Why triple encryption instead of split+encrypt?

[solman at MIT.EDU]

> There are two separate operations here.  One is splitting the plaintext:
> 
> 	P0, P1 = S_KS(P)
> 
> The other is generation of the splitting key.  I assume independent
> generation of the splitting key both because it maximizes the total
> keyspace and because it avoids the confusion that I believe is evidenced
> by the above quoted paragraph.  To wit:  You have suggested generating
> the split key with a one-way hash of the DES keys:
> 
> 	KS = hash(concat(K0,K1))
> 
> If the concatenation of the DES keys is 112 bits, then there are 2^112
> possible values of the concatenation.  However, the hashing of this
> value is not the first of the two encryptions; the splitting of the
> plaintext is the first encryption, and the hash is merely a mechanism
> for generating the splitting key.  The domain of KS is the determinant
> of the size of the intermediate memory in a brute-force
> meet-in-the-middle attack.

Agreed so far.

> Furthermore, even for an independently generated splitting key, if the
> size of the domain of KS is greater than the size of the domain of K0
> or K1, then the DES-decrypted values can be stored as the intertext,
> requiring no more memory than that required for decrypting double DES.

Yeah. You're right. Make a table of the backwards DES, then match
against that when attacking the spliting part of the algorithm. I
don't know how I missed that.

> This greatly shortens the amount of memory required for the search,
> making the algorithm much less secure than double DES.  You may respond
> by suggesting improvements to the splitting algorithm, such as
> multiple-bit dependency; but there are doubtless other weaknesses that
> could be exploited.  I did not spend a lot of time on the above
> technique; persons more qualified than I am, devoting serious time to
> the problem, will certainly develop better cryptanylitic attacks.  I
> think you will be very hard pressed to develop an algorithm anywhere
> near as secure as DES.

Agreed (although I'll point out that my splitting algorithm IS dependent
on both keys/) If I want a fast hash based symetric cipher, I'll use
MDC or Luby-Rackoff.

*sigh*

JWS