Breaking 104 bit WEP in less than 60 seconds
Erik Tews, Ralf-Philipp Weinmann, and Andrei Pyshkin
?
<e tews,weinmann,pyshkin@cdc.informatik.tu-darmstadt.de>
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 2
20
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
key
1
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and superseded by Wi-Fi Protected Access (WPA) [18], this protocol is still is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.
Fig. 1.
A 802.11 frame encrypted using WEP
802.11 Header
BSS ID Initialization vector (IV) Destination address
Logical Link Control
Data
Integrity Check Value
Encrypted using
RC4(IV || RK)
Plaintext
Subnetwork Access Protocol Header
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
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%
inverse permutation by
P
−
1
; meaning
P
[
i
] =
j
⇔
P
−
1
[
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
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
S
k
and
j
k
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,
S
0
is the identity permutation and
j
0
= 0. After the
first key byte has been processed,
j
1
= 202 and
S
1
[0] = 202,
S
1
[202] = 0, and
S
1
[
x
] =
S
0
[
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
K
u
= (
K
u
[0]
, . . . ,
K
u
[
m
]) =
(
IV
u
k
Rk
) the
u
-th packet key and by
X
u
= (
X
u
[0]
, . . . ,
X
u
[
m
−
1]) the first
m
bytes of the
u
th key stream, where 1
≤
u
≤
w
. Assume that an attacker knows
the pairs (
IV
u
,
X
u
) – we shall refer to them as
samples
– and tries to find
Rk
.
In [7], Klein showed that there is a map
F
i
: (
Z
/n
Z
)
i
→
Z
/n
Z
with 1
≤
i
≤
m
such that
F
i
(
K
[0]
, . . . ,
K
[
i
−
1]
,
X
[
i
−
1]) =
(
K
[
i
]
,
with Prob
≈
1
.
36
n
a
6
=
K
[
i
]
,
with Prob
<
1
n
for all
a
So
F
i
can be seen as a kind of approximation for
K
[
i
], and we can write
F
i
≈
n
K
[
i
]. If the first
i
bytes of a packet key are known, then the internal
permutation
S
i
−
1
and the index
j
at the (
i
−
1)th step of the RC4 key setup
algorithm can be found. We have
F
i
(
K
[0]
, . . . ,
K
[
i
−
1]
,
X
[
i
−
1]) =
S
−
1
i
−
1
[
i
−
X
[
i
−
1]]
−
(
j
i
−
1
+
S
i
−
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
Prob(
P
[
j
] +
P
[
P
[
i
] +
P
[
j
] mod
n
] =
i
mod
n
) =
2
n
Prob(
P
[
j
] +
P
[
P
[
i
] +
P
[
j
] mod
n
] =
c
mod
n
) =
n
−
2
n
(
n
−
1)
where
i, c
∈ {
0
, . . . , n
−
1
}
are fixed, and
c
6
=
i
.
Proof.
see [7].
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
,
S
i
+
n
[
S
i
+
n
[
i
] +
S
i
+
n
[
j
] mod
n
], and
S
i
+
n
[
j
] =
S
i
+
n
−
1
[
i
].
Next, the equality
S
i
[
i
] =
S
i
+
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
Prob(
S
i
[
i
] =
S
i
+
n
−
1
[
i
]) =
1
−
1
n
n
−
2
≈
e
−
1
Moreover, we have
S
i
[
i
] =
S
i
−
1
[
j
i
] =
S
i
−
1
[
j
i
−
1
+
S
i
−
1
[
i
] +
K
[
i
] mod
n
].
Combining this with Theorem 1, we get the probability that
K
[
i
] =
S
−
1
i
−
1
[
i
−
S
i
+
n
−
1
[
S
i
+
n
−
1
[
i
] +
S
i
+
n
−
1
[
j
] mod
n
] mod
n
]
−
(
j
i
−
1
+
S
i
−
1
[
i
])
is approximately
1
−
1
n
n
−
2
2
n
+
1
−
1
−
1
n
n
−
2
!
n
−
2
n
(
n
−
1)
≈
1
.
36
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
K
[
i
]
≈
n
S
−
1
i
[
i
−
X
[
i
−
1]]
−
(
S
i
[
i
] +
j
i
)
(1)
K
[
i
+ 1]
≈
n
S
−
1
i
+1
[(
i
+ 1)
−
X
[(
i
+ 1)
−
1]]
−
(
S
i
+1
[
i
+ 1] +
j
i
+1
)
(2)
We may write
j
i
+1
as
j
i
+
S
i
[
i
] +
K
[
i
]. By replacing
j
i
+1
in equation 2, we
get an approximation for
K
[
i
] +
K
[
i
+ 1]:
K
[
i
] +
K
[
i
+ 1]
≈
n
S
−
1
i
+1
[(
i
+ 1)
−
X
[(
i
+ 1)
−
1]]
−
(
S
i
+1
[
i
+ 1] +
j
i
+
S
i
[
i
]) (3)
2
Some publications approximate
`
1
−
1
n
´
n
−
2
by
1
e
. We will use
`
1
−
1
n
´
n
−
2
for the
rest of this paper.
By repeatedly replacing
j
i
+
k
, we get an approximation for
P
i
+
k
l
=
i
K
[
l
]. Because
we are mostly interested in
P
3+
i
l
=3
K
[
l
] =
P
i
l
=0
Rk
[
l
] in a WEP scenario, we will
use the symbol
σ
i
for this sum.
σ
i
≈
n
S
−
1
3+
i
[(3 +
i
)
−
X
[2 +
i
]]
−
j
3
+
i
+3
X
l
=3
S
l
[
l
]
!
= ˜
A
i
(4)
The right side of equation 4 still depends on the key bytes
K
[3] to
K
[
i
−
1],
because they are needed to compute
S
l
and
S
−
1
3+
i
. By replacing them with
S
3
, we
get another approximation
A
i
for
σ
i
, which only depends on
K
[0] to
K
[2].
σ
i
≈
n
S
−
1
3
[(3 +
i
)
−
X
[2 +
i
]]
−
j
3
+
i
+3
X
l
=3
S
3
[
l
]
!
=
A
i
(5)
Under idealized conditions, Klein derives the following probability for the
event ˜
A
i
=
σ
i
:
Prob
σ
i
= ˜
A
i
≈
1
−
1
n
n
−
2
·
2
n
+
1
−
1
−
1
n
n
−
2
!
·
n
−
2
n
(
n
−
1)
(6)
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
A
i
still taking the correct value. By replacing
S
l
and
S
i
+3
with their previous
values, we have reduced that probability slightly.
S
k
+3
[
k
+ 3] differs from
S
3
[
k
+ 3] only if one of the values of
j
3
to
j
k
+2
has
been
k
+ 3. All values of
S
l
[
l
] will be correct, if for all
j
z
with 3
≤
z
≤
3 +
i
the
condition
j
z
/
∈ {
z, . . . ,
3 +
i
}
holds. Assuming
j
changes randomly, this happens
with probability
Q
i
k
=1
1
−
k
n
. Additionally
S
3+
i
[
j
i
+3
] should not be changed
between iteration 3 and 3 +
i
. This is true if
j
does not take the value of
j
i
+3
in a
previous round, which happens with probability
≈
1
−
1
n
i
and
i
does not take
the value of
j
i
+3
, which happens with probability
≈
1
−
i
n
. To summarize,
the probability that replacing all occurrences of
S
in ˜
A
i
with
S
3
did not change
anything is:
q
i
=
1
−
1
n
i
·
1
−
i
n
·
i
Y
k
=1
1
−
k
n
(7)
This results in the following probability
p
correct
i
being a lower bound for
A
i
taking the correct value for
σ
i
.
Prob (
σ
i
=
A
i
)
≈
q
i
·
1
−
1
n
n
−
2
·
2
n
+
1
−
q
i
·
1
−
1
n
n
−
2
!
·
n
−
2
n
(
n
−
1)
(8)
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
Fig. 2.
Cleartext of ARP request and response packets
XX
AA AA 03 00 00 00 08 06 00 01 08 00 06 04 00 01
LLC/SNAP Header
ARP Header
Opcode = Request
arp who-has 192.168.1.2 tell 192.168.1.3
arp reply 192.168.1.2 is-at 00:01:02:03:04:05
XX
AA AA 03 00 00 00 08 06 00 01 08 00 06 04 00 02
LLC/SNAP Header
ARP Header
Opcode = Response
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
σ
i
from
σ
0
to
σ
12
, and every
recovered key stream, we calculate
A
i
as described in equation 5 and call the
result a
vote
for
σ
i
having the value
A
i
. We keep track of those votes in separate
tables for each
σ
i
.
Having processed all available key streams, we assume that the correct value
for every
σ
i
is the one with the most votes received. The correct key is simply
Rk
[0] =
σ
0
for the first key byte and
Rk
[
i
] =
σ
i
−
σ
i
−
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
σ
0
to
σ
4
.
6.1
Key ranking
If only a low number of samples is available, the correct value for
σ
i
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
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
M
i
of possible values
σ
i
might have.
At the beginning,
M
i
is only initialized with the top voted value for
σ
i
from the
table. Until the correct key is found, we look for an entry ˜
σ
i
/
∈
M
i
in all tables
having a minimum distance to the top voted entry in table
i
. We then add ˜
σ
i
to
M
i
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
S
3
to be an approximation of
S
3+
i
. This assumption
is wrong for a fraction of the key space. We call these keys
strong keys
. For these
keys, the value for
j
i
+3
with high probability is taken by
j
in a iteration before
i
+ 3 and after 3. This results in
S
[
j
i
+3
] being swapped with an unknown value,
depending on the previous key bytes and the
IV
. In iteration
i
+ 3, this value
instead of
S
3
[
j
i
+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
k
=
l
(
Rk
[
k
] + 3 +
k
)
≡
n
0
(9)
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
j
l
+3
from iteration
l
+ 3 to
i
+ 3, making
j
i
+3
taking his previous value
j
l
+3
.
This results in the value
q
i
of equation 7 being close to 0 and Prob(
σ
i
=
A
i
) is
very close to
1
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
σ
i
should
appear with probability
≈
p
correct
i
(see equation 8). We assume that all
other values are equidistributed with probability
p
wrong
i
=
(
1
−
p
correcti
)
n
−
1
. If
Rk
[
i
] is a strong key byte we assume that all values are equidistributed with
probability
p
equal
=
1
n
.
Fig. 3.
Distribution of votes for a strong and a normal key byte
0.003
0.004
0.005
0.006
fraction of all votes
Weak key byte after 35000
wrong value
correct value
0.003
0.004
0.005
0.006
fraction of all votes
Normal key byte after 35000
wrong value
correct value
0.003
0.004
0.005
0.006
fraction of all votes
Weak key byte after 300000
wrong value
correct value
0.003
0.004
0.005
0.006
fraction of all votes
Normal key byte after 300000
wrong value
correct value
Let
N
i
b
the fraction of votes for which
σ
i
=
b
holds. We calculate
err
strong
i
=
n
X
j
=0
N
i
j
−
p
equal
2
(10)
err
normal
i
=
max
b
(
N
i
b
)
−
p
correct
i
2
+
n
X
j
=0
,j
6
=argmax
b
(N
ib
)
N
i
j
−
p
wrong
i
2
(11)
If enough samples are available, this can be used as a test if err
strong
i
is
smaller than err
normal
i
. 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,
err
strong
i
−
err
normal
i
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
]:
Rk
[
i
]
≡
n
−
3
−
i
−
i
−
1
X
j
=
l
(
Rk
[
j
] + 3 +
j
)
(12)
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
method as described in Section 6.1. Instead of taking possible values for
σ
i
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
σ
i
−
1
+
Rk
[
i
] was top voted in the table. Possible values for
σ
i
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!
≈
2
28
.
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
XX
AA AA 03 00 00 00 08 00 45 00 YY YY ZZ ZZ 40
LLC/SNAP Header
IPv4 Header
Flags, Offset
Identification
Total Length
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.
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
σ
10
and
σ
11
are
not determined by statistical tests, because we cannot recover
X
[12] and
X
[13].
Instead, we just iterate over all 2
16
possible values when it comes to determine
these values. To prevent a slowdown of our attack by a factor of 2
16
, we do less
key ranking.
To determine the value of
σ
12
, we now introduce the concept of a ”weighted
vote”. Until now, we counted the output of the function
A
i
as a vote for
σ
i
having
a specific value. We now calculate
A
12
two times, once under the assumption
that
X
[12] = 64 (which is equivalent to
don’t fragment
flag set), and count it
as a
220
256
vote for
σ
12
, and once with the assumption that
X
[12] = 0 (which is
equivalent to no flags set), and count it as a
36
256
vote for
σ
12
.
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
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 /
∈
M
i
is added to a set
M
i
. 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 err
strong
i
−
err
normal
i
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 (
IV
i
,
X
i
) are chosen at
random. If the key stream generated using
IV
i
||
Rk
is identical to
X
i
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
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
20000
25000
30000
35000
40000
45000
50000
55000
60000
65000
70000
75000
80000
85000
probability of success
number of keystreams collected
keylimit 1,000,000
5% randomized keylimit 1,000,000
keylimit 5,000
linux iv keylimit 1,000,000
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.
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.
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.
http://lasecwww.epfl.ch/pub/lasec/doc/cha06.
pdf
.
4. Stefan D¨
orh¨
ofer.
Empirische Untersuchungen zur WLAN-Sicherheit mittels
Wardriving. Diplomarbeit, RWTH Aachen, September 2006. (in German).
5. Scott R. Fluhrer, Itsik Mantin, and Adi Shamir. Weaknesses in the key scheduling
algorithm of RC4. In Serge Vaudenay and Amr M. Youssef, editors,
Selected Areas
in Cryptography 2001
, volume 2259 of
Lecture Notes in Computer Science
, pages
1–24. Springer, 2001.
6. David Hulton (h1kari).
bsd-airtools.
http://www.dachb0den.com/projects/
bsd-airtools.html
.
7. Andreas Klein. Attacks on the RC4 stream cipher.
submitted to Designs, Codes
and Cryptography
, 2007.
8. KoreK. chopchop (experimental WEP attacks).
http://www.netstumbler.org/
showthread.php?t=12489
, 2004.
9. KoreK.
Next generation of WEP attacks?
http://www.netstumbler.org/
showpost.php?p=93942&postcount=35
, 2004.
10. Subhamoy Maitra and Goutam Paul. Many keystream bytes of RC4 leak secret key
information. Cryptology ePrint Archive, Report 2007/261, 2007.
http://eprint.
iacr.org/
.
11. Toshihiro Ohigashi, Hidenori Kuwakado, and Masakatu Morii. A key recovery
attack on WEP with less packets. to be published, 2007.
12. Yuko Ozasa, Yoshiaki Fujikawa, Toshihiro Ohigashi, Hidenori Kuwakado, and
Masakatu Morii. A study on the Tews, Weinmann, Pyshkin attack against WEP.
In
IEICE Tech. Rep.
, volume 107 of
ISEC2007-47
, pages 17–21, Hokkaido, July
2007. Thu, Jul 19, 2007 - Fri, Jul 20 : Future University-Hakodate (ISEC, SITE,
IPSJ-CSEC).
13. D. C. Plummer. RFC 826: Ethernet Address Resolution Protocol: Or converting
network protocol addresses to 48.bit Ethernet address for transmission on Ethernet
hardware, November 1982.
14. Jon Postel. Internet Protocol. Request for Comments (Standard) 791, Internet
Engineering Task Force, September 1981.
15. Adam Stubblefield, John Ioannidis, and Aviel D. Rubin. A key recovery attack
on the 802.11b wired equivalent privacy protocol (WEP).
ACM Transactions on
Information and System Security
, 7(2):319–332, May 2004.
16. The Aircrack-NG team. Aircrack-ng suite, 2007.
http://www.aircrack-ng.org
.
17. Serge Vaudenay and Martin Vuagnoux.
Passive-only key recovery attacks on
RC4. In
Selected Areas in Cryptography 2007
, Lecture Notes in Computer Sci-
ence. Springer, 2007. to appear.
18. Wi-Fi Alliance. Wi-Fi Protected Acccess (WPA), 2003.
http://www.wi-fi.org
.