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SubjectRe: [RFC][PATCH] Make cryptoapi non-optional?
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Val Henson  wrote:
>On Thu, Aug 14, 2003 at 07:40:25PM +0000, David Wagner wrote:
>> I don't see where you are getting this from. Define
>> F(x) = first80bits(SHA(x))
>> G(x) = first80bits(SHA(x)) xor last80bits(SHA(x)).
>> What makes you think that F is a better (or worse) hash function than G?
>
>See Matt Mackall's earlier post on correlation, excerpted at the end
>of this message. Basically, with two strings x and y, the entropy of
>x alone or y alone is always greater than or equal to the entropy of x
>xored with y.
>
>entropy(x) >= entropy(x xor y)
>entropy(y) >= entropy(x xor y)

Sorry; that's not accurate. Here's a counterexample. Let x and y be
two 80-bit strings. Assume that x is either 0 or 1 (equal probability
for both possibilities). Assume y is either 0 or 2 (equal probability
for both possibilities), and is independent of x. Then
entropy(x) = 1 bit
entropy(y) = 1 bit
entropy(x xor y) = 2 bits

The difference between F and G is very small, and there is not much
basis for choosing one over the other.
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