Permutation-diffusion Structure Research Articles

A hyperchaotic image encryption algorithm based on LSTM neural network and lifting wavelet transform

In order to solve the problems of simple permutation-diffusion structure, low encryption efficiency and small chaos range of existing chaotic systems, this paper proposes a hyperchaotic image encryption algorithm based on LSTM neural network and lifting wavelet transform. By building upon the Lorenz chaotic system, we construct a new hyperchaotic system in this paper, which has more complex dynamic characteristics and higher Lyapunov exponent. Then, the image is encrypted by lifting wavelet transform and zigzag conversion algorithm. Finally, the trained LSTM neural network is used to process the Henon chaotic sequence to obtain the second key for encryption, which can effectively resist chosen-plaintext attack. The experimental findings indicate that the proposed encryption algorithm has good performance in key security, differential attack, statistical analysis and operation efficiency, which indicates that the algorithm has high security.

A finite-time sliding mode control technique for synchronization chaotic fractional-order laser systems with application on encryption of color images

In recent years, fractional order Laser chaotic systems have gained popularity in both theory and applications, and various classes of these systems have been introduced. This paper presents a dynamic-free sliding mode control (SMC) methodology to synchronize a class of unknown fractional order (FO) Laser chaotic systems with input saturation. The proposed method uses a defined continuous function instead of the discrete sign function and is based on the FO version of the Lyapunov stability theorem. The result is a novel finite-time SMC (FTSMC) methodology that effectively suppresses chaotic behavior in FO Laser chaotic systems without undesirable chattering. This approach is designed to take advantage of the boundedness feature of the FO chaotic system. The efficacy of the FTSMC is demonstrated by applying the method to a chaotic FO Laser system at two different non-integer orders, and its practical applicability is demonstrated by using it to encrypt/decrypt color pictures. The suggested encryption/decryption methodology uses an adaptation of the pre-diffusion permutation-diffusion structure to increase security. Performance and security analyses, including histogram analysis, neighboring pixel correlation analysis, and information entropy analysis, provide further support for the suggested encryption system's superiority.

A Memristive Synapse Control Method to Generate Diversified Multistructure Chaotic Attractors

Due to the synapse-like nonlinearity and memory characteristics, memristor is often used to construct memristive neural networks with complex dynamical behaviors. However, memristive neural networks with multistructure chaotic attractors have not been found yet. In this article, a novel method for designing multistructure chaotic attractors in memristive neural networks is proposed. By utilizing a multipiecewise memristive synapse control in a Hopfield neural network (HNN), various complex multistructure chaotic attractors can be produced. Theoretical analysis and numerical simulation demonstrate that multiple multistructure chaotic attractors with different topologies can be generated by conducting the memristive synapse-control in different synaptic coupling positions. Differing from traditional multiscroll attractors, the generated multistructure attractors contain multiple irregular shapes instead of simple scrolls. Meanwhile, the number of structures can be easily controlled with the memristor control parameters. Furthermore, we design a module-based analog memristive neural network circuit and the arbitrary number of multistructure attractors can be obtained by selecting corresponding control voltages. Finally, based on the memristive HNNs, a novel image encryption cryptosystem with a permutation-diffusion structure is designed and evaluated, exhibiting its excellent encryption performances, especially the extremely high key sensitivity.

A one-round medical image encryption algorithm based on a combined chaotic key generator.

Medical images of patients must be securely transmitted and kept private in telemedicine. To secure such medical images, this paper proposes a single round chaotic image encryption scheme based on a permutation-diffusion structure. A combined chaotic key generator (CCKG) is proposed to enhance key sensitivity and generation in order to improve the security of medical images to be encrypted. CCKG is used to produce the initial seeds for the fractional order chaotic system (FOCS) and Lorenz system (LS) for the permutation and diffusion processes, respectively. CCKG together with proposed permutation and diffusion methods enhances cipher image security in single round. Using zigzag transform (ZT) scanning, the plain image is first permuted block by block. The type of scanning used on each block is heavily influenced by the ZT selection from FOCS and LS. Following block-wise permutation, the permutation order (PO) generated from LS performs overall permutation. Based on the pixel positions, the overall permuted image is divided into odd and even parts. Then these parts of the images are diffused separately by the random pixel matrices generated by LS and FOCS. The cipher image is formed by combining the odd and even parts after diffusion. Secret key analysis, statistical analysis, differential attack analysis, and simulations confirm that with a single round of image encryption, the proposed system is competent, robust and effective.

Security Analysis of the Image Encryption Algorithm Based on a Two-Dimensional Infinite Collapse Map.

This paper analyzes the security of the image encryption algorithm based on a two-dimensional (2D) infinite collapse map. The encryption algorithm adopts a permutation–diffusion structure and can perform two or more rounds to achieve a higher level of security. By cryptanalysis, it is found that the original diffusion process can be split into a permutation–diffusion structure, which comes after the original permutation, so these two permutations can be merged into one. Then, some theorems about round-down operation are summarized, and the encryption and decryption equations in the diffusion process are deduced and simplified accordingly. Since the chaotic sequences used in encryption algorithm are independent of the plaintext and ciphertext, there are equivalent keys. The original encryption algorithm with single-round, two-round, and multi-round of permutation–diffusion processes is cracked, and the data complexity of the cryptanalysis attacks is analyzed. Numerical simulation is carried out by MATLAB, and the experimental results and theoretical analysis show the effectiveness of the cryptanalysis attacks. Finally, some suggestions for improvement are given to overcome the shortcomings of the original encryption algorithm.

Efficient Hyperchaotic Image Encryption Algorithm Based on a Fast Key Generation Method and Simultaneous Permutation-Diffusion Structure

To provide faster encryption speed for protecting image data privacy, a highly efficient hyperchaotic image encryption algorithm using a fast key generation method and simultaneous permutation-diffusion structure is proposed in this paper. Firstly, we design a novel fast key generation method to obtain four key matrixes with the size of W × H (W and H are the width and height of an image) with the hyperchaotic Lorenz system only iterating 2W times. And within the key generation process, the piecewise linear chaotic map serves as a random selector to further enhance the randomness and unpredictability. Secondly, we introduce vectorization technique to parallelize the cipher blockchain-based encryption process. Hence, an image can be fast and sufficiently encrypted row by row and column by column through a four-round and interlinked diffusion process. Furthermore, during the diffusion process, the pixels are simultaneously scrambled by the Chebyshev map to enhance the antiattack capability of the proposed algorithm. Thirdly, we utilize a secure hash function to generate a plaintext-related secret key. Finally, cipher images can successfully pass common security tests with the correlation coefficients on the verge of 0, the entropies are greater than 7.99, and NPCR and UACI values are close to the expected values. Combined with other experimental results and analysis, we can safely conclude that the proposed algorithm has strong robustness against statistical, brute-force, differential, and some other common attacks. Moreover, only 0.009 s of encrypting a 256 × 256 image indicates that our algorithm has extensive application prosperity for real-time communications of massive digital images.

Exploiting LSB Self-quantization for Plaintext-related Image Encryption in the Zero-trust Cloud

The zero-trust (ZT) principle is a promising way to ensure data security in cloud storage. This principle stated that data confidentiality is guaranteed by encryption. However, in ZT image cloud storage scenarios, traditional symmetric cryptosystems and image encryption schemes based on the permutation-diffusion structure cannot balance between efficiency and security against some cryptanalysis. Existing plaintext-related image encryption schemes improve such problems but cause additional keys overhead for different plaintexts, additional ciphertexts overhead, or decryption failure under clipping and noise attacks. Thus, these encryption schemes cannot meet the requirements of ZT in both reducing implementation overhead and resisting multiple attacks. By using least significant bit (LSB) embedding in pixels, we propose a self-adaptive process driven by LSB self-quantization, which forms a novel plaintext-related encryption scheme in a provided ZT model. In our analysis, two pixel-level properties can be obtained through LSB repetitive embedding, LSB extraction, bitwise-XOR, and cyclic-shift operations. With these properties, the plaintext-related key stream is generated to encrypt pixel positions and pixel values, and its disturbance value can be spontaneously extracted from the LSB for decryption. As a result, the proposed scheme needs only one-round execution, resists multiple cryptanalysis without additional keys and ciphertexts, and ensures decryption under clipping or noise attacks. Further simulation results demonstrate that the scheme is efficient and has good resistance to these attacks, which indicates its good application potential for ZT image cloud storage scenarios.

Cryptanalysis of a New Chaotic Image Encryption Technique Based on Multiple Discrete Dynamical Maps.

Recently, a new chaotic image encryption technique was proposed based on multiple discrete dynamic maps. The authors claim that the scheme can provide excellent privacy for traditional digital images. However, in order to minimize the computational cost, the encryption scheme adopts one-round encryption and a traditional permutation–diffusion structure. Through cryptanalysis, there is no strong correlation between the key and the plain image, which leads to the collapse of cryptosystem. Based on this, two methods of chosen-plaintext attacks are proposed in this paper. The two methods require 3 pairs and 258 pairs of plain and cipher images, respectively, to break the original encryption system. The simulation results show the effectiveness of the two schemes.

An image encryption scheme based on double chaotic cyclic shift and Josephus problem

In recent years, image encryption has become a very popular and effective method to protect digital images. Among many image encryption methods, the image encryption algorithm based on chaotic map has extensive application and profound theoretical basis. In this paper, a novel image encryption algorithm is proposed by combining chaotic map with Josephus problem. The whole encryption process adopts the classical permutation–diffusion structure. In the permutation process, the double chaotic cycle shift algorithm has been proposed by improving the chaotic shift transform method. In the diffusion stage, we extend the definition of Josephus problem by using chaotic map to preserve the Josephus sequence diversity. We then divide the image into sub-blocks and pick one randomly according to Josephus sequence. Furthermore, we change the pixel values of the image through performing modular addition and XOR operations on the pixels between blocks. Through the above process, we get the image encryption algorithm based on double chaotic cycle shift and Josephus problem (JP-DCCS). In the simulation experiment and security analysis, we compare JP-DCCS with the other advanced image encryption algorithms. The results show that JP-DCCS has better performance and higher security.

A Novel Image Encryption Scheme Based on PWLCM and Standard Map

In the past decades, considerable attention has been paid to the chaos-based image encryption schemes owing to their characteristics such as extreme sensitivity to initial conditions and parameters, pseudo-randomness, and unpredictability. However, some schemes have been proven to be insecure due to using a single chaotic system. To increase the security, this work proposes a novel image encryption scheme based on the piecewise linear chaotic map (PWLCM) and the standard map. To the best of our knowledge, it is the first chaos-based image encryption scheme combining the PWLCM with the standard map, which adopts permutation-diffusion structure. Unlike the traditional scrambling way, a hierarchical diffusion strategy, which not only changes the pixel position but also modifies the value, is employed in the permutation phase. The operation model of row-by-row and column-by-column is further used to enhance the efficiency in the diffusion process. Consequently, a good trade-off efficiency and security can be achieved. Furthermore, the numerical simulations and performance analyses illustrate that the proposed encryption scheme can be used in practical application scenarios requiring lightweight security.

A Low-Overhead, Confidentiality-Assured, and Authenticated Data Acquisition Framework for IoT

In the presence of several critical issues during data acquisition in industrial-informatics-based applications, like Internet of Things (IoT) and smart grid, this article proposes a novel framework based on compressive sensing (CS) and a cascade chaotic system (CCS). This framework can ensure low overhead, confidentiality, and authentication. Based on CS and the CCS, three technologies, including CCS-driven CS, CCS-driven local perturbation, and authentication mechanism, are introduced in the proposed data acquisition framework in this article. CCS-driven CS generates the measurement matrix with chaotic initial conditions and avoids the transmission of a large-size measurement matrix. CCS-driven local perturbation only perturbs a small number of elements in the original measurement matrix for each sampling and avoids the regeneration of the large-size measurement matrix. The authentication mechanism employs the authentication password and the access password to deal with the passive tampering attack and the active tampering attack, respectively. Moreover, the permutation-diffusion structure is used to encrypt the obtained measurements to enhance the security. Both theoretical and experimental analyses validate low overhead, confidentiality, and effective authentication of the proposed data acquisition framework for a number of industrial-informatics-based applications, such as IoT.

Novel multiple images encryption algorithm using CML system and DNA encoding

In this study, the authors advance a novel multiple images encryption algorithm using the coupled map lattices (CML) system and DNA encoding. The algorithm adopts a permutation-diffusion structure. First, the initial values and parameters of the CML system are determined by given values and SHA hash key of original images. Secondly, several plain images are grouped and permuted among groups. Next, different groups are combined into eight blocks of the same size, each of which is independently coded and scrambled. Thirdly, in the diffusion process, a DNA-level multiplication operation is redefined, and required key matrices are resulted from a small key connected with original images. Finally, dynamic DNA coding/decoding is adopted, and the coding and decoding rules are determined by original images. The evaluation of the simulation experiment shows that the proposed algorithm is safe and feasible, and has good encryption effect.

Plaintext-related image encryption scheme using hyperchaotic system and DNA computing

We propose a hyperchaotic image encryption algorithm based on plaintext information and DNA computing. Compared to the traditional permutation-diffusion structure, the proposed method enhances the relationship between pixel position, gray value, and the plaintext image. First, the algorithm’s hyperchaotic system iteratively generates multiple pseudorandom matrices and globally scrambles the image position by operating on the pseudorandom matrices and plaintext information. Then, the pseudorandom matrices and the scrambled image are encoded into DNA sequences for subsequent algebraic operations, and a new vector is constructed to modulate the sequence to obtain robust encryption performance. Finally, the processed DNA sequence is decoded and a XOR operation is applied to the binary pseudorandom sequence to obtain a final cipher image. Based on the experimental results and security analysis, the proposed algorithm not only demonstrates excellent encryption but also resists various typical attacks.

An Image Encryption Algorithm Based on Time-Delay and Random Insertion.

An image encryption algorithm is presented in this paper based on a chaotic map. Different from traditional methods based on the permutation-diffusion structure, the keystream here depends on both secret keys and the pre-processed image. In particular, in the permutation stage, a middle parameter is designed to revise the outputs of the chaotic map, yielding a temporal delay phenomena. Then, diffusion operation is applied after a group of random numbers is inserted into the permuted image. Therefore, the gray distribution can be changed and is different from that of the plain-image. This insertion acts as a one-time pad. Moreover, the keystream for the diffusion operation is designed to be influenced by secret keys assigned in the permutation stage. As a result, the two stages are mixed together to strengthen entirety. Experimental tests also suggest that our algorithm, permutation– insertion–diffusion (PID), performs better when expecting secure communications for images.

A Simple Chaotic Map-Based Image Encryption System Using Both Plaintext Related Permutation and Diffusion.

Recently, to conquer most non-plain related chaos-based image cryptosystems’ security flaws that cannot resist the powerful chosen/knownn plain-text attacks or differential attacks efficiently for less plaintext sensitivity, many plain related chaos-based image cryptosystems have been developed. Most cryptosystems that have adopted the traditional permutation–diffusion structure still have some drawbacks and security flaws: (1) most plaintext related image encryption schemes using only plaintext related confusion operation or only plaintext related diffusion operation relate to plaintext inadequately that cannot achieve high plaintext sensitivity; (2) in some algorithms, the generation of security key that needs to be sent to the receiver is determined by the original image, so these algorithms may not applicable to real-time image encryption; (3) most plaintext related image encryption schemes have less efficiency because more than one round permutation–diffusion operation is required to achieve high security. To obtain high security and efficiency, a simple chaotic based color image encryption system by using both plaintext related permutation and diffusion is presented in this paper. In our cryptosystem, the values of the parameters of cat map used in permutation stage are related to plain image and the parameters of cat map are also influenced by the diffusion operation. Thus, both the permutation stage and diffusion stage are related to plain images, which can obtain high key sensitivity and plaintext sensitivity to resist chosen/known plaintext attacks or differential attacks efficiently. Furthermore, only one round of plaintext related permutation and diffusion operation is performed to process the original image to obtain cipher image. Thus, the proposed scheme has high efficiency. Complete simulations are given and the simulation results prove the excellent security and efficiency of the proposed scheme.

Cryptanalysis and improvement in an image encryption scheme using combination of the 1D chaotic map

In this paper, we evaluate the security of an image cipher recently proposed. Three different cryptographic primitives, i.e., permutation, diffusion, and cyclic rotation, were integrated in this cipher so as to obtain a satisfactory security performance within a single encryption round. It is found that the equivalent key stream elements can be derived under chosen-plaintext attack. Both mathematical proof and experimental validation are given in detail. Concerning the presented analysis and some common defects of chaos-based image ciphers, an enhanced image cryptosystem based on the single-round permutation–diffusion structure is further developed. Natural and medical images are introduced for experimental verification and performance comparison. The results demonstrate the security superiority of the improved cryptosystem.

A Symmetric Plaintext-Related Color Image Encryption System Based on Bit Permutation.

Recently, a variety of chaos-based image encryption algorithms adopting the traditional permutation-diffusion structure have been suggested. Most of these algorithms cannot resist the powerful chosen-plaintext attack and chosen-ciphertext attack efficiently for less sensitivity to plain-image. This paper presents a symmetric color image encryption system based on plaintext-related random access bit-permutation mechanism (PRRABPM). In the proposed scheme, a new random access bit-permutation mechanism is used to shuffle 3D bit matrix transformed from an original color image, making the RGB components of the color image interact with each other. Furthermore, the key streams used in random access bit-permutation mechanism operation are extremely dependent on plain image in an ingenious way. Therefore, the encryption system is sensitive to tiny differences in key and original images, which means that it can efficiently resist chosen-plaintext attack and chosen-ciphertext attack. In the diffusion stage, the previous encrypted pixel is used to encrypt the current pixel. The simulation results show that even though the permutation-diffusion operation in our encryption scheme is performed only one time, the proposed algorithm has favorable security performance. Considering real-time applications, the encryption speed can be further improved.

Cryptanalysis of a chaotic image encryption scheme based on permutation-diffusion structure

Chaos-based image encryption algorithms have been widely studied since the permutation-diffusion structure (PDS) was proposed. However, the PDS is not secure from attacks, which may lead to security vulnerabilities of PDS based chaotic cryptosystems. In this study, the security problems of PDS are investigated. Then, a new PDS based chaotic image encryption scheme is cryptanalyzed. In the original scheme, a 3D bit matrix permutation was used to address the intrinsic deficiencies of traditional pixel/bit level permutation of image encryption. The double random position permutation provides a high security level. However, it is not unattackable. In this study, a novel attack method will be introduced where all the chaotic mappings or parameters which are functionally equivalent to the keys used in the permutation and diffusion stages of the original cryptosystem can fully be revealed. The encrypted images can then be completely recovered without knowing the secret keys. Both mathematical analysis and experimental results are given to illustrate the effectiveness of the proposed method.

Security Analysis of Some Diffusion Mechanisms Used in Chaotic Ciphers

As a variant of the substitution–permutation network, the permutation–diffusion structure has received extensive attention in the field of chaotic cryptography over the last three decades. Because of the high implementation speed and nonlinearity over GF([Formula: see text]), the Galois field of two elements, mixing modulo addition/multiplication and Exclusive OR becomes very popular in various designs to achieve the desired diffusion effect. This paper reports that some diffusion mechanisms based on modulo addition/multiplication and Exclusive OR are not resistant to plaintext attacks as claimed. By cracking several recently proposed chaotic ciphers as examples, it is demonstrated that a good understanding of the strength and weakness of these crypto-primitives is crucial for designing more practical chaotic encryption algorithms in the future.

Chosen-plaintext attack of an image encryption scheme based on modified permutation–diffusion structure

Since the first appearance in Fridrich’s design, the usage of permutation–diffusion structure for designing digital image cryptosystem has been receiving increasing research attention in the field of chaos-based cryptography. Recently, a novel chaotic image cipher using a single-round modified permutation–diffusion pattern (ICMPD) was proposed. Unlike traditional permutation–diffusion structure, the permutation of ICMPD is operated on bit level instead of pixel level and its diffusion stage is operated on masked pixels, which are obtained by carrying out the classical affine cipher, instead of plain pixels. Following a divide-and-conquer strategy, this paper reports that ICMPD can be compromised by a chosen-plaintext attack efficiently and the involved data complexity is linear to the size of the plain-image. Moreover, the relationship between the cryptographic kernel at the diffusion stage of ICMPD and the classical modulo addition then XORing operation is explored thoroughly.