How random are commercial TRNGS

Question

I'm thinking about buying a USB TRNG. How do I evaluate its randomness? I'm sure some are better than others but which is which? Are thermal-noise better than radio-noise TRNGs?

Answer 1

Evaluating a TRNG device positively requires knowing its structure, both to evaluate the actual amount of entropy it produces, and the possibility to detect a field failure.

Some devices sold as TRNG are in fact a TRNG subsystem followed by a PRNG, which produces the output of the device. In that case, if the PRNG is any good, the output of the device may appear random even though the TRNG subsystem produces no or little entropy, opening the possibility of an attack (perhaps just by enumerating the possible outputs of the TRNG subsystem), especially for an attacker knowing enough about the PRNG.

To illustrate: consider an hypothetical Smart Card with an RNG amounting to a TRNG subsystem followed by an LFSR-based PRNG, which task is to hide any small imperfection of the TRNG subsystem. In case of total failure of the TRNG subsystem, perhaps induced by very cold temperature (as obtained non-destructively by evaporation of a liquefied gas poured on the card), it is easy to guess future output from past one (if the PRNG has few state bits, the output has a short period; even with many state bits, the full state is known after that many bits have been output, with knowledge of the LFSR feedback; even when that's unknown, Berlekamf-Massey allows an efficient attack). There might be less obvious failure modes at different temperatures. If the PRNG is fair (e.g. based on the ASG and enough state bits) but secret, only those in the know of the PRNG design are in a good position to detect the failure, or exploit it.

To avoid this, a modern Smart Card RNG may keep the same basic structure, but with hardware to detect total failure of the TRNG subsystem (e.g. when it outputs constant 0 or constant 1), with some access by the software to the output of the TRNG, to enable testing and certification. Any cryptographic TRNG should have some monitoring system able to detect its failures. In the case of a USB RNG, mere accidental under-voltage could cause the source to fail; and USB ports fuses, hubs and their power supply do fail! Monitoring is a must in contexts where an adversary is in a position induce failure. The monitoring system can be hardware or software, internal or external.

This is a requirement in the AIS31 scheme for common-criteria security evaluation of TRNG (index in German, linking to documents in English; see also how French authorities have been using AIS31 method, including some reservation in section 5). This the best such methodology I've used, although I find it much more complex than necessary to the point of being confusing, and not free from error especially in the examples. My advice if you want to assess by yourself the soundness of a TRNG (rather than delegate that to security certification) is to follow the principles behind AIS31, which I can loosely outline as:

• the structure of the RNG must be known and it must guide the evaluation;
• the TRNG hardware source must be modeled in some way;
• there should be some access to the output of that TRNG hardware source, allowing to check experimentally that the model is sound;
• some system must monitor and detect possible failures of the TRNG hardware source, and in that event prevent operation (such monitoring system typically uses the output of the TRNG hardware source);
• the model of the TRNG hardware source must support the effectiveness of that monitoring system;
• before actual use as key material, the output of the TRNG hardware source must be post-processed by a PRNG, preferably a cryptographically strong PRNG;
• the model of the TRNG hardware source must support that comfortably more entropy is fed in the (CS)PRNG than is necessary for security of the output of the (CS)PRNG in any situation where the monitoring system allows operation;
• the false alarm rate of the monitoring system should be functionally tolerable (that one tends to be hard to demonstrate).

With access to a raw bit stream produced by a TNRG hardware source, at a point amounting to the output of an analog comparator followed by sampling with a clock, one could do worse than experimentally evaluating the entropy in sub-samples of say 4 to 16 bits (depending on RAM resources and time allowance) by frequency counting, computing experimental entropy from that; doing this as monitoring, with some threshold comfortably below the experimental value; assuming the real entropy is a small fraction of what the threshold supports; and post-processing the whole output with a CSPRNG.

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A note on thermal noise vs "radio noise" TRNG sources: I've never met the later, and suspect that it is hard to prove that an attacker can't beam some RF signal towards the TRNG source, strong enough to turn its output into a square wave under the attacker's control.

Thermal noise TRNGs are more classic. They are known to be susceptible to temperature variations; in theory, the colder the less entropy; but high temperatures can introduce undesirable effects in the detector following the source. This might need to be considered (it is very relevant in a Smart Card, not much to something hooked to a PC operated in a trusted environment).

My limited understanding of physics make me see thermal noise as having its origin in quantum noise. I'm equally confident in either as a source of unguessable bits for cryptographic purposes. In my opinion, what matters more than the quantum vs thermal origin of the noise is how it is extracted and converted to bits, and the robustness of that with respect to failure modes and external influence.

This is one area where CSPRNG post-processing helps: in a cryptographic context, it insures that an attacker must have near perfect control of the TRNG source to gain an advantage. As soon as about 160 bits (give or take a factor of two) of actual entropy has been fed into the CSPRNG (without the output being observable by the adversary meanwhile, as rightly pointed by @CodesInChaos), and baring any attack on its design or implementation, the output is indistinguishable from random for any practical purpose (that's even though any CSPRNG using finite memory and no more seeding has a finite period; we are considering computationally bounded adversaries).

The output of any TRNG can't be better than that! On the contrary, in my experience, the unconditioned output of a TRNG source is never free from some detectable bias. If a stream of bits of arbitrary length has odds of 0 vs 1 passing a basic chi-squared test (and especially when that stands taking the effect of temperature and device variation into consideration), this is strong indication that it is not the output of an unconditioned TRNG. And again, any post-processing of the TRNG source must be known and taken into account (in addition to the nature of the source) when assessing the TRNG, and especially the effectiveness of its monitoring.