combining entropy

Jon Callas jon at
Fri Oct 24 15:42:59 EDT 2008

On Sep 29, 2008, at 5:13 AM, IanG wrote:

> 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?
> 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.

It's within epsilon for a good many epsilon.

I'm presuming you want the resultant size to be X, as well. Otherwise,  
the suggestion that Ben has, concatenation is obviously better, and  
you can solve obvious problems.

Another solution is to hash the N pools together with a suitably  
secure function. (Most the available algorithms are suitably secure  
for this purpose.) The downside of this is that you are capping your  
entropy at the size of the hash function. It's better than XOR because  
it's not linear, blah, blah, blah.

However, if you had three pools, each relatively large, it doesn't  
hurt anything to XOR them together. It's pretty easy to prove that the  
result does not decrease entropy, but I think it's impossible to prove  
that it increases it. XORing is really taking the max of the N pools.

You have to realize that XOR is bad if there's a chance to leak the  
entropy pool, XOR is a bad function. If whoever produced pool X sees  
X^Y, then they know Y. But you know that, too.


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