From: Benjamin Scott <[EMAIL PROTECTED]>
Date: Sun, 15 May 2005 20:42:38 -0400 (EDT)
<snip>
If the series is statistically random, then the probability of getting
*any*
set of N characters it the same. If you have a statistically random penny,
for example, and you flip it 20 times, you have just as much a chance of
getting 20 heads as you do 10 heads, because each individual flip is
strictly
50/50, and each flip has no bearing on any other flip. The fact that you
get
10 heads in a row does not mean the next one should be tails to "start
making
up for the previous 10 heads".
You said you... flunked? combinatronics. :)
If I take my... statistically random penny... and flip it 20 times, the
probability of getting 20 heads is (1/2)^20, or 1/2^20.
The probability of getting 10 heads in 20 flips is:
20C10 (1/2)^10 (1/2)^(20-10) = 20C10 1/2^20
without even calculating 20C10, you can see this is 20C10 times more
likely than getting 20 heads.
The reason for this is that the 20 trials *are* related to each other
in one important way: you're counting them.
Of course, as [EMAIL PROTECTED] discovered, when it comes to matters of
crypto, one's own tools tend to be the first source of trouble. This is why
peer review of crypto software is absolutely critical.
I think the lessons learned here are:
(1) Always double check your crypto.
(2) Never use Perl BigInt's for anything ever... especially crypto.
(3) When in doubt, use LISP.
:)
--
Ben <[EMAIL PROTECTED]>
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