False strange attractors as sources of pseudo randomness

In this work, the use of false chaotic attractors in enhancing the security of chaos-based encryption applications will be explored. False attractors result from rearranging the solution trajectories of a nonlinear dynamical system, leading to novel shapes in the 3D space. This way, a single solution trajectory of a chaotic system can be used to generate numerous new false trajectories. Examples of such attractors are provided for the Lorenz system, and a system with line equilibrium from Moysis et al (2019). By formalizing the method of constructing false attractors, and generalizing it by adding a series of elementary operations, the key parameters of this procedure can be used as part of the secret key in symmetric encryption applications, effectively increasing the key space. Specifically, the key space increases significantly with respect to the simulation time, and the system’s dimension. Moreover, due to its fast implementation, this technique can be used as a less complex, but much lighter alternative to full scale permutation. The usability of the false attractors as sources of randomness is showcased through the design of a chaotic pseudo-random bit generator. The generator can output 64 bits per iteration, and is equally effective under any false attractor of the chaotic system.