1D Chaotic Maps Research Articles

Proposed Biometric Security System Based on Deep Learning and Chaos燗lgorithms

Nowadays, there is tremendous growth in biometric authentication and cybersecurity applications. Thus, the efficient way of storing and securing personal biometric patterns is mandatory in most governmental and private sectors. Therefore, designing and implementing robust security algorithms for users’ biometrics is still a hot research area to be investigated. This work presents a powerful biometric security system (BSS) to protect different biometric modalities such as faces, iris, and fingerprints. The proposed BSS model is based on hybridizing auto-encoder (AE) network and a chaos-based ciphering algorithm to cipher the details of the stored biometric patterns and ensures their secrecy. The employed AE network is unsupervised deep learning (DL) structure used in the proposed BSS model to extract main biometric features. These obtained features are utilized to generate two random chaos matrices. The first random chaos matrix is used to permute the pixels of biometric images. In contrast, the second random matrix is used to further cipher and confuse the resulting permuted biometric pixels using a two-dimensional (2D) chaotic logistic map (CLM) algorithm. To assess the efficiency of the proposed BSS, (1) different standardized color and grayscale images of the examined fingerprint, faces, and iris biometrics were used (2) comprehensive security and recognition evaluation metrics were measured. The assessment results have proven the authentication and robustness superiority of the proposed BSS model compared to other existing BSS models. For example, the proposed BSS succeeds in getting a high area under the receiver operating characteristic (AROC) value that reached 99.97% and low rates of 0.00137, 0.00148, and 0.00157 for equal error rate (EER), false reject rate (FRR), and a false accept rate (FAR), respectively.

Dual Image Cryptosystem Using Henon Map and Discrete Fourier Transform

This paper introduces an efficient image cryptography system. The proposed image cryptography system is based on employing the two-dimensional (2D) chaotic henon map (CHM) in the Discrete Fourier Transform (DFT). The proposed DFT-based CHM image cryptography has two procedures which are the encryption and decryption procedures. In the proposed DFT-based CHM image cryptography, the confusion is employed using the CHM while the diffusion is realized using the DFT. So, the proposed DFT-based CHM image cryptography achieves both confusion and diffusion characteristics. The encryption procedure starts by applying the DFT on the image then the DFT transformed image is scrambled using the CHM and the inverse DFT is applied to get the finally encrypted image. The decryption procedure follows the inverse procedure of encryption. The proposed DFT-based CHM image cryptography system is examined using a set of security tests like statistical tests, entropy tests, differential tests, and sensitivity tests. The obtained results confirm and ensure the superiority of the proposed DFT-based CHM image cryptography system. These outcomes encourage the employment of the proposed DFT-based CHM image cryptography system in real-time image and video applications.

Steganography Encryption Secret Message in Video Raster Using DNA and Chaotic Map

Recently, much secured data has been sent across the internet and networks. Steganography is very important because it conceals secure data in images, texts, audios, protocols, videos, or other mediums. Video steganography is the method of concealing data in frames of video format. A video is a collection of frames or images used for hidden script messages. This paper proposes a technique to encrypt secret messages using DNA and a 3D chaotic map in video frames using the raster method. This technique uses three steps: Firstly, converting video frames into raster to extract features from each frame. Secondly, encryption of secret messages using encoded forms of DNA bases, inverse/inverse complements of DNA, and utilizing 3D chaotic maps, Thirdly, hiding encryption secret messages in that raster video frame by using a secret key in the four corners of each video frame. This technique hides large amounts of secret data because the video frame is large and accepts any message size. The outcomes are efficient, robust, highly secure, and can tolerate high capacity. These outcomes have been obtained from a set of tests like: peak signal to noise ratio (PSNR), mean square error (MSE), entropy, correlation coefficient, and histogram and capacity.

Chaotic honey badger algorithm for single and double photovoltaic cell/module

PV cell/module/characteristic array accuracy is mainly influenced by their circuit elements, based on established circuit characteristics, under varied radiation and temperature operating conditions. As a result, this study provides a modified accessible Honey Badger algorithm (HBA) to identify the trustworthy parameters of diode models for various PV cells and modules. This approach relies on modifying the 2D chaotic Henon map settings to improve HBA’s searching ability. A series of experiments are done utilizing the RTC France cell and SLP080 solar module datasets for the single and double-diode models to validate the performance of the presented technique. It is also compared to other state-of-the-art methods. Furthermore, a variety of statistical and non-parametric tests are used. The findings reveal that the suggested method outperforms competing strategies regarding accuracy, consistency, and convergence rate. Moreover, the primary outcomes clarify the superiority of the proposed modified optimizer in determining accurate parameters that provide a high matching between the estimated and the measured datasets.

Color image encryption based on 2D enhanced hyperchaotic logistic-sine map and two-way Josephus traversing

To improve the chaotic behavior of the chaotic map, this paper proposes a new two-dimensional (2D) chaotic map, namely, 2D enhanced hyperchaotic Logistic-sine map (2D-EHLM), which is derived from the idea of the 2D Logistic map and the Sine map. The performance analyses demonstrate that the 2D-EHLM has significantly better hyperchaotic property, unpredictability characteristics in terms of their Lyapunov exponents, trajectories, and 0-1test in comparison to some existing 2D chaotic maps. Such as the 2D-EHLM performs chaotic behavior when their control parameter μ within (−3,4), which indicates a large chaotic range comparing with other 2D dynamical systems. To investigate its application, this paper proposes a new image confusion strategy based on the two-way Josephus traversing (TJT) to efficiently scramble the color image components and pixel positions. Combining 2D-EHLM and TJT operation, a new color image encryption scheme is proposed. The stimulation experiments and security analysis demonstrate that the proposed algorithm is able to protect the image information with a high security as well as to resist common types of attacks, which also verify the superior hyperchaotic behaviors of the 2D-EHLM from the aspect of encryption effect.

Enhancement of the CAST Block Algorithm Based on Novel S-Box for Image Encryption.

due to the rapid growth of data communication and multimedia system applications, security becomes a critical issue in the communication and storage of images. This study aims to improve encryption and decryption for various types of images by decreasing time consumption and strengthening security. An algorithm is proposed for encrypting images based on the Carlisle Adams and Stafford Tavares CAST block cipher algorithm with 3D and 2D logistic maps. A chaotic function that increases the randomness in the encrypted data and images, thereby breaking the relation sequence through the encryption procedure, is introduced. The time is decreased by using three secure and private S-Boxes rather than using six S-Boxes, as in the traditional method. Moreover, the CAST encryption algorithm was modified to be used on the private keys and substitution stage (S-Boxes), with the keys and S-Boxes of the encryption algorithm being generated according to the 2D and 3D chaotic map functions. The proposed system passed all evaluation criteria, including (MSE, PSNR, EQ, MD, SC, NC, AD, SNR, SIM, MAE, Time, CC, Entropy, and histograms). Moreover, the results also illustrate that the created S-Boxes passed all evaluation criteria; compared with the results of the traditional method that was used in creating S-Box, the proposed method achieved better results than other methods used in the other works. The proposed solution improves the entropy which is between (7.991-7.999), reduces the processing time which is between (0.5-11 s/Images), and improves NCPR, which is between (0.991-1). The proposed solution focuses on reducing the total processing time for encryption and decryption and improving transmission security. Finally, this solution provides a fast security system for surgical telepresence with secure real-time communication. The complexity of this work needs to know the S-Box creation method used, the chaotic method, the values of the chaotic parameters, and which of these methods was used in the encryption process.

A Secure Medical Image Transmission System Based On 2D Logistic Map and Diffie-Hellman Key Exchange Mechanisms

With the tremendous growth of searchable visual media, the content-based medical image retrieval and computer-aided diagnosis systems have become popular in recent years to improve knowledge and provide facilities for radiologists. Medical images transferred throughout public networks demand a mechanism that guarantees image privacy, ownership and source of origin reliability, and image integrity verification. For this reason, secure image retrieval and diagnosis scheme have been given considerable interest due to users’ security concerns. This work proposed a secure framework based on a two-dimensional (2D) chaotic map with Diffie–Hellman key exchange protocols to ensure patient information privacy and security. Consequently, from a security and protection perspective, the objective is to provide a privacy procedure for medical image retrieval systems through image encryption technique combined with a secure key exchange procedure to minimize the possibility of secret key interception by an unauthorized person. Simulation results and security analysis show that the suggested technique could protect images with minimal time complexity and a high level of security while also resisting numerous attacks.

Constructing keyed strong S-Box with higher nonlinearity based on 2D hyper chaotic map and algebraic operation

As the only nonlinear component, S-Box plays an important role in cryptography. To overcome the problems in some 1D chaotic maps such as poor randomness and lacking ergodicity, we constructed a 2D exponential quadratic chaotic map (2D-EQCM), and analyzed its dynamic behavior through phase diagram, Lyapunov exponent, Kolmogorov entropy, correlation dimension and randomness testing. The results demonstrated that the 2D-EQCM with ergodicity and better randomness can be served as pseudo-random number generator (PRNG). Furthermore, to generate a large number of S-Boxes with higher nonlinearity, we designed a keyed strong S-Box construction algorithm using the 2D-EQCM and algebraic operation based on seed S-Boxes. Experimental results verified the effectiveness of the proposed keyed strong S-Box construction algorithm.

Design of cross-plane colour image encryption based on a new 2D chaotic map and combination of ECIES framework

Design of cross-plane colour image encryption based on a new 2D chaotic map and combination of ECIES framework

Cryptanalysis and Improved Image Encryption Scheme Using Elliptic Curve and Affine Hill Cipher

In the present era of digital communication, secure data transfer is a challenging task in the case of open networks. Low-key-strength encryption techniques incur enormous security threats. Therefore, efficient cryptosystems are highly necessary for the fast and secure transmission of multimedia data. In this article, cryptanalysis is performed on an existing encryption scheme designed using elliptic curve cryptography (ECC) and a Hill cipher. The work shows that the scheme is vulnerable to brute force attacks and lacks both Shannon’s primitive operations of cryptography and Kerckchoff’s principle. To circumvent these limitations, an efficient modification to the existing scheme is proposed using an affine Hill cipher in combination with ECC and a 3D chaotic map. The efficiency of the modified scheme is demonstrated through experimental results and numerical simulations.

Construction of high-dimensional cyclic symmetric chaotic map with one-dimensional chaotic map and its security application.

Classical one-dimensional chaotic map has many ideal characteristics which is quite suitable for many different kinds of scientific fields, especially cryptography. In this paper, we propose an idea of constructing high-dimensional (HD) cyclic symmetric chaotic maps by using one-dimensional (1D) chaotic map. Two constructed 3D cyclic symmetric chaotic maps are taken as the examples, named three-dimensional cyclic symmetric logistic map (3D-CSLM) and three-dimensional cyclic symmetric Chebyshev map (3D-CSCM), respectively. Numerical experiments show that the new maps possesses better dynamical performances, and their parameters have a wider range, compared with the original map. Furthermore, to verify its effect in image encryption, a novel image encryption algorithm based on 3D-CSLM and DNA coding is proposed. DNA method for image encryption can improve the efficiency of permutation and diffusion. Firstly, the algorithm uses 3D-CSLM to generate chaotic sequences for DNA operation rule selection and pixel permutation. Then through the DNA XOR operation to achieve diffusion, and finally form an encrypted image. Several simulation tests results indicate that the proposal has a promising security performance and strong anti-attack ability.

Constructing Strong S-Box by 2D Chaotic Map with Application to Irreversible Parallel Key Expansion

Cryptanalysis of key expansion algorithms in AES and SM4 revealed that (1) there exists weaknesses in their S-Boxes, and (2) the round key expansion algorithm is reversible, i.e. the initial key can be recovered from any round key, which may be explored by the attacker. To solve these problems, first we constructed a nondegenerate 2D exponential hyper chaotic map (2D-EQCM), derived a recursion formula to calculate the number of S-Boxes, and designed a strong S-Box construction algorithm without such weakness. Then based on 2D-EQCM and S-Box, we designed an irreversible parallel key expansion algorithm, which could transform the initial key to any number of relatively independent round keys. Security and statistical analysis demonstrated the flexibility and effectiveness of the proposed irreversible parallel key expansion algorithm.

Formula omitted]-Dimensional Chaotic Map with application in secure communication

When applied to practical applications, existing chaotic systems exhibit many weaknesses, including discontinuous chaotic intervals and easily predicted chaotic signals. This study proposes an n-dimensional chaotic model (nD-CM) to resolve the weaknesses of existing chaotic systems. nD-CM can produce chaotic maps with any desired dimension utilizing existing 1D chaotic maps as seed chaotic maps. To demonstrate the effect of nD-CM, we generate three 2D and one 3D chaotic map as examples, utilizing three 1D chaotic maps as the seed maps. The evaluation and experiment results show that these newly generated chaotic maps can obtain continuous and wider chaotic intervals and better performance using the indicators of the Lyapunov exponent, sample entropy and correlation dimension, compared to existing maps. To further show the practicality of nD-CM, the generated maps are additionally applied to secure communication. The experimental results show that these chaotic maps exhibit much better performance in resisting transmission noise in this application than existing chaotic maps.

A cluster of 1D quadratic chaotic map and its applications in image encryption

Chaotic systems are widely used in designing encryption algorithms for their ideal dynamical performances. One-dimensional (1D) chaotic maps have the highest efficiency in implementation and have achieved great attention. However, 1D chaotic maps have a common security weakness, which is that their key space is relatively small. Therefore, in this paper, a cluster of 1D quadratic chaotic maps is proposed according to the topological conjugate theory. The 1D chaotic map has three tunable parameters which have a significant expansion in parameter space than the traditional 1D chaotic maps. The 1D map is proved to be chaotic theoretically since it is topologically conjugated with a logistic chaotic map. An example of a 1D quadratic chaotic map is provided in this paper, and several numerical simulation results indicate that this 1D quadratic map has ideal chaotic characteristics, which are consistent with the theoretical analysis. To verify the effectiveness of this 1D quadratic map, a novel image encryption algorithm is proposed. The security of this image encryption algorithm is completely dependent on the properties of the 1D quadratic map. Security experimental test results show that this image encryption algorithm has a high-security level, and is quite competitive with other chaos-based image encryption algorithms.

An Improved Gumowski–Mira Map with Symmetric Lyapunov Exponents

The symmetric Lyapunov exponents (LEs) are known to be an inherent property of continuous-time conservative systems. However, the research on this interesting phenomenon in a discrete-time chaotic map has not been reported. Thus, this paper presents an improved 2D chaotic map based on Gumowski–Mira (GM) transformation, which has a stable fixed point or an unstable fixed point depending on its control parameters. Furthermore, it can display symmetric LEs and an infinite number of coexisting attractors with different amplitudes and different shapes. To demonstrate the complex dynamics of the 2D chaotic map, this paper studies its control parameters related to dynamical behaviors employing numerical analysis methods. Then, the hardware implementation based on STM32 platform is established for illustrating the numerical simulation results. Next, the random performance of the 2D chaotic map is tested by NIST FIPS140-2 suite. Finally, an image encryption algorithm based on the 2D chaotic map is designed, and the results obtained reveal that the proposed chaotic map has excellent randomness and is more suitable for many chaos-based image encryptions.

Constructing a 3D Exponential Hyperchaotic Map with Application to PRNG

Some weaknesses of 1D chaotic maps, such as lacking of ergodicity, multiple bifurcations, dense periodic windows, and short iteration period, limit their practical applications in cryptography. A higher-dimensional chaotic map with ergodicity can solve these problems. Based on 1D quadratic map, a 3D exponential hyperchaotic map (3D-EHCM) is constructed, and its dynamic behaviors, such as phase diagram, Lyapunov exponent spectrum, Kolmogorov entropy (KE), correlation dimension, approximate entropy and randomness, are analyzed and tested. The results demonstrate that the 3D-EHCM has ergodicity in a larger range of control parameter, and its state points have a longer period. To counteract dynamical degradation and make it suitable for a PRNG, the periodic point detection and random impulsive perturbation are applied to lengthen the aperiodic time sequence, and statistical results demonstrate that a full-period sequence can be obtained.

Construction of a Nondegenerate 2D Chaotic Map with Application to Irreversible Parallel Key Expansion Algorithm

The key expansion algorithm is an important part of a general iterated block cipher, because its security determines the security level of the encryption scheme. Thus, generating secure round keys with statistical independence and sensitivity is desirable. An irreversible parallel key expansion algorithm is proposed based on a chaotic map in this paper. First, an enhanced nondegenerate 2D exponential chaotic map (2D-ECM) with ergodicity is constructed, with analysis results demonstrating that it has better dynamical characteristics. Then, an irreversible key expansion algorithm is designed based on the 2D-ECM, which has high sensitivity to initial key with independence between round keys. Experimental results and performance analysis demonstrate that the algorithm is feasible and can resist the side channel power attack.

Performance Analysis of Chaotic Neural Network and Chaotic Cat Map Based Image Encryption

Nowadays, chaotic systems are used quite often, especially in image encryption applications. Hypersensitivity to the initial conditions, limited field-changing signs and irregular movements make these systems one of the critical elements in scientific matters such as cryptography. These systems are divided in two parts as discrete time and continuous time in terms of their dimensions and properties. Gray level image encryption applications generally use one-dimensional and color image encryption applications generally use multi-dimensional chaotic systems. In this study, Tent Map, Cat Map, Lorenz, Chua, Lu chaotic systems were used for chaotic neural network based image coding application and Logistic Map and 3D Cat Map chaotic systems were used for 3D chaotic Cat Map based image encryption application. The encrypted image and the original image were examined by various analysis methods. As a result of these analyzes, it was seen that both applications gave very successful results. Analyzes have shown that the chaotic neural network based image coding algorithm is more secure and successful.

Image lossless encoding and encryption method of SPECK based on 1D chaotic map

In order to satisfy the requirements of high quality and security during image transmission and storage, this paper proposes an image lossless compression encryption algorithm based on 1D chaotic map and Set Partitioned Embedded block encoder (SPECK). Initially, this paper proposes a new 1D chaotic map, and applies the chaotic sequences generated by it to each stage of the compression encryption algorithm. In addition, according to the feature that the degree of energy concentration in the wavelet coefficient matrix gradually decreases from low frequency to high frequency, this paper proposes a wavelet coefficient encryption algorithm, which can balance security and compression performance. Furthermore, multiple encryption points are introduced in the SPECK encoding process, and a secure SPECK encoding algorithm is proposed. Finally, theoretical analysis and simulation results show that the proposed algorithm is close to the theoretical value in terms of information entropy, correlation coefficient, mean square error of reconstructed image and other related indicators. Therefore, the algorithm has high security and lossless compression performance.

RGB image encryption based on symmetric keys using Arnold transform, 3D chaotic map and affine hill cipher

In this work, we propose a novel color image encryption scheme based on symmetric keys using the synergistic approach of Arnold transform, 3D logistic chaotic map with XOR operation, and affine hill cipher technique. All these methods work together and generate a strong cipher to abstain people from illegal access to data. The simulation results of the quality indicators and comparison with the existing algorithms ensure the security, performance, and effectiveness of our proposed scheme.