Image encryption method based on fractional order pseudo-random number generator and DNA coding and decoding

Abstract

The embodiment of the invention discloses an image encryption method and system based on a fractional order pseudo-random number generator and DNA coding and decoding, and the method comprises the steps: determining the length of a key string required for encryption based on a partitioned image, and generating a high-randomness key string according to the fractional order pseudo-random number generator, the problems that a traditional integer order chaotic system is insufficient in randomness and limited in secret key space are solved, a CBC chain type encryption mode is introduced to conduct inter-block encryption on each block of image after block division, generation of each ciphertext block depends on a previous ciphertext, inter-block relevance is established, the problem that the inter-block relevance is missing due to the independent encryption characteristic is solved, and the encryption efficiency is improved. According to the method, the image is encrypted, the differential attack resistance of the image is enhanced, the DNA coding and decoding rule is dynamically selected based on the key string, and the image block is encrypted on the basis, so that the defect that the static coding rule is easily subjected to exhaustive attack is overcome, the real-time dynamic coding mechanism is realized, and the attack resistance of image encryption is improved.

Description

Technical Field

[0001] This invention belongs to the field of chaotic system application and pseudo-random number generation technology, and relates to an image encryption method and system based on a fractional pseudo-random number generator and DNA encoding / decoding. Background Technology

[0002] With the widespread application of digital images in medical image transmission, IoT terminal communication, and cloud storage sharing, efficient and secure protection of image data has become a key research direction in information security. Compared to text data, images, due to their large data volume, high redundancy, and strong spatial correlation between pixels, are difficult for traditional symmetric encryption algorithms (such as AES and RSA) to directly adapt to, easily leading to low encryption efficiency or residual statistical features. To address this, researchers have proposed image encryption technology based on chaotic systems. This technology utilizes the pseudo-randomness, initial value sensitivity, and unpredictability of chaotic mappings, combined with pixel scrambling, diffusion, and biological computing models (such as DNA encoding) to achieve multi-level obfuscation, gradually becoming the mainstream lightweight encryption scheme. Early chaotic image encryption technologies mainly relied on a single chaotic mapping (such as Logistic mapping and Henon mapping) to generate key sequences, destroying plaintext statistical features through pixel position scrambling and value diffusion operations. With the upgrading of computational attack methods, such schemes have gradually exposed defects such as limited key space and weak resistance to phase space reconstruction due to the low dimensionality and dense periodic windows of chaotic systems. In recent years, researchers have enhanced randomness by introducing complex chaotic systems (such as hyperchaotic systems and fractional-order models) and have attempted to improve the nonlinear transformation capabilities of pixels by combining the base complementarity rules of DNA encoding. For example, some schemes utilize the eight encoding rules of DNA sequences to convert pixel values ​​into base strings, and then achieve multi-level encryption through operations such as permutation and XOR. In addition, block encryption modes (such as CBC and CFB) have been introduced to enhance inter-block dependencies and weaken the statistical regularity of ciphertext through chained operations.

[0003] However, existing technologies still face multiple challenges. On the one hand, the dynamic complexity of chaotic systems urgently needs improvement: most schemes employ integer-order chaotic models, whose dynamic behavior is limited by the periodicity of continuous iterations, making it difficult to generate highly random key sequences; while a few schemes involving fractional-order chaotic systems suffer from inefficient numerical solution algorithms (such as Caputo definition solution under uniform grids), making it difficult to meet real-time encryption requirements. On the other hand, the collaborative mechanism between DNA encoding and block encryption is not yet perfect: static encoding rules are easily cracked by rule exhaustive attacks, while the independent encryption characteristics of traditional block modes (such as ECB) lead to a lack of inter-block correlation, making it difficult to resist differential attacks. How to construct a dynamically adaptive multi-level encryption framework that balances the computational complexity of chaotic systems with key randomness has become the key to improving the robustness of image encryption. Summary of the Invention

[0004] The purpose of this invention is to solve the problems in the existing collaborative mechanism of DNA encoding and block encryption, where static encoding rules are easily cracked by rule exhaustive attacks, and the independent encryption characteristics lead to the lack of inter-block correlation, making it difficult to resist differential attacks and resulting in poor image encryption effect. The invention provides an image encryption method and system based on a fractional pseudo-random number generator and DNA encoding and decoding.

[0005] To achieve the above objectives, the present invention employs the following technical solution: An image encryption method based on a fractional-order pseudo-random number generator and DNA encoding / decoding includes the following steps: Divide the image to be encrypted into blocks and obtain the image after block division; Determine the length of the key string required for encryption based on the segmented image, construct a fractional pseudo-random number generator, and generate the key string required for encryption based on the length of the required key string and the fractional pseudo-random number generator. A CBC chain encryption mode is introduced to encrypt each image block after it is divided into blocks. The image blocks after inter-block encryption are obtained. Based on the key string, DNA encoding and decoding rules are dynamically selected. The image blocks after inter-block encryption are encrypted within the blocks by using DNA encoding and decoding rules to obtain the encrypted ciphertext. The encrypted image is obtained based on the encrypted ciphertext of all image blocks.

[0006] A further improvement of the present invention is that: The construction of the fractional-order pseudo-random number generator, based on the required key string length and the fractional-order pseudo-random number generator generating the key string required for encryption, includes: A fractional-order pseudo-random number generator is constructed using the fractional-order Chen-Lu system and the generalized bimodal Logistic system. Secret information and a key are obtained based on a fractional-order pseudo-random number generator. The secret information is used for inter-block encryption, and the key is used to generate a key string.

[0007] The key includes: Seed of a fractional pseudo-random number generator α c , α l Initial values ​​Xc(0), Xl(0), system parameters ( a c , b c , c c ()( a l , b l , cl ), which constitute the chaotic parameters p and initial value Xst(0) of the chaotic map that forms the non-uniform grid.

[0008] The introduction of the CBC chain encryption mode, which performs inter-block encryption on each block of the image after segmentation, includes: Random secret information IV is generated based on a fractional pseudo-random number generator. Based on the secret information IV, a bit-XOR operation is performed on the first image block to obtain the image blocks encrypted between blocks.

[0009] The method of dynamically selecting DNA encoding / decoding rules based on a key string to perform intra-block encryption on image blocks after inter-block encryption to obtain encrypted ciphertext includes: Obtain the key string KDNAe from the key string, and use the decimal numbers represented by each 3-bit binary sequence in the key string KDNAe to determine the dynamic DNA encoding and decoding rules as the image encoding rules. Encode the image block based on the determined image encoding rules and convert it into a DNA base sequence. The DNA base sequence is subjected to DNA complement substitution, then the DNA base sequence is converted into a DNA base matrix, and then the DNA base matrix is ​​scrambled using 2D cat mapping. Based on the key string KDNAe, the decoding rules are dynamically selected to decode the scrambled DNA base matrix and convert the DNA base matrix into a binary sequence. The binary sequence is obfuscated twice using a discrete logistic mapping to obtain the ciphertext after encrypting the first image block. Based on the ciphertext encrypted from the first image block, perform a bitwise XOR operation on the next image block, and then repeat the above intra-block encryption steps until all image blocks are encrypted.

[0010] The process of obtaining the encrypted image from the encrypted ciphertext of all image blocks includes: Set the number of encryption loops. After all image blocks have completed the first round of encryption, use the ciphertext of the last image block in the first round as input to perform bit XOR operation and intra-block encryption on the first image block. The encryption of each image block is used as the input for the bit XOR operation of the next image block, and the encryption is performed on each image block in turn, both between and within the block, until the number of iterations is reached. Then, the encrypted image is obtained based on the current encryption of all image blocks.

[0011] The encryption cycle count is greater than or equal to 2, meaning that all image blocks are encrypted at least twice.

[0012] An image encryption system based on a fractional-order pseudo-random number generator and DNA encoding / decoding includes: The image segmentation module is used to segment the image to be encrypted into blocks and obtain the segmented image. The key string generation module is used to determine the length of the key string required for encryption based on the segmented image, construct a fractional pseudo-random number generator, and generate the key string required for encryption based on the length of the required key string and the fractional pseudo-random number generator. The encryption module is used to introduce the CBC chain encryption mode, perform inter-block encryption on each image block after it is divided into blocks, obtain the image block after inter-block encryption, dynamically select DNA encoding and decoding rules based on the key string, perform intra-block encryption on the image block after inter-block encryption through the DNA encoding and decoding rules, obtain the encrypted ciphertext, and obtain the encrypted image based on the encrypted ciphertext of all image blocks.

[0013] A terminal 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 steps of any of the methods described above.

[0014] A computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of any of the methods described herein.

[0015] Compared with the prior art, the present invention has the following beneficial effects: This invention discloses an image encryption method based on a fractional-order pseudo-random number generator and DNA encoding / decoding. The method determines the length of the key string required for encryption based on the segmented image and generates a highly random key string using a fractional-order pseudo-random number generator. This overcomes the problems of insufficient randomness and limited key space in traditional integer-order chaotic systems. A CBC chain encryption mode is introduced to perform inter-block encryption on each segmented image, ensuring that the generation of each ciphertext block depends on the previous ciphertext block, establishing inter-block correlation and overcoming the problem of missing inter-block correlation caused by independent encryption characteristics. This enhances the image's resistance to differential attacks. Based on the key string, DNA encoding / decoding rules are dynamically selected, and intra-block encryption is performed on image blocks accordingly. This overcomes the vulnerability of static encoding rules to exhaustive attacks, achieving real-time dynamic encoding of the encoding mechanism and improving the image encryption's resistance to attacks.

[0016] Furthermore, in this invention, the image blocks are encrypted in multiple rounds of cyclic encryption, which avoids the security weakening caused by insufficient local randomness or repeated use of parameters in single-round encryption, thereby improving the encryption effect of the image. Attached Figure Description

[0017] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 This is a schematic diagram of an image encryption method based on a fractional-order pseudo-random number generator and DNA encoding / decoding provided by the present invention; Figure 2 This is a schematic diagram of the intra-block and inter-block encryption process provided in an embodiment of the present invention. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, 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. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0020] Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0021] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0022] In the description of the embodiments of the present invention, it should be noted that if terms such as "upper," "lower," "horizontal," or "inner" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, or the orientation or positional relationship commonly used when the product of the invention is in use, they are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the present invention. Furthermore, terms such as "first" and "second" are only used to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0023] Furthermore, the use of the term "horizontal" does not imply that the component must be absolutely horizontal, but rather that it can be slightly tilted. For example, "horizontal" simply means that its direction is more horizontal than "vertical," and does not mean that the structure must be completely horizontal, but can be slightly tilted.

[0024] In the description of the embodiments of the present invention, it should also be noted that, unless otherwise explicitly specified and limited, the terms "set," "install," "connect," and "link" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in the present invention according to the specific circumstances.

[0025] The present invention will now be described in further detail with reference to the accompanying drawings: See Figures 1 to 2 This invention discloses an image encryption method based on a fractional-order pseudo-random number generator and DNA encoding / decoding. The method enhances the key space by outputting a key string from a fractional-order chaotic pseudo-random number generator, and combines DNA biological coding characteristics with a chain-like encryption architecture to effectively improve the anti-attack capability of image encryption. The method includes the following steps: Example 1 See Figure 1 This embodiment discloses an image encryption method based on a fractional-order pseudo-random number generator and DNA encoding / decoding, including the following steps: Step 1: Preprocess the image by dividing it into blocks; Furthermore, in this step, the image preprocessing steps include: adjusting the image size to a multiple of 32×32; and dividing the image into blocks of size B. 0, B1, ...B K-1 K blocks, each block is 32×32 pixels.

[0026] Step 2: Use a fractional pseudo-random number generator to generate a key string with guaranteed randomness; Furthermore, in this step, the fractional pseudo-random number generator generates a chaotic random output with guaranteed randomness by combining the outputs of three fractional systems (fractional Chen and Lu systems and a generalized bimodal Logistic system). Specifically, the fractional Chen and Lu systems are iteratively solved using the ABM prediction-verification calculation method based on the Caputo fractional differential definition using a non-uniform grid; the generalized bimodal Logistic mapping is iteratively solved using the piecewise constant approximation method based on the fractional integral definition.

[0027] Furthermore, in this step, the seed of the fractional-order pseudo-random number generator is the core key of the encryption algorithm, including the order α of the fractional-order system. c α l Initial values ​​Xc(0), Xl(0), system parameters (a c , b c , c c(a) l , b l , c l ) as well as the chaotic parameters and initial values ​​of the chaotic mapping that constitutes the non-uniform grid.

[0028] Step 3: Encrypt the image in blocks using CBC mode, with the XOR operation between blocks depending on the previous ciphertext block; Step 4: Combine dynamic selection DNA encoding / decoding, cat mapping, discrete logistic mapping, etc. to perform base conversion and permutation operations on the pixels within the block to encrypt the image pixels.

[0029] Furthermore, in this step, the basic process of the block encryption method includes: Step 4.1: Process the first image block B1: P1′=B1⊕IV; Step 4.2: Intra-block encryption: Combining dynamic DNA encoding / decoding and discrete logistic obfuscation operations, intra-block encryption is performed on each image block sequentially; Step 4.3: Inter-block chaining: Current ciphertext block C i Use it as the XOR input for inter-block encryption; Step 4.4: Loop Encryption: Perform another round of CBC encryption on the encrypted image block, where the XOR input IV from step 4.1 is replaced with the last encrypted image block C. k .

[0030] Specifically, the intra-block encryption method and steps are as follows: Step 4.1.1: Dynamic DNA Encoding: Select an encoding rule based on the output of the fractional-order chaotic pseudo-random number generator to convert the image patch into a DNA base sequence; Step 4.1.2: DNA Operations: Perform complementation and substitution operations (e.g., A... T, C G); Step 4.1.3: 2D cat mapping scrambling: Perform 2D cat mapping scrambling on the DNA bases within the block; Step 4.1.4: Dynamic DNA Encoding: Based on the output of the fractional-order chaotic pseudo-random number generator, a decoding rule is selected to convert the DNA base sequence into image patches; Step 4.1.5: Discrete Logistic Diffusion: Use discrete logistic mapping to perform secondary obfuscation on the decoded pixels.

[0031] Furthermore, in this step, there are a total of 8 DNA encoding and decoding rules, each representing a different 2-bit value and the corresponding DNA base pair.

[0032] Furthermore, in this step, the mathematical expression for the 2D cat mapping is: , The cat mapping scrambling parameters (u,v,rl,rc) are dynamically adjusted by the pseudo-random number generator output, M is the length and width of the resized DNA base block, and A0 can be represented as:

[0033] Furthermore, in this step, the specific method of the discrete Logistic diffusion method is as follows: Each 32-bit unit of the decoded sequence is considered as a unit, and each 32-bit unit is XORed with the output of the discrete Logistic mapping. The output of the discrete Logistic mapping is the iterative value x(n) obtained by taking the previous 32-bit unit as input x(n-1) and using the following mathematical expression:

[0034] If it is the first unit of the first encrypted block, the mapping input for the XOR operation is generated by the output of the fractional-order chaotic pseudo-random number generator; for the first unit of the remaining blocks, the mapping input for the XOR operation is the last unit of the previous block.

[0035] Step 5: Perform the above encryption process twice to obtain the encrypted image.

[0036] Example 2 This embodiment uses an encrypted image of size 256 as an example. Taking a 256-bit grayscale image as an example, an image encryption method based on a fractional-order pseudo-random number generator and DNA encoding / decoding is disclosed, including the following steps: Step 1: Divide the image to be encrypted into blocks and obtain the image after block division; In example 256 A 256-level grayscale image is divided into 64 32-level segments. 32-bit size (bs = 32) A pixel block (32 = 1024) is designated by B0, B1, ... B... K-1 This indicates that K=64.

[0037] Step 2: Determine the length of the key string required for encryption based on the segmented image, construct a fractional pseudo-random number generator, and generate the key string required for encryption based on the length of the key string and the fractional pseudo-random number generator; First, set and save the algorithm's secret information and key.

[0038] The secret information is a randomly generated IV used for the XOR operation of the first image block, with a length of 1 / 2 bps. 8 bits; The key for the algorithm is the seed from a fractional-order pseudo-random number generator. αc , α c Initial values ​​Xc(0), Xl(0), system parameters ( a c , b c , c c ()( a l , b l , cl It consists of the chaotic parameter p and the initial value Xst(0) of the chaotic mapping that constitutes the non-uniform grid.

[0039] Secondly, based on the image size, calculate the length of the key string required for two rounds of encryption.

[0040] Finally, using the key as a seed, a fractional pseudo-random number generator is used to generate a 32-bit random number sequence to form a key string of the required length for subsequent image encryption processes.

[0041] Step 3: Introduce the CBC chain encryption mode to perform inter-block encryption on each image block after segmentation, obtain the image block after inter-block encryption, dynamically select the DNA encoding and decoding rule based on the key string, and perform intra-block encryption on the image block after inter-block encryption through the DNA encoding and decoding rule to obtain the encrypted ciphertext, and obtain the encrypted image based on the encrypted ciphertext of all image blocks.

[0042] In this step, image blocks influence each other and hide pixel values ​​through bit XOR, while pixels within blocks are permuted and confused through dynamic DNA encoding, DNA substitution, 2D cat mapping scrambling, dynamic DNA decoding, and discrete Logistic diffusion.

[0043] Step 3.1: For the first image block B0 of the first round of encryption: Perform a bitwise XOR operation on pixels B0(0) to B0(bs-1) with the randomly generated IV; for each pixel after XOR, encode it according to the dynamic DNA encoding and decoding rules determined by the decimal numbers represented by each 3-bit binary sequence in the key string KDNAe, and convert the pixel value in B0 into a DNA sequence of 4096 bases. Step 3.2: Perform DNA complementation substitution on the base sequence; then, convert the DNA base sequence to 64-base sequence. A 64-base DNA matrix is ​​used to perform position scrambling operations on the DNA base matrix, with Kpm provided by the key string as the scrambling parameters (u,v,rl,rc) for the improved 2D cat mapping. Step 3.3: For every 4 scrambled DNA bases, decode them according to the dynamic DNA encoding and decoding rules represented by every 3 bits in the key string KDNAd, and convert the DNA bases into a binary sequence.

[0044] The binary sequence is divided into groups of 32 bits each. Each group of 32 bits is XORed with the output of a 32-bit discrete Logistic mapping. Specifically, the first group of 32 bits is XORed with the output of the discrete Logistic mapping with the key string KPm as input; the XORed objects of the remaining groups of bits are the iterative outputs of the Logistic mapping with the decimal values ​​represented by the previous group of 32 bits as input, resulting in the encrypted image C0.

[0045] Furthermore, regarding encrypted image block B i For i=1,...,K-1, perform the following operations: First, pixel block B i Same as C i-1 Perform bitwise XOR on the inner pixels; Secondly, for each pixel B i (k), k=0,1,2,..., bs-1 XORed result, performs the operation as described in the first image encryption above. Specifically, the KDNAe, Kpm, and KDNAd encryption sequences are extracted from the key string and updated in each block; for B... i The first group of 32 bits, the input of the discrete Logistic mapping is C. i-1 The last 4 pixels make up 32 bits.

[0046] Furthermore, for the first image block in the second round of encryption, the encryption method is the same as the inter-block and intra-block encryption methods described above. The object of the XOR operation is the last encrypted image block C from the first round of encryption. K-1 The input bits C of the discrete logistic mapping K-1 The last 4 pixels make up 32 bits.

[0047] For the other image blocks in the second round of encryption, the encryption method is the same as that for image block B in the first round. i The encryption method for i=1,...,K-1.

[0048] This embodiment discloses an image encryption method based on a fractional-order pseudo-random number generator and DNA encoding / decoding. The method determines the length of the key string required for encryption based on the segmented image and generates a highly random key string using a fractional-order pseudo-random number generator. This overcomes the problems of insufficient randomness and limited key space in traditional integer-order chaotic systems. A CBC chain encryption mode is introduced to perform inter-block encryption on each segmented image, ensuring that the generation of each ciphertext block depends on the previous ciphertext block, establishing inter-block correlation and overcoming the problem of missing inter-block correlation caused by independent encryption characteristics. This enhances the image's resistance to differential attacks. Based on the key string, DNA encoding / decoding rules are dynamically selected, and intra-block encryption is performed on image blocks accordingly. This overcomes the vulnerability of static encoding rules to exhaustive attacks, achieving real-time dynamic encoding of the encoding mechanism and improving the image encryption's resistance to attacks.

[0049] This embodiment also discloses an image encryption system based on a fractional-order pseudo-random number generator and DNA encoding / decoding, including: The image segmentation module is used to segment the image to be encrypted into blocks and obtain the segmented image. The key string generation module is used to determine the length of the key string required for encryption based on the segmented image, construct a fractional pseudo-random number generator, and generate the key string required for encryption based on the length of the required key string and the fractional pseudo-random number generator. The encryption module is used to introduce the CBC chain encryption mode, perform inter-block encryption on each image block after it is divided into blocks, obtain the image block after inter-block encryption, dynamically select DNA encoding and decoding rules based on the key string, perform intra-block encryption on the image block after inter-block encryption through the DNA encoding and decoding rules, obtain the encrypted ciphertext, and obtain the encrypted image based on the encrypted ciphertext of all image blocks.

[0050] A schematic diagram of a terminal device according to an embodiment of the present invention. The terminal device of this embodiment includes: a processor, a memory, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the steps in the various method embodiments described above. Alternatively, when the processor executes the computer program, it implements the functions of each module / unit in the various device embodiments described above.

[0051] The computer program can be divided into one or more modules / units, which are stored in the memory and executed by the processor to complete the present invention.

[0052] The terminal device can be a desktop computer, laptop computer, cloud server, or other device with strong computing power. The terminal device may include, but is not limited to, a processor and memory.

[0053] The optimal choice for the processor is a multi-core high-speed central processing unit (CPU).

[0054] The memory can be used to store the computer program and / or module. The processor implements various functions of the terminal device by running or executing the computer program and / or module stored in the memory and calling the data stored in the memory.

[0055] If the modules / units integrated into the terminal device are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the methods of the above embodiments can also be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include: any entity or device capable of carrying the computer program code, recording media, USB flash drives, portable hard drives, magnetic disks, optical disks, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signals, telecommunication signals, and software distribution media, etc. It should be noted that the content included in the computer-readable medium can be appropriately added or removed according to the requirements of legislation and patent practice in the jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, computer-readable media do not include electrical carrier signals and telecommunication signals.

[0056] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. An image encryption method based on a fractional-order pseudo-random number generator and DNA encoding / decoding, characterized in that, Includes the following steps: Divide the image to be encrypted into blocks and obtain the image after block division; Determine the length of the key string required for encryption based on the segmented image, construct a fractional pseudo-random number generator, and generate the key string required for encryption based on the length of the required key string and the fractional pseudo-random number generator. A CBC chain encryption mode is introduced to encrypt each image block after it is divided into blocks. The image blocks after inter-block encryption are obtained. Based on the key string, DNA encoding and decoding rules are dynamically selected. The image blocks after inter-block encryption are encrypted within the blocks by using DNA encoding and decoding rules to obtain the encrypted ciphertext. The encrypted image is obtained based on the encrypted ciphertext of all image blocks.

2. The image encryption method based on a fractional-order pseudo-random number generator and DNA encoding / decoding according to claim 1, characterized in that, The construction of the fractional-order pseudo-random number generator, based on the required key string length and the fractional-order pseudo-random number generator generating the key string required for encryption, includes: A fractional-order pseudo-random number generator is constructed using the fractional-order Chen-Lu system and the generalized bimodal Logistic system. Secret information and a key are obtained based on a fractional-order pseudo-random number generator. The secret information is used for inter-block encryption, and the key is used to generate a key string.

3. The image encryption method based on a fractional-order pseudo-random number generator and DNA encoding / decoding according to claim 2, characterized in that, The key includes: Seed of a fractional pseudo-random number generator α c , α l Initial values ​​Xc(0), Xl(0), system parameters ( a c , b c , c c ()( a l , b l , cl ), which constitute the chaotic parameters p and initial value Xst(0) of the chaotic map that forms the non-uniform grid.

4. The image encryption method based on a fractional-order pseudo-random number generator and DNA encoding / decoding according to claim 1, characterized in that, The introduction of the CBC chain encryption mode, which performs inter-block encryption on each block of the image after segmentation, includes: Random secret information IV is generated based on a fractional pseudo-random number generator. Based on the secret information IV, a bit-XOR operation is performed on the first image block to obtain the image blocks encrypted between blocks.

5. The image encryption method based on a fractional-order pseudo-random number generator and DNA encoding / decoding according to claim 4, characterized in that, The method of dynamically selecting DNA encoding / decoding rules based on a key string to perform intra-block encryption on image blocks after inter-block encryption to obtain encrypted ciphertext includes: Obtain the key string KDNAe from the key string, and use the decimal numbers represented by each 3-bit binary sequence in the key string KDNAe to determine the dynamic DNA encoding and decoding rules as the image encoding rules. Encode the image block based on the determined image encoding rules and convert it into a DNA base sequence. The DNA base sequence is subjected to DNA complement substitution, then the DNA base sequence is converted into a DNA base matrix, and then the DNA base matrix is ​​scrambled using 2D cat mapping. Based on the key string KDNAe, the decoding rules are dynamically selected to decode the scrambled DNA base matrix and convert the DNA base matrix into a binary sequence. The binary sequence is obfuscated twice using a discrete logistic mapping to obtain the ciphertext after encrypting the first image block. Based on the ciphertext encrypted from the first image block, perform a bitwise XOR operation on the next image block, and then repeat the above intra-block encryption steps until all image blocks are encrypted.

6. The image encryption method based on a fractional-order pseudo-random number generator and DNA encoding / decoding according to claim 5, characterized in that, The process of obtaining the encrypted image from the encrypted ciphertext of all image blocks includes: Set the number of encryption loops. After all image blocks have completed the first round of encryption, use the ciphertext of the last image block in the first round as input to perform bit XOR operation and intra-block encryption on the first image block. The encryption of each image block is used as the input for the bit XOR operation of the next image block, and the encryption is performed on each image block in turn, both between and within the block, until the number of iterations is reached. Then, the encrypted image is obtained based on the current encryption of all image blocks.

7. The image encryption method based on a fractional-order pseudo-random number generator and DNA encoding / decoding according to claim 6, characterized in that, The encryption cycle count is greater than or equal to 2, meaning that all image blocks are encrypted at least twice.

8. An image encryption system based on a fractional-order pseudo-random number generator and DNA encoding / decoding, characterized in that, include: The image segmentation module is used to segment the image to be encrypted into blocks and obtain the segmented image. The key string generation module is used to determine the length of the key string required for encryption based on the segmented image, construct a fractional pseudo-random number generator, and generate the key string required for encryption based on the length of the required key string and the fractional pseudo-random number generator. The encryption module is used to introduce the CBC chain encryption mode, perform inter-block encryption on each image block after it is divided into blocks, obtain the image block after inter-block encryption, dynamically select DNA encoding and decoding rules based on the key string, perform intra-block encryption on the image block after inter-block encryption through the DNA encoding and decoding rules, obtain the encrypted ciphertext, and obtain the encrypted image based on the encrypted ciphertext of all image blocks.

9. A terminal device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the method as described in any one of claims 1-7.

10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the steps of the method as described in any one of claims 1-7.

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