Re: Why triple encryption instead of split+encrypt?

[John Douceur <johndo@microsoft.com>]

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>From:  <solman@MIT.EDU>
>Date: Monday, July 18, 1994 4:18PM

>Clearly, if you have access to P0, P1; C0 and C1 this attack crushes the
>algorithm. In most books I've seen, it is assumed that you do not have
>access to this.

The assumptions about the information available to the cryptanalyst
vary with the type of attack.  The essence of a known-plaintext attack
is that both plaintext and cyphertext of several messages are known,
and the task is to deduce the key.  This is more practical than it may
sound, since there may be (for example) header information that has
small or no variability among messages.

>Nonetheless, your cryptanalytic algorithm makes clear an additional
>constraints that must be placed on the system which I had not realized:

>From the algorithm, the plaintext, and the cypher text, in must not be
>possible to reconstruct both the plaintext, and the cyphertext for either
>half of the message.

>To that end I would suggest the improvement of making the splitting
>operation dependent on the keys.

For that matter, one could have a third key which is used by the
splitting algorithm.  If one chooses to make this splitting key a
function of the two DES keys, then this approach reduces to your
suggestion, at the expense of a smaller keyspace.  It could be said
that, in the code fragment of my previous message, the splitting key
is fixed at 0x55555555.

So now the meet-in-the-middle attack regains its earlier applicability:
A known-plaintext attack would encrypt P with the splitter, decrypt
C0 with DES, and attempt to meet in the middle to discover key K0;
similarly, decrypting with C1 to get K1.  If you can design a splitter
that is as cryptographically secure as DES (good luck), then the
resulting algorithm is as secure as double DES.  Actually, the
computational complexity of a cryptanalysis would be somewhere between
one and two times that of double DES, since it requires one encryption
analysis and two decryption analyses.

In your previous message, you commented:

>I have a hunch that if I'm wrong, its because the time required to do secure
>non-redundant secret splitting is as large as the time I'm saving.

If your secret-splitting algorithm is as secure as DES, then it probably
runs as slowly as DES does, making your hunch correct.  However, even if
this were not the case, the security of this scheme is significantly less
than that of triple DES.

JD

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