Fully Digital Chaotic Oscillators Applied to Pseudo Random Number Generation

Handle URI:
http://hdl.handle.net/10754/224712
Title:
Fully Digital Chaotic Oscillators Applied to Pseudo Random Number Generation
Authors:
Mansingka, Abhinav S.
Abstract:
This thesis presents a generalized approach for the fully digital design and implementation of chaos generators through the numerical solution of chaotic ordinary differential equations. In particular, implementations use the Euler approximation with a fixed-point twos complement number representation system for optimal hardware and performance. In general, digital design enables significant benefits in terms of power, area, throughput, reliability, repeatability and portability over analog implementations of chaos due to lower process, voltage and temperature sensitivities and easy compatibility with other digital systems such as microprocessors, digital signal processing units, communication systems and encryption systems. Furthermore, this thesis introduces the idea of implementing multidimensional chaotic systems rather than 1-D chaotic maps to enable wider throughputs and multiplier-free architectures that provide significant performance and area benefits. This work focuses efforts on the well-understood family of autonomous 3rd order "jerk" chaotic systems. The effect of implementation precision, internal delay cycles and external delay cycles on the chaotic response are assessed. Multiplexing of parameters is implemented to enable switching between chaotic and periodic modes of operation. Enhanced chaos generators that exploit long-term divergence in two identical systems of different precision are also explored. Digital design is shown to enable real-time controllability of 1D multiscroll systems and 4th order hyperchaotic systems, essentially creating non-autonomous chaos that has thus far been difficult to implement in the analog domain. Seven different systems are mathematically assessed for chaotic properties, implemented at the register transfer level in Verilog HDL and experimentally verified on a Xilinx Virtex 4 FPGA. The statistical properties of the output are rigorously studied using the NIST SP. 800-22 statistical testing suite. The output is adapted for pseudo random number generation by truncating statistically defective bits. Finally, a novel post-processing technique using the Fibonacci series is proposed and implemented with a non-autonomous driven hyperchaotic system to provide pseudo random number generators with high nonlinear complexity and controllable period length that enables full utilization of all branches of the chaotic output as statistically secure pseudo random output.
Advisors:
Salama, Khaled Nabil
Committee Member:
Alouini, Mohamed-Slim ( 0000-0003-4827-1793 ) ; Fahmy, Hossam A.H.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Program:
Electrical Engineering
Issue Date:
May-2012
Type:
Thesis
Appears in Collections:
Theses; Electrical Engineering Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.advisorSalama, Khaled Nabilen
dc.contributor.authorMansingka, Abhinav S.en
dc.date.accessioned2012-05-19T09:50:27Z-
dc.date.available2012-05-19T09:50:27Z-
dc.date.issued2012-05en
dc.identifier.urihttp://hdl.handle.net/10754/224712en
dc.description.abstractThis thesis presents a generalized approach for the fully digital design and implementation of chaos generators through the numerical solution of chaotic ordinary differential equations. In particular, implementations use the Euler approximation with a fixed-point twos complement number representation system for optimal hardware and performance. In general, digital design enables significant benefits in terms of power, area, throughput, reliability, repeatability and portability over analog implementations of chaos due to lower process, voltage and temperature sensitivities and easy compatibility with other digital systems such as microprocessors, digital signal processing units, communication systems and encryption systems. Furthermore, this thesis introduces the idea of implementing multidimensional chaotic systems rather than 1-D chaotic maps to enable wider throughputs and multiplier-free architectures that provide significant performance and area benefits. This work focuses efforts on the well-understood family of autonomous 3rd order "jerk" chaotic systems. The effect of implementation precision, internal delay cycles and external delay cycles on the chaotic response are assessed. Multiplexing of parameters is implemented to enable switching between chaotic and periodic modes of operation. Enhanced chaos generators that exploit long-term divergence in two identical systems of different precision are also explored. Digital design is shown to enable real-time controllability of 1D multiscroll systems and 4th order hyperchaotic systems, essentially creating non-autonomous chaos that has thus far been difficult to implement in the analog domain. Seven different systems are mathematically assessed for chaotic properties, implemented at the register transfer level in Verilog HDL and experimentally verified on a Xilinx Virtex 4 FPGA. The statistical properties of the output are rigorously studied using the NIST SP. 800-22 statistical testing suite. The output is adapted for pseudo random number generation by truncating statistically defective bits. Finally, a novel post-processing technique using the Fibonacci series is proposed and implemented with a non-autonomous driven hyperchaotic system to provide pseudo random number generators with high nonlinear complexity and controllable period length that enables full utilization of all branches of the chaotic output as statistically secure pseudo random output.en
dc.language.isoenen
dc.subjectChaosen
dc.subjectRandom Number Generationen
dc.subjectNISTen
dc.subjectnonlinear dynamicsen
dc.subjectdigital circuiten
dc.subjectfield programmable gate arrayen
dc.titleFully Digital Chaotic Oscillators Applied to Pseudo Random Number Generationen
dc.typeThesisen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
thesis.degree.grantorKing Abdullah University of Science and Technologyen_GB
dc.contributor.committeememberAlouini, Mohamed-Slimen
dc.contributor.committeememberFahmy, Hossam A.H.en
thesis.degree.disciplineElectrical Engineeringen
thesis.degree.nameMaster of Scienceen
dc.person.id113166en
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