Reaking 104 bit WEP in less than 60 seconds

Nội dung text: Reaking 104 bit WEP in less than 60 seconds

1. Breaking 104 bit WEP in less than 60 seconds Erik Tews, Ralf-Philipp Weinmann, and Andrei Pyshkin ? TU Darmstadt, FB Informatik Hochschulstrasse 10, 64289 Darmstadt, Germany Abstract. We demonstrate an active attack on the WEP protocol that is able to recover a 104-bit WEP key using less than 40,000 frames with a success probability of 50%. In order to succeed in 95% of all cases, 85,000 packets are needed. The IV of these packets can be randomly chosen. This is an improvement in the number of required frames by more than an order of magnitude over the best known key-recovery attacks for WEP. On a IEEE 802.11g network, the number of frames required can be ob- tained by re-injection in less than a minute. The required computational effort is approximately 220 RC4 key setups, which on current desktop and laptop CPUs is negligible. 1 Introduction Wired Equivalent Privacy (WEP) is a protocol for encrypting wirelessly trans- mitted packets on IEEE 802.11 networks. In a WEP protected network, all pack- ets are encrypted using the stream cipher RC4 under a common key, the root key1 Rk. The root key is shared by all radio stations. A successful recovery of this key gives an attacker full access to the network. Although known to be insecure and superseded by Wi-Fi Protected Access (WPA) [18], this protocol is still is in widespread use almost 6 years after practical key recovery attacks were found against it [5,15]. In this paper we present a new key-recovery attack against WEP that outperforms previous methods by at least an order of magnitude. First of all we describe how packets are encrypted: For each packet, a 24-bit initialization vector (IV) IV is chosen. The IV concatenated with the root key yields the per packet key K = IV||Rk. Over the data to be encrypted, an Integrity Check Value (ICV) is calculated as a CRC32 checksum. The key K is then used to encrypt the data followed by the ICV using the RC4 stream cipher. The IV is transmitted in the header of the packet. Figure 1 shows a simplified version of an 802.11 frame. A first analysis of the design failures of the WEP protocol was published by Borisov, Goldberg and Wagner [2] in 2001. Notably, they showed that the ICV merely protects against random errors but not against malicious attackers. ? Supported by a stipend of the Marga und Kurt-M¨ollgaard-Stiftung. 1 The standard actually allows for up to four different root keys; in practice however, only a single root key is used.
2. Fig. 1. A 802.11 frame encrypted using WEP 802.11 Header Plaintext BSS ID Initialization vector (IV) Destination address Logical Link Control Subnetwork Access Protocol Header Encrypted using Data RC4(IV || RK) Integrity Check Value Furthermore, they observed that old IV values could be reused, thus allowing to inject messages. In the same year, Fluhrer, Mantin and Shamir presented a related-key ciphertext-only attack against RC4 [5]. In order for this attack to work, the IVs need to fulfill a so-called ”resolved condition”. This attack was suspected to be applicable to WEP, which was later demonstrated by Stubble- field et al [15]. Approximately 4 million different frames need to be captured to mount this attack. Vendors reacted to this attack by filtering IVs fulfilling the resolved condition, so-called ”weak IVs’. This countermeasure however proved to be insufficient: In 2004, a person using the pseudonym KoreK posted a family of statistical attacks against WEP that does not need weak IVs [9,3]; moreover the number of frames needed for key-recovery was reduced to about 500,000 packets. More recently, Klein [7] showed an improved way of attacking RC4 using related keys that does not need the ”resolved condition” on the IVs and gets by with a significantly reduced number of frames. Table 1 shows a statistic of employed encryption methods in a sample of 490 networks, found somewhere in the middle of Germany in March 2007. Another survey of more than 15.000 networks was performed in a larger German city in September 2006 [4]. Both data sets demonstrate that WEP still is a popular method for securing wireless networks. Similar observations have been made by Bittau, Handley and Lackey [1]. Their article also give an excellent history of WEP attacks and describes a real-time decryption attack based on packet fragmentation that does not recover the key. The structure of the paper is as follows: In Section 2 we introduce the nota- tion that is used throughout the rest of this paper, in Section 3.1 we present a summary of Klein’s attack on RC4, in Section 4 we specialize Klein’s Attack to WEP, Section 5 describes how sufficient amounts of key stream can be obtained for the attack, Section 6 describes extensions of the attack such as key ranking techniques in detail and Section 7 gives experimental results. 2 Notation For arrays or vectors we use the [·] notation, as used in many programing lan- guages like in C or Java. All indices start at 0. For a permutation P denote the
3. Table 1. Methods used for securing wireless networks Time No Encryption WEP WPA1/2 March 2007 21.8% 46.3% 31.9% Middle of 2006 23.3% 59.4% 17.3% −1 −1 inverse permutation by P ; meaning P[i] = j ⇔ P [j] = i. We will use x ≈n y as a short form for x ≈ y mod n. Rk is the WEP or root key and IV is the initialization vector for a packet. K = Rk||IV is the session or per packet key. X is a key stream generated using K. We will refer to a key stream X with the corresponding initialization vector IV as a session. 3 The stream cipher RC4 RC4 is a widely used stream cipher that was invented by Ron Rivest in 1987. It was a trade secret of RSA Security until 1994 when the algorithm was published anonymously on the Internet. RC4’s internal state consists of a 256-byte array S defining a permutation as well as two integers 0 ≤ i, j ≤ 255 acting as pointers into the array. The RC4 key setup initializes the internal state using a key K of up to 256 bytes. By exchanging two elements of the state in each step, it incrementally transforms the identity permutation into a ”random” permutation. The quality of randomness of the permutation after the key setup will be analyzed in Section 3.1. The RC4 key stream generation algorithm updates the RC4 internal state and generates one byte of key stream. The key stream is XORed to the plaintext to generate the ciphertext. Listing 1.1. RC4 key setup 1 for i ← 0 to 255 do 2 S[i ] ← i 3 end 4 j ← 0 5 for i ← 0 to 255 do 6 j ← j+S[i]+K[i mod len(K)] mod 256 7 swap(S, i, j) 8 end 9 i ← 0 10 j ← 0
4. Listing 1.2. RC4 key stream generation 1 i ← i + 1 mod 256 2 j ← j + S[i] mod 256 3 swap(S, i, j) 4 return S[ S[i ] + S[j] mod 256 ] We have a closer look at the RC4 key setup algorithm described in listing 1.1, especially at the values for S, i and j. After line 4, S is the identity permutation and j has the value 0. We will use Sk and jk for the values of S and j after k iterations of the loop starting in line 5 have been completed. For example, if the key CA FE BA BE is used, S0 is the identity permutation and j0 = 0. After the first key byte has been processed, j1 = 202 and S1[0] = 202, S1[202] = 0, and S1[x] = S0[x] = x for 0 6= x 6= 202. 3.1 Klein’s attack on RC4 Suppose w key streams were generated by RC4 using packet keys with a fixed root key and different initialization vectors. Denote by Ku = (Ku[0], , Ku[m]) = (IVukRk) the u-th packet key and by Xu = (Xu[0], , Xu[m − 1]) the first m bytes of the uth key stream, where 1 ≤ u ≤ w. Assume that an attacker knows the pairs (IVu, Xu) – we shall refer to them as samples – and tries to find Rk. i In [7], Klein showed that there is a map Fi :(Z/nZ) → Z/nZ with 1 ≤ i ≤ m such that ( 1.36 K[i], with Prob ≈ n Fi(K[0], , K[i − 1], X[i − 1]) = 1 a 6= K[i], with Prob < n for all a So Fi can be seen as a kind of approximation for K[i], and we can write Fi ≈n K[i]. If the first i bytes of a packet key are known, then the internal permutation Si−1 and the index j at the (i − 1)th step of the RC4 key setup algorithm can be found. We have −1 Fi(K[0], , K[i − 1], X[i − 1]) = Si−1[i − X[i − 1]] − (ji−1 + Si−1[i]) mod n The attack is based on the following properties of permutations. Theorem 1 For a random number j ∈ {0, . . . , n−1} and a random permutation P, we have 2 Prob(P[j] + P[P[i] + P[j] mod n] = i mod n) = n n − 2 Prob(P[j] + P[P[i] + P[j] mod n] = c mod n) = n(n − 1) where i, c ∈ {0, . . . , n − 1} are fixed, and c 6= i. Proof. see [7].
5. In the case of n = 256, the first probability is equal to 2−7 ≈ 0.00781, and the second one is approximately equal to 0.00389. From Theorem 1 it follows that for RC4 there is a correlation between i, Si+n[Si+n[i] + Si+n[j] mod n], and Si+n[j] = Si+n−1[i]. Next, the equality Si[i] = Si+n−1[i] holds with high probability. The theoret- ical explanation of this is the following. If we replace the line 6 of the RC4 key setup, and the line 2 of the RC4 key stream generator by j ← RND(n), 2 then  1 n−2 Prob(S [i] = S [i]) = 1 − ≈ e−1 i i+n−1 n Moreover, we have Si[i] = Si−1[ji] = Si−1[ji−1 + Si−1[i] + K[i] mod n]. Combining this with Theorem 1, we get the probability that −1 K[i] = Si−1[i − Si+n−1[Si+n−1[i] + Si+n−1[j] mod n] mod n] − (ji−1 + Si−1[i]) is approximately !  1 n−2 2  1 n−2 n − 2 1.36 1 − + 1 − 1 − ≈ n n n n(n − 1) n 4 Extension to multiple key bytes With Klein’s attack, it is possible to iteratively compute all secret key bytes, if enough samples are available. This iterative approach has a significant disad- vantage: In this case the key streams and IVs need to be saved and processed for every key byte. Additionally correcting falsely guessed key byte is expensive, because the computations for all key bytes following K[i] needs to be repeated if K[i] was incorrect. We extend the attack such that is it possible to compute key bytes indepen- dently of each other and thus make efficient use of the attack possible by using key ranking techniques. Klein’s attack is based on the the fact that −1 K[i] ≈n Si [i − X[i − 1]] − (Si[i] + ji) (1) −1 K[i + 1] ≈n Si+1[(i + 1) − X[(i + 1) − 1]] − (Si+1[i + 1] + ji+1) (2) We may write ji+1 as ji + Si[i] + K[i]. By replacing ji+1 in equation 2, we get an approximation for K[i] + K[i + 1]: −1 K[i] + K[i + 1] ≈n Si+1[(i + 1) − X[(i + 1) − 1]] − (Si+1[i + 1] + ji + Si[i]) (3) 2 ` 1 ´n−2 1 ` 1 ´n−2 Some publications approximate 1 − n by e . We will use 1 − n for the rest of this paper.
6. Pi+k By repeatedly replacing ji+k, we get an approximation for l=i K[l]. Because P3+i Pi we are mostly interested in l=3 K[l] = l=0 Rk[l] in a WEP scenario, we will use the symbol σi for this sum. i+3 ! −1 X ˜ σi ≈n S3+i[(3 + i) − X[2 + i]] − j3 + Sl[l] = Ai (4) l=3 The right side of equation 4 still depends on the key bytes K[3] to K[i − 1], −1 because they are needed to compute Sl and S3+i. By replacing them with S3, we get another approximation Ai for σi, which only depends on K[0] to K[2]. i+3 ! −1 X σi ≈n S3 [(3 + i) − X[2 + i]] − j3 + S3[l] = Ai (5) l=3 Under idealized conditions, Klein derives the following probability for the event A˜i = σi: !    1 n−2 2  1 n−2 n − 2 Prob σ = A˜ ≈ 1 − · + 1 − 1 − · (6) i i n n n n(n − 1) The first part of sum represents the probability that S[i + 3] remains un- changed until X[2 + i] is generated, the second part represents the probability that S[i + 3] is changed during key scheduling or key stream generation with Ai still taking the correct value. By replacing Sl and Si+3 with their previous values, we have reduced that probability slightly. Sk+3[k + 3] differs from S3[k + 3] only if one of the values of j3 to jk+2 has been k + 3. All values of Sl[l] will be correct, if for all jz with 3 ≤ z ≤ 3 + i the condition jz ∈/ {z, . . . , 3 + i} holds. Assuming j changes randomly, this happens Qi k
   with probability k=1 1 − n . Additionally S3+i[ji+3] should not be changed between iteration 3 and 3+i. This is true if j does not take the value of ji+3 in a 1
   i previous round, which happens with probability ≈ 1 − n and i does not take i
   the value of ji+3, which happens with probability ≈ 1 − n . To summarize, the probability that replacing all occurrences of S in A˜i with S3 did not change anything is: i i  1   i  Y  k  q = 1 − · 1 − · 1 − (7) i n n n k=1 This results in the following probability pcorrecti being a lower bound for Ai taking the correct value for σi.
7. !  1 n−2 2  1 n−2 n − 2 Prob (σ = A ) ≈ q · 1 − · + 1 − q · 1 − · (8) i i i n n i n n(n − 1) Experimental results using more than 50,000,000,000 simulations with 104 bit WEP keys show that this approximations differs less than 0.2% from values determined from these simulations. 5 Obtaining sufficient amounts of key stream The Internet Protocol (IP) is the most widely deployed network protocol. For our attack to work, we assume that version 4 (IPv4) of this protocol is used on the wireless networks we attack. If host A wants to send an IP datagram to host B, A needs the physical address of host B or the gateway through which B can be reached. To resolve IP addresses of hosts to their physical address, the Address Resolution Protocol (ARP) [13] is used. This works as follows: Host A sends an ARP request to the link layer broadcast address. This request announces that A is looking for the physical address of host B. Host B responds with an ARP reply containing his own physical address to host A. Since the Address Resolution Protocol is a link layer protocol it is typically not restricted by any kind of packet filters or rate limiting rules. ARP requests and ARP replies are of fixed size. Because the size of a packet is not masked by WEP, they can usually be easily distinguished from other traffic. The first 16 bytes of cleartext of an ARP packet are made up of a 8 byte long 802.11 Logical Link Control (LLC) header followed by the first 8 bytes of the ARP packet itself. The LLC header is fixed for every ARP packet (AA AA 03 00 00 00 08 06). The first 8 bytes of an ARP request are also fixed. Their value is 00 01 08 00 06 04 00 01. For an ARP response, the last byte changes to 02, the rest of the bytes are identical to an ARP request. An ARP request is always sent to the broadcast address, while an ARP response is sent to a unicast address. Because the physical addresses are not encrypted by WEP, it is easy to distinguish between an encrypted ARP request and response. By XORing a captured ARP packet with these fixed patterns, we can recover the first 16 bytes of the key stream. The corresponding IV is transmitted in clear with the packet. To speed up key stream recovery, it is possible to re-inject a captured ARP request into the network, which will trigger another reply. The destination an- swers the request with a new response packet that we can add to our list of key streams. If the initiator and the destination of the original request have been both wireless stations, every re-injected packet will generate three new pack- ets, because the transmission will be relayed by the access point. Because ARP replies expire quickly, it usually takes only a few seconds or minutes until an
8. Fig. 2. Cleartext of ARP request and response packets Opcode = Request AA AA 03 00 00 00 08 06 00 01 08 00 06 04 00 01 XX LLC/SNAP Header ARP Header arp who-has 192.168.1.2 tell 192.168.1.3 Opcode = Response AA AA 03 00 00 00 08 06 00 01 08 00 06 04 00 02 XX LLC/SNAP Header ARP Header arp reply 192.168.1.2 is-at 00:01:02:03:04:05 attacker can capture an ARP request and start re-injecting it. The first pub- lic implementation of a practical re-injection attack was in the BSD-Airtools package [6]. It is even possible to speed up the time it takes to capture the first ARP request. A de-authenticate message can be sent to a client in the network, telling him that he has lost contact with the base station. In some configurations we saw clients rejoining the network automatically and at the same time flushing their ARP cache. The next IP packet sent by this client will cause an ARP request to look up the Ethernet address of the destination. 6 Our attack on WEP The basic attack is straightforward. We use the methods described in Section 5 to generate a sufficient amount of key stream under different IVs. Initially we assume that a 104 bit WEP key was used. For every σi from σ0 to σ12, and every recovered key stream, we calculate Ai as described in equation 5 and call the result a vote for σi having the value Ai. We keep track of those votes in separate tables for each σi. Having processed all available key streams, we assume that the correct value for every σi is the one with the most votes received. The correct key is simply Rk[0] = σ0 for the first key byte and Rk[i] = σi − σi−1 for all other key bytes. If the correct key was a 40 bit key instead of a 104 bit key, the correct key is just calculated from σ0 to σ4. 6.1 Key ranking If only a low number of samples is available, the correct value for σi is not always the most voted one in the table, but tends to be one of the most voted. Figure 3 contains an example in which the correct value has the second most votes after 35.000 sessions. Instead of collecting more samples, we use another method for finding the correct key. Checking if a key is the correct key is simple, because we have collected a lot of key streams with their corresponding IV. We can just
9. generate a key stream using an IV and a guessed key, and compare it with the collected one. If the method used for key stream recovery did not always guess the key stream right, the correct value just needs to match a certain fraction of some key streams. For every key byte K[i], we define a set Mi of possible values σi might have. At the beginning, Mi is only initialized with the top voted value for σi from the table. Until the correct key is found, we look for an entryσ ˜i ∈/ Mi in all tables having a minimum distance to the top voted entry in table i. We then addσ ˜i to Mi and test all keys which can now be constructed from the sets M that have not been tested previously. 6.2 Handling strong keys For equation 5 we assumed S3 to be an approximation of S3+i. This assumption is wrong for a fraction of the key space. We call these keys strong keys. For these keys, the value for ji+3 with high probability is taken by j in a iteration before i + 3 and after 3. This results in S[ji+3] being swapped with an unknown value, depending on the previous key bytes and the IV. In iteration i + 3, this value instead of S3[ji+3] is now swapped with S[i]. More formally, let Rk be a key and Rk[i] a key byte of Rk. Rk[i] is a strong key byte, if there is an integer l ∈ {1, . . . , i} where i X (Rk[k] + 3 + k) ≡n 0 (9) k=l A key Rk is a strong key, if at least one of its key bytes is a strong key byte. On the contrary, key bytes that are not strong key bytes are called normal key bytes and keys in which not a single strong key byte occurs are called normal keys. Assuming that S is still the identity permutation, the value 0 will be added to jl+3 from iteration l + 3 to i + 3, making ji+3 taking his previous value jl+3. This results in the value qi of equation 7 being close to 0 and Prob(σi = Ai) is 1 very close to n . Figure 3 shows the distribution of votes for a strong and a non strong key byte after 35.000 and 300.000 samples. It is easy to see that the correct value for strong key byte has not received the most votes of all key bytes any longer. An alternative way must be used to determine the correct value for this key byte. Our approach can be divided into two steps: 1. Find out which key bytes are strong key bytes: If a key byte Rk[i] is a normal key byte, the correct value for σi should appear with probability ≈ pcorrecti (see equation 8). We assume that all (1−pcorrect ) other values are equidistributed with probability p = i . If wrongi n−1 Rk[i] is a strong key byte we assume that all values are equidistributed with 1 probability pequal = n .
10. Fig. 3. Distribution of votes for a strong and a normal key byte Weak key byte after 35000 Normal key byte after 35000 0.006 0.006 wrong value wrong value correct value correct value 0.005 0.005 0.004 0.004 fraction of all votes fraction of all votes 0.003 0.003 Weak key byte after 300000 Normal key byte after 300000 0.006 0.006 wrong value wrong value correct value correct value 0.005 0.005 0.004 0.004 fraction of all votes fraction of all votes 0.003 0.003 Let Nib the fraction of votes for which σi = b holds. We calculate n X
    2 errstrongi = Nij − pequal (10) j=0  2 errnormal = max(Ni ) − pcorrect + i b b i n X
    2 Nij − pwrongi (11) j=0,j6=argmaxb(Nib ) If enough samples are available, this can be used as a test if errstrongi is smaller than errnormali . If that is the case, it is highly likely that key byte Rk[i] is a strong key byte. If only a small number of samples are available, errstrongi − errnormali can be used as an indicator for the likelihood of key byte Rk[i] being a strong key byte. 2. Find the correct values for these key bytes: Assuming that Rk[i] is a strong key byte and all values for Rk[0] Rk[i − 1] are known, we can use equation 9 and get the following equation for Rk[i]: i−1 X Rk[i] ≡n −3 − i − (Rk[j] + 3 + j) (12) j=l Because there at most i possible values for l, we can try every possible value for l and restrict Rk[i] to at most i possible values (12 if Rk[i] is the last key byte for a 104 bit key). This method can be combined with the key ranking
11. method as described in Section 6.1. Instead of taking possible values for σi from the top voted value in the table for key byte i, we ignore the table and use the values calculated with equation 12 for Rk[i] and assume that σi−1 + Rk[i] was top voted in the table. Possible values for σi for all assumed to be normal key bytes are still taken from the top voted values in their tables. This approach is only feasible if the number of strong bytes in the key is small. For a 104 bit key all 12 key bytes can be strong key bytes. For such a key, we need to test up to 12! ≈ 228.8 different keys, which is possible, but slows down our attack. Because Klein’s attack as described in Section 3.1 is not hindered by strong keys, we suggest to additionally implement this attack without key ranking, to be able to attack even keys with the maximum number of strong key bytes in a reasonable time. 6.3 A passive version For the attack in the previous section we assumed that an attacker obtains a sufficient amount of encrypted ARP packets by actively injecting ARP requests into the network. This attack strategy however might be detected by an intrusion detecting system (IDS). In this section we present a passive version of the attack. As we have seen, an ARP packet can be detected by its destination address and size. For our attack we will assume every packet which is not an ARP packet to be an IPv4 packet. This is expected to be true with a high probability for most networks in use today. Figure 4 shows the first 15 bytes of an IPv4 packet [14]. Fig. 4. First 15 bytes of a 802.11 frame containing an IPv4 packet Identification Total Length Flags, Offset AA AA 03 00 00 00 08 00 45 00 YY YY ZZ ZZ 40 XX LLC/SNAP Header IPv4 Header There are three fields in the first 7 bytes of the the IPv4 header which do not contain fixed values. These are: Total Length This is the total length of the packet, starting from the IPv4 header. We can calculate this value from the length of the 802.11 frame, which can be observed. Identification This field is used to keep track of packets for the reassembly of fragments and must be assumed to be random.
12. Flags and Fragment Offset This byte contains the most significant bits of the fragment offset and two control flags. Because IPv4 packets are usually short, the most significant bits of the fragment offset can be assumed to be zero, even if the packet was fragmented. After having analyzed traffic from various sources, we found that about 85% of all packets were sent with the don’t fragment flag set and about 15% had all flags cleared. In total, this means that we cannot guess two bytes at all, and one byte can be restricted to two possible values with high probability. We can now modify our attack as follows. The values for σ10 and σ11 are not determined by statistical tests, because we cannot recover X[12] and X[13]. Instead, we just iterate over all 216 possible values when it comes to determine these values. To prevent a slowdown of our attack by a factor of 216, we do less key ranking. To determine the value of σ12, we now introduce the concept of a ”weighted vote”. Until now, we counted the output of the function Ai as a vote for σi having a specific value. We now calculate A12 two times, once under the assumption that X[12] = 64 (which is equivalent to don’t fragment flag set), and count it 220 as a 256 vote for σ12, and once with the assumption that X[12] = 0 (which is 36 equivalent to no flags set), and count it as a 256 vote for σ12. Of course, the exact success rate of this passive attack heavily depends on the nature of the traffic captured, but some simulations have shown that it works with reasonable reliability and just needs some more captured packets than the active version just using ARP packets. Most of the work on the passive attack has been done by Martin Beck who also integrated our attack in the aircrack-ng toolsuite [16]. 6.4 Breaking implementations using larger WEP keys Some vendors implemented WEP using root keys longer than 104 bit. We have seen implementations using up to 232 bit key length for the root key. Attacking such networks is not as easy as attacking a 104 bit key, because only the first 16 bytes of cleartext of an ARP packet are known, but 31 bytes of the cleartext would be needed. The missing 15 bytes are constant for every request or response, if only a single ARP packet was used for injection. Using the chopchop attack invented by KoreK [8] or the fragmentation attack published by Bittau, Handley and Lackey [1] allows us do decrypt the request packet we used and one of the response packets. The decrypted packets can then be used for the ARP injection attack. Because ARP responses contain packet-unique values, we can assume that all other responses contain exactly the same plaintext. This allows us to recover enough plaintext for breaking even implementations with root keys longer than 232 bit. 7 Experimental Results We wrote an implementation using the parallelized computation as described in Section 4 and the key ranking methods described in Section 6.1 and 6.2. At
13. the beginning an upper bound on the number of keys to be tested is fixed (key limit). A limit of 1,000,000 keys seems a reasonable choice for a modern PC or laptop. Three different scenarios of attacks cover the most likely keys: scenario 1 tests 70% of the limit and uses key ranking as described in Section 6.1. As long as the set of possible keys does not exceed 70% of the key limit, a new value v∈ / Mi is added to a set Mi. The value v is chosen to have minimal distance to the top voted entry. scenario 2 tests 20% of the limit and uses the key ranking method in combina- tion with strong byte detection. We use the difference errstrongi − errnormali to determine which key byte is the most likely to be strong. We then use equation 12 to get possible values for this key byte. As long as the number of possible keys does not exceed 20% of the key limit all other key bytes are determined as in scenario 1. scenario 3 tests 10% of the limit and works like scenario 2, with the exception that 2 key bytes are assumed to be strong. To verify a possible key Rk for correctness, 10 sessions (IVi, Xi) are chosen at random. If the key stream generated using IVi||Rk is identical to Xi in the first 6 bytes for all sessions, we assume the key to be correct. If all three scenarios where unsuccessful, the attack is retried using just 10% of the key limit, this time under the assumption that the root key is a 40 bit key instead of a 104 bit one. Figure 5 shows the result from a simulation, showing that a 50% success rate is possible using just 40,000 packets. Fig. 5. Success rate 1 keylimit 1,000,000 0.9 5% randomized keylimit 1,000,000 keylimit 5,000 0.8 linux iv keylimit 1,000,000 0.7 0.6 0.5 0.4 0.3 probability of success 0.2 0.1 0 20000 25000 30000 35000 40000 45000 50000 55000 60000 65000 70000 75000 80000 85000 number of keystreams collected To test whether this attack works in a real world scenario we used the aircrack-ng tool suite [16]. aircrack-ng contains aireplay-ng, a tool which is able to capture and replay 802.11 frames; for example, frames containing ARP re- quests or other kinds of packets that cause traffic on the target network. Ad- ditionally, airodump-ng can be used to capture and save the generated traffic including all needed IEEE 802.11 headers.
14. On a mixed IEEE 802.11 b/g network, consisting of cards with chipsets from Atheros, Broadcom, Intersil and Intel, we achieved a rate of 764 different cap- tured packets per second, using aireplay-ng and a network card with a PrismGT chipset for injecting and an Atheros based card for capturing. This number might vary, depending on the chipsets and the quality of the signal. This allowed us to recover 40,492 key streams in 53 seconds. Additional 2 seconds can be added for deauthenticating one or all clients forcing them to send out new ARP requests. The final cryptographic computation requires 1 to 3 seconds of CPU-time, de- pending on the CPU being used. For a 104 bit key we were able to consistently and successfully recover keys from a packet capture in less than 3 seconds on a Thinkpad T41p (1.7 GHz Pentium-M CPU) – this includes reading and parsing the dump file, recovering key streams and performing the actual attack. On more recent multi-core CPUs we expect this figure can be brought down to less than a second with a parallelized key space search. This results in 54 to 58 seconds to crack a 104 bit WEP key, with probability 50%. Main memory requirements for an efficient implementation are quite low. Our implementation needs less than 3 MB of main memory for data structures. Most of the memory is consumed by a bit field for finding duplicate IVs, this is 2 MB in size. CPU-time scales almost linearly with the number of keys tested. By reducing the number of keys tested to 5,000, this attack is suitable for PDA or embedded system usage too, by only reducing its success probability a little bit. The success rate with this reduced key limit is included in Figure 5 with label keylimit 5,000. 7.1 Robustness of the attack The key stream recovery method we used might not always be correct. For example, any kind of short packet (TCP, UDP, ICMP) might be identified as an ARP reply resulting in an incorrect key stream. To find out how our attack performs with some incorrect values in key streams, we ran a simulation with 5% of all key streams replaced with random values. The result is included in Figure 5, labeled ”5% randomized key limit 1,000,000”. Depending on the number of packets collected, the success rate is slightly reduced by less than 10%. If enough packets are available, there is no visible difference. In all previous simulations, we assumed that IVs are generated independently, using any kind of pseudo random function. Some drivers in fact do use an PRNG to generate the IV value for each packet, however others use a counter with some modifications. For example the 802.11 stack in the Linux 2.6.20 kernel uses an counter, which additionally skips IVs which where used for an earlier attack on RC4 by Fuller, Mantin and Shamir which became known as FMS-weak-IVs. Using this modified IV generation scheme, the success rate of our attack (label linux iv keylimit 1,000,000 ) was slightly reduced by less than 5%, depending on the number of packets available. As before, there are no noticeable differences, if a high number of packets are available.
15. 8 Related and further work After we made a draft of this paper available on the IACR’s Cryptology ePrint Archive in early April 2007, other researchers published similar analyses. Sub- hamoy Maitra and Goutam Paul gave an independent analysis [10] of Klein’s attack with results similar to our multiple key bytes extension. Additionally, they found new correlations in RC4 independent of Klein’s analysis. Vaudenay and Vuagnoux presented a similar attack at SAC2007 [17], which additionally makes use of the fact that the RC4 key is stretched to 256 bytes by repeating it. The same trick was discovered by Ohigashi, Ozasa, Fujikawa, Kuwadako and Morii [12], who developed an improved version of our attack. Vau- denay and Vuagnoux additionally make use of a modified FMS attack, to improve their results. Still ongoing research of Ohigashi, Ozasa, Fujikawa, Kuwadako and Morii is expected to halve the number of packets needed for similar success rates as ours [11]. 9 Conclusion We have extended Klein’s attack on RC4 and have applied it to the WEP proto- col. Our extension consists in showing how to determine key bytes independently of each other and allows us to dramatically decrease the time complexity of a brute force attack on the remaining key bytes. We have carefully analyzed cases in which a straightforward extension of Klein’s attack will fail and have shown how to deal with these situations. The number of packets needed for our attack is so low that opportunistic attacks on this security protocol will be most probable. Although it has been known to be insecure and has been broken by a key-recovery attack for almost 6 years, WEP is still seeing widespread use at the time of writing this paper. While arguably still providing a weak deterrent against casual attackers in the past, the attack presented in this paper greatly improves the ease with which the security measure can be broken and will likely define a watershed moment in the arena of practical attacks on wireless networks. References 1. Andrea Bittau, Mark Handley, and Joshua Lackey. The final nail in WEP’s coffin. In IEEE Symposium on Security and Privacy, pages 386–400. IEEE Computer Society, 2006. 2. Nikita Borisov, Ian Goldberg, and David Wagner. Intercepting mobile communi- cations: the insecurity of 802.11. In ACM MobiCom 2001, pages 180–189. ACM Press, 2001. 3. Rafik Chaabouni. Break WEP faster with statistical analysis. Technical report, EPFL, LASEC, June 2006. pdf. 4. Stefan D¨orh¨ofer. Empirische Untersuchungen zur WLAN-Sicherheit mittels Wardriving. Diplomarbeit, RWTH Aachen, September 2006. (in German).
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