An image visual security method based on compressed sensing and discrete wavelet transform

Abstract

The application discloses an image visual security method based on compressed sensing and discrete wavelet transform, and belongs to the technical field of information security. The application designs an image visual security algorithm based on compressed sensing and discrete wavelet transform in view of the problems that the histogram of the image is not uniform enough, the information entropy is not close to the ideal value enough, and there is no visual meaning after the image is only subjected to compressed sensing and simple encryption. The method uses a one-dimensional chaotic equation as a pseudo-random sequence generator, uses Arnold cat mapping to scramble the original image, uses compressed sensing technology to compress the scrambled image, then uses a shift XOR operation to replace the pixel value to improve security, and finally embeds the intermediate state ciphertext to obtain a visual security image. Through theoretical analysis and experimental simulation, the application has excellent encryption performance, the embedding method can achieve visual security, the embedded image can be losslessly extracted and reconstructed, and the application has wide application value in real-time transmission networks.

Description

Technical Field

[0001] This invention belongs to the field of information security technology, specifically relating to an image visual security method based on compressed sensing and discrete wavelet transform. Background Technology

[0002] With the rapid development of information technology in the Internet era, people are increasingly using images to acquire and convey information. In real-time communication, sometimes images are directly encrypted to ensure privacy, making them undecipherable for others and attackers. However, sometimes, to avoid attracting the attention of attackers, an already encrypted image needs to be embedded into the carrier image using embedding technology to ensure the visual security of important information. Therefore, researching a highly secure encryption method and a highly feasible embedding method is a key research area.

[0003] Compressed sensing is widely used in image signal processing because it can achieve the Aynurs sampling rate without losing important information. Compressed sensing can quickly compress images and recover the main information of the image to the greatest extent. However, compressed sensing alone is not secure enough against statistical attacks, so other encryption techniques are often used before and after compression. In the past, people usually used operations such as shifting and transposing to encrypt text or convert images into one-dimensional data for encryption. However, this ignores the two-dimensional nature of the image and cannot guarantee security during transmission. Therefore, many new encryption technologies currently use different encryption techniques such as chaotic systems [1-5], DNA encoding technology [6-8], cellular automata [9,10], matrix encoding technology [11,12], optics [13,14] and quantum conversion [15,16] to encrypt images into snowflake-shaped ciphertext images. However, these technologies cannot achieve visual security, thus attracting the attention of some attackers. Visual security algorithms combine compression encryption with embedding. This method compresses and encrypts the image before embedding it into the carrier image. Attackers cannot determine whether the image carries secret information, thus improving transmission security to a greater extent. For example, Chai et al.

[17] used compressed sensing and zigzag obfuscation for compression encryption, decomposed the carrier image using DWT, and embedded the decomposition coefficients to obtain a visual security image. This method is highly efficient, but the distortion rate of the carrier image is high, and the visual effect of the visual security image is generally poor. It is suitable for application scenarios with high efficiency requirements. Hua et al.

[12] proposed a visual security image encryption scheme based on adaptive threshold sparsity and PCS. They used matrix coding technology to embed the secret image into the carrier image. This method can recover a high-quality reconstructed image. The matrix coding technology reduces the distortion rate of the carrier image, and the encryption algorithm is more secure.

[0004] This invention studies compressed sensing and discrete wavelet embedding methods to improve the visual quality of images after compression and reconstruction. At the same time, it uses a highly complex encryption algorithm to ensure the security of the intermediate ciphertext of the image. The embedded visually secure image is structurally highly similar to the carrier image, thus ensuring the visual security of the image. Summary of the Invention

[0005] The purpose of this invention is to address the fact that many images currently only use traditional encryption techniques to encrypt them into snowflake-shaped ciphertext images. However, these images attract the attention of attackers during real-time transmission over channels and are easily cracked. Therefore, researching a visually meaningful method can enhance security. Specifically, this invention claims protection for an image visual security method based on compressed sensing and discrete wavelet transform, including its overall algorithm and specific implementation methods.

[0006] The technical solution adopted by this invention to solve the above-mentioned technical problems is: an image visual security method based on compressed sensing and discrete wavelet transform. This solution mainly includes two modules: compression encryption and discrete wavelet transform embedding.

[0007] 1. Chaotic systems and pseudo-random generators

[0008] One-dimensional logistic chaotic systems and one-dimensional sine mappings are two classic one-dimensional chaotic systems. Based on these two classic chaotic systems, a new highly stochastic one-dimensional chaotic system is designed, and its equations are expressed as follows:

[0009] x n+1 =a sin(π) 2 a 2 x n (1-x n ))(a-sin(π 2 a 2 sin(πx n (1-x n (1)

[0010] Where 'a' is a control parameter, when the control parameter is greater than 200, its Lyapunov exponent reaches 24. The Lyapunov exponent represents the orbital separation velocity, indicating that the equation has strong randomness. A plaintext image is subjected to a SHA-256 operation to obtain a 256-bit binary number. This binary number is converted to decimal and rounded down to its decimal value as the initial value of the system. The system is iterated 4*M*N times, where M and N are the length and width of the plaintext image. The first M*N values ​​are discarded, and the last 3*M*N values ​​are divided into three equal parts to obtain the random sequence {x}. n},{y n},{z n} is used for the encryption and measurement matrix generation steps.

[0011] 2. Compression and Encryption Scheme Design

[0012] To ensure both visual security and the security of the intermediate ciphertext, this invention employs compressed sensing and embedding, along with a complex encryption algorithm. First, let's understand the principles of compressed sensing and the construction and optimization of the measurement matrix:

[0013] 2.1 Compressed Sensing Principle

[0014] Compressed sensing is a new sampling theory that allows the Nyquist sampling rate to be achieved without losing important information

[18] . When a signal is sparse or sparsely represented, it can still be reconstructed without distortion even if the signal is much lower than the Nyquist sampling rate. The compressed sensing process is as follows:

[0015] Y=ΦX=ΦψS=ΘS (2)

[0016] Where the sparse basis is the measurement matrix of size and is the sensing matrix. During the reconstruction stage, equation (2) needs to be solved. Since the unknown N is greater than the measurement equation M, the signal X cannot be obtained by general methods. We solve it by adding constraints. For a signal in the domain, we find the vector with the smallest coefficient in the domain, i.e., the one with the smallest norm, as shown below:

[0017]

[0018] This is an NP-hard non-convex optimization problem. Generally, relaxation techniques are used to approximate convex problems. Common methods for solving convex problems (i.e., methods for reconstructing signals) include basis pursuit (BP), orthogonal matched pursuit (OMP), and smoothing norm (SL0). This method will use the orthogonal matched pursuit (OMP) to reconstruct the signal.

[0019] 2.2 Construction and Optimization of Measurement Matrix

[0020] The generated pseudo-random sequence {x n The following method is used to generate the measurement matrix:

[0021]

[0022] 2.3 Compression and Encryption Scheme

[0023] First, perform a multi-dimensional discrete wavelet transform on the plaintext image, sparsify the wavelet coefficients after the transformation, that is, set a threshold and set all values less than the threshold to zero. Then, perform an Arnold scrambling on the wavelet sparse coefficients to obtain a preliminary encrypted matrix. Next, perform compressive measurement on this matrix to obtain compressive sensing measurement values. Then, perform a diffusion XOR operation on these measurement values associated with the plaintext to obtain a relatively secure intermediate state compressed encrypted image.

[0024] 3. Embedding Scheme Design

[0025] To ensure visual security, while using compressive sensing and non-linear encryption, this invention also uses the embedding method of discrete wavelet transform. The specific method is as follows:

[0026] First, perform a discrete wavelet transform on the carrier image (with size M×N) to obtain four high and low frequency components CA, CH, CV, CD (all with size Take the mean MV of the high frequency component CA; then use formula X and X to obtain H1 and H2 (both with size ). Then, make a judgment. If CA>MV, replace the values at the corresponding positions of H1 into CH, and replace the values at the corresponding positions of H2 into CV. If CA<MV, replace the values at the corresponding positions of H1 into CV, and replace the values at the corresponding positions of H2 into CH. Then, perform an inverse discrete wavelet transform on the four replaced component matrices to obtain the visually secure image, that is, the embedding operation is completed.

[0027] H1(i,j) = P(i,j) mod 10 (5)

[0028] H2(i,j) = floor(P(i,j) / 10) (6)

[0029] 4. Compressive Performance and Security Analysis

[0030] In this section, through experimental simulations and tests, experimental results and data are generated to visually demonstrate the security of the algorithm.

[0031] 4.1 Key Stream Test

[0032] Usually, we analyze a large number of pseudo-random sequences generated by the chaotic sequence to judge its randomness, and thus evaluate the performance of this chaotic equation. Generally, the NIST SP800 test of the National Security and Technology Council of the United States is adopted. Among them, take 100 groups of pseudo-random sequence key streams with 1,000,000 bits for testing. The closer the Pass Rate is to 1, the better. The P-Value needs to be greater than the threshold 0.01, otherwise it is considered a failed test. The results are shown in the following table:

[0033] Table l NIST SP800 Test Results

[0034]

[0035] The results in Table 1 show that the pseudo-random key stream generated by the one-dimensional highly random chaotic equation proposed in this invention has good randomness and can provide good randomness and security.

[0036] 4.2 Key Space Analysis

[0037] Since this method uses hashing to generate initial values, it generates 256-bit binary numbers from plaintext images. According to the IEEE 754-2008 standard, these numbers are stored in double-precision (binary64) format, with eight bytes representing one double-precision number. Therefore, the key space for this method is 2^64 bytes. 256 We typically consider the key space to be greater than 2. 100 It is safe and can resist brute-force attacks.

[0038] 4.3 Performance Analysis of Compression and Reconstruction

[0039] The visual quality of the reconstructed image after compression is also an important indicator of an algorithm's performance. We typically use Peak Signal-to-Noise Ratio (PSNR) to calculate the difference between corresponding pixels in the original and reconstructed images to measure the quality of the reconstructed image. Generally, a PSNR above 25 indicates that the image is visually indistinguishable from the original, and the higher the value, the closer the reconstructed image is to the original. The formula for calculating PSNR is as follows:

[0040]

[0041]

[0042] To verify the compression and reconstruction performance of this invention, we selected standard images from the USC-SIPI database for testing, and the results are shown below:

[0043] Table 2. PSNR (dB) of the reconstructed images after compression and encryption.

[0044]

[0045] The results in Table 2 show that the reconstructed image still has high visual quality at a low compression ratio, while its visual quality is highly similar to that of the plaintext image when the compression ratio is high.

[0046] 4.4 Correlation Analysis of Adjacent Pixels in Intermediate-State Ciphertext Images

[0047] Adjacent pixel correlation reflects the degree of correlation between pixel values ​​at adjacent positions in an image. A good image encryption algorithm can reduce the correlation between adjacent pixels, aiming for near-zero correlation. Generally, it involves analyzing three aspects: horizontal, vertical, and diagonal pixels. The correlation coefficient is defined as follows:

[0048]

[0049] Table 5 Correlation Analysis of Adjacent Pixels

[0050]

[0051] The results in Table 5 show that this method can minimize the correlation between adjacent pixels in plaintext images and has good security.

[0052] 4.5 Information Entropy Analysis

[0053] The information entropy of an image reflects its randomness. For ciphertext of length T, the formula for calculating its information entropy is as follows:

[0054]

[0055] The ideal value for information entropy is 8. The closer the encrypted image is to 8, the better its randomness. We tested the information entropy of the encrypted images of Lena, Female, Tree, House, and Cameraman (256*256) at a compression ratio of 0.5. The results are shown below:

[0056] Table 6. Information Entropy Analysis Results

[0057]

[0058] The results shown in Table 6 demonstrate that the encryption method of the present invention has excellent randomness. Attached Figure Description

[0059] Figure 1 is a flowchart of the algorithm of the present invention;

[0060] Figure 2 shows the intermediate ciphertext image and the reconstructed image of the compressed encryption of the present invention; where (a)-(d) are plaintext images, (e)-(h) are intermediate ciphertext images, and (i)-(l) are reconstructed decrypted images;

[0061] Figure 3 shows the visual security images and their histograms of the intermediate-state encrypted image of Figure 2 embedded into different carrier images; where (a)-(d) are carrier images, (e)-(h) are histograms of carrier images, (i)-(l) are embedded visual security images, and (m)-(p) are histograms of visual security images. Detailed Implementation

[0062] The present invention will be further described below with reference to embodiments. 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 protection scope of the present invention.

[0063] The image compression and encryption method proposed in this invention mainly includes the following steps:

[0064] The first step is to select an image X of size M×N, perform a hash operation on it to obtain a 256-bit binary number, convert it to a decimal number and fractionalize it to obtain the initial key x0 of the equation.

[0065] The second step involves inputting the initial key x0 into a one-dimensional highly random chaotic equation and iterating 4×M×N times. To ensure good randomness of the pseudo-random sequence, the first M×N numbers are discarded, and the pseudo-random sequence of length 3×M×N is divided into three equal segments to obtain {x n},{y n},{z n Then generate three key streams. The specific generation method is as follows:

[0066]

[0067]

[0068]

[0069] The third step is to use multidimensional discrete wavelet transform on the image X to obtain wavelet coefficients. Then, a threshold T = 0.080 is set, and wavelet coefficients smaller than the threshold T are set to zero to further sparsify the image, resulting in a sparse matrix D.

[0070] The fourth step is to perform the Arnold transformation on the sparse matrix D. The specific method is as follows:

[0071]

[0072] Where is the matrix coordinate position, and is the transformed matrix coordinate position.

[0073] Fifth step, using the pseudo-random sequence {x} n Generate a measurement matrix, set the compression ratio to CR, and obtain a measurement matrix Φ of size CR×M×N. Then, perform compressed sensing measurement on the sparse matrix D. The calculation formula is as follows:

[0074] Y = ΦD (15)

[0075] This yields a scrambled matrix D′ of size CR×M×N;

[0076] The sixth step is to convert the scrambled matrix D′ into a one-dimensional array in preparation for the diffusion operation. The specific operation is as follows:

[0077]

[0078] E i =D i-1 <<<mod(x) i *10 14 ,4) (17)

[0079]

[0080] Where i = 2, ..., CR×M×N, and P is the intermediate state ciphertext image.

[0081] Step 7: Select a carrier image of size M′×N′ and embed the intermediate ciphertext image into the carrier image using the least significant bit method. Specifically, first perform discrete wavelet transform on the carrier image to obtain four high-frequency and low-frequency components. Then, selectively embed the intermediate ciphertext image into the high-frequency or low-frequency components at positions where the value is greater than or less than the mean, respectively, to obtain the visual security image.

[0082] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

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Claims

1. An image visual security method based on compressed sensing and least significant bit, which is implemented in the following seven steps: The first step is to select an image X of size M×N, perform a hash operation on it to obtain a 256-bit binary number, convert it to a decimal number and fractionalize it to obtain the initial key x0 of the equation. The second step involves inputting the initial key x0 into a one-dimensional highly random chaotic equation and iterating 4×M×N times. To ensure good randomness of the pseudo-random sequence, the first M×N numbers are discarded, and the pseudo-random sequence of length 3×M×N is divided into three equal segments to obtain {x n },{y n },{z n Then generate three key streams. The specific generation method is as follows: The third step is to use multidimensional discrete wavelet transform on the image X to obtain wavelet coefficients. Then, a threshold T = 0.080 is set, and wavelet coefficients smaller than the threshold T are set to zero to further sparsify the image, resulting in a sparse matrix D. The fourth step is to perform the Arnold transformation on the sparse matrix D. The specific method is as follows: in, Let be the matrix coordinate position, and be the transformed matrix coordinate position; Fifth step, using the pseudo-random sequence {x} n Generate a measurement matrix, set the compression ratio to CR, and obtain a measurement matrix Φ of size CR×M×N. Then, perform compressed sensing measurement on the sparse matrix D. The calculation formula is as follows: Y=ΦD (5) This yields a scrambled matrix D′ of size CR×M×N; The sixth step is to convert the scrambled matrix D′ into a one-dimensional array in preparation for the diffusion operation. The specific operation is as follows: E i =D i-1 <<<mod(x i *10 14 ,4) (7) Where i = 2, ..., CR×M×N, and P is the intermediate state ciphertext image; Step 7: Select a carrier image of size M′×N′ and embed the intermediate ciphertext image into the carrier image using the least significant bit method. Specifically, first perform discrete wavelet transform on the carrier image to obtain four high-frequency and low-frequency components. Then, selectively embed the intermediate ciphertext image into the high-frequency or low-frequency components at positions where the value is greater than or less than the mean, respectively, to obtain the visual security image.

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