##Infinite Noise Multiplier
The Infinite Noise Multiplier is an architecture for true random number generators (TRNG). Besides being simple, low-cost, and fast, it is easy to get right, unlike other TRNGs.
The Problem: Noise Sensitivity, and Signal Injection
True random number generators are very difficult to get right. Generally, they amplify a tiny noise signal, perhaps only a microvolt in amplitude, by a factor of millions or billions, until the signal is an unpredictable digital signal. This signal is then sampled to see if it's a 0 or 1.
The problem with this aproach is the weak noise source can easily be overridden by other nearby signals, which may be under the control of an attacker. Power supply noise can cause zener diodes to avalanche with predictable timing. Thermal noise can be overridden by nearby radio sources, such as EMI from a CPU. Oscillator drift can be controlled through syncrhonous power-supply noise. Jitter can be controlled through cross-talk and power rail droop. On ICs, substrate currents can override thermal noise. Cross talk strong enough to override these tiny sources of noise can be introduced through radio waves, inductive coupling, capacitive coupling, or even "microphonics", due to physical vibrations in the system. These circuits are sometimes even light sensitive.
Systems built with massive amplification of tiny noise sources often require power supply filters, EMI shielding, and even light shielding, and even then remain difficult to prove secure. Such systems can be difficult to audit, because their signal traces are inaccessible behind layers of shields.
Intel's RDRAND instruction is a perfect example. It uses massive amplification of thermal noise to determine the power-up state of a latch. Unfortunately, this source of entropy is highly power-supply, cross-talk, and substrate current sensitive. Intel claims to have carefully shielded their thermal noise source, but without a thorough pubic audit of both the design and layout, including all potential sources of interference, it is not possible to trust the RDRAND instruction as the source of entropy for cryptography.
With such strong sensitivity, these TRNG architectures are potential targets for signal injection by an attacker, who can cause the TRNG to generate his desired output rather than true random data.
The Solution: Modular Multiplication
Unpredictable noise sources are tiny, and must be massively amplified to be used by an TRNG. Other TRNG architectures amplify these signals until they saturate, becoming digital 1's and 0's. They rely on careful design and shielding to keep outside signals from influencing the noise source.
For example, if we amplify a tiny noise source by 1 billion in a system that saturates at 3.3V, then 1uV of noise will be amplified causing the output to be about 3.3V. An attacker need only introduce at least -1uV to cause the TRNG to saturate at 0V instead. An attacker even this tiny influence over the noise source can entirely control the output.
This is the wrong aproach. Instead, TRNGs should use modular multiplication to amplify their noise source, because modular multiplication never saturates.
If we multiply a 1uV peak by 1 billion modulo 3.3V, then the result will be about 0.3V, which will result in a ditital 0. If an attacker subtracts 1uV, causing our noise source to be at 0.0V, then after amplification, the output is 0V, which still results in a 0. In fact, without knowing the current amplituded of the noise source, there is no signal an attacker can add to our noise source that will result in a desired output. He may be able to flip the output bit, but since it was already random, his signal injection fails to control the result, which is still random. In fact, an attacker's injected signal causes the output to be more random, since an attacker is a nice unpredictable source of entropy! Infinite Noise Multipliers add entropy from all noise sources, even those from an attacker.
Variations
There are currently 3 versions of Infinite Noise Multipliers documented here. The infnoise_small directory describes a low part-count design that works well with op-amps which have rail-to-rail inputs and outputs. The infnoise_fast directory contains a faster design that uses a few more resistors and an additional op-amp. This design is suitable for use with a wide range of op-amps.
Because Infinite Noise Mulitpliers are switched-capacitor circuits, it is important to use components with low leakage. Op-amps with below 1nA of input bias current will enable running at lower frequencies with less power.
There is also a CMOS version described here.
Free As in Freedom
I, Bill Cox, came up with The Infinite Noise Multiplier architecture in 2013. I hereby renounce any claim to copyright and patent rigts related to this architecture. I'm giving it away emphatically freely. Furthermore, I am aware of no infringing patents and believe there are none. It should be entirely safe for use in any application.