Iterated function system has been found to be an important method to generate fractal sets. Hilbert space-filling curve is one kind of fractal sets which has been applied widely in digital image processing, such as image encoding, image clustering, image encryption, image storing/retrieving, and pattern recognition. In this paper, we will explore the generation of Hilbert-type space-filling curves via iterated function system based approach systematically. Cooperating a recursive calling of the common Hilbert's original space-filling curve at resolution n-1 and an IFS consisting of four affine transformations, one can generate the vertices for Hilbert-type space-filling curves at any resolution n. The merit is that the recursive algorithm is easy to implement and can be generalized to produce any other Hilbert-type space-filling curves and their variation versions.

This paper puts forward a novel image encryption scheme based on ordinary differential equation system. Firstly, a hyper-chaotic differential equation system is used to generate two hyper-chaotic orbit sequences. Introducing the idea of hybrid orbit, two orbits are mixed to generate a hybrid hyper-chaotic sequence which is used to be the initial chaotic key stream. Secondly, the final encryption key stream is generated through two rounds of diffusion operation which is related to the initial chaotic key stream and plain-image. Therefore, the algorithm’s key stream not only depends on the cipher keys but also depends on plain-image. Last but not least, the security and performance analysis have been performed, including key space analysis, histogram analysis, correlation analysis, information entropy analysis, peak signal-to-noise ratio analysis, key sensitivity analysis, differential analysis etc. All the experimental results show that the proposed image encryption scheme is secure and suitable for practical image and video encryption.

A multi-orbit hybrid image encryption scheme based on discrete chaotic dynamical systems is proposed. One generalized Arnold map is adopted to generate three orbits for three initial conditions. Another chaotic dynamical system, tent map, is applied to generate one pseudo-random sequence to determine the hybrid orbit points from which one of the three orbits of generalized Arnold map. The hybrid orbit sequence is then utilized to shuffle the pixels’ positions of plain-image so as to get one permuted image. To enhance the encryption security, two rounds of pixel gray values’ diffusion is employed as well. The proposed encryption scheme is simple and easy to manipulate. The security and performance of the proposed image encryption have been analyzed, including histograms, correlation coefficients, information entropy, key sensitivity analysis, key space analysis, differential analysis, etc. All the experimental results suggest that the proposed image encryption scheme is robust and secure and can be used for secure image and video communication applications.

A great many chaos-based image encryption schemes have been proposed in the past decades. Most of them use the permutation-diffusion architecture in pixel level, which has been proved insecure enough as they are not dependent on plain-images and so cannot resist chosen/known plain-image attack usually. In this paper, we propose a novel image encryption scheme comprising of one permutation process and one diffusion process. In the permutation process, the image sized is expanded to one sized by dividing the plain-image into two parts: one consisting of the higher 4bits and one consisting of the lower 4bits. The permutation operations are done row-by-row and column-by-column to increase the speed of permutation process. The chaotic cat map is utilized to generate chaotic sequences, which are quantized to shuffle the expanded image. The chaotic sequence for permutation process is dependent on plain-image and cipher keys, resulting in good key sensitivity and plain-image sensitivity. To achieve more avalanche effect and larger key space, a chaotic Bernoulli shift map based bilateral (i.e., horizontal and vertical) diffusion function is applied as well. The security and performance of the proposed image encryption have been analyzed, including histograms, correlation coefficients, information entropy, key sensitivity analysis, key space analysis, differential analysis, encryption rate analysis etc. All the experimental results suggest that the proposed image encryption scheme is robust and secure and can be used for secure image and video communication applications.

A secure image encryption scheme based on 2D skew tent map is proposed for the encryption of color images. The proposed encryption scheme is composed of one permutation process and one substitution process. The 3D color plain-image matrix is converted to 2D image matrix first, then 2D skew tent map is utilized to generate chaotic sequences, which are used for both permutation process and substitution process. The chaotic sequence for permutation process is dependent on plain-image and cipher keys, resulting in good key sensitivity and plaintext sensitivity. The substitution process is first initiated with the initial vectors generated by the cipher keys and 2D skew tent map, then the gray values of row and column pixels of 2D image matrix are mixed with the pseudorandom number sequences via bitxoring operation. Both permutation process and substitution process are executed row-by-row and column-by-column instead of pixel-by-pixel to improve the speed of encryption. The security and performance of the proposed image encryption have been analyzed, including histograms, correlation coefficients, information entropy, key sensitivity analysis, key space analysis, differential analysis, encryption/decryption rate analysis etc. All the experimental results suggest that the proposed image encryption scheme is robust and secure and can be used for secure image and video communication applications.

This paper proposes an image encryption scheme based on chaotic system with changeable parameters depending on plain-image. A generalized Arnold map, whose control parameters are changeable and image-dependent during the iteration procedure, is utilized to generate chaotic orbits applied to permute the pixel positions. A diffusion function is also designed to realize the diffusion effect by piece-wise linear chaotic map. In both the permutation process and the diffusion process, the keystreams generated by chaotic maps are all strongly dependent on plain-image, and thereby can improve the encryption security efficiently. The major merits of the proposed image encryption scheme include a huge key space, good statistical nature resisting statistical analysis attack, differential attack, and good resistance against known-plaintext attack and chosen-plaintext attack, etc. Experimental results have been carried out with detailed analysis to show that the proposed scheme can be a potential candidate for practical image encryption.

A novel image encryption scheme based on chaotic system is proposed. The proposed encryption scheme utilizes one tent map to generate a pseudo-random sequence and then shift the bits of the expanding 0-1 image circularly so as to shuffle the image gray values. To make the encryption scheme resist differential attack efficiently, generalized Arnold maps and Bernoulli shift maps are applied to produce two pseudo-random gray value sequences and then diffuse the gray values bi-directionally. The bit circular shift process and diffusion processes greatly confuse the statistical nature between plain-images and cipher-images. Security analyses including key sensitivity analysis, key space analysis, statistical analysis, differential attack analysis and information entropy analysis are performed. All the experimental results demonstrate that the proposed image encryption scheme possesses large key space to frustrate brute-force attack efficiently and can resist statistical attack, differential attack, etc.

In this paper, a chaotic image encryption scheme with an efficient permutation–diffusion mechanism is constructed, where six generalized Bernoulli shift maps and one six-dimensional Arnold map are utilized to generate one hybrid chaotic orbit applied to disorder the pixel positions in the permutation process while four generalized Bernoulli shift maps and one Arnold map are employed to yield two random gray value sequences to change the gray values by a two-way diffusion process. Several merits of the proposed image encryption scheme are achieved, including a huge key space, good statistical properties resisting statistical attack and differential attack, desirable robustness against malicious attacks on cipher-images, such as cropping, noising, JPEG compression, etc. Experimental results have been carried out with detailed analysis to show that the proposed scheme can be a potential candidate for practical image encryption.

Linear congruential generator has been widely applied to generate pseudo-random numbers successfully. This paper proposes a novel chaos-based image encryption scheme using affine modular maps, which are extensions of linear congruential generators, acting on the unit interval. A permutation process utilizes two affine modular maps to get two index order sequences for the shuffling of image pixel positions, while a diffusion process employs another two affine modular maps to yield two pseudo-random gray value sequences for a two-way diffusion of gray values. Experimental results are carried out with detailed analysis to demonstrate that the proposed image encryption scheme possesses large key space to frustrate brute-force attack efficiently and can resist statistical attack, differential attack, known-plaintext attack as well as chosen-plaintext attack thanks to the yielded gray value sequences in the diffusion process not only being sensitive to the control parameters and initial conditions of the considered chaotic maps, but also strongly depending on the plain-image processed.

An image encryption scheme based on the 3D sawtooth map is proposed in this paper. The 3D sawtooth map is utilized to generate chaotic orbits to permute the pixel positions and to generate pseudo-random gray value sequences to change the pixel gray values. The image encryption scheme is then applied to encrypt the secret image which will be imbedded in one host image. The encrypted secret image and the host image are transformed by the wavelet transform and then are merged in the frequency domain. Experimental results show that the stego-image looks visually identical to the original host one and the secret image can be effectively extracted upon image processing attacks, which demonstrates strong robustness against a variety of attacks.

An image scrambling method based on the itinerary of the improved 3D Baker map is proposed in this paper. The standard 3D Baker map is improved by the tent map, so that the itinerary becomes more complicated and can be used to encode the image pixel positions to scramble the image. The scrambling method is applied to the preprocessing in watermarking. The watermark bits are embedded in the discrete wavelet transform (DWT) spectral domain based on the scrambling of watermark, the odd-even adjustment rule and the neighbor mean value. The watermark bits are embedded in medium coefficients in DWT domain of the host image. Experimental results show that the watermarked image looks visually identical to the original one and the watermark can be effectively extracted upon image processing attacks, which demonstrates strong robustness against a variety of attacks.

This paper proposes a chaos-based image encryption scheme where one 3D skew tent map with three control parameters is utilized to generate chaotic orbits applied to scramble the pixel positions while one coupled map lattice is employed to yield random gray value sequences to change the gray values so as to enhance the security. Experimental results have been carried out with detailed analysis to demonstrate that the proposed image encryption scheme possesses large key space to resist brute-force attack and possesses good statistical properties to frustrate statistical analysis attacks. Experiments are also performed to illustrate the robustness against malicious attacks like cropping, noising, JPEG compression.

Thanks to the exceptionally good properties in chaotic systems, such as sensitivity to initial conditions and control parameters, pseudo-randomness and ergodicity, chaos-based image encryption algorithms have been widely studied and developed in recent years. Standard map is chaotic so that it can be employed to shuffle the positions of image pixels to get a totally visual difference from the original images. This paper proposes two novel schemes to shuffle digital images. Different from the conventional schemes based on Standard map, we disorder the pixel positions according to the orbits of the Standard map. The proposed shuffling schemes don’t need to discretize the Standard map and own more cipher leys compared with the conventional shuffling scheme based on the discretized Standard map. The shuffling schemes are applied to encrypt image and disorder the host image in watermarking scheme to enhance the robustness against attacks. Experimental results show that the proposed encryption scheme yields good secure effects. The watermarked images are robust against attacks as well.