Generation of n-scroll chaos using nonlinear transconductors

Microelectronics Journal

Barakat

et al. 2013

Self Cite

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.

Section: Introductionmentioning

confidence: 99%

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

Mansingka

Microelectronics Journal

Barakat

et al. 2013

Self Cite

“…In particular, multi-scroll chaos is well understood [9]- [14] and has been realized through analog circuits [13], [15] but the limited dynamic range of analog components and low supply voltages has restricted the number of scrolls that can be realized [16] unless mixed-signal approaches are used [17]. Digital design enables reliable and fully digital chaotic oscillators [14], [18] for direct application in digital systems.…”

Section: Introductionmentioning

confidence: 99%

Secure DS-CDMA spreading codes using fully digital multidimensional multiscroll chaos

Mansingka

2013 IEEE 56th International Midwest Symposium on Circuits and Systems (MWSCAS)

Radwan

et al. 2013

Abstract-This paper introduces a generalized fully digital hardware implementation of 1-D, 2-D and 3-D multiscroll chaos through sawtooth nonlinearities in a 3rd order ODE with the Euler approximation, wherein low-significance bits pass all NIST SP. 800-22 tests. The low-significance bits show good performance as spreading code for multiple-access DS-CDMA in AWGN and multipath environments, equivalent to Gold codes. This system capitalizes on complex nonlinear dynamics afforded by multiscroll chaos to provide higher security than conventional codes with the same BER performance demonstrated experimentally on a Xilinx Virtex 4 FPGA with logic utilization less than 1.25% and throughput up to 10.92 Gbits/s.

“…In addition, multi-scrolls attractors are proven to have better properties, like having higher entropy for random number generation, compared to normal attractors [Yalcin, 2007]. The implementation of these generators ranges from using discrete elements and operational amplifiers Elwakil & Kennedy, 2001;Salama et al, 2003], completely MOS based [Radwan et al, 2004;Tavas et al, 2010],to fully integrated [Elwakil et al, 2002b]. Hybrid analog/digital implementation was introduced in [Radwan et al, 2007].…”

Section: Introductionmentioning

confidence: 99%

Controllable v-Shape Multiscroll Butterfly Attractor: System and Circuit Implementation

Int. J. Bifurcation Chaos

Radwan

Salama

2012

In this paper, a new controllable V-shape multiscroll attractor is presented, where a variety of symmetrical and unsymmetrical attractors with a variable number of scrolls can be controlled using new staircase nonlinear function and the parameters of the system. This attractor can be used to generate random signals with a variety of symbol distribution. Digital implementation of the proposed generator is also presented using a Xilinx Virtex® 4 Field Programmable Gate Array and experimental results are provided. The digital realization easily fits into a small area (<1.5% of the total area) and expresses a high throughput (4.3 Gbit/sec per state variable).