Image encryption method based on one-dimensional improved Logistic mapping parallelism

Abstract

The invention discloses a parallel image encryption method based on one-dimensional improved Logistic mapping, which relates to the technical field of image encryption, and is characterized by comprising the following steps: S1, designing improved one-dimensional Logistic mapping; s2, generating a key of a password system from the plaintext information; s3, a color image to be encrypted is split into three independent color channels, and preparation is made for parallel processing; and S4, generating a key stream of the cryptosystem by using the key and the improved one-dimensional Logistic mapping. The technical problem to be solved by the invention is to provide an image encryption method based on one-dimensional improved Logistic mapping parallelism, and a chaotic sequence is generated through improved Logistic mapping, so that pixel-by-pixel encryption processing is carried out on an image. According to the method, the confidentiality and the attack resistance of the image data are enhanced, and the encryption speed is increased, so that the method is suitable for scenes such as real-time image transmission and large-scale image storage.

Description

Technical Field

[0001] The present invention relates to the technical field of image encryption, and more specifically, to an image encryption method based on parallel one-dimensional improved Logistic mapping. Background Art

[0002] With the rapid development of information technology, digital images are increasingly widely used in daily life, such as social media, e-commerce, telemedicine, and intelligent monitoring. These applications not only facilitate the dissemination and sharing of information but also expose potential security risks in the transmission and storage of image data. Potential security issues include data leakage, tampering, and unauthorized access. The emergence of these problems has put forward higher requirements for user privacy protection and data security.

[0003] The protection technology of image data, especially image encryption technology, has become the key to ensuring the security of digital images. Traditional encryption algorithms are mostly based on symmetric encryption and asymmetric encryption methods. However, they often face problems such as slow speed and weak anti-attack ability. Although one-dimensional chaotic mapping performs well in some applications, there are still some problems that need to be solved urgently. Among them, relatively poor chaotic performance is one of its main defects. This means that the generated chaotic sequence may lack the required randomness and cannot effectively meet the needs of high-security applications. Specifically, lower chaotic performance may lead to increased predictability of the sequence, enabling attackers to deduce partial information by analyzing the output data during the encryption process, thus threatening data confidentiality. In addition, the one-dimensional chaotic mapping also has the problem of periodic windows, which is particularly prominent. Under specific parameter settings or initial conditions, the output sequence will repeat within a limited range. This not only reduces the complexity of the sequence but also may lead to a significant decrease in security because attackers can use this regularity to crack the encrypted information. The existence of periodic phenomena, especially when dealing with long sequences or large-scale data, will limit the anti-attack ability of the encryption system and thus affect its practical application in high-security environments. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide an image encryption method based on parallel one-dimensional improved Logistic mapping, which generates a chaotic sequence through the improved Logistic mapping and then performs pixel-by-pixel encryption on the image. This method not only enhances the confidentiality and anti-attack ability of image data but also improves the encryption speed, making it suitable for scenarios such as real-time image transmission and large-scale image storage.

[0005] The present invention adopts the following technical solutions to achieve the invention purpose: An image encryption method based on parallel one-dimensional improved Logistic mapping, characterized by comprising the following steps: S1: Design an improved one-dimensional Logistic map; S2: Generate the key of the cryptosystem from the plaintext information; S3: Split the color image to be encrypted into three independent color channels to prepare for parallel processing; S4: Use the key and the improved one-dimensional Logistic map to generate the key stream of the cryptosystem; S5: Implement a parallel encryption algorithm for each color channel, and independently encrypt the pixel values of each channel using the generated chaotic sequence.

[0006] As a further limitation of this technical solution, the improved one-dimensional Logistic map designed in S1 is specifically: (1); Where: and represent the current state and the next state of the chaotic sequence respectively; is the control parameter.

[0007] As a further limitation of this technical solution, S2 specifically includes: S21; Calculate the sum SU of the pixel values of the plaintext image and scale it to a value as the initial value y(1); S22: Use the improved one-dimensional Logistic map for iterative calculation, generate the y sequence through loop, and perform 25 iterations; (2); Where: represents the number of iterations, starts from 1 and iterates 25 times; S23: Scale the 25th iteration value y(25) to generate the parameter and store the 24th value y(24) in x(1) for subsequent calculation.

[0008] As a further limitation of this technical solution, S3 specifically includes: (3); Where: PR , PG and PB are the red, green and blue channels of the plaintext image respectively, and the sizes of the three are ; Perform information fusion on the red, green and blue channels to obtain new three channels: NPR ,NPG and NPB ; (4).

[0009] As a further limitation of this technical solution, S4 specifically includes: Using control parameters and the initial value x(1), and generating a key stream using an improved one-dimensional Logistic map, (5); Iterating times to generate a key stream x and generating a key stream for diffusion X 1、 X 2 and X 3: (6); Wherein: is used to calculate the remainder after dividing two integers; is the floor function; Generating a key stream for scrambling S 1、 S 2 and S 3: (7); For S 1、 S 2 and S 3, use sortrows to sort and obtain matrix S 1', S 2' and S 3', respectively find the positions of each element in S 1', S 2' and S 3 in S 1、 S 2 and S 3, and record the position matrix as NS 1、 NS 2 and NS 3: (8); Wherein: The sortrows function sorts all rows of matrix S 1、 S 2 and S 3 in ascending order to obtain matrix S 1', S 2' and S 3', and returns the sorted matrix to obtain matrix S 1', S 2' and S3' position in the original matrix S 1, S 2 and S 3. NS 1, NS 2 and NS 3.

[0010] As a further limitation of the present technical solution, the S5 specifically includes: Process the NPR , NPG and NPB dimensions so that they are converted from to : (9); Encrypt the new npr , npg and npb to obtain ciphertexts CR , CG and CB ; (10); Process the dimensions of the ciphertexts CR , CG and CB so that they are converted from to ; ; Output the ciphertexts CR , CG and CB .

[0011] Compared with the prior art, the advantages and positive effects of the present invention are: 1. This patent proposes an improved Logistic map (1D-Optimized Logistic Map, 1D-OLP), which enhances the available parameter space of the Logistic map. By expanding the available parameter space, the performance of the key stream is significantly improved. This improvement makes the generated key stream more complex and random, reduces the repeatability and predictability of the key stream, and thus enhances the security of the encryption algorithm. In addition, the optimized parameter configuration enables the key stream to adapt to different application scenarios and security requirements, providing stronger anti-attack capabilities and resisting potential cracking attempts.

[0012] 2. This patent proposes a parallel color image encryption algorithm. By processing the three channels of a color image simultaneously, this method achieves the purpose of parallel processing and improves the efficiency of the algorithm. Specifically, the algorithm uses a chaotic sequence generated by an improved Logistic map to perform independent encryption processing on each color channel. This parallel encryption method allows each channel to be operated simultaneously on different processing units. The feature of independently encrypting each data channel provides greater flexibility, allowing for personalized adjustment of encryption parameters according to different security requirements. At the same time, it enhances the anti-attack ability of the system, ensuring data security and reliability. This parallel processing not only improves performance but also meets the needs of large-scale data encryption, which is an important development direction of modern information security technology.

[0013] 3. This patent systematically evaluates and tests the ciphertext correlation of the proposed encryption method to ensure that the encrypted data has a low correlation, enhancing the security and reliability of the encryption result. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 is a flowchart of the present invention.

[0015] Figure 2 is an attractor graph of the improved one-dimensional Logistic map of the present invention; Figure 2 In (a) is the attractor graph of the improved one-dimensional Logistic map ( ); Figure 2 In (b) is the attractor graph of the improved one-dimensional Logistic map ( ); Figure 2 In (c) is the attractor graph of the improved one-dimensional Logistic map ( ).

[0016] Figure 3 is the bifurcation diagram analysis of the improved one-dimensional Logistic map of the present invention.

[0017] Figure 4 is the simulation result graph of "Lena" of the present invention; Figure 4 In (a) is the red channel of the original "Lena" image; Figure 4 In (b) is the green channel of the original "Lena" image; Figure 4 In (c) is the blue channel of the original "Lena" image; Figure 4 In (d) is the red channel of the encrypted "Lena" image; Figure 4 In (e) is the green channel of the encrypted "Lena" image; Figure 4 In (f) is the blue channel of the encrypted "Lena" image. DETAILED DESCRIPTION OF THE INVENTION

[0018] The following will describe in detail a specific embodiment of the present invention in conjunction with the accompanying drawings, but it should be understood that the protection scope of the present invention is not limited by the specific embodiment.

[0019] For a color plaintext image , with a size of . An image encryption method based on parallel one-dimensional improved Logistic mapping provided by the present invention, the flowchart of the encryption method is as Figure 1 shown, and includes the following steps: S1: Design an improved one-dimensional Logistic mapping.

[0020] The Logistic mapping, also known as the unimodal map or Logistic function, Logistic equation, is a quadratic polynomial mapping (recursive relation), and is often used as a typical example to illustrate how complex chaotic phenomena are generated from very simple non-linear dynamic equations.

[0021] The specific improved one-dimensional Logistic mapping (1D-OLP) designed in S1 is as follows: (1); Where: and respectively represent the current state and the next state of the chaotic sequence; the value ranges of both are (0, 1); is the control parameter, by adjusting , the chaoticity of the mapping and the randomness of the sequence can be changed, has a value range of (0.5, 100).

[0022] Conduct dynamic behavior analysis on 1D-OLP respectively, as Figure 2 and Figure 3 shown. Figure 2 is the trajectory of 1D-OLP under different parameters and , Figure 3 is the bifurcation diagram analysis of 1D-OLP.

[0023] Figure 2 is the attractor graph of the improved one-dimensional Logistic mapping provided by the embodiment of the present invention. As gradually increases, the area filled by 1D-OLP becomes larger and larger. It shows that the generated sequence has good randomness.

[0024] Figure 2 In: (a) is the attractor graph of the improved one-dimensional Logistic mapping ( ); (b) is the attractor graph of the improved one-dimensional Logistic map ( ); (c) is the attractor graph of the improved one-dimensional Logistic map ( ).

[0025] Figure 3 This is the bifurcation graph analysis of the improved one-dimensional Logistic map provided by the embodiments of the present invention. The bifurcation graph analysis shows that the parameter space where the dynamic behavior of 1D-OLP is in a chaotic state is significantly better than that of the Logistic map.

[0026] S2: Generate the key of the cryptosystem from the plaintext information.

[0027] The specific steps of S2 include: S21; Calculate the sum SU of the pixel values of the plaintext image and scale it to a smaller value as the initial value y(1); S22: Use the improved one-dimensional Logistic map for iterative calculation, generate the y sequence through looping, and perform 25 iterations; (2); Where: represents the number of iterations, starts from 1 and iterates 25 times; S23: Scale the 25th iteration value y(25) to generate the parameter and store the 24th value y(24) in x(1) for subsequent calculations.

[0028] x is a sequence generated by the improved one-dimensional Logistic map, and x(1) is the initial value of the improved one-dimensional Logistic.

[0029] This process is used to generate the initial key parameters for the chaotic encryption algorithm.

[0030] S3: Split the color image to be encrypted into three independent color channels (red, green, blue) to prepare for parallel processing.

[0031] The specific steps of S3 include: (3); Where: PR , PG and PB are the red, green, and blue channels of the plaintext image respectively, and the size of the three is ; Fuse the information of the red, green, and blue channels to obtain three new channels: NPR , NPG and NPB ; (4);

[0032] NPR , NPG and NPB have a size of .

[0033] S4: Generate the key stream of the cryptosystem using the secret key and the improved one-dimensional Logistic map.

[0034] The specific steps of S4 include: Use the control parameter and the initial value x(1), along with the improved one-dimensional Logistic map to generate the key stream, (5); Iterate times to generate the key stream x and generate the key stream X 1, X 2 and X 3 for diffusion: (6); Where: is used to calculate the remainder after dividing two integers; is the floor function; Generate the key stream S 1, S 2 and S 3 for scrambling: (7); The sortrows function is used to sort a matrix according to specific rows or columns in the matrix. Sort S 1, S 2 and S 3 using sortrows to obtain the matrix S 1', S 2' and S 3'. Respectively find the positions of each element in S 1', S 2' and S 3' in S 1, S 2 and S 3, and record the position matrix as NS 1, NS 2 and NS 3: (8); Among them: The sortrows function sorts all rows of the matrix S 1, S 2 and S 3 in ascending order to obtain the matrix S 1', S 2' and S 3', and returns the sorted matrix to obtain the matrix S 1', S 2' and S 3' in the original matrix S 1, S 2 and S 3 of the positions NS 1, NS 2 and NS 3.

[0035] S5: Implement a parallel encryption algorithm for each color channel, and use the generated chaotic sequence to independently encrypt the pixel values of each channel.

[0036] The specific content of the said S5 includes: Process the dimensions of NPR , NPG and NPB to make it change from to : (9); Encrypt the new npr , npg and npb to obtain the ciphertext CR , CG and CB ; (10); In this step npr , npg and npb are carried out synchronously to complete the parallel operation; Process the dimensions of the ciphertext CR , CG and CB to make it change from to ; ;

[0037] Output the ciphertext CR , CG and CB .

[0038] Taking Lena as an example, Figure 4This is the "Lena" simulation result diagram provided by the embodiments of the present invention.

[0039] Figure 4 Among them: (a) is the red channel of the "Lena" original image; (b) is the green channel of the "Lena" original image; (c) is the blue channel of the "Lena" original image; (d) is the red channel of the "Lena" encrypted image; (e) is the green channel of the "Lena" encrypted image; (f) is the blue channel of the "Lena" encrypted image.

[0040] S6: Evaluate and test the ciphertext correlation of the proposed encryption method.

[0041] The specific content of S6 includes: Use the following formula to analyze the correlation of adjacent pixels of the plaintext and ciphertext: (11); (12); Among them: and are adjacent pixel values.

[0042] When is close to 1, it indicates that the correlation of adjacent pixels is very large. When is close to 0, it indicates that the correlation of adjacent pixels is very small. The test results of the proposed algorithm in the correlation analysis of Lena are shown in Table 1.

[0043] Table 1 Correlation of adjacent pixels of plaintext and ciphertext of Lena

[0044] The above-disclosed are only specific embodiments of the present invention. However, the present invention is not limited thereto, and any changes that can be conceived by those skilled in the art should fall within the protection scope of the present invention.

Claims

1. A parallel image encryption method based on one-dimensional improved Logistic mapping, characterized in that: The following steps are involved: S1: Design an improved one-dimensional Logistic mapping; S2: Generate the cryptographic key from the plaintext information; S3: Split the color image to be encrypted into three independent color channels to prepare for parallel processing; S4: Generate the key stream of the cryptographic system using the key and the improved one-dimensional Logistic map; S5: Implement a parallel encryption algorithm for each color channel and use the generated chaotic sequence to independently encrypt the pixel values ​​of each channel.

2. The image encryption method based on one-dimensional improved Logistic mapping parallelism according to claim 1 is characterized in that: The improved one-dimensional Logistic mapping designed in S1 is specifically: （1）； in: and Respectively represent the current state and next state of the chaotic sequence; is the control parameter.

3. The image encryption method based on one-dimensional improved Logistic mapping parallelism according to claim 2 is characterized in that: The S2 specifically includes: S21; Calculate the plaintext image The sum of the pixel values ​​SU is scaled to a value as the initial value y(1); S22: Use the improved one-dimensional Logistic map to perform iterative calculations, generate the y sequence through a loop, and perform 25 iterations; （2）； in: represents the number of iterations, Start from 1 and iterate 25 times; S23: Scale the 25th iteration value y(25) to generate the parameter , and stores the 24th value y(24) in x(1) for subsequent calculations.

4. The image encryption method based on one-dimensional improved Logistic mapping parallelism according to claim 3 is characterized in that: The S3 specifically includes: （3）； in: PR , PG and PB Plaintext images The red, green and blue channels are ; The red, green and blue channels are fused to obtain three new channels: NPR , NPG and NPB ; （4）。 5. The image encryption method based on one-dimensional improved Logistic mapping parallelism according to claim 4 is characterized in that: The S4 specifically includes: Use control parameters and initial value x(1), and the improved one-dimensional Logistic map to generate the key stream, （5）； Iteration times, generate the key stream x, generate the key stream for diffusion X 1. X 2 and X 3: （6）； in: Used to calculate the remainder after dividing two integers; is the floor function; Generate key stream for scrambling S 1. S 2 and S 3: （7）； right S 1. S 2 and S 3 Use sortrows to sort the matrix S 1', S 2' and S 3', respectively, look for S 1', S 2' and S Each element in 3' S 1. S 2 and S 3, the recorded position matrix is NS 1. NS 2 and NS 3: （8）； Among them: sortrows function for matrix S 1. S 2 and S Sort all rows of 3 in ascending order to get the matrix S 1', S 2' and S 3', and return the sorted matrix to get the matrix S 1', S 2' and S 3' in the original matrix S 1. S 2 and S Position in 3 NS 1. NS 2 and NS 3.

6. The image encryption method based on one-dimensional improved Logistic mapping parallelism according to claim 5 is characterized in that: The S5 specifically includes: right NPR , NPG and NPB The dimension is processed so that it changes from Convert to : （9）； For new npr , npg and npb Encrypt to get ciphertext CR , CG and CB ; （10）； Ciphertext CR , CG and CB The dimension is processed so that it changes from Convert to ; ； Output ciphertext CR , CG and CB .

Images