Cryptography Reference
In-Depth Information
Chapter 9
Variants of RC4
We already discussed many cryptanalytic results on RC4 KSA and PRGA in
the previous chapters. In order to remove the weaknesses and improve the
cipher, many modifications and variants of RC4 have been proposed so far.
In this chapter, we outline these works.
9.1 Byte-Oriented Variants
At FSE 2004, two variants of RC4 were proposed. One is VMPC and the
other is RC4A. VMPC [192] is a generalization of RC4. The key scheduling
of VMPC transforms a secret key K of length l bytes (typically, 16 ≤l ≤ 64)
into a permutation S of Z N and initializes a variable j. An optional IV of
length l may be used. Another 16-bit variable m is used as a counter.
The name VMPC comes from Variably Modified Permutation Composition
which is a transformation of permutation P into the permutation Q. A k-level
VMPC function is defined as
Q[x] = P[P k [P k−1 [...[P 1 [P[x]]]...]]],0 ≤ x≤ N −1,
where P i [x] = (P[x]+i) mod N. VMPC cipher uses this transformation in its
PRGA to output the keystream bytes and update S through shu e-exchanges.
RC4A [139] tries to increase the security of RC4 by using two S-boxes S 1
and S 2 . The key scheduling of RC4A is the same as the RC4 KSA, except
that it uses two different secret keys two construct the two S-boxes. Hence
we do not give the RC4A KSA separately. The keystream generation part
is in the same line of RC4 PRGA. Two pseudo-random indices j 1 and j 2 are
used corresponding to S 1 and S 2 respectively to update them through shu e-
exchanges. The only modification is that the index S 1 [i] + S 1 [j] evaluated on
S 1 produces output from S 2 and vice-versa. The RC4A PRGA is given in
Algorithm 9.1.3
RC4A uses fewer CPU cycles per keystream output byte than RC4. To
produce two successive output bytes, the index i is incremented once in case
of RC4A, but twice in RC4.
The first distinguishing attacks on VMPC and RC4A appeared in [113].
According to [113], the distinguisher for VMPC requires around 2 54 keystream
 
 
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