This discussion will progress more smoothly and more rapidly if we clarify some of the concepts and terminology.
There are at least four concepts on the table: 1) At one extreme, there is 100% entropy density, for example 32 bits of entropy in a 32-bit word. I'm talking about real physics entropy, the kind of hard-core industrial-strength randomness that will never get cracked by anybody, ever. 2) It is also possible to have lesser entropy density, such as 3 bits of entropy in a 32-bit word. Such a word is partly predicable and partly not. Remark: I emphatically recommend that we pay attention to cases where we have a provable lower bound on the entropy, even if the entropy density starts out less than 100%, because the density can be increased to virtually 100% by hashing. This is how turbid works. 3) At the other extreme, there is complete determinism, such as the decimal digits of π, or even the decimal digits of 1/3rd. 4) Last but not least, there is the "squish" category. This case is covered by Murphy's law. That means: -- If you wanted the symbol to be predictable, it would not be reliably predictable. -- If you wanted the symbol to be unpredictable, it would not be reliably unpredictable. Illustration: Back when I was 17 years old, I needed a random number generator. The pointy-haired boss directed me to use the value of the instruction pointer at each interrupt. I had to explain to him that it was an event-driven system, so with high likelihood, the IP pointed to the idle loop. It was clearly a squish. You couldn't rely on it being predictable, but you also couldn't rely on it being unpredictable. =========== To say the same thing yet again: For non-adversarial situations, you can do pretty much whatever you like, and you might reasonably care about the typical case ... but a great many applications of randomness, including gaming and cryptography, are highly adversarial. That demands a minimax approach. The best case doesn't much matter and the typical case doesn't much matter; we need to focus attention on the worst case. Absence of proof is not proof of absence. For the important applications, we need a provably-good RNG. The second law of thermodynamics provides the required guarantees. ============ Here's another way of looking at almost the same issues. People on this list have been talking about combining every possible source of "randomness" ... the more the merrier. Again there is a crucial distinction to be made: a) In the linux "random" device, /any/ user can mix stuff into the driver's pool. This is a non-privileged operation. The idea is that it can't hurt and it might help. So far so good. b) Contributions of the type just mentioned do *not* increase the driver's estimate of the entropy in the pool. If you want to increase the entropy-estimate, you need to issue a privileged ioctl. If we want to have a meaningful discussion, we must distinguish between a) mixing in all sorts of squish, and b) mixing in some real entropy /and taking credit for it/. Again, step (a) cannot get anybody into trouble. Step (b) gets you into trouble if you claim credit for more entropy than was actually contributed. ============== Let's be clear: There is a huge difference between contributing worthless squish and contributing real entropy. IMHO the key distinction is whether or not you have a hard /lower bound/ on the amount of entropy, so you can claim credit for it, and be confident of the claim. I strongly recommend not bothering with things that /might/ be unpredictable, and focusing instead on things that are absolutely guaranteed to be unpredictable, as guaranteed by the laws of physics. On 09/12/2013 07:38 PM, Thor Lancelot Simon wrote: > The audio subsystem actually posed *two* obvious opportunities: amplifier > noise from channels with high final stage gain but connected by a mixer > to muted inputs, and clock skew between system timers and audio sample > clocks. I wouldn't have said that. In a multi-stage amplifier, the noise figure is set by the /first/ stage, not the "final stage". More importantly, it hardly matters which stage contributes which part of the gain, so long as there is "enough" gain before the signal is digitized. Most computer audio systems have enough gain to make the Johnson noise observable. This gives us a source of hard-core, industrial-strength, guaranteed physics entropy. In typical cases, increasing the gain helps a tiny bit, but doubling the gain does /not/ double the amount of entropy per sample; it only increases it by one bit. Muting the inputs cannot help and might hurt. It might well drop the entropy production to zero. Things like clock skew are usually nothing but squish ... not reliably predictable, but also not reliably unpredictable. I'm not interested in squish, and I'm not interested in speculation about things that "might" be random. I'm interested in things that /guarantee/ a usable amount of entropy. The second law of thermodynamics provides such a guarantee. ============ The word "random" means different things to different people. There is nothing to be gained by arguing over the definition. Feel free to use this word however you like. In contrast, please do not use the word "entropy" loosely. There is a very well-defined and well-understood notion of physics entropy. Tacking on additional metaphorical or just plain sloppy usages just pollutes the discussion and serves no useful purpose. There is a huuuuge difference between squishy randomness and real physics entropy. _______________________________________________ The cryptography mailing list firstname.lastname@example.org http://www.metzdowd.com/mailman/listinfo/cryptography