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Date: Fri, 15 Aug 2003 18:11:21 +1000
From: Nick Piggin <piggin@cyberone.com.au>
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To: =?ISO-8859-1?Q?M=E5ns_Rullg=E5rd?= <mru@users.sourceforge.net>
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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.