A new 1D parameter-control chaotic framework

Recently, due to the initial sensitivity, ergodicity, boundedness, and unpredictability of chaos, it has been widely used in the fields of secure communication, signal processing, chaotic synchronization, etc. Moreover, due to the low complexity of hardware implementation, widespread attention to one-dimensional (1D) chaotic maps has been paid from researchers. However, some existing 1D maps have simple chaotic behaviors and discrete chaotic intervals, which have significantly affected the practical application. To address these shortcomings, this paper proposes a 1D chaotic model based on the absolute value function and the cosine function called the cosine-coupled chaotic model (CCCM). It can use existing 1D chaotic maps as seed maps to construct a series of 1D chaotic maps with continuous chaotic intervals and complex chaotic behaviors. To verify the effectiveness of the CCCM, we first generate three new chaotic maps using the CCCM, and then their chaotic properties are analyzed by using various measures including Lyapunov exponent (LE), sample entropy (SE), correlation dimension (CD), 0-1 test and sensitivity. The experimental results confirm that the new chaotic maps have wider chaotic intervals and more complex chaotic behaviors than the corresponding seed maps and some other advanced chaotic maps. Then we use a field programmable gate array (FPGA) as the hardware platform for simple hardware implementations of the new chaotic maps. And a new pseudo-random number generator (PRNG) is introduced to verify practical applications of the new maps. Finally, experimental results show that the new chaotic maps can be implemented on FPGA and the proposed PRNG has strong random properties.

This paper shows a digital noise generator designed in FPGA, based on a variant of the one‐dimensional (1D) chaotic tent map (T‐1D). The T‐1D map is a piecewise linear 1D chaotic map that defines the statistical behavior of the generated sequences using its control parameter. In this way, the proposed noise generator is a highly competitive alternative in cryptographic systems when the statistical behavior of the sequences is closer to the uniform statistical distribution. The proposed system uses the inverted tent chaotic map (IT‐1D), which has the same statistical behavior as the T‐1D map. The fundamental algorithm used in this system was developed based on a 64‐bit double precision format according to the numerical representation of floating point numbers defined in the IEEE‐754 standard. The proposed system is analized using mechanical statistic tools and some statistical tests defined in the NIST 800‐22SP (USA) standard. The main contribution of this work is the possibility of generating binary sequence of pseudorandom appearance by a procedure implemented in an FPGA device that translates real numbers to natural numbers preserving the statistical properties of sequences of real numbers that can be generated with the tent chaotic map in its original definition domain.

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

Chaotic systems are widely used in various aspects such as information security, signal processing, and synchronous control. The structural complexity and the chaotic behavior of chaotic systems are two significant factors affecting their practical applications. In this paper, we propose a universal two-dimensional (2D) absolute-cosine chaotic model (ACCM). The 2D-ACCM is composed of a nonlinear bounded cosine function and an absolute value function. It can construct new chaotic maps with simple structures and complex chaotic behaviors on the basis of existing chaotic systems. To verify the effectiveness of the proposed system, we first choose two existing one-dimensional (1D) chaotic maps and one existing 2D chaotic map as the seed maps of the 2D-ACCM to generate two new maps, respectively. The results of chaotic behavior analysis show that these two new maps have more complex chaotic behavior and wider chaotic ranges than seed maps and some advanced chaotic maps. Then a hardware experiment platform based on a field-programmable gate array (FPGA) is used for the hardware implementation of the new maps. Finally, a simple chaos-based pseudo-random number generator (PRNG) is introduced to show the practical application. The experimental results show that the new maps can be easily implemented on the FPGA and the chaos-PRNGs can generate pseudo-random numbers with excellent randomness.

In this paper, a chaotic image encryption algorithm is suggested combining with double chaotic maps, SHA‐3 (Secure Hash Algorithm‐3), and auto‐updating system. To shuffle pixel positions, a matrix having same size of the plain‐image is generated dependent on the plain‐image in stage of permutation. Then, SHA‐3 is taken to calculate its hash values used to produce control parameter and initial condition of Logistic map. After that, total permutation is implemented for row and column to exchange pixels, where auto‐updating systems are established by different images acting like one‐time pad. Furthermore, 3D chaotic cat map is employed to enlarge key space in diffusion process. Permuted image is firstly divided into four sub‐blocks, which are queued randomly according to the key of Logistic map. The last sub‐block is picked out to calculate the hash values using SHA‐3, of which are assigned into three groups to update the initial conditions of 3D chaotic cat map performing like one‐time pad again. Current sub‐block is designed to influence next sub‐block in diffusion process. As a result, the proposed algorithm can resist efficiently the chosen‐plaintext and known‐plaintext attacks. Experimental results are also given to explain the high security of the proposed method. Copyright © 2016 John Wiley & Sons, Ltd.

Compressive sensing based encryption achieves simultaneous compression-encryption by utilizing a low complex sampling process, which is computationally secure. In this paper, a new novel 1D–chaotic map is proposed that is used to construct an incoherence rotated chaotic measurement matrix. The chaotic property of the proposed map is experimentally analysed. The linear measurements obtained are confused and diffused using the chaotic sequence generated using the proposed map. The chaos based measurement matrix construction results in reduced data storage and bandwidth requirements. As it needs to store only the parameters required to generate the chaotic sequence. Also, the sensitivity of the chaos to the parameters makes the data transmission secure. The secret key used in the encryption process is dependent on both the input data and the parameter used to generate the chaotic map. Hence the proposed scheme can resist chosen plaintext attack. The key space of the proposed scheme is large enough to thwart statistical attacks. Experimental results and the security analysis verifies the security and effectiveness of the proposed compression-encryption scheme.

A novel compression-based 2D-chaotic sine map for enhancing privacy and security of biometric identification systems

Stream ciphers are a type of symmetric encryption algorithm, and excel in speed and efficiency compared with block ciphers. They are applied in various applications, particularly in digital communications and real-time transmissions. In this paper, we propose lightweight chaotic keystream generators that utilize original one-dimensional (1D) chaotic maps with a counter to fit the requirement of a stream cipher for secure communications in the Internet of Things (IoT). The proposed chaotic scheme, referred to as expanded chaos, improves the limit of the chaotic range for the original 1D chaos. It can resist brute-force attacks, chosen-ciphertext attacks, guess-and-determine attacks, and other known attacks. We implement the proposed scheme on the IoT platform Raspberry Pi. Under NIST SP800-22 tests, the pass rates for the proposed improved chaotic maps with a counter and the proposed the mutual-coupled chaos are found to be at least about 90% and 92%, respectively.

In this paper a novel data hiding method has been proposed which is based on Non-Linear Feedback Shift Register and Tinkerbell 2D chaotic map. So far, the major work in Steganography using chaotic map has been confined to image steganography where significant restrictions are there to increase payload. In our work, 2D chaotic map and NLFSR are used to developed a video steganography mechanism where data will be embedded in the segregated frames. This will increase the data hiding limit exponentially. Also, embedding position of each frame will be different from others frames which will increase the overall security of the proposed mechanism. We have achieved this randomized data hiding points by using a chaotic map. Basically, Chaotic theory which is non-linear dynamics physics is using in this era in the field of Cryptography and Steganography and because of this theory, little bit changes in initial condition makes the output totally different. So, it is very hard to get embedding position of data without knowing the initial value of the chaotic map.

A secure image steganography based on LSB technique and 2D chaotic maps

Image encryption algorithm based on the finite fields in chaotic maps

In this paper, a novel one dimensional chaotic map $ K(x) = \frac{\mu x(1\, -x)}{1+ x} $, $ x\in [0, 1], \mu > 0 $ is proposed. Some dynamical properties including fixed points, attracting points, repelling points, stability and chaotic behavior of this map are analyzed. To prove the main result, various dynamical techniques like cobweb representation, bifurcation diagrams, maximal Lyapunov exponent, and time series analysis are adopted. Further, the entropy and probability distribution of this newly introduced map are computed which are compared with traditional one-dimensional chaotic logistic map. Moreover, with the help of bifurcation diagrams, we prove that the range of stability and chaos of this map is larger than that of existing one dimensional logistic map. Therefore, this map might be used to achieve better results in all the fields where logistic map has been used so far.

Recently, a novel bit-level color image encryption scheme based on improved one-dimension (1D) chaotic map has been proposed. It was claimed that the proposed scheme is secure due to the improved 1D chaotic map with better chaotic performance. Some security analyses and simulation experiments were presented to show that it could resist various attacks. However, we found that there are some security loopholes in the original scheme, and then proposed an effective attack strategy utilizing chosen-plaintext attack (CPA) in this paper. The proposed strategy mainly includes two attacks. The first is to obtain the equivalent secret key of the diffusion right shift phase, and the second is to obtain the permutation right shift rule. The effectiveness and feasibility of the proposed method are verified by both theoretical analyses and experimental results. Some proposals are also given for improving the security of the original encryption scheme.

Symmetric stream cipher with chaotic maps have been proven to be feasible and secure for digital image encryption, where 2D Cat map as well as Baker map are usually employed to permute pixels and 1D chaotic maps are employed to diffuse the values of pixels. In this paper, a new permutation method with perturbation strategy is proposed, which is used to enhance the performance of Cat map and hence the security degree of the image cryptosystem. Moreover, a chaotic orbit perturbation mechanism is introduced in diffusion procedure to further enhance the security of the cryptosystem. Intensive security analysis is carried out and the results demonstrate that the proposed cryptosystem is suitable for high secure image transmission applications.

A modern method for gray image enciphering depends on two techniques which are; DNA Exclusive-OR operation and 2D Chaotic Map is introduced. In preprocessing level, Arnold Transform is first applied on plain gray image for shuffling. Then, a DNA 2D matrix is resulted from encoding the shuffled gray image. Next, each of Henon Map and Ikeda Map are employed in keys generation to be used in the substitution and permutation process, respectively. The last process is decoding the resulted 2D matrix, and the enciphered image is obtained. The introduced method can acquire fine enciphering effect; has very low correlation (correlation close to zero), as well attains satisfactory entropy value close to 8, a wide secret key's space, strong sensitivity to secret key was the NPCR over 99% and UACI up to 33%, and has the abilities of resisting exhaustive attack and statistic attack as the investigational outcome and security analysis showed.