Image Encryption using Seven-Dimensional Logistic-Sine-Tan (7D-LST) Hyperchaotic Map

In chaos-based image encryption, it is desired that the pseudorandom source has to survive simultaneously to statistical, differential and brute-force attacks with the aid of dynamical complexity, sensitivity to initial conditions and key space. The limited key space and narrow chaotic windows in low-dimensional chaotic map inspire the construction of chaotic map in high dimension. This paper proposes a new seven dimensional hyperchaotic Logistic–Sine–Tan (7D-LST) map, which interleaves three nonlinear kernels – logistic, sinusoidal and hyperbolic tangent – in a repeating sequence L→S→T, and has two propagation connecting coefficients γ, δ between any nonlinear kernel that can be bidirectional, causing the map to create a circulant coupling graph between the nonlinear kernels that are not adjacent. Thus, the situation lacks periodicity in the vicinity of a fold point and corresponds to a larger phase-space mixing as compared to a homogeneous logistic or sine system. The key space for the 640-bit secret key (eight initial states, the control parameter μ and two values for the coupling weights) is 2⁶⁴⁰ ≈ 4.6×10¹⁹², which is much larger than 2¹²⁸, the AES-256 key space. These properties make the 7D-LST map a good pseudo random generator in image high-security encryption.