Re: permutation mappings
From: duffman (samarthsanghavi_at_gmail.com)
Date: 09/28/04
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Date: 28 Sep 2004 08:58:09 -0700
any ideas?? anyone??
samarthsanghavi@gmail.com (duffman) wrote in message news:<f73e3e68.0409271917.7af11f5d@posting.google.com>...
> Let PI be a permutation of the integers 0,1,2,3...2^(n-1), such that
> PI(m) gives the permuted value of m, 0 <= m < 2^n. Put another way,
> PI maps the set of n-bit integers into itself and no two integers map
> into the same integer. DES (Data Encryption Standard, for those who
> don't know a really popular way of encrypting data in a block-cipher
> fashion) is such a permutation for 64 bit integers. We say that PI
> has a fixed point at m if PI (m) = m. That is, if PI is an encryption
> mapping, then a fixed point comes points to a message that encrypts to
> itself. We are interested in the probability that PI has no fixed
> points. Show the somewhat unexpected result that over 60% of mappings
> will have at least one fixed point.
>
> any ideas?
>
> thanks,
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- In reply to: duffman: "permutation mappings"
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