Messages in this thread | | | Date | Fri, 15 Aug 2003 14:22:35 -0600 | From | Val Henson <> | Subject | Re: [RFC][PATCH] Make cryptoapi non-optional? |
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On Fri, Aug 15, 2003 at 09:55:03AM +0200, Andries Brouwer wrote: > The lemma that you believe in, applied to x and z, says > > entropy(x) >= entropy(x xor z) > entropy(z) >= entropy(x xor z) [snip] > This "lemma", formulated in this generality, is just plain nonsense.
Indeed. In the context of x = first 80 bits of SHA-1 hash, y = second 80 bits of SHA-1 hash, we are assuming that the entropy of x and y are basically equal. Then xoring them together gives us no benefit over taking just one or the other, and may reduce the entropy if the output of SHA-1 is correlated between the two halves in any way (which seems more likely than not).
Including a little more context, then:
If entropy(x) == entropy(y), then:
entropy(x) >= entropy(x xor y) entropy(y) >= entropy(x xor y)
Amusingly, someone already worked their way backwards from my post without the benefit of any context to find that it implied that entropy(x) == entropy(y). I should know better than to assume that people have read the entire thread before posting.
Apologies to Matt for sidetracking the discussion. He has come up with a nice solution despite our kibitzing.
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