Messages in this thread | | | Date | Fri, 15 Aug 2003 18:11:21 +1000 | From | Nick Piggin <> | Subject | Re: [RFC][PATCH] Make cryptoapi non-optional? |
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Måns Rullgård wrote:
>Andries Brouwer <aebr@win.tue.nl> writes: > > >>>>>entropy(x) >= entropy(x xor y) >>>>>entropy(y) >= entropy(x xor y) >>>>> >>>>Is this trolling? Are you serious? >>>> >>>These lemma are absolutely true. >>> >>David, did you read this line: >> >> >>>>Try to put z = x xor y and apply your insight to the strings x and z. >>>> >>Let us do it. Let z be an abbreviation for x xor y. >> >>The lemma that you believe in, applied to x and z, says >> >> entropy(x) >= entropy(x xor z) >> entropy(z) >= entropy(x xor z) >> >>But x xor z equals y, so you believe for arbitrary strings x and y that >> >> entropy(x) >= entropy(y) >> entropy(x xor y) >= entropy(y). >> >>This "lemma", formulated in this generality, is just plain nonsense. >> > >Not quite non-sense, but it would mean that for any strings x and y, > > entropy(x) == entropy(y), > >which seems incorrect. >
Well, just the line entropy(x) >= entropy(y) is incorrect. ie. proof by contradiction.
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