RC4

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In cryptography, RC4 (also known as ARC4 or ARCFOUR) is the most widely-used software stream cipher and is used in popular protocols such as Secure Sockets Layer (SSL) (to protect Internet traffic) and WEP (to secure wireless networks). While remarkable for its simplicity and speed in software, RC4 is vulnerable to attacks when the beginning of the output keystream is not discarded, or a single keystream is used twice; some ways of using RC4 can lead to very insecure cryptosystems such as WEP.


Contents

[edit] History

RC4 was designed by Ron Rivest of RSA Security in 1987. While it is officially termed "Rivest Cipher 4", the RC acronym is alternatively understood to stand for "Ron's Code"[1] (see also RC2, RC5 and RC6).

RC4 was initially a trade secret, but in September 1994 a description of it was anonymously posted to the Cypherpunks mailing list[2]. It was soon posted on the sci.crypt newsgroup, and from there to many sites on the Internet. The leaked code was confirmed to be genuine as its output was found to match that of proprietary software using licensed RC4. Because the algorithm is known, it is no longer a trade secret. The name "RC4" is trademarked, however. RC4 is often referred to as "ARCFOUR" or "ARC4" (meaning Alleged RC4, because RSA has never officially released the algorithm), to avoid possible trademark problems. It has become part of some commonly used encryption protocols and standards, including WEP and WPA for wireless cards and TLS.

The main factors which helped its deployment over such a wide range of applications consisted in its impressive speed and simplicity. Implementations in both software and hardware are very easy to develop.

[edit] Description

RC4 generates a pseudorandom stream of bits (a keystream) which, for encryption, is combined with the plaintext using XOR; decryption is performed the same way. (This is similar to the Vernam cipher except that pseudorandom bits, rather than random bits, are used.) To generate the keystream, the cipher makes use of a secret internal state which consists of two parts:

  1. A permutation of all 256 possible bytes (denoted "S" below).
  2. Two 8-bit index-pointers (denoted "i" and "j").

The permutation is initialized with a variable length key, typically between 40 and 256 bits, using the key-scheduling algorithm (KSA). Once this has been completed, the stream of bits is generated using the pseudo-random generation algorithm (PRGA).

[edit] The key-scheduling algorithm (KSA)

The key-scheduling algorithm is used to initialize the permutation in the array "S". "keylength" is defined as the number of bytes in the key and can be in the range 1 ≤ keylength ≤ 256, typically between 5 and 16, corresponding to a key length of 40 – 128 bits. First, the array "S" is initialized to the identity permutation. S is then processed for 256 iterations in a similar way to the main PRGA algorithm, but also mixes in bytes of the key at the same time.

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

[edit] The pseudo-random generation algorithm (PRGA)

The lookup stage of RC4. The output byte is selected by looking up the values of S(i) and S(j), adding them together modulo 256, and then looking up the sum in S; S(S(i) + S(j)) is used as a byte of the key stream, K.
The lookup stage of RC4. The output byte is selected by looking up the values of S(i) and S(j), adding them together modulo 256, and then looking up the sum in S; S(S(i) + S(j)) is used as a byte of the key stream, K.

For as many iterations as are needed, the PRGA modifies the state and outputs a byte of the keystream. In each iteration, the PRGA increments i, adds the value of S pointed to by i to j, exchanges the values of S[i] and S[j], and then outputs the value of S at the location S[i] + S[j] (modulo 256). Each value of S is swapped at least once every 256 iterations.

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

[edit] Implementation

Many stream ciphers are based on linear feedback shift registers (LFSRs), which while efficient in hardware are less so in software. The design of RC4 avoids the use of LFSRs, and is ideal for software implementation, as it requires only byte manipulations. It uses 256 bytes of memory for the state array, S[0] through S[255], k bytes of memory for the key, key[0] through key[k-1], and integer variables, i, j, and k. Performing a modulus 256 can be done with a bitwise AND with 255 (or on most platforms, simple addition of bytes ignoring overflow).

Here is a simple implementation in Python:

class WikipediaARC4:
    def __init__(self, key = None):
        self.state = range(256) # Initialize state array with values 0 .. 255
        self.x = self.y = 0 # Our indexes. x, y instead of i, j
 
        if key is not None:
            self.init(key)
        
    # KSA
    def init(self, key):
        for i in range(256):
            self.x = (ord(key[i % len(key)]) + self.state[i] + self.x) & 0xFF
            self.state[i], self.state[self.x] = self.state[self.x], self.state[i]
        self.x = 0
            
    # PRGA
    def crypt(self, input):
        output = [None]*len(input)
        for i in xrange(len(input)):
            self.x = (self.x + 1) & 0xFF
            self.y = (self.state[self.x] + self.y) & 0xFF
            self.state[self.x], self.state[self.y] = self.state[self.y], self.state[self.x]
            r = self.state[(self.state[self.x] + self.state[self.y]) & 0xFF]
            output[i] = chr(ord(input[i]) ^ r)
        return ''.join(output)
            
if __name__ == '__main__':
    test_vectors = [['Key', 'Plaintext'], \
                    ['Wiki', 'pedia'], \
                    ['Secret', 'Attack at dawn']]
    for i in test_vectors:
        print WikipediaARC4(i[0]).crypt(i[1]).encode('hex').upper()

[edit] Test vectors

These test vectors are not official, but convenient for anyone testing their own RC4 program. The inputs are ASCII, the output is in hexadecimal.

RC4( "Key", "Plaintext" ) == BBF316E8D940AF0AD3

RC4( "Wiki", "pedia" ) == 1021BF0420

RC4( "Secret", "Attack at dawn" ) == 45A01F645FC35B383552544B9BF5

[edit] Security

RC4 falls short of the standards set by cryptographers for a secure cipher in several ways, and thus is not recommended for use in new applications.

Unlike a modern stream cipher (such as those in eSTREAM), RC4 does not take a separate nonce alongside the key. This means that if a single long-term key is to be used to securely encrypt multiple streams, the cryptosystem must specify how to combine the nonce and the long-term key to generate the stream key for RC4. One approach to addressing this is to generate a "fresh" RC4 key by hashing a long-term key with a nonce. However, many applications that use RC4 simply concatenate key and nonce; RC4's weak key schedule then gives rise to a variety of serious problems.

[edit] Biased Outputs of the RC4

The keystream generated by the RC4 is biased in varying degrees towards certain sequences. The best such attack is due to Itsik Mantin and Adi Shamir who showed that the second output byte of the cipher was biased toward zero with high probability. Such bias can be detected by observing only 256 bytes.

Souradyuti Paul and Bart Preneel of COSIC showed that the first and the second bytes of the RC4 were also biased. The number of required samples to detect this bias is 225 bytes.

Fluhrer and McGrew also showed such attacks which distinguished the keystream of the RC4 from a random stream given a gigabyte of output.[3]

[edit] Fluhrer, Mantin and Shamir attack

Main article: Fluhrer, Mantin, and Shamir attack

In 2001 a new and surprising discovery was made by Fluhrer, Mantin and Shamir: over all possible RC4 keys, the statistics for the first few bytes of output keystream are strongly non-random, leaking information about the key. If the long-term key and nonce are simply concatenated to generate the RC4 key, this long-term key can be discovered by analysing a large number of messages encrypted with this key. This and related effects were then used to break the WEP ("wired equivalent privacy") encryption used with 802.11 wireless networks. This caused a scramble for a standards-based replacement for WEP in the 802.11 market, and led to the IEEE 802.11i effort and WPA.

Cryptosystems can defend against this attack by discarding the initial portion of the keystream. Such a modified algorithm is traditionally called "RC4-drop[n]", where n is the number of initial keystream bytes that are dropped. The SCAN default is n = 768 bytes, but a conservative value would be n = 3072 bytes. [4]

[edit] Klein's Attack

In 2005, Andreas Klein presented an analysis of the RC4 stream cipher showing more correlations between the RC4 keystream and the key. Erik Tews, Ralf-Philipp Weinmann, and Andrei Pyshkin used this analysis to create aircrack-ptw, a tool which cracks 104-bit RC4 used in 128-bit WEP in under a minute[5] Whereas the Fluhrer, Mantin, and Shamir attack used around 10 million messages, aircrack-ptw can break 104-bit keys in 40,000 frames with 50% probability, or in 85,000 frames with 95% probability.

[edit] Combinatorial problem

A combinatorial problem related to the number of inputs and outputs of the RC4 cipher was first posed by Itsik Mantin and Adi Shamir in 2001, whereby, of the total 256 elements in the typical state of RC4, if x number of elements (x ≤ 256) are only known (all other elements can be assumed empty), then the maximum number of elements that can be produced deterministically is also x in the next 256 rounds. This conjecture was put to rest in 2004 with a formal proof given by Souradyuti Paul and Bart Preneel.

[edit] RC4-based cryptosystems

Where a cryptosystem is marked with "(optionally)", RC4 is one of several ciphers the system can be configured to use.

[edit] See also

[edit] References

  1. ^ Rivest FAQ
  2. ^ Thank you Bob Anderson. Cypherpunks mailing list (1994-09-09). Retrieved on 2007-05-28.
  3. ^ Scott R. Fluhrer and David A. McGrew, Statistical Analysis of the Alleged RC4 Keystream Generator. FSE 2000, pp19 – 30 (PDF)
  4. ^ "RC4-drop(nbytes)" in the "Standard Cryptographic Algorithm Naming" database
  5. ^ Erik Tews, Ralf-Philipp Weinmann, Andrei Pyshkin. Breaking 104-bit WEP in under a minute.

[edit] External links

RC4

RC4 in WEP

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