Symmetric encryption algorithms using chaotic and non-chaotic generators: A review
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paper_title: Image Encryption Based on Diffusion and Multiple Chaotic Maps

paper_content:

In the recent world, security is a prime important issue, and encryption is one of the best alternative way to ensure security. More over, there are many image encryption schemes have been proposed, each one of them has its own strength and weakness. This paper presents a new algorithm for the image encryption/decryption scheme. This paper is devoted to provide a secured image encryption technique using multiple chaotic based circular mapping. In this paper, first, a pair of sub keys is given by using chaotic logistic maps. Second, the image is encrypted using logistic map sub key and in its transformation leads to diffusion process. Third, sub keys are generated by four different chaotic maps. Based on the initial conditions, each map may produce various random numbers from various orbits of the maps. Among those random numbers, a particular number and from a particular orbit are selected as a key for the encryption algorithm. Based on the key, a binary sequence is generated to control the encryption algorithm. The input image of 2-D is transformed into a 1- D array by using two different scanning pattern (raster and Zigzag ) and then divided into various sub blocks. Then the position permutation and value permutation is applied to each binary matrix based on multiple chaos maps. Finally the receiver uses the same sub keys to decrypt the encrypted images. The salient features of the proposed image encryption method are loss-less, good peak signal –to noise ratio (PSNR), Symmetric key encryption, less cross correlation, very large number of secret keys, and key-dependent pixel value replacement.
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paper_title: Color Image Encryption Algorithm Combining Compressive Sensing with Arnold Transform

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A new color image encryption algorithm combining compressive sensing with Arnold transform is proposed, which can encrypt the color image into a gray image. Considering the dimensional reduction and random projection of compressive sensing, we utilize compressive sensing to encrypt and compress the three color components of color image simultaneously. The three encrypted and compressed color components’ dimensions are smaller than the original image, thus they can be grouped into a gray image, and then the gray image is scrambled by Arnold transform to enhance the security. The proposed algorithm can also be applied in the multiple-image encryption. The experimental results show the validity and the reliability of the proposed algorithm.
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paper_title: Chaos-based Cryptography: Theory, Algorithms and Applications

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Chaos-based cryptography, attracting many researchers in the past decade, is a research field across two fields, i.e., chaos (nonlinear dynamic system) and cryptography (computer and data security). It Chaos' properties, such as randomness and ergodicity, have been proved to be suitable for designing the means for data protection.The book gives a thorough description of chaos-based cryptography, which consists of chaos basic theory, chaos properties suitable for cryptography, chaos-based cryptographic techniques, and various secure applications based on chaos. Additionally, it covers both the latest research results and some open issues or hot topics. The book creates a collection of high-quality chapters contributed by leading experts in the related fields. It embraces a wide variety of aspects of the related subject areas and provide a scientifically and scholarly sound treatment of state-of-the-art techniques to students, researchers, academics, personnel of law enforcement and IT practitioners who are interested or involved in the study, research, use, design and development of techniques related to chaos-based cryptography.
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paper_title: A novel image encryption algorithm based on a 3D chaotic map

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Abstract Recently [Solak E, Cokal C, Yildiz OT Biyikogˇlu T. Cryptanalysis of Fridrich’s chaotic image encryption. Int J Bifur Chaos 2010;20:1405–1413] cryptanalyzed the chaotic image encryption algorithm of [Fridrich J. Symmetric ciphers based on two-dimensional chaotic maps. Int J Bifur Chaos 1998;8(6):1259–1284], which was considered a benchmark for measuring security of many image encryption algorithms. This attack can also be applied to other encryption algorithms that have a structure similar to Fridrich’s algorithm, such as that of [Chen G, Mao Y, Chui, C. A symmetric image encryption scheme based on 3D chaotic cat maps. Chaos Soliton Fract 2004;21:749–761]. In this paper, we suggest a novel image encryption algorithm based on a three dimensional (3D) chaotic map that can defeat the aforementioned attack among other existing attacks. The design of the proposed algorithm is simple and efficient, and based on three phases which provide the necessary properties for a secure image encryption algorithm including the confusion and diffusion properties. In phase I, the image pixels are shuffled according to a search rule based on the 3D chaotic map. In phases II and III, 3D chaotic maps are used to scramble shuffled pixels through mixing and masking rules, respectively. Simulation results show that the suggested algorithm satisfies the required performance tests such as high level security, large key space and acceptable encryption speed. These characteristics make it a suitable candidate for use in cryptographic applications.
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paper_title: MOS realization of the modified Lorenz chaotic system

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Abstract A new chaotic oscillator circuit that realizes three attractors, the modified Lorenz system, Lorenz attractor “Butterfly attractor” and unsymmetrical modified Lorenz system [IEEE Trans. Circ. Syst. I 48 (2001) 289] is given in the paper. The general block diagram of this circuit is introduced based on gm–C integrators. The overall circuit realization using MOS transistors and using low supply voltage is given. The proposed circuit depends on the use of grounded capacitors which provides the freedom to be off chip. A new block diagram called voltage controlled current direction is also introduced and its realization using MOS transistors is given. Numerical and PSpice simulations are also provided to confirm its functionality.
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paper_title: Comparative Image Encryption Method Analysis Using New Transformed - Mapped Technique

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Several traditional encryption schemes have been analysed and based on the literature survey, it has been found that chaotic sequences are very much useful to create randomness. In this paper, a new encryption scheme has been proposed with two phases. In the first phase the input image is transformed using a new transformation technique whereas in the second phase .Chirikov Standard Map is used for pixel shuffling and modified Logistic Map is used for diffusion. Chirikov standard map , decor relate the strong relationship among adjacent pixels hence employed to shuffle the pixel positions of the plain image. The modified logistic map is used for generating the random sequence which is completed the purpose of changing pixel values. Various images and standard lena image is used to demonstrate the validity of the proposed algorithm. The results of experiments show that the proposed algorithm for image cryptosystems provides a no correlation between the original image and cipher image. The scheme is key sensitive and shows impressive resistance against brute force attack and statistical attack.
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paper_title: The fractional-order modeling and synchronization of electrically coupled neuron systems

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In this paper, we generalize the integer-order cable model of the neuron system into the fractional-order domain, where the long memory dependence of the fractional derivative can be a better fit for the neuron response. Furthermore, the chaotic synchronization with a gap junction of two or multi-coupled-neurons of fractional-order are discussed. The circuit model, fractional-order state equations and the numerical technique are introduced in this paper for individual and multiple coupled neuron systems with different fractional-orders. Various examples are introduced with different fractional orders using the non-standard finite difference scheme together with the Grunwald-Letnikov discretization process which is easily implemented and reliably accurate.
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paper_title: Gray code permutation algorithm for high-dimensional data encryption

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Abstract We present a novel permutation algorithm for fast encryption of a large amount of data, such as 3D images and real-time videos. The proposed P-Box algorithm takes advantage of Gray code properties and allows fast encryption with high information diffusion. The algorithm is optimized for integer q -bit operations ( q = 8 , 16 , 32 , … ), allowing a direct implementation in almost any hardware platform, while avoiding rounding errors of floating-point operations. By combining the P-Box with chaotic S-Box based on the logistic map, we design a complete, highly secure and fast cryptosystem.
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paper_title: Hardware stream cipher with controllable chaos generator for colour image encryption

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This study presents hardware realisation of chaos-based stream cipher utilised for image encryption applications. A third-order chaotic system with signum non-linearity is implemented and a new post processing technique is proposed to eliminate the bias from the original chaotic sequence. The proposed stream cipher utilises the processed chaotic output to mask and diffuse input pixels through several stages of XORing and bit permutations. The performance of the cipher is tested with several input images and compared with previously reported systems showing superior security and higher hardware efficiency. The system is experimentally verified on XilinxVirtex 4 field programmable gate array (FPGA) achieving small area utilisation and a throughput of 3.62 Gb/s.
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paper_title: A fractal-based image encryption system

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This study introduces a novel image encryption system based on diffusion and confusion processes in which the image information is hidden inside the complex details of fractal images. A simplified encryption technique is, first, presented using a single-fractal image and statistical analysis is performed. A general encryption system utilising multiple fractal images is, then, introduced to improve the performance and increase the encryption key up to hundreds of bits. This improvement is achieved through several parameters: feedback delay, multiplexing and independent horizontal or vertical shifts. The effect of each parameter is studied separately and, then, they are combined to illustrate their influence on the encryption quality. The encryption quality is evaluated using different analysis techniques such as correlation coefficients, differential attack measures, histogram distributions, key sensitivity analysis and the National Institute of Standards and Technology (NIST) statistical test suite. The obtained results show great potential compared to other techniques.
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paper_title: Some basic cryptographic requirements for chaos-based cryptosystems

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In recent years, a large amount of work on chaos-based cryptosystems have been published. However, many of the proposed schemes fail to explain or do not possess a number of features that are fundamentally important to all kind of cryptosystems. As a result, many proposed systems are difficult to implement in practice with a reasonable degree of security. Likewise, they are seldom accompanied by a thorough security analysis. Consequently, it is difficult for other researchers and end users to evaluate their security and performance. This work is intended to provide a common framework of basic guidelines that, if followed, could benefit every new cryptosystem. The suggested guidelines address three main issues: implementation, key management and security analysis, aiming at assisting designers of new cryptosystems to present their work in a more systematic and rigorous way to fulfill some basic cryptographic requirements. Meanwhile, several recommendations are made regarding some practical aspects of analog chaos-based secure communications, such as channel noise, limited bandwith and attenuation.
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paper_title: The image encryption algorithm based on the novel diffusion transformation

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In order to improve the capability of scrambling encryption and anti-aggressive, we introduced a digital image encryption algorithm in the paper, which was based on the three-dimensional Arnold transformation and a whole novel diffusion transformation. The large number of simulation results show that the proposed algorithm has very good permutation and diffusion properties and is a very effective encryption algorithm.
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paper_title: Self-adaptive permutation and combined global diffusion for chaotic color image encryption

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As to color image encryption, most of the previous algorithms are to encrypt its R, G, B components, respectively, which neglected the correlations among R, G, B components. To overcome this problem, a type of chaotic color encryption scheme was proposed by Wang et al. based on combined permutation and combined diffusion. Unfortunately, there are some drawbacks in the scheme and it has been cryptanalyzed soon. To strength the security performance, a new scheme based on coupled logistic map, self-adaptive permutation, S8 S-boxes transform and combined global diffusion is proposed in this paper. Simulation results and analyses show that our cryptosystem is immune to some well-known attacks and has high security for practical color image encryption applications.
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paper_title: Image encryption with chaotically coupled chaotic maps

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Abstract We present a novel secure cryptosystem for direct encryption of color images, based on chaotically coupled chaotic maps. The proposed cipher provides good confusion and diffusion properties that ensures extremely high security because of the chaotic mixing of pixels’ colors. Information is mixed and distributed over a complete image using a complex strategy that makes known plaintext attack unfeasible. The encryption algorithm guarantees the three main goals of cryptography: strong cryptographic security, short encryption/decryption time, and robustness against noise and other external disturbances. Due to the high speed, the proposed cryptosystem is suitable for application in real-time communication systems.
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paper_title: Diffusion-substitution based gray image encryption scheme

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In this paper, an encryption algorithm for gray images using a secret key of 128-bits size is proposed. Initially, visual quality of image is degraded by the mixing process. Resultant image is partitioned into key dependent dynamic blocks and, further, these blocks are passed through key dependent diffusion and substitution processes. Total sixteen rounds are used in the encryption algorithm. Proposed technique is simple to implement and has high encryption rate. Simulation experiment results have been given to validate the high security features and effectiveness of proposed system.
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paper_title: A fast chaotic block cipher for image encryption

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Image encryption schemes based on chaos usually involve real number arithmetic operations to generate the chaotic orbits from the chaotic system. These operations are time-consuming and are normally performed with high-end processors. To overcome this drawback, this paper proposes a one round encryption scheme for the fast generation of large permutation and diffusion keys based on the sorting of the solutions of the Linear Diophantine Equation (LDE) whose coefficients are integers and dynamically generated from any type of chaotic systems. The high security and low computational complexity are achieved not only by using large permutation based on the sorting of the solutions of LDE but also by generating only one permutation from the sorting of the solutions of the LDE, then by dynamically updating d number of integers (d>2) in the permutation. The performance of the proposed scheme is evaluated using various types of analysis such as entropy analysis, difference analysis, statistical analysis, key sensitivity analysis, key space analysis and speed analysis. The experimental results indicate that the proposed algorithm is secure and fast as compared to the two round encryption scheme.
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paper_title: A novel image encryption scheme based on spatial chaos map

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In recent years, the chaos-based cryptographic algorithms have suggested some new and efficient ways to develop secure image encryption techniques, but the drawbacks of small key space and weak security in one-dimensional chaotic cryptosystems are obvious. In this paper, spatial chaos system are used for high degree security image encryption while its speed is acceptable. The proposed algorithm is described in detail. The basic idea is to encrypt the image in space with spatial chaos map pixel by pixel, and then the pixels are confused in multiple directions of space. Using this method one cycle, the image becomes indistinguishable in space due to inherent properties of spatial chaotic systems. Several experimental results, key sensitivity tests, key space analysis, and statistical analysis show that the approach for image cryptosystems provides an efficient and secure way for real time image encryption and transmission from the cryptographic viewpoint.
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paper_title: An image encryption scheme using lightweight bit-level confusion and cascade cross circular diffusion

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Abstract Recently, quite a lot of chaos-based image encryption schemes have been proposed. Most of them adopt the traditional permutation and diffusion operations. The drawbacks are: (1) the architecture is not sensitive to changes in the plain-image; (2) they are insecure upon chosen/known plain-image attack. Due to the favorable properties of bit-level permutation, we propose a lightweight bit-level confusion and cascade cross circular diffusion to enhance the security of the cryptosystem and to reduce the computation redundancy in traditional architectures. Simulations have been carried out and the results demonstrate the superior security and high efficiency of the proposed scheme.
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paper_title: A simple and robust gray image encryption scheme using chaotic logistic map and artificial neural network

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A robust gray image encryption scheme using chaotic logistic map and artificial neural network (ANN) is introduced. In the proposed method, an external secret key is used to derive the initial conditions for the logistic chaotic maps which are employed to generate weights and biases matrices of the multilayer perceptron (MLP). During the learning process with the backpropagation algorithm, ANN determines the weight matrix of the connections. The plain image is divided into four subimages which are used for the first diffusion stage. The subimages obtained previously are divided into the square subimage blocks. In the next stage, different initial conditions are employed to generate a key stream which will be used for permutation and diffusion of the subimage blocks. Some security analyses such as entropy analysis, statistical analysis, and key sensitivity analysis are given to demonstrate the key space of the proposed algorithm which is large enough to make brute force attacks infeasible. Computing validation using experimental data with several gray images has been carried out with detailed numerical analysis, in order to validate the high security of the proposed encryption scheme.
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paper_title: A novel chaotic image encryption algorithm based on water wave motion and water drop diffusion models

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Abstract This paper will put forward a novel chaotic image encryption algorithm with confusion–diffusion architecture. First of all, secret keys will be processed by key generator before they can really be used in the encryption scheme, and in this stage this paper associates plain image with secret keys; Secondly, by imitating the trajectory of water wave movement, encryption algorithm will do scrambling operations to the image. Thirdly, this paper combines water drop motion and dynamic look up table to realize diffusion operations. For an 8 bits pixel, this algorithm will just dispose the higher 4 bits, which is because the higher 4 bits contain the vast majority of information of the image. At last, the experiment results and security analysis show that this proposed algorithm has a desirable encryption effect. Its key space is large enough, it is sensitive to keys and plain image, its encryption speed is fast and it can resist cryptanalysis such as brute attack, differential attack, etc.
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paper_title: An image encryption scheme using reverse 2-dimensional chaotic map and dependent diffusion

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Abstract In recent years, a variety of chaos-based image cryptosystems have been studied. Most of them adopt the traditional confusion–diffusion architecture, which is considered insecure upon chosen/known plain-image attacks. In this paper, a nonlinear traverse on the plain-image using dependent diffusion and reverse cat map is proposed to replace the traditional linear traverse performed in the confusion phase. Two cryptosystems are designed and are implemented by software means. Simulation results and numerical analysis justify their high efficiency and sufficient strength.
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paper_title: A new 1D chaotic system for image encryption

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This paper introduces a simple and effective chaotic system using a combination of two existing one-dimension (1D) chaotic maps (seed maps). Simulations and performance evaluations show that the proposed system is able to produce many 1D chaotic maps with larger chaotic ranges and better chaotic behaviors compared with their seed maps. To investigate its applications in multimedia security, a novel image encryption algorithm is proposed. Using a same set of security keys, this algorithm is able to generate a completely different encrypted image each time when it is applied to the same original image. Experiments and security analysis demonstrate the algorithm's excellent performance in image encryption and various attacks.
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paper_title: A symmetric color image encryption algorithm using the intrinsic features of bit distributions

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Abstract In recent years, a variety of chaos-based image encryption algorithms have been proposed. Most of them employ the confusion-diffusion architecture and operate at the pixel level. In this paper, we analyze the intrinsic features of the bit distributions, the high correlation among bit planes and other issues related to the bit information of an image. Due to the superior characteristics of bit-level operations and the intrinsic bit features of the image, an expand-and-shrink strategy is employed to shuffle the image with reconstructed permuting plane. Simulations have been carried out and the results demonstrate the superior security and high efficiency of the proposed scheme.
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paper_title: An image encryption scheme based on constructing large permutation with chaotic sequence

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Abstract This paper proposes a chaos-based image encryption scheme with a permutation–diffusion structure. In the proposed scheme, the large permutation with the same size as the plain-image is used to shuffle the positions of image pixels totally. An effective method is also presented to construct the large permutation quickly and easily by combining several small permutations, where small permutations are directly generated using a chaotic map. In the diffusion stage, the pixel is enciphered by exclusive or with the previous ciphered pixel and a random number produced by the Logistic map with different initial conditions. Test results and analysis by using several security measures have shown that the proposed scheme is efficient and reliable, and can be applied to real-time image encryption.
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paper_title: A novel image encryption–compression scheme using hyper-chaos and Chinese remainder theorem

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Abstract Hyper-chaos has more than one positive Lyapunov exponents and it has more complex dynamical characteristics than chaos. Hence it becomes a better choice for secure image encryption schemes. In this paper, we propose a new image encryption scheme integrated with compression simultaneously. Specifically, we first use 2D hyper-chaos discrete nonlinear dynamic system to shuffle the plain image, and then we apply Chinese remainder theorem (well known in number theory) to diffuse and compress the shuffled image, simultaneously. This new scheme can be used to change the plain image information drastically and compress the plain image with a given compression ratio k , which is most crucial in multimedia transmission. Theoretical and experimental analyses both confirm the security and the validity of the proposed algorithm.
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paper_title: A Non-adaptive Partial Encryption of Grayscale Images based on Chaos☆

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Research papers published in recent times have focused towards different kinds of image encryption techniques. Image encryption based on Chaos became very popular for cryptography since properties of Chaos are related to two basic properties of good cipher-Confusion and Diffusion. In this paper, A Non-adaptive Partial Encryption of Grayscale Images Based on Chaoshas been proposed. In Partial encryption speed and time is the main factor. We decompose the original grayscale image into its corresponding binary eight bit planes then encrypted using couple tent map based pseudorandom binary number generator (PRBNG). The four significant bit planes, determined by 5% level of significance on contribution of a bit-plane in determination of a pixel value, are encrypted using keys which are obtained by applying the recurrence relation of tent map based PRBNG. Then the four insignificant bit planes along with encrypted significant bit planes are combined to form the final cipher image. In order to evaluate performance, the proposed algorithm was measured through a series of tests to measure the security and effectiveness of the proposed algorithm. These tests includes visual test through histogram analysis, measures of central tendency and dispersion, correlation-coefficient analysis, key sensitivity test, key space analysis, information entropy test, Measurement of Encryption Quality – MSE, PSNR, NPCR, UACI. Experimental results show that the new cipher has satisfactory security and efficient.
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paper_title: A novel chaos-based image encryption scheme with an efficient permutation-diffusion mechanism☆

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Abstract This paper proposes a novel chaos-based image encryption scheme with an efficient permutation-diffusion mechanism, in which permuting the positions of image pixels incorporates with changing the gray values of image pixels to confuse the relationship between cipher-image and plain-image. In the permutation process, a generalized Arnold map is utilized to generate one chaotic orbit used to get two index order sequences for the permutation of image pixel positions; in the diffusion process, a generalized Arnold map and a generalized Bernoulli shift map are employed to yield two pseudo-random gray value sequences for a two-way diffusion of gray values. The yielded gray value sequences are not only sensitive to the control parameters and initial conditions of the considered chaotic maps, but also strongly depend on the plain-image processed, therefore the proposed scheme can resist statistical attack, differential attack, known-plaintext as well as chosen-plaintext attack. Experimental results are carried out with detailed analysis to demonstrate that the proposed image encryption scheme possesses large key space to resist brute-force attack as well.
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paper_title: Substitution-diffusion based Image Cipher

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In this paper, a new image encryption scheme using a secret key of 128-bit size is proposed. In the algorithm, image is partitioned into several key based dynamic blocks and further, each block passes through the eight rounds of diffusion as well as substitution process. In diffusion process, sequences of block pixels are rearranged within the block by a zigzag approach whereas block pixels are replaced with another by using difference calculation of row and column in substitution process. Due to high order of substitution and diffusion, common attacks like linear and differential cryptanalysis are infeasible. The experimental results show that the proposed technique is efficient and has high security features.
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paper_title: Design of image cipher using latin squares

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In this paper, we introduce a symmetric-key Latin square image cipher (LSIC) for grayscale and color image encryption. Our main contributions include (1) we propose new Latin square image encryption primitives including Latin Square Whitening, Latin Square S-box and Latin Square P-box; (2) we develop probabilistic image encryption by embedding random noise into the least significant bit-plane of images; and (3) we design a new loom-like 2D substitution-permutation network maintaining good confusion and diffusion properties with extra error tolerance. Theoretical analysis and simulation results show that the proposed method has many desired properties of a secure cipher, shows robustness against different attack models, and outperforms state of the art suggested by many peer algorithms. Open-source implementation can be found on the webpage https://sites.google.com/site/tuftsyuewu/source-code.
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paper_title: Integrated confusion-diffusion mechanisms for chaos based image encryption

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A new kind of color image encryption algorithm based on integrated confusion-diffusion mechanisms and chaos is put forward. Firstly, generate three values by iterating two-dimensional logistic maps, which are used as the three offset values of RGB components respectively. Secondly, choose three variables from the four-dimensional hyper-chaos to generate four different combinations. Next, XOR operation is conducted between the chosen combination and the original image with three offset values. Thus, integration confusion with diffusion is achieved. The experimental results demonstrate that this algorithm has advantages of large key space and high security, and moreover, it is sensitive to the secret keys, his electronic document is a “live” template.
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paper_title: A Novel Encryption Method for Image Security

paper_content:

Image encryption is one of the most methods of information hiding. A novel secure encryption method for image hiding is presented in this paper. The proposed method provides good confusion and diffusion properties that ensures high security due to mixing the two Boolean operations: XOR and Rotation that are done on the bits of the pixels in the image. This method is implemented by firstly doing a sequential XOR operation on all the bits of pixels in the image, and secondly makes a circular rotate right of these bits. These two operations are repeated many times during the encryption phase. The security and performance of the proposed encryption method have been evaluated by applying it on images and analyze the recorded results using key space analysis, key sensitivity analysis, and statistical analysis. The performance experiments show that the proposed method is promising to use effectively in wide fields of image encryption.
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paper_title: Encryption and decryption of images with chaotic map lattices.

paper_content:

We propose a secure algorithm for direct encryption and decryption of digital images with chaotic map lattices. The basic idea is to convert, pixel by pixel, the image color to chaotic logistic maps one-way coupled by initial conditions. After small numbers of iterations and cycles, the image becomes indistinguishable due to inherent properties of chaotic systems. Since the maps are coupled, the image can be completely recovered by the decryption algorithm if map parameters, number of iterations, number of cycles, and the image size are exactly known.
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paper_title: Control and switching synchronization of fractional order chaotic systems using active control technique

paper_content:

This paper discusses the continuous effect of the fractional order parameter of the Lu system where the system response starts stable, passing by chaotic behavior then reaching periodic response as the fractional-order increases. In addition, this paper presents the concept of synchronization of different fractional order chaotic systems using active control technique. Four different synchronization cases are introduced based on the switching parameters. Also, the static and dynamic synchronizations can be obtained when the switching parameters are functions of time. The nonstandard finite difference method is used for the numerical solution of the fractional order master and slave systems. Many numeric simulations are presented to validate the concept for different fractional order parameters.
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paper_title: Color Image Encryption Algorithm Combining Compressive Sensing with Arnold Transform

paper_content:

A new color image encryption algorithm combining compressive sensing with Arnold transform is proposed, which can encrypt the color image into a gray image. Considering the dimensional reduction and random projection of compressive sensing, we utilize compressive sensing to encrypt and compress the three color components of color image simultaneously. The three encrypted and compressed color components’ dimensions are smaller than the original image, thus they can be grouped into a gray image, and then the gray image is scrambled by Arnold transform to enhance the security. The proposed algorithm can also be applied in the multiple-image encryption. The experimental results show the validity and the reliability of the proposed algorithm.
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paper_title: NPCR and UACI Randomness Tests for Image Encryption

paper_content:

The number of changing pixel rate (NPCR) and the unified averaged changed intensity (UACI) are two most common quantities used to evaluate the strength of image encryption algorithms/ciphers with respect to differential attacks. Conventionally, a high NPCR/UACI score is usually interpreted as a high resistance to differential attacks. However, it is not clear how high NPCR/UACI is such that the image cipher indeed has a high security level. In this paper, we approach this problem by establishing a mathematical model for ideally encrypted images and then derive expectations and variances of NPCR and UACI under this model. Further, these theoretical values are used to form statistical hypothesis NPCR and UACI tests. Critical values of tests are consequently derived and calculated both symbolically and numerically. As a result, the question of whether a given NPCR/UACI score is sufficiently high such that it is not discernible from ideally encrypted images is answered by comparing actual NPCR/UACI scores with corresponding critical values. Experimental results using the NPCR and UACI randomness tests show that many existing image encryption methods are actually not as good as they are purported, although some methods do pass these randomness tests.
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paper_title: Color Image Encryption Algorithm Combining Compressive Sensing with Arnold Transform

paper_content:

A new color image encryption algorithm combining compressive sensing with Arnold transform is proposed, which can encrypt the color image into a gray image. Considering the dimensional reduction and random projection of compressive sensing, we utilize compressive sensing to encrypt and compress the three color components of color image simultaneously. The three encrypted and compressed color components’ dimensions are smaller than the original image, thus they can be grouped into a gray image, and then the gray image is scrambled by Arnold transform to enhance the security. The proposed algorithm can also be applied in the multiple-image encryption. The experimental results show the validity and the reliability of the proposed algorithm.
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paper_title: Color Image Encryption Algorithm Combining Compressive Sensing with Arnold Transform

paper_content:

A new color image encryption algorithm combining compressive sensing with Arnold transform is proposed, which can encrypt the color image into a gray image. Considering the dimensional reduction and random projection of compressive sensing, we utilize compressive sensing to encrypt and compress the three color components of color image simultaneously. The three encrypted and compressed color components’ dimensions are smaller than the original image, thus they can be grouped into a gray image, and then the gray image is scrambled by Arnold transform to enhance the security. The proposed algorithm can also be applied in the multiple-image encryption. The experimental results show the validity and the reliability of the proposed algorithm.
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paper_title: NPCR and UACI Randomness Tests for Image Encryption

paper_content:

The number of changing pixel rate (NPCR) and the unified averaged changed intensity (UACI) are two most common quantities used to evaluate the strength of image encryption algorithms/ciphers with respect to differential attacks. Conventionally, a high NPCR/UACI score is usually interpreted as a high resistance to differential attacks. However, it is not clear how high NPCR/UACI is such that the image cipher indeed has a high security level. In this paper, we approach this problem by establishing a mathematical model for ideally encrypted images and then derive expectations and variances of NPCR and UACI under this model. Further, these theoretical values are used to form statistical hypothesis NPCR and UACI tests. Critical values of tests are consequently derived and calculated both symbolically and numerically. As a result, the question of whether a given NPCR/UACI score is sufficiently high such that it is not discernible from ideally encrypted images is answered by comparing actual NPCR/UACI scores with corresponding critical values. Experimental results using the NPCR and UACI randomness tests show that many existing image encryption methods are actually not as good as they are purported, although some methods do pass these randomness tests.
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paper_title: The effect of numerical techniques on differential equation based chaotic generators

paper_content:

In this paper, we study the effect of the numerical solution accuracy on the digital implementation of differential chaos generators. Four systems are built on a Xilinx Virtex 4 FPGA using Euler, mid-point, and Runge-Kutta fourth order techniques. The twelve implementations are compared based on the FPGA used area, maximum throughput, maximum Lyapunov exponent, and autocorrelation confidence region. Based on circuit performance and the chaotic response of the different implementations, it was found that less complicated numerical solution has better chaotic response and higher throughput.
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paper_title: Control and switching synchronization of fractional order chaotic systems using active control technique

paper_content:

This paper discusses the continuous effect of the fractional order parameter of the Lu system where the system response starts stable, passing by chaotic behavior then reaching periodic response as the fractional-order increases. In addition, this paper presents the concept of synchronization of different fractional order chaotic systems using active control technique. Four different synchronization cases are introduced based on the switching parameters. Also, the static and dynamic synchronizations can be obtained when the switching parameters are functions of time. The nonstandard finite difference method is used for the numerical solution of the fractional order master and slave systems. Many numeric simulations are presented to validate the concept for different fractional order parameters.
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paper_title: MOS realization of the modified Lorenz chaotic system

paper_content:

Abstract A new chaotic oscillator circuit that realizes three attractors, the modified Lorenz system, Lorenz attractor “Butterfly attractor” and unsymmetrical modified Lorenz system [IEEE Trans. Circ. Syst. I 48 (2001) 289] is given in the paper. The general block diagram of this circuit is introduced based on gm–C integrators. The overall circuit realization using MOS transistors and using low supply voltage is given. The proposed circuit depends on the use of grounded capacitors which provides the freedom to be off chip. A new block diagram called voltage controlled current direction is also introduced and its realization using MOS transistors is given. Numerical and PSpice simulations are also provided to confirm its functionality.
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paper_title: Image encryption in the fractional-order domain

paper_content:

This paper presents a new image encryption scheme based on the fractional-order Lorenz system which gives more degrees of freedom in key generation. In the modified fractional-order system, the key length is doubled using the three fractional-orde r parameters beside the three initial conditions, which makes it invulnerable to brute-force attacks. In addition, using a very simple algorithm, based on pixel confusion only, strongly encrypted images are produced. Such an algorithm can be used in real time applications. To evaluate the algorithm and analyze the encryption results, a standard image is used. A comparison of the colored correlation coefficients (horizontal, vertical, diagonal) for different cases with respect to a fractional-order parameter and another system parameter are introduced. Moreover, the encrypted image shows high sensitivity to the fractional-order key, which appears from the wrong decryption with 0.1% change of the fractional-order parameter.
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paper_title: CONTROLLABLE V-SHAPE MULTISCROLL BUTTERFLY ATTRACTOR: SYSTEM AND CIRCUIT IMPLEMENTATION

paper_content:

In this paper, a new controllable V-shape multiscroll attractor is presented, where a variety of symmetrical and unsymmetrical attractors with a variable number of scrolls can be controlled using new staircase nonlinear function and the parameters of the system. This attractor can be used to generate random signals with a variety of symbol distribution. Digital implementation of the proposed generator is also presented using a Xilinx Virtex® 4 Field Programmable Gate Array and experimental results are provided. The digital realization easily fits into a small area (<1.5% of the total area) and expresses a high throughput (4.3 Gbit/sec per state variable).
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paper_title: The effect of numerical techniques on differential equation based chaotic generators

paper_content:

In this paper, we study the effect of the numerical solution accuracy on the digital implementation of differential chaos generators. Four systems are built on a Xilinx Virtex 4 FPGA using Euler, mid-point, and Runge-Kutta fourth order techniques. The twelve implementations are compared based on the FPGA used area, maximum throughput, maximum Lyapunov exponent, and autocorrelation confidence region. Based on circuit performance and the chaotic response of the different implementations, it was found that less complicated numerical solution has better chaotic response and higher throughput.
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paper_title: NPCR and UACI Randomness Tests for Image Encryption

paper_content:

The number of changing pixel rate (NPCR) and the unified averaged changed intensity (UACI) are two most common quantities used to evaluate the strength of image encryption algorithms/ciphers with respect to differential attacks. Conventionally, a high NPCR/UACI score is usually interpreted as a high resistance to differential attacks. However, it is not clear how high NPCR/UACI is such that the image cipher indeed has a high security level. In this paper, we approach this problem by establishing a mathematical model for ideally encrypted images and then derive expectations and variances of NPCR and UACI under this model. Further, these theoretical values are used to form statistical hypothesis NPCR and UACI tests. Critical values of tests are consequently derived and calculated both symbolically and numerically. As a result, the question of whether a given NPCR/UACI score is sufficiently high such that it is not discernible from ideally encrypted images is answered by comparing actual NPCR/UACI scores with corresponding critical values. Experimental results using the NPCR and UACI randomness tests show that many existing image encryption methods are actually not as good as they are purported, although some methods do pass these randomness tests.
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paper_title: Design of pseudo random keystream generator using fractals

paper_content:

This paper presents a novel method for designing a pseudo random keystream generator (PRKG) based on fractal images. Although a fractal image has high correlation between its pixels, the proposed technique succeeds in almost eliminating this correlation and the output stream passes the NIST statistical test suite. The post-processing on the fractals is based only on a confusion process and uses a nonlinear network with a delay block to randomize the output stream. Many statistical measures and the NIST suite have been used to evaluate the processed fractals and the results are promising. As an example to validate the PRKG, the output stream is used in a simple image encryption system. The encrypted image is tested by calculating pixel correlations, differential attack measures, entropy and it also passes the NIST test suite.
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paper_title: Control and switching synchronization of fractional order chaotic systems using active control technique

paper_content:

This paper discusses the continuous effect of the fractional order parameter of the Lu system where the system response starts stable, passing by chaotic behavior then reaching periodic response as the fractional-order increases. In addition, this paper presents the concept of synchronization of different fractional order chaotic systems using active control technique. Four different synchronization cases are introduced based on the switching parameters. Also, the static and dynamic synchronizations can be obtained when the switching parameters are functions of time. The nonstandard finite difference method is used for the numerical solution of the fractional order master and slave systems. Many numeric simulations are presented to validate the concept for different fractional order parameters.
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paper_title: An image encryption scheme using lightweight bit-level confusion and cascade cross circular diffusion

paper_content:

Abstract Recently, quite a lot of chaos-based image encryption schemes have been proposed. Most of them adopt the traditional permutation and diffusion operations. The drawbacks are: (1) the architecture is not sensitive to changes in the plain-image; (2) they are insecure upon chosen/known plain-image attack. Due to the favorable properties of bit-level permutation, we propose a lightweight bit-level confusion and cascade cross circular diffusion to enhance the security of the cryptosystem and to reduce the computation redundancy in traditional architectures. Simulations have been carried out and the results demonstrate the superior security and high efficiency of the proposed scheme.
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paper_title: An image encryption scheme based on constructing large permutation with chaotic sequence

paper_content:

Abstract This paper proposes a chaos-based image encryption scheme with a permutation–diffusion structure. In the proposed scheme, the large permutation with the same size as the plain-image is used to shuffle the positions of image pixels totally. An effective method is also presented to construct the large permutation quickly and easily by combining several small permutations, where small permutations are directly generated using a chaotic map. In the diffusion stage, the pixel is enciphered by exclusive or with the previous ciphered pixel and a random number produced by the Logistic map with different initial conditions. Test results and analysis by using several security measures have shown that the proposed scheme is efficient and reliable, and can be applied to real-time image encryption.
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paper_title: A novel chaos-based image encryption scheme with an efficient permutation-diffusion mechanism☆

paper_content:

Abstract This paper proposes a novel chaos-based image encryption scheme with an efficient permutation-diffusion mechanism, in which permuting the positions of image pixels incorporates with changing the gray values of image pixels to confuse the relationship between cipher-image and plain-image. In the permutation process, a generalized Arnold map is utilized to generate one chaotic orbit used to get two index order sequences for the permutation of image pixel positions; in the diffusion process, a generalized Arnold map and a generalized Bernoulli shift map are employed to yield two pseudo-random gray value sequences for a two-way diffusion of gray values. The yielded gray value sequences are not only sensitive to the control parameters and initial conditions of the considered chaotic maps, but also strongly depend on the plain-image processed, therefore the proposed scheme can resist statistical attack, differential attack, known-plaintext as well as chosen-plaintext attack. Experimental results are carried out with detailed analysis to demonstrate that the proposed image encryption scheme possesses large key space to resist brute-force attack as well.
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paper_title: Integrated confusion-diffusion mechanisms for chaos based image encryption

paper_content:

A new kind of color image encryption algorithm based on integrated confusion-diffusion mechanisms and chaos is put forward. Firstly, generate three values by iterating two-dimensional logistic maps, which are used as the three offset values of RGB components respectively. Secondly, choose three variables from the four-dimensional hyper-chaos to generate four different combinations. Next, XOR operation is conducted between the chosen combination and the original image with three offset values. Thus, integration confusion with diffusion is achieved. The experimental results demonstrate that this algorithm has advantages of large key space and high security, and moreover, it is sensitive to the secret keys, his electronic document is a “live” template.
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paper_title: MOS realization of the modified Lorenz chaotic system

paper_content:

Abstract A new chaotic oscillator circuit that realizes three attractors, the modified Lorenz system, Lorenz attractor “Butterfly attractor” and unsymmetrical modified Lorenz system [IEEE Trans. Circ. Syst. I 48 (2001) 289] is given in the paper. The general block diagram of this circuit is introduced based on gm–C integrators. The overall circuit realization using MOS transistors and using low supply voltage is given. The proposed circuit depends on the use of grounded capacitors which provides the freedom to be off chip. A new block diagram called voltage controlled current direction is also introduced and its realization using MOS transistors is given. Numerical and PSpice simulations are also provided to confirm its functionality.
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paper_title: Chaos-based Cryptography: Theory, Algorithms and Applications

paper_content:

Chaos-based cryptography, attracting many researchers in the past decade, is a research field across two fields, i.e., chaos (nonlinear dynamic system) and cryptography (computer and data security). It Chaos' properties, such as randomness and ergodicity, have been proved to be suitable for designing the means for data protection.The book gives a thorough description of chaos-based cryptography, which consists of chaos basic theory, chaos properties suitable for cryptography, chaos-based cryptographic techniques, and various secure applications based on chaos. Additionally, it covers both the latest research results and some open issues or hot topics. The book creates a collection of high-quality chapters contributed by leading experts in the related fields. It embraces a wide variety of aspects of the related subject areas and provide a scientifically and scholarly sound treatment of state-of-the-art techniques to students, researchers, academics, personnel of law enforcement and IT practitioners who are interested or involved in the study, research, use, design and development of techniques related to chaos-based cryptography.
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paper_title: NPCR and UACI Randomness Tests for Image Encryption

paper_content:

The number of changing pixel rate (NPCR) and the unified averaged changed intensity (UACI) are two most common quantities used to evaluate the strength of image encryption algorithms/ciphers with respect to differential attacks. Conventionally, a high NPCR/UACI score is usually interpreted as a high resistance to differential attacks. However, it is not clear how high NPCR/UACI is such that the image cipher indeed has a high security level. In this paper, we approach this problem by establishing a mathematical model for ideally encrypted images and then derive expectations and variances of NPCR and UACI under this model. Further, these theoretical values are used to form statistical hypothesis NPCR and UACI tests. Critical values of tests are consequently derived and calculated both symbolically and numerically. As a result, the question of whether a given NPCR/UACI score is sufficiently high such that it is not discernible from ideally encrypted images is answered by comparing actual NPCR/UACI scores with corresponding critical values. Experimental results using the NPCR and UACI randomness tests show that many existing image encryption methods are actually not as good as they are purported, although some methods do pass these randomness tests.
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paper_title: Gray code permutation algorithm for high-dimensional data encryption

paper_content:

Abstract We present a novel permutation algorithm for fast encryption of a large amount of data, such as 3D images and real-time videos. The proposed P-Box algorithm takes advantage of Gray code properties and allows fast encryption with high information diffusion. The algorithm is optimized for integer q -bit operations ( q = 8 , 16 , 32 , … ), allowing a direct implementation in almost any hardware platform, while avoiding rounding errors of floating-point operations. By combining the P-Box with chaotic S-Box based on the logistic map, we design a complete, highly secure and fast cryptosystem.
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paper_title: Image encryption with chaotically coupled chaotic maps

paper_content:

Abstract We present a novel secure cryptosystem for direct encryption of color images, based on chaotically coupled chaotic maps. The proposed cipher provides good confusion and diffusion properties that ensures extremely high security because of the chaotic mixing of pixels’ colors. Information is mixed and distributed over a complete image using a complex strategy that makes known plaintext attack unfeasible. The encryption algorithm guarantees the three main goals of cryptography: strong cryptographic security, short encryption/decryption time, and robustness against noise and other external disturbances. Due to the high speed, the proposed cryptosystem is suitable for application in real-time communication systems.
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paper_title: A novel image encryption scheme based on spatial chaos map

paper_content:

In recent years, the chaos-based cryptographic algorithms have suggested some new and efficient ways to develop secure image encryption techniques, but the drawbacks of small key space and weak security in one-dimensional chaotic cryptosystems are obvious. In this paper, spatial chaos system are used for high degree security image encryption while its speed is acceptable. The proposed algorithm is described in detail. The basic idea is to encrypt the image in space with spatial chaos map pixel by pixel, and then the pixels are confused in multiple directions of space. Using this method one cycle, the image becomes indistinguishable in space due to inherent properties of spatial chaotic systems. Several experimental results, key sensitivity tests, key space analysis, and statistical analysis show that the approach for image cryptosystems provides an efficient and secure way for real time image encryption and transmission from the cryptographic viewpoint.
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paper_title: A new 1D chaotic system for image encryption

paper_content:

This paper introduces a simple and effective chaotic system using a combination of two existing one-dimension (1D) chaotic maps (seed maps). Simulations and performance evaluations show that the proposed system is able to produce many 1D chaotic maps with larger chaotic ranges and better chaotic behaviors compared with their seed maps. To investigate its applications in multimedia security, a novel image encryption algorithm is proposed. Using a same set of security keys, this algorithm is able to generate a completely different encrypted image each time when it is applied to the same original image. Experiments and security analysis demonstrate the algorithm's excellent performance in image encryption and various attacks.
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paper_title: A novel image encryption–compression scheme using hyper-chaos and Chinese remainder theorem

paper_content:

Abstract Hyper-chaos has more than one positive Lyapunov exponents and it has more complex dynamical characteristics than chaos. Hence it becomes a better choice for secure image encryption schemes. In this paper, we propose a new image encryption scheme integrated with compression simultaneously. Specifically, we first use 2D hyper-chaos discrete nonlinear dynamic system to shuffle the plain image, and then we apply Chinese remainder theorem (well known in number theory) to diffuse and compress the shuffled image, simultaneously. This new scheme can be used to change the plain image information drastically and compress the plain image with a given compression ratio k , which is most crucial in multimedia transmission. Theoretical and experimental analyses both confirm the security and the validity of the proposed algorithm.
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paper_title: A Non-adaptive Partial Encryption of Grayscale Images based on Chaos☆

paper_content:

Research papers published in recent times have focused towards different kinds of image encryption techniques. Image encryption based on Chaos became very popular for cryptography since properties of Chaos are related to two basic properties of good cipher-Confusion and Diffusion. In this paper, A Non-adaptive Partial Encryption of Grayscale Images Based on Chaoshas been proposed. In Partial encryption speed and time is the main factor. We decompose the original grayscale image into its corresponding binary eight bit planes then encrypted using couple tent map based pseudorandom binary number generator (PRBNG). The four significant bit planes, determined by 5% level of significance on contribution of a bit-plane in determination of a pixel value, are encrypted using keys which are obtained by applying the recurrence relation of tent map based PRBNG. Then the four insignificant bit planes along with encrypted significant bit planes are combined to form the final cipher image. In order to evaluate performance, the proposed algorithm was measured through a series of tests to measure the security and effectiveness of the proposed algorithm. These tests includes visual test through histogram analysis, measures of central tendency and dispersion, correlation-coefficient analysis, key sensitivity test, key space analysis, information entropy test, Measurement of Encryption Quality – MSE, PSNR, NPCR, UACI. Experimental results show that the new cipher has satisfactory security and efficient.
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paper_title: Encryption and decryption of images with chaotic map lattices.

paper_content:

We propose a secure algorithm for direct encryption and decryption of digital images with chaotic map lattices. The basic idea is to convert, pixel by pixel, the image color to chaotic logistic maps one-way coupled by initial conditions. After small numbers of iterations and cycles, the image becomes indistinguishable due to inherent properties of chaotic systems. Since the maps are coupled, the image can be completely recovered by the decryption algorithm if map parameters, number of iterations, number of cycles, and the image size are exactly known.
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Title: Symmetric encryption algorithms using chaotic and non-chaotic generators: A review

Section 1: Introduction
Description 1: Introduce the basics of symmetric encryption algorithms, their types, and the need for substitution and permutation phases. Discuss the importance of chaotic systems in encryption.

Section 2: Encryption key and evaluation criteria
Description 2: Explain the concept of the encryption key and the criteria for evaluating encryption quality, including statistical tests and sensitivity tests.

Section 3: Pixel correlation coefficients
Description 3: Describe what pixel correlation coefficients are and how they are used to measure the strength of encryption.

Section 4: Histogram analysis
Description 4: Discuss histogram analysis to evaluate the distribution of pixel values in encrypted images.

Section 5: Entropy
Description 5: Define entropy in the context of image encryption and its significance in assessing randomness.

Section 6: NIST statistical test suite
Description 6: Explain the NIST SP-800-22 statistical test suite and its role in evaluating the randomness of encrypted bit sequences.

Section 7: Differential attack measures
Description 7: Discuss the measures used to evaluate resistance to differential attacks, including NPCR and UACI.

Section 8: Sensitivity to one bit change in the encryption key
Description 8: Describe how the sensitivity of the encryption algorithm to small changes in the encryption key is evaluated using MSE.

Section 9: Substitution-only encryption algorithm
Description 9: Present different substitution techniques based on chaotic systems, generalized discrete maps, and fractals, detailing their encryption processes and evaluations.

Section 10: PRNG based on Lorenz chaotic system
Description 10: Explain the use of the Lorenz chaotic system in generating pseudo-random numbers for substitution.

Section 11: PRNG based on generalized discrete maps
Description 11: Discuss the use of generalized discrete maps in PRNG and their application in image encryption.

Section 12: PRNG based on fractals
Description 12: Detail the use of fractals in PRNG and their role in substitution encryption algorithms.

Section 13: Comparison of permutation techniques
Description 13: Compare various permutation techniques using chaotic and non-chaotic methods, such as logistic maps, Arnold's cat map, and chess-based algorithms.

Section 14: Permutation based on logistic map
Description 14: Describe the technique of using logistic maps for generating permutation matrices.

Section 15: Permutation based on indices vectors
Description 15: Explain the permutation technique using sorted row and column indices.

Section 16: Permutation based on Arnold's cat map
Description 16: Discuss the Arnold's cat map and its application in pixel permutation.

Section 17: Permutation based on Lorenz system
Description 17: Explain the use of the Lorenz system in continuous chaotic permutation.

Section 18: Permutation based on chess-algorithm
Description 18: Describe the chess-based horse move algorithm for permutation.

Section 19: Mixed permutation-substitution image encryption algorithms
Description 19: Investigate encryption algorithms combining permutation and substitution phases and evaluate their effectiveness.

Section 20: Permutation-only encryption algorithm
Description 20: Present the outputs and evaluations of permutation-only encryption algorithms.

Section 21: Permutation-substitution encryption algorithms
Description 21: Present the results and evaluations of combined permutation and substitution encryption algorithms.

Section 22: Conclusions and recommendations
Description 22: Summarize the findings of the review and provide recommendations for future research and design of secure image encryption algorithms.