DESX Whitening

From: Sebastian Faust (sfaustdeleteme@logic-software.de)
Date: 02/19/03 

From: "Sebastian Faust" <sfaustdeleteme@logic-software.de>
Date: Wed, 19 Feb 2003 21:39:28 +0100

Hi,

I read in the book from Bruce Schneider "Applied Cryptography" that when
whitening is used in the DESX case a brute-force attack requires 2^(n+m/p)
operations if K_1 = K_3 or 2^(n+m+1) if K_1 and K_2 are different and we
have 3 known plaintexts, where n is the key size, m the b lock size and p
the number of known plaintexts.
DESX is in that book defined as followed:
C = K_3 + E_(K_2)(P + K_1),
P = K_1 + D_(K_2)(C + K_3),
where E_(K_2) is encryption with DES using K_2 and D_(K_2) is decryption.
Now my question: Why 2^(n+m/p) and 2^(n+m+1)? And what has it to do with the
number of known plaintexts?

Thanks in advance
Sebastian

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