Fully digital chaotic differential equation-based systems and methods
First Claim
1. A digital circuit, comprising:
- three digital state registers; and
three digital logic modules coupled to the three digital state registers, each of the three digital logic modules configured to;
obtain a plurality of first values from two or more digital state registers of the three digital state registers, where a first digital logic module of the three digital logic modules obtains two first values of the plurality of first values from two of the three digital state registers, where a second digital logic module of the three digital logic modules obtains two first values of the plurality of first values from two of the three digital state registers, and where a third digital logic module of the three digital logic modules obtains three first values of the plurality of first values from the three digital state registers;
determine a corresponding second value based upon the two or three first values obtained by that digital logic module and a chaotic differential equation; and
provide the corresponding second value as a respective input to set a state of a corresponding one of the three digital state registers;
where the three digital logic modules are configured to determine the corresponding second values according to a Runge-Kutta Fourth-order numerical solution, a mid-point numerical solution, or an Euler numerical solution to the chaotic differential equation.
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Abstract
Various embodiments are provided for fully digital chaotic differential equation-based systems and methods. In one embodiment, among others, a digital circuit includes digital state registers and one or more digital logic modules configured to obtain a first value from two or more of the digital state registers; determine a second value based upon the obtained first values and a chaotic differential equation; and provide the second value to set a state of one of the plurality of digital state registers. In another embodiment, a digital circuit includes digital state registers, digital logic modules configured to obtain outputs from a subset of the digital shift registers and to provide the input based upon a chaotic differential equation for setting a state of at least one of the subset of digital shift registers, and a digital clock configured to provide a clock signal for operating the digital shift registers.
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Citations
31 Claims
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1. A digital circuit, comprising:
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three digital state registers; and three digital logic modules coupled to the three digital state registers, each of the three digital logic modules configured to; obtain a plurality of first values from two or more digital state registers of the three digital state registers, where a first digital logic module of the three digital logic modules obtains two first values of the plurality of first values from two of the three digital state registers, where a second digital logic module of the three digital logic modules obtains two first values of the plurality of first values from two of the three digital state registers, and where a third digital logic module of the three digital logic modules obtains three first values of the plurality of first values from the three digital state registers; determine a corresponding second value based upon the two or three first values obtained by that digital logic module and a chaotic differential equation; and provide the corresponding second value as a respective input to set a state of a corresponding one of the three digital state registers; where the three digital logic modules are configured to determine the corresponding second values according to a Runge-Kutta Fourth-order numerical solution, a mid-point numerical solution, or an Euler numerical solution to the chaotic differential equation. - View Dependent Claims (2, 3, 4, 5)
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6. A digital circuit, comprising:
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three digital state registers; and three digital logic modules coupled to the three digital state registers, each of the three digital logic modules configured to; obtain a plurality of first values from two or more digital state registers of the three digital state registers, where a first digital logic module of the three digital logic modules obtains two first values of the plurality of first values from two of the three digital state registers, where a second digital logic module of the three digital logic modules obtains two first values of the plurality of first values from two of the three digital state registers, and where a third digital logic module of the three digital logic modules obtains three first values of the plurality of first values from the three digital state registers; determine a corresponding second value based upon the two or three first values obtained by that digital logic module and a chaotic differential equation, where the chaotic differential equation is a nonlinear jerk equation; and provide the corresponding second value as a respective input to set a state of a corresponding one of the three digital state registers, where the corresponding second value determined by one of the three digital logic modules comprises a linear component provided to set the state of one of the two or more digital state registers and a nonlinear component provided to set a state of a fourth digital state register. - View Dependent Claims (7, 8, 9)
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10. A digital circuit, comprising:
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three digital state registers; and three digital logic modules coupled to the three digital state registers, each of the three digital logic modules configured to; obtain a plurality of first values from two or more digital state registers of the three digital state registers, where a first digital logic module of the three digital logic modules obtains two first values of the plurality of first values from two of the three digital state registers, where a second digital logic module of the three digital logic modules obtains two first values of the plurality of first values from two of the three digital state registers, and where a third digital logic module of the three digital logic modules obtains three first values of the plurality of first values from the three digital state registers; determine a corresponding second value based upon the two or three first values obtained by that digital logic module and a chaotic differential equation, where the three digital logic modules are configured to determine the corresponding second values using shift operations without multiplication operations, where all coefficients of the chaotic differential equation are a power of two; and provide the corresponding second value as a respective input to set a state of a corresponding one of the three digital state registers. - View Dependent Claims (11, 12, 13, 14, 15, 16)
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17. A digital circuit, comprising:
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a plurality of digital shift registers, each of the plurality of digital shift registers configured to obtain an input and provide an output; a plurality of digital logic modules coupled to the plurality of digital shift registers, where the plurality of digital logic modules do not include multipliers, each of the plurality of digital logic modules configured to; obtain outputs from a subset of two or more of the plurality of digital shift registers, where a first digital logic module of the plurality of digital logic modules obtains a first output from two of the plurality of digital shift registers, where a second digital logic module of the plurality of digital logic modules obtains a second output from two of the plurality of digital shift registers, and where a third digital logic module of the plurality of digital logic modules obtains a third output from three of the plurality of digital shift registers; and provide the input for setting a state of at least one of the subset of two or more of the plurality of digital shift registers, the plurality of digital logic modules each configured to provide the input according to a portion of a numeric solution to a chaotic differential equation, the numeric solution based upon the outputs obtained by that digital logic module; and a digital clock configured to provide a digital clock signal for operating the plurality of digital shift registers. - View Dependent Claims (18, 19, 20, 21, 22, 23, 24, 25)
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26. A method, comprising:
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receiving a clock signal having a first clock state and a second clock state; obtaining, by each of a plurality of at least three digital logic modules, first values from a subset of a plurality of digital state registers when the clock signal enters the first clock state, where a first one of the plurality of at least three digital logic modules obtains two first values from two of the plurality of digital state registers, where a second one of the plurality of at least three digital logic modules obtains two first values from two of the plurality of digital state registers, and where at least a third one of the plurality of at least three digital logic modules obtains at least three first values from at least three of the plurality of digital state registers; transforming the first values in each of the plurality of at least three digital logic modules into a corresponding second value based upon a numerical solution to one or more chaotic differential equations, where the one or more chaotic differential equations corresponds to a multi-scroll butterfly attractor; writing the corresponding second values into a corresponding one of the plurality of digital state registers when the clock signal enters the second clock state; and providing a control signal to adjust parameters of the chaotic differential equations to modify the multi-scroll butterfly attractor. - View Dependent Claims (27, 28, 29, 30, 31)
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Specification