True Random Number Generator for a True Hacker

How can you generate random bits? Some people think it’s not easy, others will tell you that it’s pretty damn hard, and then there are those who wonder if it is possible at all. Of course, it is easy to create a very long pseudorandom sequence in software, but even the best PRNG (Pseudorandom Number Generator) needs a good random seed, as we don’t want to get the same sequence each time we switch on the unit, do we? That’s why we need a TRNG (True Random Number Generator), but that requires special hardware.

Some high-end microprocessors are equipped with an internal hardware TRNG, but it is, unfortunately, not true for most low-cost microcontrollers. There are a couple of tricks hackers use to compensate. They usually start the internal free running counter and fetch its contents when some external event occurs (user presses a button, or so). This works, but not without disadvantages. First, there is the danger of “locking” those two events, as a timer period may be some derivative of input scan routine timing. Second, the free running time (between switching on and the moment the unit requests a random number) is often too short, resulting in the seed being too close to the sequence start, and thus predictable. In some cases even, there is no external input before the unit needs a random seed!

Despite what has already been discussed, microcontrollers do have a source of true randomness inside them. While it might not be good enough for crypto applications, it still generates high enough entropy for amusement games, simulations, art gadgets, etc.

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Generating truly random sequences

Your brain can’t generate random numbers, and computers can’t either. Most of the ‘random’ numbers we come across in our lives are actually pseudorandom numbers; random enough for their purpose, but ordered enough to throw statistical analyses for a loop. [Giorgio] thought generating random sequences would make for an excellent project, so he whipped up a random sequence generator out of a few Opamps, resistors, and a handful of caps.

[Giorgio] used a Chua Circuit – a circuit that models nonlinear equations – to create a chaotic system. When pairs of points from these systems of equations are plotted on a graph, a fabulous and chaotic ‘double scroll’ pattern (seen above) can be found. After taking oscilloscope probes to different points on his Chua circuit, [Giorgio] watched chaos magically appear on his ‘oscope screen.

The double scroll pattern isn’t exactly random, but since the Z signal of his circuit chaotically varies between positive and negative, the only thing needed to create a random sequence of 1s and 0s is sending the Z signal through a comparator.

After calibrating and sampling his circuit [Giorgio] captured thousands of samples at a rate of 5 samples per second. From a cursory glance, it looks like [Giorgio]’s circuit is at least as good as flipping a coin, but proper tests for randomness require many more samples.

A very, very cool piece of work that is much, much more elegant than getting random bits from a Geiger counter.