There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Image encryption using 2D Logistic-adjusted-Sine map

Cosine-transform-based chaotic system for image encryption

A new color image encryption using combination of the 1D chaotic map

A color image cryptosystem based on dynamic DNA encryption and chaos

2D Sine Logistic modulation map for image encryption

2D Logistic-Sine-coupling map for image encryption

Chaotic maps are widely used in different applications. Motivated by the cascade structure in electronic circuits, this paper introduces a general chaotic framework called the cascade chaotic system (CCS). Using two 1-D chaotic maps as seed maps, CCS is able to generate a huge number of new chaotic maps. Examples and evaluations show the CCS’s robustness. Compared with corresponding seed maps, newly generated chaotic maps are more unpredictable and have better chaotic performance, more parameters, and complex chaotic properties. To investigate applications of CCS, we introduce a pseudo-random number generator (PRNG) and a data encryption system using a chaotic map generated by CCS. Simulation and analysis demonstrate that the proposed PRNG has high quality of randomness and that the data encryption system is able to protect different types of data with a high-security level.

Zhongyun Hua

Papers

2D Sine Logistic modulation map for image encryption

Image encryption using 2D Logistic-adjusted-Sine map

Cosine-transform-based chaotic system for image encryption

2D Logistic-Sine-coupling map for image encryption

Cascade Chaotic System With Applications