Method and apparatus for generating secure random numbers using chaos

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 .phi. 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.

An apparatus for generating a random number from a deterministic circuit comprising:

• 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 .phi. 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.