From: alain@elevia.UUCP (W.A.Simon)
Newsgroups: sci.crypt

Subject: eating pretzels
Message-ID: <1991Jul2.105754.11804@elevia.UUCP>
Date: 2 Jul 91 10:57:54 GMT
Followup-To: sci.crypt
Organization: The Electronic Path - Global Village
Lines: 44

Eating pretzels:

I will show that a 2 stream braids is weaker than a simple XOR.

If we split a plaintext into two more or less equal parts and braid
them together, we have in effect done a transposition.  A braid is a
particular case of the more general random shuffle.  This is a shuffle
that has constraints on the valid keys that can be used to randomize
the order of the bits.  We are working with a reduced key space.
Therefore, the two stream braid is weaker than the unconstrained shuffle
or transposition.  But we know that moving bits around at random is
weaker than flipping bits at random (for each shuffle, there is an XOR
that can produce it, but the reverse is not true).  So we can safely
conclude that a two braid stream is weaker than a XOR.
This doesn't spell the end of the Braided Streams approach.  It just
proves that a TWO stream braid is weaker than a XOR.  The braiding
itself would be of no interest if it were not for the immeasurable
strength added by the presence of a totally unpredictable input stream
which can't be psyched out through known cryptographical methods (known
plaintext attacks would certainly not work here).  As a result, we have
seen that it is possible to extract any "known" plaintext.  This is also
reinforced by the possibility of braiding more than two streams at one
time, and the benefit of added security at each iteration through the

These qualities would also be present (to an even greater extent) in the
unconstrained Shuffle or XOR of the composite string, but braids lends
themselves well to applications that require encryption "as we go", such
as live radio or telephone communications, remote sensing and remote
control, and any real time usage, where the blocking of data, and the
deferred encryption/decryption cycles would introduce unacceptable
weakening and delaying elements.  In a normal shuffle or a normal XOR,
any extra pass through the system would require that the whole message
has been processed once, or that arbitrary blocking be performed.  With
braids, by the simple device of using as many streams as one would like
passes through the system, we achieve the required result without batching
the messages.

To be continue, I am sure.

      William "Alain" Simon                          alain@elevia.UUCP
      Frank Zappa for President of the United States of North America!