🚀 go-pugleaf

In <unruh.719212856@physics.ubc.ca> unruh@unixg.ubc.ca (Bill Unruh) writes:

>phr@telebit.com (Paul Rubin) writes:

>>I heard that someone in Eastern Germany recently proved a stronger
>>result, that DES generates the alternating group on 2^64 letters.

>What is the "alternating group"? Does this mean that for any two 64 bit
>words, x and y, there exists some sequence of DES transformations that
>take x into y?, or that for any 1-1 onto mapping from the set of all {x}
>to itself, there exists a sequence of DES which generates that mapping
>(ie, that the DES group contains 2^(2^64) elements)?

It's larger than 2^(2^64); it's (2^64)!/2.  The result is saying that half
of all possible permutations of the word-space (2^64) are attainable by
some combination of DES transformations.


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Arthur L. Rubin: a_rubin@dsg4.dse.beckman.com (work) Beckman Instruments/Brea
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