ABSTRACT
Chaotic systems implemented by artificial neural networks are good candidates for data encryption. In this manner, this paper introduces the cryptographic application of the Hopfield and the Hindmarsh-Rose neurons. The contribution is focused on finding suitable coefficient values of the neurons to generate robust random binary sequences that can be used in image encryption. This task is performed by evaluating the bifurcation diagrams from which one chooses appropriate coefficient values of the mathematical models that produce high positive Lyapunov exponent and Kaplan-Yorke dimension values, which are computed using TISEAN. The randomness of both the Hopfield and the Hindmarsh-Rose neurons is evaluated from chaotic time series data by performing National Institute of Standard and Technology (NIST) tests. The implementation of both neurons is done using field-programmable gate arrays whose architectures are used to develop an encryption system for RGB images. The success of the encryption system is confirmed by performing correlation, histogram, variance, entropy, and Number of Pixel Change Rate (NPCR) tests.
ABSTRACT
Synchronizing chaotic oscillators has been a challenge to guarantee successful applications in secure communications. That way, three synchronization techniques are applied herein to twenty two chaotic oscillators, three of them based on piecewise-linear functions and nineteen proposed by Julien C. Sprott. These chaotic oscillators are simulated to generate chaotic time series that are used to evaluate their Lyapunov exponents and Kaplan-Yorke dimension to rank their unpredictability. The oscillators with the high positive Lyapunov exponent are implemented into a field-programmable gate array (FPGA), and afterwards they are synchronized in a master-slave topology applying three techniques: the seminal work introduced by Pecora-Carroll, Hamiltonian forms and observer approach, and open-plus-closed-loop (OPCL). These techniques are compared with respect to their synchronization error and latency that is associated to the FPGA implementation. Finally, the chaotic oscillators providing the high positive Lyapunov exponent are synchronized and applied to a communication system with chaotic masking to perform a secure image transmission. Correlation analysis is performed among the original image, the chaotic channel and the recovered image for the three synchronization schemes. The experimental results show that both Hamiltonian forms and OPCL can recover the original image and its correlation with the chaotic channel is as low as 0.00002, demonstrating the advantage of synchronizing chaotic oscillators with high positive Lyapunov exponent to guarantee high security in data transmission.
