combining entropy

Stephan Neuhaus neuhaus at
Fri Oct 24 09:37:45 EDT 2008

On Oct 24, 2008, at 14:29, John Denker wrote:

> On 09/29/2008 05:13 AM, IanG wrote:
>> My assumptions are:
>> * I trust no single source of Random Numbers.
>> * I trust at least one source of all the sources.
>> * no particular difficulty with lossy combination.
>> If I have N pools of entropy (all same size X) and I pool them
>> together with XOR, is that as good as it gets?
> Yes.
> The second assumption suffices to prove the result,
> since (random bit) XOR (anything) is random.

Ah, but for this to hold, you will also have to assume that the N  
pools are all independent.  If they are not, you cannot even guarantee  
one single bit of "entropy" (whatever that is).  For example, if N =  
2, your trusted source is pool 1, and I can read pool 1 and control  
pool 2, I set pool 2 = pool 1, and all you get is zeros. And that  
surely does not contain X bits of "entropy" for any reasonable  
definition of "entropy".



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