An optical information hiding and decoding method based on pixel-free extension
Patent Information
- Application Number
- CN202311207952.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2023-09-19
- Publication Date
- 2026-10-23
- Estimated Expiration
- 2043-09-19
AI Technical Summary
[0005]另一方面，前几种视觉密码都会存在像素扩展问题，这样分享图像往往比秘密信息图像具有更大的尺寸，例如对于(k,n)门限的视觉密码，理想情况的像素扩展度为m＝2k-1，即一个像素加密为2k-1个子像素，为分享图像的存储以及传输带来了很大的不便
[0057]本发明通过无像素扩展的视觉密码方案对秘密信息图像进行编码，再进行隐藏可保证分享图像与恢复后的秘密信息图像与原始秘密信息图像大小相同，节省了存储空间，提高传输效率。
Smart Images
Figure CN117201696B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of visual cryptography, and in particular to a method for hiding and decoding optical information based on pixel-free extension. Background Technology
[0002] As an important technology for information security, the idea of secret sharing was proposed by Shamir and Blakey in 1979, primarily to solve the problem of key management. Shamir and Blakey implemented the first (k,n) threshold scheme using Lagrange interpolation and the properties of points in multidimensional space, respectively. The characteristic of this scheme is that any k or more participants can recover the secret information, while fewer than k participants cannot obtain it. The initial intention of secret sharing technology was to protect the key through distributed storage. However, when the shared object is an image containing rich information, general secret sharing schemes become difficult to implement. Based on this, in 1994, at the European Conference on Cryptography, Naor and Shamir proposed a new cryptographic scheme that can provide complete confidentiality and can be decrypted solely through the human visual system—this is visual cryptography.
[0003] Visual cryptography originates from threshold secret sharing technology. When encrypting a secret information image, operations are performed on a pixel-by-pixel basis, resulting in several shared copies. Because each shared copy is as chaotic as random noise, attackers cannot directly decipher the secret information from the ciphertext. Visual cryptography has attracted widespread attention from scholars since its inception, leading to extensive research in this field. Current research on visual cryptography generally includes: visual cryptography of binary images, grayscale images, color images, visual cryptography of images with multiple secret information, enhanced visual cryptography, and pixel-free visual cryptography.
[0004] Traditional visual cryptography uses pure amplitude images as ciphertext, which easily attracts the attention of attackers, leading to encryption failure. To address this issue, in 2017, Shi Yishi's research group proposed an indirect method to achieve invisible visual cryptography using diffraction optics. This transforms the visible pure amplitude image into a phase image invisible to the human eye and intensity detectors, further improving the security of visual cryptography. In coherent diffraction imaging phase retrieval algorithms, the GS algorithm is the first practical iterative phase reconstruction algorithm, initially proposed by Gerchberg and Saxton in 1971 when studying the phase retrieval problem in electron microscopy. The GS algorithm involves two planes and two constraints: the plane containing the light field to be measured and the plane containing its Fresnel diffraction field. The plane containing the light field to be measured is called the input plane, and the plane containing the Fresnel diffraction field is called the output plane. The output plane constraint is the light intensity recorded by the detector on the diffraction plane. Typically, the square root of the light intensity is used to replace the amplitude of the light field distribution function while preserving phase information. The input plane constraint is the light field intensity distribution on the light field to be measured.
[0005] On the other hand, the first few types of visual ciphers all suffer from pixel expansion problems, meaning the shared image is often larger than the secret information image. For example, for a visual cipher with a (k,n) threshold, the ideal pixel expansion is m = 2. k -1 That is, one pixel is encrypted as 2 k-1 The use of individual pixels creates significant inconvenience for storing and transmitting shared images. Summary of the Invention
[0006] The purpose of this invention is to provide an optical information hiding and decoding method based on pixel-free expansion, which can ensure that the shared image and the recovered secret information image are the same size as the original secret information image, saving storage space and improving transmission efficiency.
[0007] To achieve the above objectives, the present invention provides the following solution:
[0008] An optical information hiding method based on pixel-free expansion, the method comprising:
[0009] Select the secret information image;
[0010] The secret information image is encoded using a pixel-free visual cryptography scheme to obtain three shared images. The pixel-free visual cryptography scheme involves randomly transforming each row of a 3*4 basic matrix based on the secret information image, and obtaining the three shared images based on each row of the transformed 3*4 basic matrix.
[0011] The three shared images are hidden in a phase key using a phase retrieval algorithm; the phase key includes the diffraction distance and the diffraction wavelength.
[0012] Optionally, the phase recovery algorithm is the GS algorithm.
[0013] Optionally, a pixel-free visual cryptography scheme is used to encode the secret information image, resulting in three shared images, specifically including:
[0014] The secret information image is divided into multiple 2x2 pixel blocks;
[0015] A visual cryptography scheme without pixel expansion is used to encode each pixel block, resulting in three shared sub-images corresponding to each pixel block.
[0016] Optionally, a pixel-free visual cryptography scheme is used to encode each pixel block to obtain three shared sub-images corresponding to each pixel block, specifically including:
[0017] A fundamental matrix is selected based on the number of black and white pixels in the pixel block, and a random column transformation is performed on the fundamental matrix to obtain the transformed fundamental matrix; the fundamental matrix is either a first fundamental matrix or a second fundamental matrix.
[0018] The first fundamental matrix is:
[0019]
[0020] The second fundamental matrix is:
[0021]
[0022] Each row of the transformed base matrix is mapped to a shared image template to obtain three shared sub-images; the shared image template is a 2*2 size empty pixel block;
[0023] Among them, S 0 S represents the first fundamental matrix; 1 This represents the second fundamental matrix; 1 represents black; 0 represents white.
[0024] Optionally, a fundamental matrix is selected based on the number of black and white pixels in the pixel block, and a random column transformation is performed on the fundamental matrix to obtain a transformed fundamental matrix, specifically including:
[0025] If the pixel block includes four black pixels, then the fundamental matrix is determined to be the first fundamental matrix;
[0026] Perform a random column transformation on the first fundamental matrix to obtain the transformed fundamental matrix;
[0027] If the pixel block includes three black pixels and one white pixel, then the fundamental matrix is determined to be the second fundamental matrix;
[0028] Then, the white pixels are assigned to the all-zero column in the second basic matrix, and the other three columns are randomly transformed to obtain the transformed basic matrix;
[0029] If the pixel block includes two white pixels or three white pixels, then the fundamental matrix is determined to be the second fundamental matrix;
[0030] Then, randomly select a white pixel corresponding to the all-zero column in the second basic matrix, and perform random column transformation on the other three columns to obtain the transformed basic matrix;
[0031] If the pixel block includes four white pixels, then the fundamental matrix is the second fundamental matrix;
[0032] Perform a random column transformation on the second fundamental matrix to obtain the transformed fundamental matrix.
[0033] Optionally, a phase retrieval algorithm is used to hide the three shared images in a phase key, specifically including:
[0034] Let the value of k be 1;
[0035] Based on the input surface amplitude and the input surface phase of the k-th iteration, the complex amplitude P of the input surface in the k-th iteration is obtained. k (x,y):
[0036]
[0037] Fresnel diffraction is performed on the complex amplitude of the input surface in the k-th iteration to obtain the complex amplitude P of the first output surface in the k-th iteration. k (u,v) is:
[0038]
[0039] Using the amplitude of shared images Replace the actual amplitude |P of the complex amplitude of the first output surface in the k-th iteration k (u,v)|, yielding the complex amplitude P of the second output surface in the k-th iteration. k ′(u,v):
[0040]
[0041] Inverse Fresnel diffraction is performed on the complex amplitude of the second output surface in the k-th iteration to obtain the phase of the input surface in the (k+1)-th iteration;
[0042] Determine whether the iteration termination condition is met, and obtain the first determination result;
[0043] If the first judgment result is negative, then the value of k is increased by 1, and the complex amplitude P of the input surface in the kth iteration is obtained based on the input surface amplitude and the input surface phase in the kth iteration. k The steps for (x,y);
[0044] If the first judgment result is yes, then output θ. k (x,y) is used as the phase key;
[0045] Where j represents the imaginary part; exp[] represents the exponential function; (x,y) represents the input surface coordinates; (u,v) represents the output surface coordinates; FrT{·} represents the Fresnel transform; θ represents the phase of the complex amplitude of the second output surface in the k-th iteration; k (x,y) represents the input surface phase in the k-th iteration; U(x,y) represents the input surface light intensity. O(u,v) represents the amplitude of the input surface; O(u,v) represents the light intensity of the shared image.
[0046] A pixel-free optical information decoding method is provided, wherein the pixel-free optical information decoding method is applied to the aforementioned pixel-free optical information hiding method, and the pixel-free optical information decoding method includes:
[0047] Obtain the phase key;
[0048] The phase key is processed using Fresnel diffraction to obtain three output plane amplitude images;
[0049] The secret information image is obtained by superimposing the three output surface amplitude images and performing threshold segmentation.
[0050] Optionally, the optical information hiding system based on pixel-free expansion includes:
[0051] The selection module is used to select images containing secret information.
[0052] The encoding module is used to encode the secret information image using a pixel-free visual cryptography scheme to obtain three shared images; the pixel-free visual cryptography scheme is to randomly transform each row of a 3*4 basic matrix based on the secret information image, and obtain the three shared images based on each row of the transformed 3*4 basic matrix.
[0053] A hiding module is used to hide the three shared images in a phase key using a phase recovery algorithm; the phase key includes diffraction distance and diffraction wavelength.
[0054] An electronic device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, implements the pixel-free optical information hiding method as described above.
[0055] A computer-readable storage medium storing a computer program that, when executed, implements the pixel-free optical information hiding method as described above.
[0056] According to specific embodiments provided by the present invention, the present invention discloses the following technical effects:
[0057] This invention encodes secret information images using a pixel-free visual cryptography scheme and then hides them, ensuring that the shared image and the recovered secret information image are the same size as the original secret information image, thus saving storage space and improving transmission efficiency. Attached Figure Description
[0058] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0059] Figure 1 This is a flowchart of an optical information hiding and decoding method based on pixel-free expansion in an embodiment of the present invention;
[0060] Figure 2 This is a rule diagram for visual cryptographic encoding without pixel extension in an embodiment of the present invention;
[0061] Figure 3 This is an overlay result of any two shared images from this invention;
[0062] Figure 4 This is a superimposed image of any two output surface amplitude images of the present invention. Detailed Implementation
[0063] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0064] The purpose of this invention is to provide an optical information hiding and decoding method based on pixel-free expansion, which can ensure that the shared image and the recovered secret information image are the same size as the original secret information image, saving storage space and improving transmission efficiency.
[0065] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.
[0066] Example 1
[0067] like Figure 1 As shown, the present invention provides an optical information hiding method based on pixel-free expansion, the optical information hiding method based on pixel-free expansion comprising:
[0068] Select the secret information image.
[0069] The secret information image is encoded using a pixel-free visual cryptography scheme to obtain three shared images. The pixel-free visual cryptography scheme involves randomly transforming each row of a 3*4 basic matrix based on the secret information image, and obtaining the three shared images based on each row of the transformed 3*4 basic matrix.
[0070] For example: First, select an image containing secret information and encode it using a visual cryptography scheme without pixel expansion. The encoding process involves selecting 2x2 pixel blocks each time. Based on the number of black and white pixels in each block, the encoding scheme can be divided into five cases, such as... Figure 2 As shown.
[0071] The three shared images are hidden in a phase key using a phase retrieval algorithm; the phase key includes the diffraction distance and the diffraction wavelength.
[0072] As a specific embodiment, the phase recovery algorithm is the GS algorithm.
[0073] As a specific embodiment, a pixel-free visual cryptography scheme is used to encode the secret information image, resulting in three shared images, specifically including:
[0074] The secret information image is divided into multiple 2x2 pixel blocks.
[0075] A visual cryptography scheme without pixel expansion is used to encode each pixel block, resulting in three shared sub-images corresponding to each pixel block.
[0076] As a specific embodiment, a pixel-free visual cryptography scheme is used to encode each pixel block to obtain three shared sub-images corresponding to each pixel block, specifically including:
[0077] A fundamental matrix is selected based on the number of black and white pixels in the pixel block, and a random column transformation is performed on the fundamental matrix to obtain the transformed fundamental matrix; the fundamental matrix is either a first fundamental matrix or a second fundamental matrix.
[0078] The first fundamental matrix is:
[0079]
[0080] The second fundamental matrix is:
[0081]
[0082] Each row of the transformed base matrix is mapped to a shared image template to obtain three shared sub-images; the shared image template is a 2*2 size empty pixel block.
[0083] Among them, S 0 S represents the first fundamental matrix; 1 This represents the second fundamental matrix; 1 represents black; 0 represents white.
[0084] As a specific embodiment, a basic matrix is selected based on the number of black pixels and white pixels in the pixel block, and a random column transformation is performed on the basic matrix to obtain the transformed basic matrix, specifically including:
[0085] If the pixel block includes four black pixels, then the fundamental matrix is determined to be the first fundamental matrix.
[0086] Perform a random column transformation on the first fundamental matrix to obtain the transformed fundamental matrix.
[0087] If the pixel block includes three black pixels and one white pixel, then the fundamental matrix is determined to be the second fundamental matrix.
[0088] The white pixels are then assigned to the all-zero column in the second basic matrix, and the other three columns are subjected to random column transformation to obtain the transformed basic matrix.
[0089] If the pixel block includes two white pixels or three white pixels, then the fundamental matrix is determined to be the second fundamental matrix.
[0090] Then, randomly select a white pixel to correspond to the all-zero column in the second basic matrix, and perform random column transformation on the other three columns to obtain the transformed basic matrix.
[0091] If the pixel block includes four white pixels, then the fundamental matrix is the second fundamental matrix.
[0092] Perform a random column transformation on the second fundamental matrix to obtain the transformed fundamental matrix.
[0093] In practical implementation, when the secret information image contains white pixels, the superimposed results of the shared copies are the same. Therefore, the basic matrix corresponding to the visual cryptography scheme without pixel expansion consists of two matrices, namely...
[0094]
[0095]
[0096] Where 1 represents black and 0 represents white, when a white pixel exists in the secret information pixel block, the fundamental matrix S is used. 1 To share, select S only when all four pixels are black. 0 Let's share our findings. Based on the varying number of black and white pixels in the four pixels, we can discuss four different scenarios for the sharing algorithm.
[0097] 1) When all four pixels are black, then for S 0 Perform a random column transformation and map each row of the transformed base matrix to the corresponding shared sub-image.
[0098] 2) When all four pixels are white, then for S 1 Perform a random column transformation and map each row of the transformed base matrix to the corresponding shared sub-image.
[0099] 3) If the four pixels are three black and one white, then let the white pixel correspond to S. 1 The base matrix consists of all zero columns, and the other three columns are randomly transformed. Each row of the transformed base matrix is then mapped to the corresponding shared sub-image.
[0100] 4) If two or more of the four pixels are white, then randomly select a white pixel to correspond to S. 1 The base matrix consists of all zero columns, and the other three columns are randomly transformed. Each row of the transformed base matrix is then mapped to the corresponding shared sub-image.
[0101] As a specific embodiment, a phase retrieval algorithm is used to hide the three shared images in a phase key, specifically including:
[0102] Let the value of k be 1.
[0103] Based on the input surface amplitude and the input surface phase of the k-th iteration, the complex amplitude P of the input surface in the k-th iteration is obtained. k (x,y):
[0104]
[0105] Fresnel diffraction is performed on the complex amplitude of the input surface in the k-th iteration to obtain the complex amplitude P of the first output surface in the k-th iteration. k (u,v) is:
[0106]
[0107] Using the amplitude of shared images Replace the actual amplitude |P of the complex amplitude of the first output surface in the k-th iteration k (u,v)|, yielding the complex amplitude P of the second output surface in the k-th iteration. k ′(u,v):
[0108]
[0109] Inverse Fresnel diffraction is performed on the complex amplitude of the second output surface in the k-th iteration to obtain the phase of the input surface in the (k+1)-th iteration.
[0110] Determine if the iteration termination condition is met to obtain the first determination result. The iteration termination condition is reaching the set number of iterations.
[0111] If the first judgment result is negative, then the value of k is increased by 1, and the complex amplitude P of the input surface in the kth iteration is obtained based on the input surface amplitude and the input surface phase in the kth iteration. k The steps for (x,y).
[0112] If the first judgment result is yes, then output θ. k (x,y) is used as the phase key.
[0113] Where j represents the imaginary part; exp[] represents the exponential function; (x,y) represents the input surface coordinates; (u,v) represents the output surface coordinates; FrT{·} represents the Fresnel transform; θ represents the phase of the complex amplitude of the second output surface in the k-th iteration; k (x,y) represents the input surface phase in the k-th iteration; U(x,y) represents the input surface light intensity. O(u,v) represents the amplitude of the input surface; O(u,v) represents the light intensity of the shared image.
[0114] After the above steps, the secret information image is hidden in the phase key.
[0115] Example 2
[0116] like Figure 1 As shown, an optical information decoding method based on pixel-free extension is proposed. This method is applied to the optical information hiding method based on pixel-free extension described in Example 1. The optical information decoding method based on pixel-free extension includes:
[0117] Obtain the phase key.
[0118] The phase key was processed using Fresnel diffraction to obtain three output plane amplitude images.
[0119] If you directly overlay any two shared images, the result will be as follows: Figure 3 The results shown confirm the feasibility of pixel-free extended visual cryptography.
[0120] Still as Figure 1 As shown, the secret information image is obtained by superimposing the three output surface amplitude images and performing threshold segmentation.
[0121] If only any two output plane amplitude images are superimposed, the following will occur: Figure 4 The results shown further confirm the feasibility of an invisible visual cryptography without pixel expansion.
[0122] In practice, to extract the image, the correct diffraction distance and wavelength must first be known. Then, the obtained phase key is reproduced using Fresnel diffraction to obtain the output surface amplitude image. Finally, the output surface amplitude images are superimposed and threshold segmentation is performed to observe the secret information image.
[0123] As one specific embodiment, the optical information hiding system based on pixel-free expansion includes:
[0124] The selection module is used to select images containing secret information.
[0125] The encoding module is used to encode the secret information image using a pixel-free visual cryptography scheme to obtain three shared images. The pixel-free visual cryptography scheme involves randomly transforming each row of a 3*4 basic matrix based on the secret information image, and obtaining the three shared images based on each row of the transformed 3*4 basic matrix.
[0126] A hiding module is used to hide the three shared images in a phase key using a phase recovery algorithm; the phase key includes diffraction distance and diffraction wavelength.
[0127] An electronic device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, implements the optical information hiding method based on pixel-free extension as described in Embodiment 1.
[0128] A computer-readable storage medium storing a computer program that, when executed, implements the pixel-free optical information hiding method as described in Embodiment 1.
[0129] The implementation process of this invention is as follows: 1) First, select a secret information image, convert the image into a binary image, and then encode it using a visual cryptography scheme without pixel expansion to obtain three shared images. 2) Use a phase recovery algorithm, such as the GS algorithm, to hide the three shared images in the phase key. In this way, the secret information is completely hidden in the phase key, which is invisible to the human eye. In this process, the diffraction distance and wavelength can be used as keys. 3) In the information extraction process, the correct diffraction distance and wavelength must first be known. Fresnel diffraction is used to reconstruct the amplitude image. 4) The secret information can be recovered by superimposing the three amplitude images obtained from diffraction and performing threshold segmentation. Superimposing any two images will not yield any valuable information.
[0130] The beneficial effects that this invention can achieve are:
[0131] 1. The advantages of pixel-free visual cryptography compared to traditional visual cryptography are: the shared image and the recovered secret information image are the same size as the original secret information image, saving storage space, transmission time and network bandwidth.
[0132] 2. Invisibility: Combining phase retrieval algorithms can convert amplitude images into phase images that are invisible to the human eye and intensity detectors, thus improving the invisibility of shared images.
[0133] 3. Security: The encoding scheme of visual cryptography, the phase recovery algorithm used, and the diffraction distance and wavelength can all be used as keys, which greatly improves the security of the system.
[0134] The encryption method proposed in this invention, which combines optics with traditional information security, ultimately transmits a phase key as the final image. The phase key is highly vulnerable and can be used to prevent fraud in online shopping and for digital watermarking.
[0135] Specific applications of this invention:
[0136] 1. Preventing Online Shopping Fraud
[0137] Online shopping involves searching for products online, submitting orders, and paying electronically. However, some criminals use fake websites or emails to steal consumers' bank card numbers and passwords. This invention proposes a pixel-free, invisible visual cipher to prevent online shopping fraud. The system consists of a bank server, merchants, and customers. Both merchants and customers register their information on the bank server. Customers first provide their username and ID to the merchant. The merchant sends the received information along with their own information to the bank server for authentication. The bank first authenticates the merchant. If authentication is successful, the bank server generates a one-time password and uses the pixel-free visual cipher to create three shared images. The GS algorithm is then used to obtain three phase key images. One phase key image is kept by the bank, one is sent to the merchant, and the third is sent to the customer. The merchant sends the received shared image to the customer, who then sends it back to the bank along with their own shared image. The bank decrypts and verifies the image. If the verification is successful, the transaction continues.
[0138] 2. Digital watermarking
[0139] With the development of network technology, the distribution and access of digital information has become very convenient. However, it is very important to ensure that digital information and the rights of information owners are not infringed. Digital watermarking is considered an effective solution for protecting copyright. Based on this invention, digital watermarking can be implemented. The digital watermark can be the signature of the information owner. First, the signature is converted into a binary image, and then three analysis images are obtained using this invention. One analysis image is embedded in the protected information, another is kept by the certification authority for authentication, and the third is kept by the information owner. When the owner requests copyright protection, the first analysis image is extracted from the protected information with the embedded watermark. Then, the owner's own analysis image is decrypted and verified together with the image kept by the certification authority. If the result is correct, the applicant's identity is confirmed.
[0140] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the systems disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the descriptions are relatively simple; relevant parts can be referred to the method section.
[0141] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.
Claims
1. A method for hiding optical information based on pixel-free expansion, characterized in that, The optical information hiding method based on pixel-free expansion includes: Select the secret information image; The secret information image is encoded using a pixel-free visual cryptography scheme to obtain three shared images; The method of encoding the secret information image using a pixel-free visual cryptography scheme to obtain three shared images specifically includes: dividing the secret information image into multiple 2*2 pixel blocks; and encoding each pixel block using a pixel-free visual cryptography scheme to obtain three shared sub-images corresponding to each pixel block. The method employing a pixel-free visual cryptography scheme to encode each pixel block, resulting in three shared sub-images corresponding to each pixel block, specifically includes: selecting a base matrix based on the number of black and white pixels in the pixel block, and performing a random column transformation on the base matrix to obtain a transformed base matrix; the base matrix is either a first base matrix or a second base matrix; the first base matrix is: ； The second fundamental matrix is: ； Each row of the transformed fundamental matrix is mapped to a shared image template, resulting in three shared sub-images; the shared image template is a 2x2 empty pixel block; wherein, Represents the first fundamental matrix; This represents the second fundamental matrix; 1 represents black; 0 represents white. The step of selecting a base matrix based on the number of black and white pixels in the pixel block and performing a random column transformation on the base matrix to obtain a transformed base matrix specifically includes: if the pixel block includes four black pixels, then the base matrix is determined to be the first base matrix; a random column transformation is performed on the first base matrix to obtain a transformed base matrix; if the pixel block includes three black pixels and one white pixel, then the base matrix is determined to be the second base matrix; then the white pixel is assigned to the all-zero column in the second base matrix, and the other three columns are randomly transformed to obtain a transformed base matrix; if the pixel block includes two or three white pixels, then the base matrix is determined to be the second base matrix; then a white pixel is randomly selected and assigned to the all-zero column in the second base matrix, and the other three columns are randomly transformed to obtain a transformed base matrix; if the pixel block includes four white pixels, then the base matrix is the second base matrix; a random column transformation is performed on the second base matrix to obtain a transformed base matrix. The three shared images are hidden in a phase key using a phase retrieval algorithm; the phase key includes the diffraction distance and the diffraction wavelength.
2. The optical information hiding method based on pixel-free expansion according to claim 1, characterized in that, The phase recovery algorithm is the GS algorithm.
3. The optical information hiding method based on pixel-free expansion according to claim 2, characterized in that, The three shared images are hidden in a phase key using a phase retrieval algorithm, specifically including: make k The value is 1; Based on the input surface amplitude and the first k The input surface phase of the nth iteration yields the nth... k The complex amplitude of the input surface in the next iteration : ； For the k The complex amplitude of the input surface in the nth iteration is subjected to Fresnel diffraction to obtain the nth... k The complex amplitude of the first output surface in the next iteration for: ； Using the amplitude of shared images Replace the first k The actual amplitude of the first output surface complex amplitude in the next iteration , obtained the k The complex amplitude of the second output surface in the next iteration : ； For the k The complex amplitude of the second output surface in the second iteration is subjected to inverse Fresnel diffraction to obtain the... k +1 iterations of input surface phase; Determine whether the iteration termination condition is met, and obtain the first determination result; If the first judgment result is negative, then let k The value is increased by 1, and the result is returned based on the input surface amplitude and the first... k The input surface phase of the nth iteration yields the nth... k The complex amplitude of the input surface in the next iteration Steps; If the first judgment result is yes, then output As a phase key; in, j The imaginary part is represented by exp[ ]; the exponential function is represented by exp[ ]. Indicates the input plane coordinates; Indicates the output plane coordinates; Represents the Fresnel transform; Indicates the first k The phase of the complex amplitude of the second output surface in the next iteration; Indicates the first k The input surface phase of the next iteration; Indicates the light intensity of the input surface; Indicates the amplitude of the input surface; This indicates the light intensity of the shared image.
4. A method for decoding optical information based on pixel-free extension, characterized in that, The pixel-free optical information decoding method is applied to the pixel-free optical information hiding method according to any one of claims 1-3, wherein the pixel-free optical information decoding method includes: Obtain the phase key; The phase key is processed using Fresnel diffraction to obtain three output plane amplitude images; The secret information image is obtained by superimposing the three output surface amplitude images and performing threshold segmentation.
5. An optical information hiding system based on pixel-free expansion, characterized in that, The optical information hiding system based on pixel-free expansion includes: The selection module is used to select images containing secret information. The encoding module is used to encode the secret information image using a pixel-free visual cryptography scheme to obtain three shared images. Specifically, the pixel-free visual cryptography scheme for encoding the secret information image to obtain three shared images includes: dividing the secret information image into multiple 2x2 pixel blocks; and encoding each pixel block using a pixel-free visual cryptography scheme to obtain three shared sub-images corresponding to each pixel block. The method employing a pixel-free visual cryptography scheme to encode each pixel block, resulting in three shared sub-images corresponding to each pixel block, specifically includes: selecting a base matrix based on the number of black and white pixels in the pixel block, and performing a random column transformation on the base matrix to obtain a transformed base matrix; the base matrix is either a first base matrix or a second base matrix; the first base matrix is: ； The second fundamental matrix is: ； Each row of the transformed fundamental matrix is mapped to a shared image template, resulting in three shared sub-images; the shared image template is a 2x2 empty pixel block; wherein, Represents the first fundamental matrix; This represents the second fundamental matrix; 1 represents black; 0 represents white. The step of selecting a base matrix based on the number of black and white pixels in the pixel block and performing a random column transformation on the base matrix to obtain a transformed base matrix specifically includes: if the pixel block includes four black pixels, then the base matrix is determined to be the first base matrix; a random column transformation is performed on the first base matrix to obtain a transformed base matrix; if the pixel block includes three black pixels and one white pixel, then the base matrix is determined to be the second base matrix; then the white pixel is assigned to the all-zero column in the second base matrix, and the other three columns are randomly transformed to obtain a transformed base matrix; if the pixel block includes two or three white pixels, then the base matrix is determined to be the second base matrix; then a white pixel is randomly selected and assigned to the all-zero column in the second base matrix, and the other three columns are randomly transformed to obtain a transformed base matrix; if the pixel block includes four white pixels, then the base matrix is the second base matrix; a random column transformation is performed on the second base matrix to obtain a transformed base matrix. A hiding module is used to hide the three shared images in a phase key using a phase recovery algorithm; the phase key includes diffraction distance and diffraction wavelength.
6. An electronic device, characterized in that, It includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, implements the method as described in any one of claims 1 to 3.
7. A computer-readable storage medium, characterized in that, The storage medium stores a computer program, which, when executed, implements the method as described in any one of claims 1 to 3.