Messages in this thread | | | Date | Fri, 15 Aug 2003 23:16:08 +0100 | From | Jamie Lokier <> | Subject | Re: [RFC][PATCH] Make cryptoapi non-optional? |
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Matt Mackall wrote: > No, it's a premise stated at the beginning of the thread. We're > assuming perfect distribution for x and y. The problem here is that x > and y can be dependent or independent. If they're independent, then > there's no issue. If they're dependent (for instance correlated or > anticorrelated) then x^y biases toward zero or one. Which clearly has > less entropy.
Sure, but that only holds when you assume a specific mix of independence and dependence among the bits.
(Bits within x are independent of each other, and also within y, while at the same time x and y are dependent.)
In general, bits from x^y do not have more bias towards zero or one than bits from x or y alone. Consider an extreme:
x = [ random_bit_0, random_bit_0 ] y = [ random_bit_1, ~random_bit_1 ]
Then:
entropy(x) = entropy(y) = 1 entropy(x^y) = 2
This is no more arbitrary a mix of dependence and independence than your assumption.
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