Exploiting one-dimensional exponential Chebyshev chaotic map and matching embedding for visually meaningful image encryption

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.

Chaotic maps used to shuffle and manipulate the image pixels are important for image encryption (IE). In this study, a novel 2D optimized chaotic map (OPMAP) using a triple-objective differential evolution (TODE) algorithm is presented for IE. A model for OPMAP with eight decision variables is empirically designed, and then its variables are determined utilizing TODE through minimizing a triple-objective function that involving Lyapunov exponent (LE), entropy and 0–1 test. OPMAP is assessed with respect to credible measurements like bifurcation, 3D phase space, LE, 0–1 test, permutation entropy (PE) and sample entropy (SE). The capability of OPMAP is then verified through an IE scheme including permutation and diffusion through various cryptanalyses: key space 2298, mean entropy 7.9995, mean correlation 13.61E-5, number of pixels changing rate (NPCR) 99.6093, unified average changing intensity (UACI) 33.4630 and encryption processing time (EPT) 0.2919 (s). A detailed review of IE schemes reported elsewhere is presented and IE performance of OPMAP is also validated by comparison with those IE schemes with and without optimization used. The 2D-OPMAP-based IE is faster and has low computational complexity. Moreover, the proposed it shows better cryptanalysis results for the most of the comparisons.

Optimized Chaotic encrypted image based on continuous raster scan method

In the last decade, the communication of images through the internet has increased. Due to the growing demands for data transfer through images, protection of data and safe communication is very important. For this purpose, many encryption techniques have been designed and developed. New and secured encryption schemes based on chaos theory have introduced methods for secure as well as fast communication. A modified image encryption process is proposed in this work with chaotic maps and orthogonal matrix in Hill cipher. Image encryption involves three phases. In the first phase, a chaotic Henon map is used for permuting the digital image. In the second phase, a Hill cipher is used whose encryption key is generated by an orthogonal matrix which further is produced from the equation of the plane. In the third phase, a sequence is generated by a chaotic tent map which is later XORed. Chaotic maps play an important role in the encryption process. To deal with the issues of fast and highly secured image processing, the prominent properties of non-periodical movement and non-convergence of chaotic theory play an important role. The proposed scheme is resistant to different attacks on the cipher image. Different tests have been applied to evaluate the proposed technique. The results of the tests such as key space analysis, key sensitivity analysis, and information entropy, histogram correlation of the adjacent pixels, number of pixel change rate (NPCR), peak signal to noise ratio (PSNR), and unified average changing intensity (UCAI) showed that our proposed scheme is an efficient encryption technique. The proposed approach is also compared with some state-of-the-art image encryption techniques. In the view of statistical analysis, we claim that our proposed encryption algorithm is secured.

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.

In 2009, Tseng et al. proposed a key agreement protocol based on chaotic maps. Tseng et al. claimed that their protocol preserve user anonymity. However, Tseng et al.’s protocol is insecure against the insider attack. Nui et al. proposed a new anonymous key agreement protocol in 2011. Unfortunately, Nui et al.’s protocol cannot provide user anonymity and has computational efficiency problem. We introduce a new key agreement protocol based on Chebyshev chaotic map. Our protocol overcomes these security problems and provides user anonymity.

This paper proposes a novel approach for generating the secure measurement matrix used for multimedia compressive sensing based on multiple chaotic maps. From the selected eight one-dimensional chaotic maps, two are randomly chosen to run random number of iterations to form random arrays. These random arrays are combined together to form a single random array, which is used as the initial seed for generating the random measurement matrix used in the compressive sensing operation. The key-based selection of initial pair of chaotic maps, the initial values of the selected chaotic maps and the number of iterations of the chaotic maps are kept as the secret information to provide the security. The proposed system is experimented with different audio, image and video CS techniques to validate the reconstruction and robustness to noise performance. From cryptanalysis it is proved that the proposed system can resist all types of attacks.

Home area network (HAN) devices send the electricity consumption and other important data to the smart meter that must remain confidential from other devices. This paper proposes a novel one-dimensional hybrid chaotic map. The proposed map shows excellent chaotic properties when analyzed by bifurcation diagram, Lyapunov exponent & Shannon entropy. We further design an encryption strategy for data transfers between the smart meter and HAN devices. The proposed encryption scheme uses the existing lightweight key management in advanced metering infrastructure (LKM-AMI) architecture for data transfers, in which the encrypted data is transferred through an insecure channel and private keys are provided by trusted third party (TTP) through secure channels. The 2-way communication between HAN devices and the smart meter sends messages that are encrypted by using the proposed novel hybrid one-dimensional chaotic map. The encryption strategy mainly consists of three steps. In the first step, the seed and the control parameters are initialized. The second phase generates two intermediate keys using the proposed hybrid chaotic map. In the last phase, we encrypt the message by applying permutation followed by diffusion using intermediate keys. The proposed encryption strategy is resistant to various attacks.

Image encryption with compound chaotic sequence cipher shifting dynamically

Image encryption scheme based on 3D baker with dynamical compound chaotic sequence cipher generator

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.

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Chaotic behavior can be observed in continuous and discrete-time systems. This behavior can appear in one-dimensional nonlinear maps; however, having at least three state variables in flows is necessary. Due to the lower mathematical complexity and computational cost of maps, lots of research has been conducted based on them. This paper aims to present a novel one-dimensional trigonometric chaotic map that is multi-stable and can act attractively. The proposed chaotic map is first analyzed using a single sinusoidal function; then, its abilities are expanded to a map with a combination of two sinusoidal functions. The stability conditions of both maps are investigated, and their different behaviors are validated through time series, state space, and cobweb diagrams. Eventually, the influence of parameter variations on the maps’ outputs is examined by one-dimensional and two-dimensional bifurcation diagrams and Lyapunov exponent spectra. Besides, the diversity of outputs with varying initial conditions reveals this map’s multi-stability. The newly designed chaotic map can be employed in encryption applications.

Session Initiation Protocol (SIP) is the most widely used signalling protocol for controlling communication, establishing, maintaining, and terminating sessions on the Internet. However, since sensitive information is often transmitted through open channels, a security authentication scheme is essential. Recently, Islam et al. proposed an authentication scheme for SIP, and argued that the scheme is immune to known attacks. However, we discover that their scheme fails to achieve user anonymity, and it cannot even resist impersonation attack. Therefore, this study proposes an enhanced mutual authentication scheme to eliminate the drawbacks of the scheme proposed by Islam et al. In addition, our proposed scheme is based on extended chaotic map, which avoids computationally expensive elliptic curve point multiplication. Then, we use Burrows-Abadi-Needham logic to prove that the proposed scheme achieves secure mutual authentication, and we use the Real-Or-Random model to analyze the formal security verification of the session key. Finally, we compare the performance and the security features of the proposed scheme with some existing schemes. Therefore, we provide better safety and efficiency than related schemes and the proposed scheme is suitable for SIP.

ABSTRACTWith the fast growth of the automatic authentication and asset tracking usage in a wide variety of applications in different fields, government, logistics, transportation and retail are among the most supportive of the radio‐frequency identification (RFID) market. Security is a crucial issue and must be addressed seriously. RFID security must meet the public demand of data protection. Recently, several lightweight RFID authentication protocols conforming to the EPCglobal Class 1 Generation 2 (EPC C1‐G2) standard have been proposed. In this paper, we present efficient attacks against the authenticated RFID security mechanism of Changet al. based on Chebyshev chaotic maps, which is the first solution that adopted the chaos in the RFID authentication process. It turns out that this protocol has fundamental weaknesses that can be used by an adversary to break the system. We will show that this protocol is vulnerable to tracking attack, secret disclosure attack, impersonation attack and desynchronization attack. The proposed attack techniques are in light of two flaws related to the message generation and the shared‐secret update process, which are not neatly scrutinized. Then, we propose an improved RFID authentication protocol based on the Chebyshev chaotic map hard problem, conforming to the EPC C1‐G2 standard with more flexibility, security and mobility for the RFID application. Copyright © 2014 John Wiley & Sons, Ltd.