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

2D Sine Logistic modulation map for image encryption

A symmetric image encryption algorithm based on mixed linear–nonlinear coupled map lattice

Color image encryption using spatial bit-level permutation and high-dimension chaotic system

A chaos-based symmetric image encryption scheme using a bit-level permutation

In recent years, the classic encryption architecture based on chaotic map—“confusion diffusion” has been investigated. Among them, a two dimension Cat map is usually employed in confusion phase as an image can be seen as a two dimension array, meanwhile the flew of Cat map is obvious, that is the key space of it is not large enough. In the proposed encryption scheme, the Cat map is not with the fixed control parameters but a variable one during the confusion phase to enlarge the key space of the encryption scheme. Simulations are carried out with detail analyses, demonstrating the high security and efficient operation of our cryptosystem.

An Image Encryption Scheme Based on Chaotic Maps

In recent years, with the development of the social network theories, how to find or mining the most significant node in social network for understanding or controlling the information dissemination has become a hot topic and a series of effective algorithms have been presented. In this paper, a new scheme to measure the dynamic influence of the nodes in a social network is proposed, in which the sum of trust values of the propagation nodes is used. Simulations have been carried out and the results show that our scheme is stable and accurate.

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Wei Zhang

Papers

A chaos-based symmetric image encryption scheme using a bit-level permutation

An Image Encryption Scheme Based on Chaotic Maps

Analysis of the Dynamic Influence of Social Network Nodes