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In developing Really Random Numbers, our focus was to find an observable and measurable event of a process that generates truly random binary data. Our definition of truly random binary data requires:
We believe we located such an event in the digital audio data stream created by the analog to digital converter of a basic PC sound card. The Really Random Numbers software observes, tracks, and stores the results of these specific events as binary data.
We have internally tested the binary data generated by our software using:
H0: Random binary data collected from Really Random Numbers matches all of the criteria listed above (iid, zero covariance, p=.5, etc.)
H1: Not H0.
We have used a variety of tests and have not found any that fail consistently more than the significance level of the test, provided the sound card settings are properly configured.
Really Random Numbers' transformations of binary data into random integers, floating point values, permutations and combinations, etc. are all based on the assumption of being able to generate truly random binary data conforming to the definition above.