Method and apparatus for generating secure random numbers using chaos
First Claim
1. A method for generating a random number from a circuit, said circuit exhibiting a positive Lyaponov exponent and characterizable by an invariant probability distribution, said method comprising:
- operating said circuit with said positive Lyapunov exponent such that operation is chaotic; and
after an interval, extracting a value of a state of said circuit at selected intervals as a random number sequence, said intervals selected to have a specified degree of uncertainty.
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Abstract
Information-theoretic notions are employed to establish the predictability of a random number generated from a circuit exhibiting chaos in order to obtain a number from a sequence of numbers with a known level of randomness and security. The method provides a measure of information loss whereby one may select the number of iterations before or between bit sampling in order to extract a secure pseudo-random number. A chaotic output is obtained by use of a sample and hold circuit coupled in a feedback loop to a variable frequency oscillator, such as a voltage controlled oscillator circuit, and operated with a positive Lyapunov exponent. A source signal generator, such as a periodic wave generator, provides a driving signal to the sample and hold circuit.
252 Citations
15 Claims
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1. A method for generating a random number from a circuit, said circuit exhibiting a positive Lyaponov exponent and characterizable by an invariant probability distribution, said method comprising:
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operating said circuit with said positive Lyapunov exponent such that operation is chaotic; and after an interval, extracting a value of a state of said circuit at selected intervals as a random number sequence, said intervals selected to have a specified degree of uncertainty. - View Dependent Claims (2, 3, 4, 5)
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6. A method for generating a random number from a deterministic circuit, said deterministic circuit comprising a signal source means for producing a source signal, first sampling means having a sample control input and a signal input coupled to said periodic signal source means, variable frequency oscillator means coupled to receive a representations of a sampled output of said first sampling means for generating a binary-valued signal having a frequency and phase state φ
- derived from said sampled output, and feedback means for feeding back in a feedback loop said binary-valued signal to control said sample control input of said first sampling means, said method comprising;
operating said deterministic circuit with a positive Lyapunov exponent such that operation is chaotic; iteratively sampling said periodic source signal at sample times determined by level of said binary-valued signal; and after an interval, extracting a binary value of a signal in said feedback loop at intervals as a random number sequence having a specified degree of uncertainty. - View Dependent Claims (7, 8, 9, 10, 11, 12, 13, 14)
- derived from said sampled output, and feedback means for feeding back in a feedback loop said binary-valued signal to control said sample control input of said first sampling means, said method comprising;
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15. An apparatus for generating a random number from a deterministic circuit comprising:
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periodic signal source means for producing a periodic source signal; first sampling means having a sample control input and a signal input coupled to said periodic signal source means; variable frequency oscillator means coupled to receive a representation of a sampled output of said first sampling means for generating a binary-valued signal having a frequency and phase state φ
derived from said sampled output;feedback means for feeding back in a feedback loop said binary-valued signal to control said sample control input of said first sampling means; means for constraining operation of said deterministic circuit with a positive Lyapunov exponent through sampling said periodic source signal at sample times determined by level of said binary-valued signal such that operation is chaotic; and means coupled to a node in said feedback loop for extracting a binary value of a signal in said feedback loop after an interval, in order to form a random number sequence having a preselected degree of uncertainty.
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Specification