Color image dual encryption method based on orthogonal frequency domain scrambling and phase steganography

Abstract

The invention discloses a color image dual encryption method based on orthogonal frequency domain scrambling and phase steganography, and belongs to the technical field of optical information encryption. According to the method, orthogonal frequency domain scrambling and phase steganography are fused, an orthogonal projection-phase reconstruction cross-domain collaborative encryption framework is constructed, and deep fusion of mathematical irreversibility and physical unclonability is realized. In a mathematical encryption layer, designing a high-dimensional orthogonal matrix to perform global linear transformation on RGB three-channel combined two-dimensional discrete cosine transform coefficients, and eliminating correlation between a frequency domain statistical law and the channels; in a physical encryption layer, orthogonal encryption data is coded into a phase image, secondary modulation is carried out through a non-interference coding aperture correlation holographic optical system, spatial domain plaintext information is destroyed by using physical unclonability of speckle noise, and a joint protection mechanism of a mathematical key and a physical key is formed. The method is suitable for scenes with extremely high requirements on encryption strength and anti-attack capability, such as secret communication and medical image security storage.

Description

Technical Field

[0001] The present invention belongs to the technical field of intersection of optical information encryption and digital image processing, and specifically relates to a cross-domain collaborative encryption method based on orthogonal frequency domain scrambling and phase steganography. The method eliminates frequency domain statistical features through mathematical orthogonal projection and realizes double encryption by combining the physical non-cloning property of interference-free coded aperture-correlated holographic system. The method is suitable for scenarios with strict requirements on encryption strength and anti-attack capabilities, such as confidential communications and secure storage of medical images. Background Art

[0002] With the rapid development of digital information technology, color images are increasingly used as information carriers, and their security has attracted significant attention. Currently, the field of image encryption is primarily divided into two technical approaches: spatial / frequency domain encryption methods based on mathematical transformations, such as wavelet transforms, chaotic systems, and compressed sensing; and physical encryption techniques based on optical principles, such as holographic encryption and phase recovery. However, existing traditional methods have significant limitations. Specifically, spatial scrambling is vulnerable to statistical analysis attacks, while frequency domain transformations preserve identifiable coefficient distribution characteristics. Schemes that rely solely on optical encryption lack flexible mathematical key management mechanisms. Furthermore, advances in modern computing power have made brute force and deep learning attacks a serious threat to existing encryption schemes. Therefore, there is an urgent need to develop new encryption schemes that combine mathematical complexity with physical unclonability to meet growing security demands.

[0003] To address challenges in current color image encryption technology, such as the leakage of inter-channel correlation features caused by independent encryption of the three RGB channels, the analyzable distribution of frequency domain coefficients after traditional Fourier transforms, the susceptibility of common pixel replacement algorithms to geometric attacks and their limited key space, and insufficient optical compatibility, this paper proposes a dual encryption mechanism based on orthogonal frequency domain scrambling and phase steganography. This mechanism establishes a theoretical framework for color image encryption that integrates orthogonal projection and analytical phase reconstruction, aiming to achieve decorrelation of frequency domain coefficient distribution, phase domain conversion of spatial information, and collaborative protection of mathematical-physical encryption. By generating a high-dimensional orthogonal matrix, the present invention effectively eliminates frequency domain statistical features and channel correlation. The encrypted data is encoded as a phase image and modulated by an interference-free coded aperture correlation holography (I-COACH) system to generate a physically unclonable holographic ciphertext, thereby achieving cross-domain collaboration between mathematical and physical encryption and ensuring the joint protection of digital and physical keys. Summary of the Invention 1. A color image dual encryption method based on orthogonal frequency-domain scrambling and phase steganography. The method is implemented using an I-COACH optical device comprising a monochromatic LED light source, a first lens, a target object or pinhole, a second lens, a polarizer, a spatial light modulator (SLM), and a CMOS image sensor. The light source uses incoherent light, which propagates through diffraction and is modulated by a coded phase mask in the SLM. The image sensor ultimately records an intensity image. The coded phase mask is a sparse point type generated using a modified GS (Gerchberg-Saxton) algorithm.

[0004] This method includes the following five steps:

[0005] S1: Divide the color image into blocks;

[0006] Divide the color image (H×W×3) with a height of H and a width of W into blocks of B×B and a sliding step of S=B / 2 to achieve overlapping blocks. The total number of blocks is The RGB channel data of the kth block are expressed as and

[0007] S2: frequency domain transformation and multi-channel joint vectorization;

[0008] Perform two-dimensional discrete cosine transform (DCT) on each channel block and merge the three-channel DCT coefficients into a vector, which is expressed as follows: Among them, D k represents the two-dimensional DCT coefficient matrix of the kth block RGB channel, X represents the input data block, DCT2(X) u,v Represents the two-dimensional DCT coefficient of block X at the frequency domain coordinate (u, v), where u and v are frequency domain indices, x and y are spatial domain pixel coordinates, and α u and α v represents the normalization coefficient, vec(·) represents the matrix column vectorization operation, d k represents the DCT coefficient vector of the k-th block, and "T" represents the transpose operation.

[0009] S3: Orthogonal projection encryption;

[0010] The orthogonal matrix Q is generated by QR decomposition, and then the DCT coefficient vector is linearly transformed to complete the first encryption. The formula is expressed as Among them, y kRepresents the encrypted measurement value, satisfying the energy conservation ||y k ||2=||d k ||2, φ represents a Gaussian random matrix whose elements obey the standard normal distribution, R represents an upper triangular matrix, Q represents an orthogonal matrix, and Q T Q=I, where I is the identity matrix.

[0011] S4: Optical Phase Steganography and Modulation;

[0012] Based on the Kramers-Kronig relationship, the causal spectrum constraint condition is established. The ciphertext generated in step S3 is embedded into the phase component θ through single sideband modulation to form a pure phase image O with an amplitude of 1. After the coded phase mask CPM (Coded Phase Mask) is modulated in the I-COACH system, the intensity recorded by the image sensor is I OH , get the final ciphertext, then replace the target object with the pinhole, and the point source hologram recorded by the image sensor is used as the key, whose intensity is I PSH , which is described by the formula Among them, “*” represents the convolution operation.

[0013] S5: Decryption and reconstruction;

[0014] Assume that the complex amplitude estimate of the reconstructed image is U, and the ciphertext and key are cross-correlated and reconstructed. The reconstructed result is the real part real(U), and then the imaginary part Im(U) is restored using the Kramers-Kronig relationship. Its expression is: Among them, F[·] and F -1 [·] denotes two-dimensional Fourier transform and inverse transform, respectively. Represents the cross-correlation operation, the Hilbert transform corresponds to the multiplier -jsgn(v), v is the vertical spatial frequency, sgn(v) is the sign function, and j represents the imaginary unit. The reconstructed phase image is obtained, and its expression is in, represents the reconstructed phase image, and arctan(·) represents the inverse tangent function.

[0015] Reconstructed phase image Decryption, this process is the reverse process of the first encryption, first orthogonal matrix Q T Back projection separates the DCT coefficients of the RGB channels and then performs inverse DCT transformation to reconstruct the color image. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 Schematic diagram of the interference-free coded aperture correlation holography used in a specific embodiment of the present invention.

[0017] Figure 2 Flowchart of a color image dual encryption method based on orthogonal frequency domain scrambling and phase steganography.

[0018] Figure 3 Encryption process: (a) plaintext, (b) first encryption result, (c) point diffusion hologram, (d) final ciphertext.

[0019] Figure 4 Decryption process: (a) cross-correlation reconstruction result, (b) reconstructed phase image, (c) decrypted image.

[0020] Figure 5 Key analysis: (a) Decrypted graph using incorrect CPM key, (b) Decrypted graph using incorrect orthogonal matrix key.

[0021] Figure 6 Robustness analysis: (a) Decrypted image after cutting the ciphertext by 1 / 6, (b) Decrypted image after adding noise to the ciphertext.

[0022] Description of reference numerals:

[0023] 1. Monochromatic LED light source, 2. First lens, 3. Target object or pinhole, 4. Second lens, 5. Polarizer, 6. Spatial Light Modulator (SLM), 7. CMOS image sensor. DETAILED DESCRIPTION

[0024] In order to better explain the implementation process of the present invention, the present invention will be further described in detail with reference to an embodiment below, but the present invention is not limited to this embodiment.

[0025] Example.

[0026] Will Figure 3 The color image shown in (a) is divided into blocks. The color image size is 256×256×3, the block size B×B is 16×16, the sliding step S=8 to achieve overlapping blocks, the total number of blocks K=31×31, and the RGB channel data of the kth block are expressed as and

[0027] Perform two-dimensional discrete cosine transform (DCT) on each channel block and merge the three-channel DCT coefficients into a vector, which is expressed as follows: Among them, D krepresents the two-dimensional DCT coefficient matrix of the kth block RGB channel, X represents the input data block, DCT2(X) u,v Represents the two-dimensional DCT coefficient of block X at the frequency domain coordinate (u, v), where u and v are frequency domain indices, x and y are spatial domain pixel coordinates, and α u and α v represents the normalization coefficient, vec(·) represents the matrix column vectorization operation, d k represents the DCT coefficient vector of the k-th block, and "T" represents the transpose operation.

[0028] Generate the orthogonal matrix Q by QR decomposition, and then perform linear transformation on the DCT coefficient vector to obtain Figure 3 The first encryption result shown in (b) is expressed as Among them, y k Represents the encrypted measurement value, satisfying the energy conservation ||y k ||2=||d k ||2, φ represents a Gaussian random matrix whose elements obey the standard normal distribution, R represents an upper triangular matrix, Q represents an orthogonal matrix, and Q T Q=I, where I is the identity matrix.

[0029] Based on the Kramers-Kronig relationship, causal spectrum constraints are established, and the ciphertext generated in step S3 is embedded as a phase component through single-sideband modulation to form a pure phase image O. The encrypted optical system is as follows Figure 1 As shown, define Z C is the distance between the target object and the second lens, Z S is the distance between the SLM and the image sensor. In the simulation experiment using MATLAB, the wavelength of the monochromatic LED light source is 532nm, and the diffraction distance Z C =50mm, Z S =50mm, the light source diffracts after passing through the object image to the plane where the SLM is located, and is received by the image sensor after being modulated by the coded phase mask CPM loaded on the SLM. The intensity recorded by the image sensor after the image O is modulated by the coded phase mask CPM in the I-COACH system is I OH , get Figure 3 The final ciphertext shown in (d) is then replaced by the pinhole, and the image sensor records Figure 3 (c) Point source hologram as key, whose intensity is I PSH , which is described by the formula Here, θ represents the phase diagram of the complex amplitude, and “*” represents the convolution operation.

[0030] Decrypt the ciphertext. Assume that the reconstructed image complex amplitude estimate is U, and reconstruct the ciphertext and key by cross-correlation, and the reconstructed result is as follows: Figure 4 As shown in (a), we take it as the real part real(U), and then use the Kramers-Kronig relationship to recover the imaginary part Im(U), which is expressed as Among them, F[·] and F -1 [·] denotes two-dimensional Fourier transform and inverse transform, respectively. Represents the cross-correlation operation, the Hilbert transform corresponds to the multiplier -jsgn(v), v is the vertical spatial frequency, sgn(v) is the sign function, and j represents the imaginary unit. The reconstructed phase image is obtained, and its expression is in, represents the reconstructed phase image, and arctan(·) represents the inverse tangent function.

[0031] Reconstructed phase image Decryption, this process is the reverse process of the first encryption, first orthogonal matrix Q T Back projection separates the RGB channel DCT coefficients and then performs inverse DCT transformation, and finally reconstructs and decrypts Figure 4 (c) Color image.

[0032] After encrypting and decrypting color images using the method of the present invention, the correlation coefficient (CC) between the plaintext image and the decrypted image reached 0.9762, the structural similarity index (SSIM) was 0.9685, and the mean square error (MSE) was approximately 0. In the encryption system of the present invention, the orthogonal matrix Q, the wavelength of the light source, the CPM, and the diffraction distance of the image are all used as keys. Figure 5 (a) and Figure 5 (b) shows the results when decrypting using the wrong CPM synthesized PSH and the wrong orthogonal matrix. The results show that no information of the original image can be extracted from the encrypted image.

[0033] In addition, the present invention also analyzes the noise resistance and anti-clipping of the method. In the MATLAB simulation, the ciphertext is cut by 1 / 6 and then decrypted. Figure 6 As shown in (a), the decrypted image can still clearly distinguish the outline of the original image, and the CC value is 0.8314. Secondly, in the simulation, Gaussian white noise with an intensity of 0.5 is added to the ciphertext to restore it, as shown in Figure 6As shown in (b), the decrypted image can still effectively distinguish the contours of the original image, with a CC value of 0.9196. Simulation results show that the encryption system has good noise and clipping resistance.

[0034] The above description is only a preferred embodiment of the present invention and does not represent the scope of protection of the present invention. Any modification, equivalent replacement, improvement, etc. made within the principle of the present invention are included in the scope of protection of the present invention.

Claims

1. A color image dual encryption method based on orthogonal frequency domain scrambling and phase steganography, characterized in that: The optical device specifically implemented by the method includes a monochromatic LED light source, a first lens, a target object, a pinhole, a second lens, a polarizer, a spatial light modulator (SLM), and a CMOS image sensor. The light source uses incoherent light, which propagates through diffraction and is modulated by a coded phase mask in the SLM. The image sensor ultimately records an intensity image, wherein the coded phase mask is a sparse point type generated by an improved GS (Gerchberg-Saxton) algorithm. The method comprises the following five steps: S1, divide the color image into blocks: Divide the color image (H×W×3) with a height of H and a width of W into blocks of B×B and a sliding step of S=B / 2 to achieve overlapping blocks. The total number of blocks is The RGB channel data of the kth block are expressed as and S2, frequency domain transformation and multi-channel joint vectorization: Perform two-dimensional discrete cosine transform (DCT) on each channel block and merge the three-channel DCT coefficients into a vector, which is expressed as follows: Among them, D k represents the two-dimensional DCT coefficient matrix of the kth block RGB channel, X represents the input data block, DCT2(X) u,v Represents the two-dimensional DCT coefficient of block X at the frequency domain coordinate (u, v), where u and v are frequency domain indices, x and y are spatial domain pixel coordinates, and α u and α v represents the normalization coefficient, vec(·) represents the matrix column vectorization operation, d k represents the DCT coefficient vector of the k-th block, "T" represents the transpose operation; S3, orthogonal projection encryption: The orthogonal matrix Q is generated by QR decomposition, and then the DCT coefficient vector is linearly transformed to complete the first encryption. The formula is expressed as Among them, y k Represents the encrypted measurement value, satisfying the energy conservation ||y k ||2=||d k ||2, φ represents a Gaussian random matrix whose elements obey the standard normal distribution, R represents an upper triangular matrix, Q represents an orthogonal matrix, and Q T Q = I, where I is the identity matrix; S4, Optical Phase Steganography and Modulation: Based on the Kramers-Kronig relationship, the causal spectrum constraint condition is established. The ciphertext generated in step S3 is embedded as a phase component through single-sideband modulation to form a pure phase image O, whose amplitude is 1. After the coded phase mask CPM (Coded Phase Mask) is modulated in the I-COACH system, the intensity recorded by the image sensor is I OH , get the final ciphertext, then replace the target object with the pinhole, and the point source hologram recorded by the image sensor is used as the key, whose intensity is I PSH , which is described by the formula Where θ represents the phase diagram of the complex amplitude, and "*" represents the convolution operation; S5, decryption and reconstruction: Assume that the reconstructed image complex amplitude estimate is, the ciphertext and key are cross-correlated and reconstructed, the reconstruction result is the real part real(U), and then the Kramers-Kronig relationship is used to recover the imaginary part Im(U), which is expressed as Among them, F[·] and F -1 [·] denotes two-dimensional Fourier transform and inverse transform, respectively. Represents the cross-correlation operation, the Hilbert transform corresponds to the multiplier -jsgn(v), v is the vertical spatial frequency, sgn(v) is the sign function, and j represents the imaginary unit; thus, the reconstructed phase image is obtained, and its expression is in, represents the reconstructed phase image, arctan(·) represents the inverse tangent function; Reconstructed phase image Decryption, this process is the reverse process of the first encryption, first orthogonal matrix Q T Back projection separates the DCT coefficients of the RGB channels and then performs inverse DCT transformation to reconstruct the color image.

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