Quantum mechanics

Pseudorandom number generator

Algorithm

Control (management)

Histogram

Chaotic

Entropy (arrow of time)

Theoretical computer science

Encryption

Degenerate energy levels

Operating system

Computer science

Physics

Singular value decomposition

Mathematics

Image (mathematics)

Lyapunov exponent

Artificial intelligence

Control theory (sociology)

Chaos Solitons & Fractals

Due to the limited machine word length of hardware devices, the dynamics of digital chaotic systems will degenerate. To combat this issue, we proposed a universal method that is based on singular value decomposition (SVD), which can reversely construct non-degenerate hyperchaotic systems with any desired number of positive Lyapunov exponents by controlling pre-specified singular values. To assess the practicability and effectiveness of the method, we construct a 6-dimensional non-degenerate hyperchaotic system as an example. Furthermore, based on the hyperchaotic system, a pseudorandom number generator (PRNG) with desirable statistical characteristics is designed for image encryption. Numerical simulations were performed to evaluate the security of the image encryption algorithm in terms of histogram, information entropy, differential attack test, etc. The proposed non-degenerate hyperchaotic system can be effectively applied in the field of multimedia data encryption and information security.

A universal method for constructing non-degenerate hyperchaotic systems with any desired number of positive Lyapunov exponents