2D Logistic Map Research Articles

FPGA Implementation of Improved Security Approach for Medical Image Encryption and Decryption

Securing medical images is a great challenge to protect medical privacy. An image encryption model founded on a complex chaos-based Pseudorandom Number Generator (PRNG) and Modified Advanced Encryption Standard (MAES) is put forward in this paper. Our work consists of the following three main points. First, we propose the use of a complex PRNG based on two different chaotic systems which are the 2D Logistic map in a complex set and Henon’s system in the key generation procedure. Second, in the MAES 128 bits, the subbytes’ operation is performed using four different S-boxes for more complexity. Third, both shift-rows’ and mix-columns’ transformations are eliminated and replaced with a random permutation method which increases the complexity. More importantly, only four rounds of encryption are performed in a loop that reduces significantly the execution time. The overall system is implemented on the Altera Cyclone III board, which is completed with an SD card interface for medical image storage and a VGA interface for image display. The HPS software runs on μClinux and is used to control the FPGA encryption-decryption algorithm and image transmission. Experimental findings prove that the propounded map used has a keyspace sufficiently large and the proposed image encryption algorithm augments the entropy of the ciphered image compared to the AES standard and reduces the complexity time by 97%. The power consumption of the system is 136.87 mw and the throughput is 1.34 Gbit/s. The proposed technique is compared to recent image cryptosystems including hardware performances and different security analysis properties, such as randomness, sensitivity, and correlation of the encrypted images and results prove that our cryptographic algorithm is faster, more efficient, and can resist any kind of attacks.

Designing Substitution Box Based on the 1D Logistic Map Chaotic System

Many researchers have tried to use the chaotic systems in generating different cryptographic tools, in order to provide high level of security to the data passing through network. In modern symmetric cryptographic systems, one of the most essential functions is a nonlinear mapping Substitution process which is responsible for creating the confusion between plaintext and ciphertext. It replaces each input bits by other bits using the lookup table S-Box. In this paper a new S-Box based on a 1D logistic map chaotic system was designed. The chaotic sequence generated from the 1D logistic map was processed to generate the hexa code values, and after that this hexa code also processed to construct the new good S-Box. This proposal was evaluated using the S-Box tests criteria including avalanche, balanced, completeness, strict avalanche, and invertibility. The analysis results show that the proposed S-Box passes all these statistical tests, has large avalanche effect and therefore the S-Box can avoid many attacks. The construction of both Substitution-Box and its inverse take only few milliseconds, so it can be used in many lightweight block ciphers.

The Design and FPGA-Based Implementation of a Stream Cipher Based on a Secure Chaotic Generator

In this study, with an FPGA-board using VHDL, we designed a secure chaos-based stream cipher (SCbSC), and we evaluated its hardware implementation performance in terms of computational complexity and its security. The fundamental element of the system is the proposed secure pseudo-chaotic number generator (SPCNG). The architecture of the proposed SPCNG includes three first-order recursive filters, each containing a discrete chaotic map and a mixing technique using an internal pseudo-random number (PRN). The three discrete chaotic maps, namely, the 3D Chebyshev map (3D Ch), the 1D logistic map (L), and the 1D skew-tent map (S), are weakly coupled by a predefined coupling matrix M. The mixing technique combined with the weak coupling technique of the three chaotic maps allows preserving the system against side-channel attacks (SCAs). The proposed system was implemented on a Xilinx XC7Z020 PYNQ-Z2 FPGA platform. Logic resources, throughput, and cryptanalytic and statistical tests showed a good tradeoff between efficiency and security. Thus, the proposed SCbSC can be used as a secure stream cipher.

Enhanced Image Encryption Using Two Chaotic Maps

Information security is an important aspect in various communication areas, multimedia frameworks, medical imaging and militant communications. However, most of them encounter issues such as insufficient robustness or security. Recently, the approach of achieving information security by using chaotic techniques has gained popularity, since they provide ergodic and random generated keys. This paper introduces a combination of two chaotic maps (3D logistic map and Arnold’s cat map) that meet the general security requirements of image transmission. First the image is encrypted using Arnold’s cat map, which shuffles the image pixels. 3D logistic map is applied to the encrypted image for transformation and permutation purposes. Then the XOR operation for the encrypted image and a chaotic sequence key are used to provide more security after the pixel values have been changed. The performance of the proposed security method was evaluated using MATLAB by analyzing the correlation between adjacent pixels, histogram analysis, and entropy information. The simulation results showed that the proposed method is robust and resilient. It can achieve an average of 7.99 for entropy information, 99.6% for NPCR, and 33.77 % for UCAI.   Â

Image Encryption Algorithm Based on Substitution Principle and Shuffling Scheme

This research presents a method of image encryption that has been designed based on the algorithm of complete shuffling, transformation of substitution box, and predicated image crypto-system. This proposed algorithm presents extra confusion in the first phase because of including an S-box based on using substitution by AES algorithm in encryption and its inverse in Decryption. In the second phase, shifting and rotation were used based on secrete key in each channel depending on the result from the chaotic map, 2D logistic map and the output was processed and used for the encryption algorithm. It is known from earlier studies that simple encryption of images based on the scheme of shuffling is insecure in the face of chosen cipher text attacks. Later, an extended algorithm has been projected. This algorithm performs well against chosen cipher text attacks. In addition, the proposed approach was analyzed for NPCR, UACI (Unified Average Changing Intensity), and Entropy analysis for determining its strength.

Further Discussions of the Complex Dynamics of a 2D Logistic Map: Basins of Attraction and Fractal Dimensions

In this paper, we study the complex dynamic characteristics of a simple nonlinear logistic map. The map contains two parameters that have complex influences on the map’s dynamics. Assuming different values for those parameters gives rise to strange attractors with fractal dimensions. Furthermore, some of these chaotic attractors have heteroclinic cycles due to saddle-fixed points. The basins of attraction for some periodic cycles in the phase plane are divided into three regions of rank-1 preimages. We analyze those regions and show that the map is noninvertible and includes Z0,Z2 and Z4 regions.

Double image encryption based on symmetry of 2D-DFT and equal modulus decomposition

This paper introduces a double image encryption scheme mainly based on symmetry of two-dimensional discrete Fourier transform (2D-DFT) and equal modulus decomposition (EMD). Firstly, the plural form is adopted to encode double image as a whole and the 2D-DFT is performed. To obtain matrices satisfying property of conjugate symmetry, the spectra are implemented addition and subtraction. Followed by truncation-superposition operations, another complex value matrix is attained and equal modulus decomposition is carried out to get two phase templates, which are further gyrator transformed to enhance security. With an orthogonal matrix, the real and imaginary parts are shared and spliced together to produce a real-valued cipherimage, which aims to make storage and transmission convenient. The initial states of 2D logistic map are closely related to the plaintext images and is employed to generate phase mask, rotation angles as well as the input of Gaussian matrix, which ensures the high level of security. Experimental results have demonstrated the feasibility and validity of the proposal in restituting plaintext images, security and resisting Gaussian noise attack.

A 2D logistic map and Lorenz-Rossler chaotic system based RGB image encryption approach

This paper presents a novel color image encryption approach. The proposed approach utilizes the basic concepts of DNA cryptography along with Lorenz and Rossler chaotic system and 2D logistic map. The proposed approach encrypts RGB images using DNA cryptography techniques. In diffusion phase, at pixel level Lorenz and Rossler chaotic system is used to encrypt the three channels of test images. Afterwards, at bit level 2D logistic map is used for performing bitwise chaotic ponytail process on these diffused Red, Green, and Blue channels in confusion phase. Simulation of the proposed approach on test images reveals that the color images have been encrypted very efficiently.

Algebra-chaos amalgam and DNA transform based multiple digital image encryption

This study suggests a novel color multiple image encryption technique using “Algebra-Chaos Amalgamated 256-length-12-bit random sequence” and DNA Transform. The proposed random sequence (S-box) has the property of occupying small computer memory space as regards to the existing S-boxes. Moreover, for simplicity and novelty, 1D sin chaotic map and 1D logistic map are mixed to generate a 1D mixed Chaotic map. Initially, a 12 × 12 (256-length-12-bit) S-box is designed by the unit elements of a chain ring, and then it is mixed with the 1-D mixed chaotic map that results triplets T1,T2 and T3 of high random behavior. A multiple digital image encryption is performed by using the triplet for substitution-permutation along with DNA transform. The proposed image encryption technique enhances key-space size. Moreover, the experimental results show that the proposed technique of encryption for digital medium has extra ordinary resistance against the well-known attacks.

An improved digital logistic map and its application in image encryption

Chaos maps are widely used in image encryption systems due to their intrinsic advantages such as extreme sensitivity to initial values., ergodicity and pseudo-randomness. 1D Logistic map has attracted the attention of researchers due to its simple structure and easy implementation, but also because of this, the map is easy to be affected by finite precision, resulting in dynamic degradation, at low precision, the sequence generated by this map not only enters a period quickly, but also has a shorter period. Thus, taking 1D Logistic map as an example, we proposed a method to suppress the dynamic degradation of digital chaotic systems by using parameter variables and state variables to influence each other, and using sine function as feedback function to destroy the state space. The simulation results show that the improved logistic mapping with the proposed method has better randomness and higher complexity than the original logistic mapping. To prove the practicability and applicability of the improved chaotic map, we design a new image encryption algorithm, which is suitable for both color image and grayscale image. The numerical results indicate that the proposed algorithm has high encryption efficiency, good resistance to various attacks and certain competitiveness with other encryption algorithms.

Chaotic image encryption algorithm based on block theory and reversible mixed cellular automata

In this paper, a new chaotic image encryption algorithm based on block theory and reversible mixed cellular automata model is proposed. Different from traditional confusion-diffusion structure, this paper employs new three-tier architecture, i.e. diffusion-confusion-diffusion. The first diffusion operation adopts the traditional diffusion method, which aims to avoid direct operation on plaintext and further enhance the encryption effect. The next scrambling and diffusion operations are based on image blocks and a new dynamical system, namely reversible mixed cellular automata model. The scrambling operation is divided into two parts, inter block scrambling and intra block scrambling, all the above operations are based on pixel level. Then, diffusion operation is performed and its implementation is based on the evolution of constructed reversible mixed cellular automata with balanced rules. In addition, the initial values and parameters of the adopted chaotic system, two dimensional (2D) Logistic map, are obtained using SHA 256 hash function related to plaintext image. The use of hash function makes the chaotic sequences completely different when encrypt different images, which enhances the ability to resist known-plaintext and chosen-plaintext attacks. Simulation results and performance analysis bear out that the encryption algorithm proposed in this paper has higher security performance and can resist different attacks efficiently.

Perceptual accessible image encryption scheme conjugating multiple chaotic maps

In the recent decade, chaos-based image encryption algorithms gained attention due to their pros and cons. The authors suggest one such algorithm of image encryption for different colour space using feed forward initial condition to pursue random permutation by combining 1D logistic map with a series of tent maps. The algorithm adds one more novel step to protect and encrypt binary image by concealing it within a cover grey image using bit-plane decomposition methods. Sensitivity towards initial condition is shown using block division of image by applying a stream of random initial conditions to each block for encryption along with XOR operation which leads the key space high . For better performance analysis, the proposed scheme has been tested with many colour space images including a binary image. The proposed technique is more efficient with respect to time complexity and resistance to vulnerability aspects.

Novel image encryption by combining dynamic DNA sequence encryption and the improved 2D logistic sine map

The one-dimensional (2D) chaotic encryption algorithm has good encryption performance. For its properties, such as the excellent complexity, pseudo-randomness, and sensitivity to the initial value of the chaotic sequence. However, compared with other methods, its biggest drawback is that the key space is too small. To address these problems, in this study, the authors introduce an improved 2D logistic sine chaotic map (2D-LSMM). A novel image encryption scheme based on dynamic DNA sequences encryption and improved 2D-LSMM is presented. The logistic map is used to control the input of the sine map. And the encoding and operation rules of DNA sequences are determined by 2D-LSMM chaotic sequences. By implementing dynamic DNA sequence encryption, the encryption process becomes more complicated and harder to be attacked. Simulation experimental results and security analysis show that the authors’ encryption scheme not only achieves proper encryption but can also resist different attacks.

Colour image encryption using Gaussian apertured real-preserving fractional Mellin transform in diffraction domain

A colour image encryption scheme based on Gaussian apertured real-preserving fractional Mellin transform (GARPFrMT) in diffraction domain and chaos permutation is proposed. Real-preserving fractional transform in diffraction domain using Gaussian aperture is constructed to ensure that the output is real, which is convenient for storage and communication. And the Gaussian aperture, as a soft aperture, can improve the intensity distributions of the output light, which contributes to prevent possible attacks for obtaining some useful information from the marginal leakage of light in the optical encryption systems. The colour space rotation transform is first used to convert the colour image from standard space to space. And then, the three new colour components are transformed by GARPFrMT with three different diffraction channels, respectively. A 3D-logistic map is utilized to further scramble the three-colour components. At last, a logistic-sine map is used to perform Xor operation with three components, respectively. Simulation results demonstrate that the proposed algorithm is feasible and robust to noise attack and data loss.

Reducing the Dynamical Degradation of Digital Chaotic Maps with Time-Delay Linear Feedback and Parameter Perturbation

Digital chaotic maps are not secure enough for cryptographic applications due to their dynamical degradation. In order to improve their dynamics, in this paper, a novel method with time-delay linear feedback and parameter perturbation is proposed. The delayed state variable is used to construct the linear feedback function and parameter perturbation function. This method is universal for all different digital chaotic maps. Here, two examples are presented: one is 1D logistic map and the other is 2D Baker map. To show the effectiveness of this method, we take some numerical experiments, including trajectory and phase space analysis, correlation analysis, period analysis, and complexity analysis. All the numerical results prove that the method can greatly improve the dynamics of digital chaotic maps and is quite competitive with other proposed methods. Furthermore, a simple pseudorandom bit generator (PRBG) based on digital Baker map is proposed to show its potential application. The proposed PRBG is completely constructed by the digital chaotic map, without any other complex operations. Several numerical results indicate that this PRBG has good randomness and high complexity level.

Iris images encryption based on QR code and chaotic map

In this paper an Iris image is encrypted based on QR (quick response) code and chaotic map. The main idea of the proposed system is generating a QR code depending on the input text and then extract the features from QR code by using convolution, these features are used for key generation. After that the permuted iris image is encrypted by using generated key, after that the resulting image will be encrypts using 2D logistic map. The randomness of generated key is tested using the measures of NIST, and quality of images that encrypted in this method are tested by using security analysis tests such as PSNR, UACI, NPCR, histogram, correlation and entropy. The security analysis shows that the proposed system is secure for iris image encryption.

A novel parallel image encryption algorithm based on hybrid chaotic maps with OpenCL implementation

Since chaotic maps have the excellent properties of unpredictability, ergodicity and sensitivity to their parameters and initial values, they are quite suitable for generating chaotic sequences for securing communication systems and are also especially useful for securing images, and a lot of chaotic map-based image encryption algorithms have been proposed. But some existing image encryption algorithms were proved that their security, encryption efficiency or computational speeds are not quite satisfactory for practical applications. Some of them using only one type of chaotic system may suffer from low key space, and some others using two or more types of chaotic system may suffer from high computational overheads. In this paper, based on the classic 1D logistic map, a 2D one-coupling logistic dynamics system and OpenCL, a novel parallel image encryption algorithm HCMO is proposed. Our algorithm consists of a confusion phase and a diffusion phase using four sub-key matrices based on the hybrid logistic dynamics systems, the linear transformation and the enlarging operation. In the confusion phase, the image’s pixel positions are first scrambled by performing row-wise and column-wise permutation operations using two sub-key matrices; then, in its diffusion phase, both the bit XOR operation and the bit cyclic shifting are applied onto the scrambled intermediate image matrix using the other two sub-key matrices. In order to reduce the whole encrypting execution time, we speed up our HCMO on an OpenCL’s heterogeneous and parallel characteristics. Compared to the implementation of Vihari’s algorithm and some other chaotic map-based algorithms referred in this paper with the OpenCL-based implementation on the CPU and on the GPU, respectively, our algorithm’s simulation demonstrates remarkable improvement in the operational speedup, and the experimental result analyses have also shown that HCMO has a higher-level security than some other referred algorithms.

Hybrid Method of Document Image Encryption using ECC and Multiple Chaotic Maps

Document imaging is one of the most important technology used to preserve, retrieve and to transmit old documents over the internet. Since open network threatens the security of such documents from being intercepted, the proposed scheme intends to provide enhanced security for such documents. The proposed hybrid algorithm includes Elliptic Curve Cryptography (ECC), and mixed chaotic system. The ECC encrypts the plain image based on the elliptic points generated by selecting a prime number. The mixed chaotic map includes two-dimensional logistic map and three-dimensional Lorenz map. The 2D logistic map is used for confusing the ECC encrypted image and 3D Lorenz map is used for diffusing the confused image. The two levels of confusion, first with byte level and second with bit level are introduced. The two levels of diffusion, first level with Lorenz map and second level with Fibonacci sequences are introduced. Better net pixel change rate and unified average change intensity with flat histogram and low correlation are achieved in this method. The key Sensitivity, Entropy, Mean Square Error, and Peak Signal to Noise Ratio analysis reveal that the proposed method is resistant to any external invasion. The encryption and decryption speed is increased by using programming techniques. The robustness of the algorithm is also checked and found to be robust against noise and loss of information.

Secure color image cryptosystem based on chaotic logistic in the FrFT domain

Recently, the digital multimedia security technology has been an interesting research theme due to fast advancement in employing real time multimedia through Internet and wireless networks. The market of multimedia streaming, such as exclusive video on demand (VoD) is a huge multi- billion-dollar market. This market is threatened by hackers. The multimedia streaming industry needs a cryptosystem that is both fast and secure. Chaotic cryptosystems have been proposed by many researchers in order to promote communication security. However, these chaotic schemes have some major problems, such as unacceptable expansion of data, slow performance speed, and shortcomings against differential attack. Therefore, this paper provides an efficient Fractional Fourier Transform (FrFT)-based logistic map (LM) color image encryption scheme by applying a 2D LM on FrFT. In the proposed FrFT-based LM color image encryption scheme, the 2D LM is employed as a confusion step to scramble the color image pixel positions in the FrFT and confuse the relationship between the cipherimage and the plainimage. For enhancing the encryption performance characteristics of the 2D LM under the FrFT, the angle of the FrFT is taken as an extra additional key in encryption. The proposed FrFT-based LM color image encryption scheme is examined and investigated using visual inspection, entropy, histograms, encryption quality, noise tests, and differential analysis. The obtained simulation tests demonstrate and verify the effectiveness of the FrFT-based LM color image encryption scheme. Moreover, our results also show a significant improvement in the performance of the confusion property with our proposed 2D LM encryption scheme using the FrFT. Also, we compared the proposed cryptosystem with recent state-of-the-art cryptosystems. Experimental results show that our proposed image cryptosystem is highly secure from the cryptographic point of view. Furthermore, the obtained test results ensured the superiority of our proposed cryptosystem for digital image transmission compared to the recent state-of-theart cryptosystems.

A lightweight and efficient digital image encryption using hybrid chaotic systems for wireless network applications

Due to limited processing capabilities and other constraints of most wireless networks, many existing security algorithms do not consider the network efficiency. This is because most of these security solutions exhibit intolerable overhead and consider only securing scalar data, which are not suitable for other data types such as digital images, hence affecting the provided security level and network performance. Thus, in this paper, we propose a lightweight and efficient security scheme based on chaotic algorithms to efficiently encrypt digital images. Our proposed algorithm handles digital images in two phases: Firstly, digital images are split into blocks and compressed by processing them in frequency domain instead of Red-Green-Blue (RGB) domain. The ultimate goal is to reduce their sizes to speed up the encryption process and to break the correlation among image pixel values. Secondly, 2D Logistic chaotic map is deployed in key generation, permutation, and substitution stages for image pixel shuffling and transposition. In addition, 2D Henon chaotic map is deployed to change the pixel values in the diffusion stage in order to enhance the required level of security and resist various security attacks. Security performance analysis based on standard test images shows that our proposed scheme overcomes the performance of other existing techniques.