# Fluhrer, Mantin and Shamir attack

In cryptography, the Fluhrer, Mantin and Shamir attack is a particular stream cipher attack, a dedicated form of cryptanalysis for attacking the widely used stream cipher RC4. The attack allows an attacker to recover the key in an RC4 encrypted stream from a large number of messages in that stream.

The Fluhrer, Mantin and Shamir attack applies to specific key derivation methods, but does not apply to RC4-based SSL (TLS), since SSL generates the encryption keys it uses for RC4 by hashing, meaning that different SSL sessions have unrelated keys.[1]

## Background

The Fluhrer, Mantin and Shamir (FMS) attack, published in a 2001 paper titled Weaknesses in the Key Scheduling Algorithm of RC4, takes advantage of a weakness in the RC4 key scheduling algorithm to reconstruct the key from a number of collected encrypted messages. The FMS attack gained popularity in tools such as AirSnort and aircrack, both of which can be used to attack WEP encrypted wireless networks.

This discussion will use the below RC4 key scheduling algorithm (KSA).

begin ksa(with int keylength, with byte key[keylength])
for i from 0 to 255
S[i] := i
endfor
j := 0
for i from 0 to 255
j := (j + S[i] + key[i mod keylength]) mod 256
swap(S[i],S[j])
endfor
end

The following pseudo-random generation algorithm (PRGA) will also be used.

begin prga(with byte S[256])
i := 0
j := 0
while GeneratingOutput:
i := (i + 1) mod 256
j := (j + S[i]) mod 256
swap(S[i],S[j])
output S[(S[i] + S[j]) mod 256]
endwhile
end

## The attack

The basis of the FMS attack lies in the use of weak initialization vectors (IVs) used with RC4. RC4 encrypts one byte at a time with a keystream output from prga(); RC4 uses the key to initialize a state machine via ksa(), and then continuously modifies the state and generates a new byte of the keystream from the new state. Theoretically, the key stream functions as a random one-time pad, as a pseudo-random number generator controls the output at each step.

With certain IVs, an attacker knowing the first byte of the keystream and the first m bytes of the key can derive the (m + 1)th byte of the key due to a weakness in the PRNG used to generate the keystream. Because the first byte of the plaintext comes from the WEP SNAP header, an attacker can assume he can derive the first byte of the keystream from B ⊕ 0xAA. From there, he only needs an IV in the form (a + 3, n − 1, x) for key index a origin 0, element value space n (256 since 8 bits make a byte), and any X. To start, the attacker needs IVs of (3, 255, x). WEP uses 24-bit IVs, making each value one byte long.

To start, the attacker utilizes the IV as the first 3 elements in K[ ]. He fills the S-box S[ ] with sequential values from 0 to n as RC4 does when initializing the S-box from a known K[ ]. He then performs the first 3 iterations of ksa() to begin initializing the S-box.

After the third step, the attacker can possibly, but not definitely, derive the fourth byte of the key using the keystream output O by computing (O − j − S[i]) mod nK[i], with the value i = 3 at this step.

At this point, the attacker does not yet have the fourth byte of the key. This algorithm does not regenerate the next byte of the key; it generates a possible value of the key. By collecting multiple messages—for example WEP packets—and repeating these steps, the attacker will generate a number of different possible values. The correct value appears significantly more frequently than any other; the attacker can determine the value of the key by recognizing this value and selecting it as the next byte. At this point, he can start the attack over again on the fifth byte of the key.

Although the attacker cannot attack words of the key out of order, he can store messages for later sequential attack on later words once he knows earlier words. Again, he only needs messages with weak IVs, and can discard others. Through this process, he can gather a large number of messages for attack on the entire key; in fact, he can store only a short portion of the beginning of those messages, just enough to carry the attack out as far as the word of the key the IV will allow him to attack.

## References

1. ^ "RSA Security Response to Weaknesses in Key Scheduling Algorithm of RC4". RSA Laboratories. 2001-09-091.