Bingbing Feng

Chengqing Li, Dongdong Lin, Bingbing Feng et al.

Recently, a chaotic image encryption algorithm based on information entropy (IEAIE) was proposed. This paper scrutinizes the security properties of the algorithm and evaluates the validity of the used quantifiable security metrics. When the round number is only one, the equivalent secret key of every basic operation of IEAIE can be recovered with a differential attack separately. Some common insecurity problems in the field of chaotic image encryption are found in IEAIE, e.g. the short orbits of the digital chaotic system and the invalid sensitivity mechanism built on information entropy of the plain image. Even worse, each security metric is questionable, which undermines the security credibility of IEAIE. Hence, IEAIE can only serve as a counterexample for illustrating common pitfalls in designing secure communication method for image data.

Chengqing Li, Bingbing Feng, Shujun Li et al.

Chaotic dynamics is widely used to design pseudo-random number generators and for other applications such as secure communications and encryption. This paper aims to study the dynamics of discrete-time chaotic maps in the digital (i.e., finite-precision) domain. Differing from the traditional approaches treating a digital chaotic map as a black box with different explanations according to the test results of the output, the dynamical properties of such chaotic maps are first explored with a fixed-point arithmetic, using the Logistic map and the Tent map as two representative examples, from a new perspective with the corresponding state-mapping networks (SMNs). In an SMN, every possible value in the digital domain is considered as a node and the mapping relationship between any pair of nodes is a directed edge. The scale-free properties of the Logistic map's SMN are proved. The analytic results are further extended to the scenario of floating-point arithmetic and for other chaotic maps. Understanding the network structure of a chaotic map's SMN in digital computers can facilitate counteracting the undesirable degeneration of chaotic dynamics in finite-precision domains, helping also classify and improve the randomness of pseudo-random number sequences generated by iterating chaotic maps.