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- Title
Constructing a 3D Exponential Hyperchaotic Map with Application to PRNG.
- Authors
Si, Yuanyuan; Liu, Hongjun; Chen, Yuehui
- Abstract
Some weaknesses of 1D chaotic maps, such as lacking of ergodicity, multiple bifurcations, dense periodic windows, and short iteration period, limit their practical applications in cryptography. A higher-dimensional chaotic map with ergodicity can solve these problems. Based on 1D quadratic map, a 3D exponential hyperchaotic map (3D-EHCM) is constructed, and its dynamic behaviors, such as phase diagram, Lyapunov exponent spectrum, Kolmogorov entropy (KE), correlation dimension, approximate entropy and randomness, are analyzed and tested. The results demonstrate that the 3D-EHCM has ergodicity in a larger range of control parameter, and its state points have a longer period. To counteract dynamical degradation and make it suitable for a PRNG, the periodic point detection and random impulsive perturbation are applied to lengthen the aperiodic time sequence, and statistical results demonstrate that a full-period sequence can be obtained.
- Publication
International Journal of Bifurcation & Chaos in Applied Sciences & Engineering, 2022, Vol 32, Issue 7, p1
- ISSN
0218-1274
- Publication type
Article
- DOI
10.1142/S021812742250095X