Cryptanalysis of RC4-like Ciphers

Abstract

Abstract. RC4, a stream cipher designed by Rivest for RSA Data Security Inc., has found several commercial applications, but little public analysis has been done to date. In this paper, alleged RC4 (hereafter called RC4) is described and existing analysis outlined. The properties of RC4, and in particular its cycle structure, are discussed. Several variants of a basic "tracking" attack are described, and we provide experimental results on their success for scaled-down versions of RC4. This analysis shows that, although the full-size RC4 remains secure against known attacks, keystreams are distinguishable from randomly generated bit streams, and the RC4 key can be recovered if a significant fraction of the full cycle of keystream bits is generated (while recognizing that for a full-size system, the cycle length is too large for this to be practical). The tracking attacks discussed provide a significant improvement over the exhaustive search of the full RC4 keyspace. For example, the state of a 5 bit RC4-like cipher can be obtained from a portion of the keystream using 2 42 steps, while the nominal keyspace of the system is 2 160 . More work is necessary to improve these attacks in the case where a reduced keyspace is used.

A Practical Attack on Broadcast RC4

“…Since the state transition in RC4 is invertible and the initial state (i = j = 0) is not of this type, RC4 can never enter these states for any key. Additional properties of the state transition graph of RC4 were analyzed by Mister and Tavares in [MT98].…”

“…A branch and bound attack that is based on the "Guess on Demand" paradigm is analyzed in [MT98] and [KMP + 98]. The attack simulates the generation process, and keeps track of all the known values in S which had been deduced so far.…”

A Survey on RC4 Stream Cipher

“…The first state recovery attack on RC4 was proposed Knudsen, Meier and Preneel [35] in 1998 where the attack complexity was found to be 2 779 for N=256. In the same year 1998, another state recovery attack was analyzed using some cycle -structures of RC4 [36] and observed that for N=32, state recovery can be done in 2 42 steps. A probabilistic approach was used for RC4 state recovery in [37], having attack complexity similar to the one obtained in [35] .…”

Attacks on the RC4 stream cipher

“…A weakness detected early was that the first byte of the pseudo random sequence is not very random (see [9] and [7]). The strongest know attack of this kind is due to S. Fluhrer, I. Mantin and A. Shamir [2].…”