Towards the Perfect Coin Flip: The NIST Randomness Beacon

Since early evening on September 5th, 2013 the US National Institute of Standards and Technology (NIST) has been publishing a 512-bit, full-entropy random number every minute of every day. What’s more, each number is cryptographically signed so that you can easily verify that it was generated by the NIST. A date stamp is included in the process, so that you can tell when the random values were created. And finally, all of the values are linked to the previous value in a chain so that you can detect if any of the past numbers in the series have been altered after the next number is published. This is quite an extensive list of features for a list of random values, and we’ll get into the rationale, methods, and uses behind this scheme in the next section, so stick around.

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Chaos Theory in Practice: Chua’s Circuit

Chua’s circuit is the simplest electronic circuit that produces chaos—the output of this circuit never repeats the same sequence, and is a truly random signal. If you need a good source of randomness, Chua’s circuit is easy to make and is built around standard components that you might have lying around. [Valentine] wrote a comprehensive guide which walks you through the process of building your own source of chaos.

The chaos of Chua’s circuit is derived from several elements, most importantly a nonlinear negative resistor. Unfortunately for us, this type of resistor doesn’t exist in a discrete form, so we have to model it with several other components. This resistor, also known as Chua’s diode, can be created with an op-amp configured as a negative impedance converter and a couple pairs of diodes and resistors. Other variations such, as the schematic above,22`01 model Chua’s diode using only op-amps and resistors.

The rest of the circuit is quite simple: only two capacitors, an inductor, and a resistor are needed. [Valentine] does note that the circuit is quite sensitive, so you might encounter issues when building it on a breadboard. The circuit is very sensitive to vibration (especially on a breadboard), and good solder connections are essential to a reliable circuit. Be sure to check out the Wikipedia article on Chua’s circuit for a brief overview of the circuit’s functionality and a rabbit trail of information on chaos theory.

Dual-mode Avalanche and RF Random Number Generator

[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

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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.

The Most Random Electronic Dice Yet

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If you’ve written a great library to generate random numbers with a microcontroller, what’s the first thing you would do? Build an electronic pair of dice, of course.

[Walter] created the entropy library for AVRs for a reliable source of true random numbers. It works by using the watchdog timer’s natural jitter; not fast by any means but most sources of entropy aren’t that fast anyway. By sampling a whole lot of AVR chips and doing a few statistical tests, it turns out this library is actually a pretty good source of randomness, at least as good as a pair of dice.

The circuit itself uses two 8×8 LED matrices from Adafruit, an Arduino, and a pair of buttons. The supported modes are 2d6, 2d4, 2d8, 2d10, 1d12, 1d20, a deck of cards, a single hex number, a single 8-bit binary number, or an eight character alphanumeric password. It’s more than enough for D&D or when you really need an unguessable password. Video demo below.

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The Two Component Random Number Generator

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[Karl] was in need of a hardware random number generator, but is needs had a few caveats: it needed to be cheap, and sufficiently random. Random number generation can get quite crazy with Geiger tubes, lava lamps, and radioactive decay, but a much smaller solution was found in an 8 pin AVR microcontroller.

The solution uses AVRentropy, a library that uses the watchdog timer’s jitter in AVR microcontrollers to provide cryptographically secure random numbers. Setting up the circuit was easy – an ATtiny45 microcontroller was connected to a cheap chinese USB to serial converter. Three wires, and the circuit is complete. The code was simple as well; it’s just a call to initialize the entropy and write the bits to the serial port.

There are a few drawbacks to this build. Because the entropy library must wait until enough entropy is gathered, it can only produce about two 32-bit numbers per second. That’s all [Karl] needed for his application, though, and with an enclosure made from a wine cork and marble, he has the prettiest and smallest random number generator around.

A hardware random number generator for your FPGA

[Zach] sent in a project he’s been working on that brings hardware random number generators to common hardware you might have lying around. It’s called Whirlyfly and it turns an FPGA dev board into a hardware random number capable of outputting random bits over a USB connection at 3 Mbps.

Previously, the whirlygig ran on a custom CPLD that interfaced to a *nix box and provided high quality random numbers via /dev/hw_random. [Zach]’s efforts takes the core of the whirlygig and ports it to the very popular and inexpensive Papilio One FPGA dev board.

As for what [Zach] can do with his random number generator, it’s extremely easy to write a Monte Carlo experiment to approximate the value of π with a better accuracy than [Ptolemy] was able to muster 1900 years ago. There’s also the aspect of encryption, and – why you would do this we have no idea – making an uncompressable file is also possible.