Fully digital jerk-based chaotic oscillators for high throughput pseudo-random number generators up to 8.77 Gbits/s

Abstract

This paper introduces fully digital implementations of four different systems in the 3rd order jerk-equation based chaotic family using the Euler approximation. The digitization approach enables controllable chaotic systems that reliably provide sinusoidal or chaotic output based on a selection input. New systems are introduced, derived using logical and arithmetic operations between two system implementations of different bus widths, with up to 100x higher maximum Lyapunov exponent than the original jerkequation based chaotic systems. The resulting chaotic output is shown to pass the NIST sp. 800-22 statistical test suite for pseudorandom number generators without post-processing by only eliminating the statistically defective bits. The systems are designed in Verilog HDL and experimentally verified on a Xilinx Virtex 4 FPGA for a maximum throughput of 15.59 Gbits/s for the native chaotic output and 8.77 Gbits/s for the resulting pseudo-random number generators.

Dynamics, Circuit Design, and Synchronization of a New Chaotic System with Closed Curve Equilibrium

“…From Figure 8 we can see that the designed circuit displays chaotic signals. The PSpice results also indicate that the circuit can emulate the theoretical model (9). It is necessary to remark that results of circuit simulation depend on the discretization step.…”

“…Combining (6) and (8), it is simple to verify that system (9) has an infinite number of equilibrium points ( * , * , 0). Remarkably, such equilibrium points are described by…”

“…Although chaos has been an object of research since the 1960s, investigating chaotic systems is still a continuing concern within nonlinear dynamics field [1][2][3][4][5][6][7]. A great amount of different chaotic systems has been reported in the literature such as modified Lorenz chaotic system [8], jerk-based chaotic oscillators [9], three-dimensional (3D) system [10], 3D autonomous chaotic system with a single cubic nonlinearity [11], chaotic system with butterfly attractor [12], systems with multiscroll chaotic attractors [13][14][15], or fractional-order chaotic systems [16,17]. Moreover, the past decade has seen the rapid development of chaos-based applications in many areas from hardware pseudorandom number generators [18], autonomous mobile robots [19], MOS oscillators [20], encryption [21], chaotic masking communication [22], to information processing [23].…”

FPGA-based Chaotic Cryptosystem by Using Voice Recognition as Access Key

“…By the same time, a CPRBG algorithm was implemented in an Arduino microcontroller [21], which was based on a pair of Logistic maps and a skewed technique with the XOR binary operation. Likewise and more recently, novel implementations have been developed by using reconfigurable hardware such as Field Programmable Gate Arrays (FPGAs), which provide an excellent balance between the computational power and the processing flexibility [17,[22][23][24][25][26][27][28]. Other FPGA implementations of chaotic systems and maps have been applied to image encryption [29].…”

On the short-term predictability of fully digital chaotic oscillators for pseudo-random number generation

“…Chaos theory is thus considered attractive for many recent applications and especially PRNG implementations due to the high sensitivities within system dynamics [1]- [16]. The digital realizations of the 1D discrete chaotic maps presented in [2], [3] are slow and large due to multiplication and have only one dimensional output.…”