[300] in cryptography@c2.net mail archive
Re: standardizing key schedules
daemon@ATHENA.MIT.EDU (yoda)
Mon Feb 24 17:45:35 1997
Date: 24 Feb 1997 07:49:40 -0000
From: yoda <yoda@nym.alias.net>
To: cryptography@c2.net
Cc: reinhold@world.std.com, mignone@isi.ee.ethz.ch
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In message <199702202133.WAA04110@isibee13.ethz.ch>
Domenico Mignone & Christoph Maeder wrote:
>A. G. Reinhold wrote:
>> The initial permutations RC4 produces are hardly random. Counting all key
>> lengths, RC4 can only produce 2**257 different permutations, a very sparse
>> subset of the 256! ~= 2**1684 possible permutations.
>
>You will reach only a subset of the possible permutations if you consider very
>short userkeys. But if the userkey is long enough then every permutation can be
>reached, as you can find in D.E.Knuth ``The Art Of Computer Programming'', Vol.2
But in the standard RC4 initialization, the maximal userkey is 256. How
do you know that this is sufficiently long?
You are claiming that the map is surjective (onto). The fact that
256^256 > 256^2 * 256! does not imply this.
>The only thing you can say is that initial permutations will probably not be
>equally distributed.
>How did you compute 2**257 as the number of different permutations that RC4 can
>produce?
>To our knowledge 256**256 different userkey can be chosen at random, using the
>full userkey length. This number is much bigger than 256!. Therefore you can
>expect that each permutation is reached at least once.
No, you cannot expect this without knowing something additional. You
can indeed use 256^256 user keys, but, as I stated above, your
conclusion does not follow unless you know that the map is surjective.
>
>Domenico Mignone & Christoph Maeder
Yoda
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Date: Mon Feb 24 07:49:39 1997 GMT
From: yoda@nym.alias.net
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