hello, I would like to discuss with you your project about a quantum random number generator, to be honest, I don’t understand why one thing is written on the diagram and a little different in the photo, for example, 2 diodes were used there although they were not in the diagram at all. Or a variable resistor that is located next to americium. I would be glad if you answer the questions or at least respond to the message

Hello, sorry for the long silence! I was experimenting with diodes as a way to create a tiny bias voltage for the amplifier, but that turned out to be unnecessary, if I remember correctly. As mentioned in the description, it took me quite a while to figure out how to get the signal out reliably. I will post the full schematic once I have assembled everything in the final housing and am sure that it actually works like that.

Many years ago, I did something similar with a zener diode. At very low currents (microamps), a zener diode can be induced into avalanche breakdown, at about the same voltage. The avalanche current is highly random. I used a coupling capacitor and a CMOS hex inverter with feedback to make a linear amplifier, and I could get a highly random voltage between Vcc and Vdd, which was then digitized.

I don't recall doing a lot of testing, other than a simple plot that showed it was much better than the Linear-Congruential random number generators of the day.

Did you write about this somewhere? Years ago I built what sounds like the very same thing and I’m wondering if I learned about it from you.

I think I may have put something on Usenet at the time, but it's been lost in the dustbin of many employer/computer changes over the years.

That sounds pretty cool. I guess you can adjust the average break down rate by adjusting the current? Would probably make for a more practical RNG that what I am planning. XD

I've tried something similar, but with a tunnel diode. The plan was to bias it to a steady state, about mid-way into the <negative resistance> region, then just amplify the noise. Doing this needs similar care to the current project as very high gain is required.

Couldn't tell you if the result was any more random than using a zener, which as you point out is much easier!

The time between independent individual detected pairs of Americium decay events is completely random. All that can be said is that during the half-life of a mass of radioactive material, any individual atom will have a 50% chance of decaying. The ionization current is an average of millions of decay events. Variations in current are likely caused by convection in the chamber or thermal effects. Quantum effects suggest the current variations are NOT random. Detection of individual events  by a GM tube and comparing the time interval between pairs of detected counts is a far better way of generating random numbers from radioactive decay.  

https://www.fourmilab.ch/hotbits/ 

I have an operational Americium system and random number server at :

https://projectmf.org/hotbits/ 

Random verification is run continuously on a 10% sample of all random numbers generated. Generated bit rate is only 66-68 bytes/second though.

Okay, so there are at least two americium random number generator hobbyists. Anyone you know who is even more into it? 

John Walker at https://www.fourmilab.ch/hotbits/how3.html has been running his Cesium-137 random number generator since 1986, so I would count him as a serious enthusiast. He figured out a scheme to use simple time intervals between pairs of Geiger tube counts to eliminate statistical bias and produce an excellent source of random numbers while eliminating variables such as radiation flux density, tube to source geometries, etc. as factors. I think this ionization chamber approach has promise as well.  It seems the number generation rate would be slower than detecting individual events, though.  Still, a very cool idea!

Originally I tried to resolve single ionisation events with the ion chamber, but was not able to. So I settled for the average current variations. It is true that I would get more randomness if I looked at the single decays, but it is not true that the average current is not random according to quantum physics. The number of decays in a given time is Poisson distributed. Since the conductivity should be proportional to the number of ions in the chamber, the conductivity should also vary similar to a Poisson distribution on the right time scales (i.e. time scales longer than the time it takes for ions to drift to the electrode).

You are right, that the relative variation goes down as the average number of decays increases, but I am not dealing with millions of events here. The activity of my Americium sample is less than 30 kBq (according to the print on the chamber), and only half of that should be emitted into the ion chamber. Also I am looking at this at time scales of ~0.1 s, so overall I am dealing with an average of at most ~1000 events. This would mean a current variation of ~3%. Less than what I see, but not a huge deal off.

That is not to say that I am certain right now, that I actually am collecting the true quantum randomness of the decays. It could be partially or even mostly something else. I will try to investigate this a bit more in detail at some point.

As for the bit rate, in some tests I was able to get in the order of 1-10 bits/second. This is not going to be a fast RNG. XD

Thank you for the explanation. I do agree that, provided the measurement window is small and the count rate not too high, the Poisson distribution should give sufficient variability to detect. 

Smoke detectors have a dual-chamber design. One chamber is exposed to the atmosphere but unvented to prevent smoke from entering. It is used as a reference chamber to eliminate variability due to humidity and atmospheric pressure changes. Another chamber is vented to outside air to allow smoke variation.

The Darlington current amplifier seems connected only to one of the two chambers. Smoke detector chips use a differential op amp in conjunction with the reference chamber to eliminate spurious current fluctuations. It appears that you are using only one of the two chambers and not compensating for pressure or humidity. It seems this might introduce a significant non-random variation into the system.

Interesting idea!!!!

I have in fact experimented a bit with the different possible combinations of which contacts of the ion chamber to connect to 9V or the preamp input. It does not make that much of a difference actually. But the setup I have at the moment has the body and the central ring connected to 9V and the Am-electrode to the preamp. Another configuration that works similarly well is having the central ring as the preamp input and the body and lower electrode on 9V. In any case the aim is to use as much of the ionised volume as possible. I might go back to the "central cathode" configuration since at least in theory it should reduce the drift time of the ions due to larger fields and shorter drift distances. And shorter drift times mean less current averaging over time.

1) What is the cutoff frequency of your RC filter? 

2) How do you separate the 1/f flicker noise generated by the darlington transistors from your quantum noise?

3) Using a schmitt trigger adds hysteresis to the comparator which might introduce bias to the randomness.

4) Have you tried recording your number stream and performing some basic randomness testing? 

5) Any idea what the probability density function is for an alpha emitter?

1) The one for the oscilloscope measurement? C=47 uF, R=1 MOhm, so tau=47 seconds. I also have a low-pass filter in there after the preamp. It has a cut-off frequency of 33 Hz.

2) So far, I don't. Without the ion source, the signal is 0, so that's something. At the end I at least want to check whether it is plausible that the randomness I see is actually caused by variations in the conductivity. But I don't think I will be able to prove that it is just that and not some other source of noise.

3) Yeah, I have a reference voltage generator circuit that should automatically adjust to get a long-term duty cycle of 50/50. But a small bias will remain.

4) I have. The raw output is not actually that good (because of the remaining bias towards either 0 or 1), but there are ways to turn a slightly biased bi stream into an unbiased one, e.g. http://www.eecs.harvard.edu/~michaelm/coinflipext.pdf

After a bit of processing, I got a bit stream that passed most of the NIST tests: https://nvlpubs.nist.gov/nistpubs/Legacy/SP/nistspecialpublication800-22r1a.pdf

I will re-visit this when I actually have the hardware finished.

5) The number of decays in a given time interval should be Poisson distributed. Starting from there I will probably try to deduce a distribution of ionisation charge, i.e. current integrated over fixed time windows. Might be enough to check whether it is at least plausible that the variations I see come from the radioactive decay itself.

The 33Hz high pass filter is likely blocking any 1/f flicker noise from the electronics. 

It's a _low_-pass filter. It is intended to get rid of any remaining 50 Hz noise while letting the slower current variations through.

Wouldn't a sealed chamber be less vulnerable to tampering? If yes i am wondering if it's possible for the typical consumer to buy such part?

You mean a sealed ion chamber? In the end it will all be container in a metal case, so I don't think it will matter much. And of course you are free to put as much EM shielding around the ion chamber in whatever place you like. Unless I misunderstand which kind of tampering you refer to.

I was thinking about introducing highly ionized air :)

Introducing ionised air would mess with things just like blowing smoke into it (see other comments below), just in the opposite direction. I have not really thought about malicious attacks like this. The best protection against this kinda thing is probably putting this somewhere where black hats cannot reach it. XD

Does introducing smoke affect the entropy?

Smoke should reduce the overall conductivity of the ion chamber. That's how these smoke detectors work. Depending on how much the conductivity drops, the signal might become too low for my circuit to use it. But even before that, if the conductivity suddenly drops, the output signal will drop below the reference voltage and thus the output will be pulled to a constant value for a while. The reference voltage will adjust automatically to get back to a 50/50 ratio of 1s and 0s at the output, but that process is deliberately slow to allow for long runs of the same value. So yeah, blowing smoke into this will mess with the randomness of the output.

The randomness of the radioactive decay (and thus the randomness of the conductivity variation itself) should not be affected.

There a very simple Windows command line program here:

https://www.fourmilab.ch/random/

...to test the random quality of a data set. Fast and easy way to test the generated data.

Ent is great, but it by no means guarantees that your random sequence is actually random. I am using a test suite published by NIST to check for the quality of the final bitstream (after some processing to get rid of biases in the raw bitstream): https://nvlpubs.nist.gov/nistpubs/Legacy/SP/nistspecialpublication800-22r1a.pdf