Designing multi-dimensional logistic map with fixed-point finite precision

In cryptographic algorithms, random sequences of longer period and higher nonlinearity are always desirable in order to increase resistance against cryptanalysis. The use of chaotic maps is an attractive choice as they exhibit properties that are suitable for cryptography. In continuous phase space...

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Bibliographic Details
Published in:Nonlinear dynamics 2019-09, Vol.97 (4), p.2147-2158
Main Authors: Munir, Fahad A., Zia, Muhammad, Mahmood, Hasan
Format: Article
Language:English
Subjects:
Algorithms
Automotive Engineering
Classical Mechanics
Computer simulation
Control
Cryptography
Dynamical Systems
Engineering
Mechanical Engineering
Nonlinear feedback
Nonlinearity
Orbits
Original Paper
Randomness
Sequences
Trajectories
Vibration
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Summary:In cryptographic algorithms, random sequences of longer period and higher nonlinearity are always desirable in order to increase resistance against cryptanalysis. The use of chaotic maps is an attractive choice as they exhibit properties that are suitable for cryptography. In continuous phase space of the logistic map, proper control parameters and initial state result into aperiodic trajectories. However, when the phase space of the logistic map is quantized, the trajectories terminate in finite and stable periodic orbits due to quantization error. The dynamic degradation of the logistic map can be mitigated using nonlinear feedback and cascading multiple chaotic maps. We propose a logistic map-based, finite precision multi-dimensional logistic map, that incorporates nonlinear feedback and modulus operations to perturb the chaotic trajectories. We present complexity, average cycle length and randomness analysis to evaluate the proposed method. The simulation results and analysis reveal that the proposed MDLM approach achieves longer period and higher randomness.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-019-05112-4