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.

NPCR and UACI Randomness Tests for Image Encryption

A new 1D chaotic system for image encryption

A novel colour image encryption algorithm based on chaos

In recent years, various image encryption algorithms based on the permutation-diffusion architecture have been proposed where, however, permutation and diffusion are considered as two separate stages, both requiring image-scanning to obtain pixel values. If these two stages are combined, the duplicated scanning effort can be reduced and the encryption can be accelerated. In this paper, a fast image encryption algorithm with combined permutation and diffusion is proposed. First, the image is partitioned into blocks of pixels. Then, spatiotemporal chaos is employed to shuffle the blocks and, at the same time, to change the pixel values. Meanwhile, an efficient method for generating pseudorandom numbers from spatiotemporal chaos is suggested, which further increases the encryption speed. Theoretical analyses and computer simulations both confirm that the new algorithm has high security and is very fast for practical image encryption.

A new chaos-based fast image encryption algorithm

This paper proposes a novel confusion and diffusion method for image encryption. One innovation is to confuse the pixels by transforming the nucleotide into its base pair for random times, the other is to generate the new keys according to the plain image and the common keys, which can make the initial conditions of the chaotic maps change automatically in every encryption process. For any size of the original grayscale image, after being permuted the rows and columns respectively by the arrays generated by piecewise linear chaotic map (PWLCM), each pixel of the original image is encoded into four nucleotides by the deoxyribonucleic acid (DNA) coding, then each nucleotide is transformed into its base pair for random time(s) using the complementary rule, the times is generated by Chebyshev maps. Experiment results and security analysis show that the scheme can not only achieve good encryption result, but also the key space is large enough to resist against common attacks.

Image encryption using DNA complementary rule and chaotic maps

Chaos-based encryption appeared recently in the early 1990s as an original application of nonlinear dynamics in the chaotic regime. In this paper, an implementation of digital image encryption scheme based on the mixture of chaotic systems is reported. The chaotic cryptography technique used in this paper is a symmetric key cryptography. In this algorithm, a typical coupled map was mixed with a one-dimensional chaotic map and used for high degree security image encryption while its speed is acceptable. The proposed algorithm is described in detail, along with its security analysis and implementation. The experimental results based on mixture of chaotic maps approves the effectiveness of the proposed method and the implementation of the algorithm. This mixture application of chaotic maps shows advantages of large key space and high-level security. The ciphertext generated by this method is the same size as the plaintext and is suitable for practical use in the secure transmission of confidential information over the Internet.

A novel algorithm for image encryption based on mixture of chaotic maps

A fast chaotic encryption scheme based on piecewise nonlinear chaotic maps

Pseudo random number generator based on quantum chaotic map

A novel scheme for image encryption based on 2D piecewise chaotic maps

During the recent years several chaotic image encryption algorithms have been proposed, but most of them encountered some drawbacks such as small key space, low speed, lack of robustness and low security. In this paper, we have proposed an image algorithm based on the combination of a one-dimensional polynomial chaotic map and a piecewise nonlinear chaotic map. Theoretical analysis and computer simulations, both confirm that the new algorithm possesses high security, robust fast encryption speed for practical image encryption and solves the problem of small key space.

Amir Akhavan

Papers

A novel algorithm for image encryption based on mixture of chaotic maps

A fast chaotic encryption scheme based on piecewise nonlinear chaotic maps

Pseudo random number generator based on quantum chaotic map

A novel scheme for image encryption based on 2D piecewise chaotic maps

A symmetric image encryption scheme based on combination of nonlinear chaotic maps