An improved image encryption algorithm with finite computing precision

Enhancing chaos-based PRNGs quality is the subject of this paper. The big problem that chaotic systems suffer from is the limited arithmetic computation size, that is; dynamical degradation in digital chaotic systems appears due to the digitization process. Quantization error, limited cycle-length and worse statistical proprieties of the chaotic sequence are in fact the most shortcomings of implementing chaotic systems on digital computers. In this paper, we have proposed a simple method for purifying as maximum as possible digital chaotic systems from aforementioned shortcomings. The method consists of using a mechanism to perturb the chaotic orbits during randomly chosen periods, and in the same time using another circuit to convert the chaotic sequence to another one that provide good statistical proprieties. The proposed scheme has been applied on the Logistic chaotic map using low arithmetic computation size, the results in terms of cycle-length and uniformity showed that the proposed scheme is so better compared to the original system and can extremely enhance the chaotic proprieties of a given digital chaotic system.

To improve the dynamical behaviors of 1D chaotic maps, a new linear-delay-modulation method (LDM) is proposed. Derived from the Sine map, a delayed Sine map (DSM) is proposed based on the LDM. Then, we substitute the Sine map in the SIMM system with DSM and obtained a delayed SIMM system (DSIMM). Its chaotic performance is analyzed through the phase diagram, Lyapunov exponent spectrum, and complexity. The results show that the delayed chaotic map can generate more complex dynamical behaviors and more random sequences. Hence, we apply the two delayed systems to a novel image encryption algorithm with the permutation-confusion-diffusion architecture. Firstly, to permutate the pixel of the image efficiently, the plain-image is scrambled by using a multilayer of the nonlinear index. Secondly, the image is confused by using the chaotic matrix generated with two chaotic sequences, and then, the ciphertext is transformed into a 1D sequence. Finally, to improve the plaintext sensitivity and facilitate key management, we enhance the sensitivity by applying a novel diffusion algorithm instead of using plaintext-related keystream. The diffusion equation contains the sum of undiffused pixels and the operation of cyclic bit-shift. Simulation results for the gray image illustrate the effectiveness of the proposed encryption algorithm.

Image encryption based on chaotic maps is an important method for ensuring the secure communication of digital multimedia on the Internet. To improve the encryption performance and security of image encryption systems, a new image encryption algorithm is proposed that employs a compound chaotic map and random cyclic shift. First, a new hybrid chaotic system is designed by coupling logistic, ICMIC, Tent, and Chebyshev (HLITC) maps. Comparison tests with previous chaotic maps in terms of chaotic trajectory, Lyapunov exponent, and approximate entropy illustrate that the new hybrid chaotic map has better chaotic performance. Then, the proposed HLITC chaotic system and spiral transformation are used to develop a new chaotic image encryption scheme using the double permutation strategy. The new HLITC chaotic system is used to generate key sequences used in the image scrambling and diffusion stages. The spiral transformation controlled by the chaotic sequence is used to scramble the pixels of the plaintext image, while the XOR operation based on a chaotic map is used for pixel diffusion. Extensive experiments on statistical analysis, key sensitivity, and key space analysis were conducted. Experimental results show that the proposed encryption scheme has good robustness against brute-force attacks, statistical attacks, and differential attacks and is more effective than many existing chaotic image encryption algorithms.

Medical image transmission and storage must be secure due to the rapid growth of digital healthcare systems and telemedicine. Medical images have high data volumes and strong pixel correlations, making conventional encryption algorithms inefficient or computationally expensive. Chaos-based encryption methods are popular due to their sensitivity to initial conditions and strong randomness, but finite precision limits key spaces and short periodicity in chaotic maps. A novel hybrid image encryption scheme is proposed that integrates long short-term memory (LSTM) networks with classical chaotic maps to generate adaptive keystreams using a hash float-seeded chaotic map and statistical features. The chaotic maps provide nonlinearity and high key sensitivity, while the LSTM extends the randomness, eliminates periodicity, and expands the key space to test its robustness. Three variants of the proposed model were experimented with: LSTM + Logistic, LSTM + sine map, and LSTM + Chebyshev map. Results demonstrate that all 3 models achieve strong encryption performance, but LSTM + Logistic map outperforms the other two in terms of randomness quality, noise, and crop attacks. The proposed model achieves 99.62% of NPCR, 39.59% of UACI, and 7.975 of entropy. Compared with conventional chaos methods and GAN encryption schemes, the proposed method provides high security, lightweight computation, and practical deployment.

Due to easy and simple implementation, normally single 1-D chaotic maps like logistic and sine maps are employed in multimedia data encryption. However, data encrypted through a single chaotic map does not provide better security in terms of resistance against various attacks. In this paper, 2D Henon chaotic map and skew tent map are deployed in the design of an efficient chaos-based image encryption algorithm. To confuse the relationship between plaintext and ciphertext images, both chaotic maps play a key role in the permutation and diffusion mechanism. In the confusion stage, firstly, the Henon chaotic map generates two different chaotic sequences, which are further applied in row and column permutation of plaintext image. The pixel values diffusion is produced by unimodal skew tent map via XOR operations. In the last stage of encryption algorithm, Hussain's substitution box is used to substitute each pixel into a new random pixel. Extensive security analysis and resistance to statistical attack prove the security of anticipated scheme.

A novel devaney chaotic map with uniform trajectory for color image encryption

The paper presents combining k-error approximate entropy with some tests in NIST's STS randomness test suite to analyze cryptographical properties of several chaotic pseudo- random sequences generated by diverse maps and quantified methods, including Logistic map, Cubic map, Henon map, Sine map, Tent map, Chebyshev map, Piecewise-linear map, Piece- wise-square-root map. Simulation results show that the k-error approximate entropy can distinguish the stability of different sequences; that the cryptological properties are influenced by quantified methods; that the sequences generated by Logistic map, Chebyshev map, Piecewise-linear map and Piecewise- square-root map have the best pseudorandom properties, while the sequences generated by Henon map and Tent map have the worst stability.

Effects of an agonist of gonadotrophin releasing hormone in cattle. I. Hormone concentrations and oestrous cycle length

An image encryption scheme based on new spatiotemporal chaos

The research on the balance of chaotic sequence has important significance to spread-spectrum communication. The relationship between the balance and the parameter of four typical chaotic maps (Chebyshev, improved Logistic, Logistic and Tent) was discussed. The new numeric ranges of initial value and fractal parameter were decided, which provided reference for the generation of chaotic spread-spectrum sequence. Through the graphs of the four chaotic sequences' balance and the error-bit rate performance of these systems with the four chaotic sequences' map parameters, the new numeric ranges were validated. Both simulation results and the analysis show that the balance of Chebyshev is the best.

The properties of chaotic maps based on Logistic map, Tent map, Improved Logistic map and Chebyshev map are analyzed in this paper .Then we discuss the performance of correlation, balance and run-length of the chaotic binary sequences . Simulation results show that the characteristics of chaotic sequences are similar to the traditional pseudo-random sequences, and chaotic sequence is suitable for direct sequence spread spectrum systems as spreading sequence.

For a gray image, every row (column) can be seen as an irregular wave. Activated by the architecture of permutation-diffusion based image encryption scheme, a chaotic image encryption algorithm is proposed to change the representation of irregular waves in the plain-image. To reduce the high correlation, permutation for both rows and columns is taken in the first stage. Due to the transposition of pixels in row/column, wave shapes will be changed according to the pseudo-random sequences generated from chaotic map. Specifically, pixels in each wave (row or column) are divided into two groups by energy (a bigger one and a smaller one). Then different groups are employed to manipulate the production of chaotic sequence. As a result, the chosen-plaintext and known-plaintext attacks will be difficult due to the plain-image dependent keystream. In the second stage, wave-by-wave diffusion in column is carried out such that any tiny change in the plain-image spreads out uniformly to the whole cipher-image. The keystream used in diffusion is designed again dependent on the permuted image obtained from the first stage. In this way, the security of the proposed algorithm can be further strengthened compared with some existing algorithms. Related security analyses also show that our method can satisfy common requirements of secure communication for daily images.

Image encryption based on 3D Cubic-Sine Logistic Coupled Map and Improved Chirikov Map

Image encryption algorithm with random scrambling based on one-dimensional logistic self-embedding chaotic map

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.