plate; the pinhole (4) is placed at the focal point of the microscope objective (3), and the focal point of the microscope objective (3) coincides with the object-side focal point of the collimating lens (5); the spatial light modulator (6) for carrying the phase distribution of the multidimensional multiplexed encrypted hologram is placed at the object-side focal point of the first lens (71); the object-side focal point of the second lens (72) coincides with the image-side focal point of the first lens (71), and the object-side focal length of the second lens (72) is equal to the image-side focal length of the first lens (73); the spatial light modulator (8) for carrying the phase distribution of the decrypted chaotic radial Hilbert mask is placed at the image-side focal point of the second lens (72).

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