Re: [PATCH RFC] random: Account for entropy loss due to overwrites

[H. Peter Anvin]

On 08/15/2012 12:30 PM, Matt Mackall wrote:
> On Mon, 2012-08-13 at 10:26 -0700, H. Peter Anvin wrote:
>> From: "H. Peter Anvin" <hpa@xxxxxxxxxxxxxxx>
>>
>> When we write entropy into a non-empty pool, we currently don't
>> account at all for the fact that we will probabilistically overwrite
>> some of the entropy in that pool.
> 
> Technically, no, nothing is overwritten. The key fact is that the mixing
> function is -reversible-. Thus, even if you mix in known data, you can't
> learn anything about the state and thus can't destroy any of the
> existing entropy.
> 
> But you are correct, mixing new actual entropy is not purely additive
> (with saturation). For that to happen, we'd need an input mixing
> function with perfect maximal cascading. Instead we effectively cascade
> across somewhere between 6 and 64 bits. So the truth lies somewhere
> between linear and your exponential estimate (which would be the case
> for mixing a single bit into the pool with XOR), but much closer to
> linear due to combinatoric expansion.
> 

I think you have it backwards; if the input was a FIFO, with no mixing
at all, and no reuse, the linear estimate would be correct.  The mixing
into an already-existent and potentially-observed pool is what causes
the exponential estimate to apply... although it is assuming perfect
mixing.  However, I believe it is still correct in the aggregate.

> On the other hand, I don't think this sort of thing matters at all.
> There is so much more fundamentally wrong with even trying to do entropy
> accounting in the first place that these sorts of details don't even
> matter. Instead we should stop fooling ourselves and just drop the
> pretense of accounting entirely. Now that we've got a much richer set of
> inputs, I think the time is ripe... but of course, I'm no longer the
> maintainer.

If we're going to fundamentally change the structure perhaps we should
actually take the suggestions long offered from the cryptographic
community, and look at structures like Fortuna.

	-hpa
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