3 ms·

Doesn't the time between events increase over time as there are fewer radioactive atoms left to decay? So E[T1] < E[T2] and you get slightly more 0 bits than 1s

Doesn't the time between events increase over time as there are fewer radioactive atoms left to decay? So E[T1] < E[T2] and you get slightly more 0 bits than 1s. I'm sure the device is on a scale where this effect is tiny, but the description sounds like the creator is aiming for absolute theoretical correctness rather than "good enough" randomness which is not so hard to come by.

shagie 4y ago
If you've got a mole of cesium (137 grams), that's 10^23 atoms. The difference between 10^23 and (10^23) - 1 would be lost in the clock resolution of the computer it is hooked up to. The statistical tests of randomness are described at https://www.fourmilab.ch/hotbits/statistical_testing/stattest.html https://www.fourmilab.ch/hotbits/statistical_testing/stattes... from ent ( https://www.fourmilab.ch/random/ https://www.fourmilab.ch/random/ ) Entropy = 7.999975 bits per byte. Optimum compression would reduce the size of this 11468800 byte file by 0 percent. Chi square distribution for 11468800 samples is 402.53, and randomly would exceed this value 0.01 percent of the times. Arithmetic mean value of data bytes is 127.5423 (127.5 = random). Monte Carlo value for Pi is 3.141486168 (error 0.00 percent). Serial correlation coefficient is -0.000053 (totally uncorrelated = 0.0). I'd be impressed to find any other data source that is more random than hotbits (autocorrect keeps wanting to make this hobbits). ---- (late edit) https://www.fourmilab.ch/hotbits/how3.html https://www.fourmilab.ch/hotbits/how3.html specifically addresses this though: > For example, you might worry about the fact that the intensity of the radiation source is slowly decreasing over time. Cæsium-137's 30.17 year half-life isn't all that long. One half-life in the future, we'll measure T1 and T2 intervals, on the average, twice as long as today. This means, then, that even on consecutive measurements there is a small bias in favour of T2 being longer than T1. How serious is this? Well, expressed in seconds, the half-life is about 9.5×108 and we receive count pulses at a rate of 1000 per second or so. So the time needed to perform the measurements to produce one random bit is on the order of 10−12 half-lives, and T2 will then tend to be longer by a factor of the same magnitude. Since the inter-count interval is around a millisecond, this means T2 will be, on average, 10−15 seconds longer than T1. This is comparable to the long-term accuracy of the best atomic time standards and is entirely negligible for our purposes. The crystal oscillator which provides the time base for the computer making the measurement is only accurate to 100 parts per million, or one part in ten thousand, and thus can induce errors ten million times as large as those due to the slow decay of the source. (This is, again, unlikely to be a real problem because most computer clocks, while prone to drifting as temperature and supply voltage vary, do not change significantly on the millisecond scale. Still, jitter due to where the clock generator happens to trigger on the oscillator waveform will still dwarf the effects of decay of the source during one measurement.)
- dmurray 4y ago
  Great analysis, but the argument at the end still seems wrong. The methodology has been carefully designed so that the clock jitter only adds random noise, not a directional bias. Even if the oscillator consistently runs fast by triggering 90 ppm early, it doesn't predictably increase the probability of a 0 or 1 bit. I suppose you could get more randomness using von Neumann's method for a biased coin - either waiting for multiple time periods, or with multiple decay sources in parallel. Or XOR the bits with a shitty but cheap source of randomness. But it's more valuable to be able to put an upper bound on your bias is - here, something like 10^-12 - and ensure that's acceptable for your application.

shagie 4y ago

If you've got a mole of cesium (137 grams), that's 10^23 atoms. The difference between 10^23 and (10^23) - 1 would be lost in the clock resolution of the computer it is hooked up to. The statistical tests of randomness are described at https://www.fourmilab.ch/hotbits/statistical_testing/stattest.html https://www.fourmilab.ch/hotbits/statistical_testing/stattes... from ent ( https://www.fourmilab.ch/random/ https://www.fourmilab.ch/random/ ) Entropy = 7.999975 bits per byte. Optimum compression would reduce the size of this 11468800 byte file by 0 percent. Chi square distribution for 11468800 samples is 402.53, and randomly would exceed this value 0.01 percent of the times. Arithmetic mean value of data bytes is 127.5423 (127.5 = random). Monte Carlo value for Pi is 3.141486168 (error 0.00 percent). Serial correlation coefficient is -0.000053 (totally uncorrelated = 0.0). I'd be impressed to find any other data source that is more random than hotbits (autocorrect keeps wanting to make this hobbits). ---- (late edit) https://www.fourmilab.ch/hotbits/how3.html https://www.fourmilab.ch/hotbits/how3.html specifically addresses this though: > For example, you might worry about the fact that the intensity of the radiation source is slowly decreasing over time. Cæsium-137's 30.17 year half-life isn't all that long. One half-life in the future, we'll measure T1 and T2 intervals, on the average, twice as long as today. This means, then, that even on consecutive measurements there is a small bias in favour of T2 being longer than T1. How serious is this? Well, expressed in seconds, the half-life is about 9.5×108 and we receive count pulses at a rate of 1000 per second or so. So the time needed to perform the measurements to produce one random bit is on the order of 10−12 half-lives, and T2 will then tend to be longer by a factor of the same magnitude. Since the inter-count interval is around a millisecond, this means T2 will be, on average, 10−15 seconds longer than T1. This is comparable to the long-term accuracy of the best atomic time standards and is entirely negligible for our purposes. The crystal oscillator which provides the time base for the computer making the measurement is only accurate to 100 parts per million, or one part in ten thousand, and thus can induce errors ten million times as large as those due to the slow decay of the source. (This is, again, unlikely to be a real problem because most computer clocks, while prone to drifting as temperature and supply voltage vary, do not change significantly on the millisecond scale. Still, jitter due to where the clock generator happens to trigger on the oscillator waveform will still dwarf the effects of decay of the source during one measurement.)

dmurray 4y ago
Great analysis, but the argument at the end still seems wrong. The methodology has been carefully designed so that the clock jitter only adds random noise, not a directional bias. Even if the oscillator consistently runs fast by triggering 90 ppm early, it doesn't predictably increase the probability of a 0 or 1 bit. I suppose you could get more randomness using von Neumann's method for a biased coin - either waiting for multiple time periods, or with multiple decay sources in parallel. Or XOR the bits with a shitty but cheap source of randomness. But it's more valuable to be able to put an upper bound on your bias is - here, something like 10^-12 - and ensure that's acceptable for your application.