What Is Entropy And How Do I Get More Of It?

November 2, 2017 by Elliot Williams 55 Comments

Let’s start off with one of my favorite quotes from John von Neumann: “Any one who considers arithmetical methods of producing random digits is, of course, in a state of sin. For, as has been pointed out several times, there is no such thing as a random number — there are only methods to produce random numbers, and a strict arithmetic procedure of course is not such a method.”

What von Neumann is getting at is that the “pseudo” in pseudorandom number generator (PRNG) is really a synonym for “not at all”. Granted, if you come in the middle of a good PRNG sequence, guessing the next number is nearly impossible. But if you know, or can guess, the seed that started the PRNG off, you know all past and future values nearly instantly; it’s a purely deterministic mathematical function. This shouldn’t be taken as a rant against PRNGs, but merely as a reminder that when you use one, the un-guessability of the numbers that it spits out is only as un-guessable as the seed. And while “un-guessability” isn’t a well-defined mathematical concept, or even a real word, entropy is.

That’s why entropy matters to you. Almost anything that your computer wants to keep secret will require the generation of a secret random number at some point, and any series of “random” numbers that a computer generates will have only as much entropy, and thus un-guessability, as the seed used. So how does a computer, a deterministic machine, harvest entropy for that seed in the first place? And how can you make sure you’ve got enough? And did you know that your Raspberry Pi can be turned into a heavy-duty source of entropy? Read on!

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Dual-mode Avalanche And RF Random Number Generator

October 31, 2014 by Ethan Zonca 28 Comments

[Paul] designed a new open-hardware RNG (random number generator) that includes two sources of entropy in a small package. The first source of entropy is a typical avalanche diode circuit, which is formed by a pair of transistors. This circuit creates high-speed random pulses which are sampled by the onboard microcontroller.

What makes this design unique is a second entropy source: a CC2531 RF receiver. The RF receiver continuously skips around channels in the 2.5Ghz band and measures the RF signal level. The least-significant bit of the signal level is captured and used as a source of entropy. The firmware can be configured to use either source of entropy individually, or to combine both. The firmware also supports optionally whitening the entropy byte stream, which evens out the number of 1’s and 0’s without reducing entropy.

The OneRNG uses the USB-CDC profile, so it shows up as a virtual serial port in most modern operating systems. With the rngd daemon and a bit of configuration, the OneRNG can feed the system entropy source in Linux. [Paul] also has a good writeup about the theory behind the entropy generator which includes images of his schematic. Firmware, drivers, and hardware design files are open-source and are available for download.

The Development Of A Hardware Random Number Generator

June 8, 2014 by Brian Benchoff 22 Comments

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[Ian] had a need for a lot of random numbers. There are dozens of commercial offerings when it comes to RNGs, but there are also hundreds of different ways for an electronics hobbyist to shoot random bits at a serial port. One of these methods is an RNG based on the avalanche breakdown noise in a PN junction. As with any circuit in hobbyist electronics, there are dozens of prototypes floating out there on the web, but not too many finished projects. [Ian] decided he would build one of these RNGs as a prototype and bring it to something resembling a finished project.

An avalanche noise RNG takes advantage of the fact that a strongly reverse-biased PN junction, like one found in a transistor, will create a condition where one electron knocks another electron out of place, leading to a sustained chain reaction. It’s quantum, it’s chaotic, it makes for a great source for a random number generator, and there are already dozens of prototype circuits around the Internet.

[Ian] took one of these circuit designs by [Will Ware] and started the iterations that would lead to a finished design. Round one was a simple PCB with the basic circuit and a power supply. Just a few transistors, resistors, and a DC/DC boost converter. Confirming the circuit was generating noise, the next iteration brought in an ADC and an ARM micro with a USB interface. Iterating over this again with an improved ADC – 20 megasamples per second – the design finally reached a point where a final PCB could be designed.

In the end, [Ian] turned a simple circuit that could have been built on a breadboard into a USB device that throws 9kB/s of random data into a computer. The data are actually good, too: the project passed most of the Dieharder test suite, making it very useful for whatever crypto or gaming application [Ian] has in mind.

Improved Hourglass Entropy

January 25, 2013 by Mike Szczys 16 Comments

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[Wardy] built himself a high quality entropy source with parts he had lying around. It’s based on the hourglass entropy project we saw in a links post earlier this month. Just like that project, he is bouncing a laser off of the falling sand and reading the result. But he brings a few innovations to the party, and has test results to back up his work.

The first change is an obvious one; motorize the hourglass so that you don’t need to flip it by hand. We thought this might mess with the laser alignment but the clip after the break proved us wrong. He changed up the sensor, using an LED connected to the base of an NPN transistor. The next change was to mount the light sensor at an angle to the laser rather than straight on. This picks up reflections of the laser and not the direct beam itself, resulting in a wider range of readings.

He used an Ethernet shield to get the system on the network. It’s pushing 420k random numbers per second and was tested with the DieHarder suite. It didn’t get a very high score, but it did pass the test.

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