Biomedical image encryption based on double-humped and fractional logistic maps

This paper presents a secured highly sensitive image encryption system suitable for biomedical applications. The pseudo random number generator of the presented system is based on two discrete logistic maps. The employed maps are: the double humped logistic map as well as the fractional order logistic map. The mixing of the map parameters and the initial conditions x0, offers a great variety for constructing more efficient encryption keys. Different analyses are introduced to measure the performance of the proposed encryption system such as: histogram analysis, correlation coefficients, MAE, NPCR as well as UACI measurements. The encryption system is proven to be highly sensitive to ±0.001% perturbation of the logistic maps parameters. The system is tested on medical images of knee MRI and a lung X-rays.

[1]  Kenneth Coiteux.  An Introductory Look at Deterministic Chaos , 2014 .

[2]  Ahmed M. Soliman,et al.  Two-port two impedances fractional order oscillators , 2016, Microelectron. J..

[3]  Ahmed M. Soliman,et al.  Generalized delayed logistic map suitable for pseudo-random number generation , 2015, 2015 International Conference on Science and Technology (TICST).

[4]  Emil E. Pacurar,et al.  Database integration of protocol-specific neurological imaging datasets , 2016, NeuroImage.

[5]  Salwa K. Abd-El-Hafiz,et al.  Symmetric encryption algorithms using chaotic and non-chaotic generators: A review , 2015, Journal of advanced research.

[6]  Vinod Patidar,et al.  Image encryption using chaotic logistic map , 2006, Image Vis. Comput..

[7]  T. Kaczorek,et al.  Fractional Differential Equations , 2015 .

[8]  Ahmed M. Soliman,et al.  Generalized fractional logistic map suitable for data encryption , 2015, 2015 International Conference on Science and Technology (TICST).

[9]  S. Salman,et al.  On a discretization process of fractional-order Logistic differential equation , 2014 .

[10]  A. Elwakil,et al.  Design equations for fractional-order sinusoidal oscillators: Four practical circuit examples , 2008 .

[11]  Joakim Munkhammar,et al.  Chaos in a fractional order logistic map , 2013 .

[12]  Ahmed M. Soliman,et al.  Fractional Order Oscillator Design Based on Two-Port Network , 2016, Circuits Syst. Signal Process..

[13]  D. Baleanu,et al.  Discrete fractional logistic map and its chaos , 2014 .

[14]  A. Radwan,et al.  Image encryption in the fractional-order domain , 2012, 2012 International Conference on Engineering and Technology (ICET).