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A Model of Information Security Governance for E-Business
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•ITGI
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Technical Issues, edited by M. Warkentin, pp. 1-15, copyright 2006 by IGI Publishing (an imprint of IGI Global).
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Chapter 7.13
Wireless LAN Setup and
Security Loopholes
Biju Issac

Swinburne University of Technology, Malaysia
Lawan A. Mohammed
Swinburne University of Technology, Malaysia
ABSTRACT
This chapter gives a practical overview of the brief
implementation details of the IEEE802.11 wireless
LAN and the security vulnerabilities involved in
VXFK QHWZRUNV 6SHFL¿FDOO\ LW GLVFXVVHV DERXW
the implementation of EAP authentication using
RADIUS server with WEP encryption options.
The chapter also touches on the ageing WEP
and the cracking process, along with the current
TKIP and CCMP mechanisms. War driving and
other security attacks on wireless networks are
DOVREULHÀ\FRYHUHG7KHFKDSWHUFRQFOXGHVZLWK
practical security recommendations that can keep
intruders at bay. The authors hope that any reader
would thus be well informed on the security vul-
nerabilities and the precautions that are associated
with 802.11 wireless networks.
INTRODUCTION
Over the recent past, the world has increasingly
becoming mobile. As mobile computing is get-
ting more popular each day, the use of wireless
local area network (WLAN) is becoming ever
more relevant. If we are connected to a wired
network, our mobility is undoubtedly affected.
From public hotspots in coffee shops to secure
WLAN in organizations, the world is moving to
ubiquitous and seamless computing environments.

IEEE 802.11 has been one of the most successful
wireless technologies, and this chapter would be
focusing more on this technology.
0RELOLW\DQGÀH[LELOLW\KDVEHHQWKHNH\QRWH
advantages of wireless networks in general.
Users can roam around freely without any inter-
ruption to their connection. Flexibility comes in
as users can get connected through simple steps
of authentication without the hassle of running
2156
Wireless LAN Setup and Security Loopholes
cables. Also, compared to the wired network,
wireless network installation costs are minimal
as the number of interface hardware is minimal.
Radio spectrum is the key resource, and the
wireless devices are set to operate in a certain
frequency band. 802.11 networks operate in the
2.4 GHz ISM band, which are generally license
free bands. The more common 802.11b devices
operate in the S-band ISM.
In the next sections, we will be explaining
the wireless LAN basic setup and implementa-
tion, WEP encryption schemes and others, EAP
authentication through RADIUS server and its
brief implementation, WEP cracking procedure,
war driving, 802.11b vulnerabilities with secu-
ULW\DWWDFNVDQG¿QDOO\FRQFOXGLQJZLWK:/$1
security safeguards.
WIRELESS LAN NETWORK AND
TECHNOLOGIES INVOLVED

Network Infrastructure
To form the wireless network, four generic types
of WLAN devices are used. These are wireless
station, access point (AP), wireless router, and
wireless bridge. A wireless station can be a note-
book or desktop computer with a wireless network
card in it. Access points act like a 2-port bridge
linking the wired infrastructure to the wireless
infrastructure. It constructs a port-address table
and operates by following the 3F rule: ÀRRG-
ing, forwarding, and ¿OWHULQJ )ORRGLQJ LV WKH
process of transmitting frames on all ports other
than the port in which the frames were received.
)RUZDUGLQJDQG¿OWHULQJLQYROYHWKHSURFHVVRI
transmitting a frame based on the port-address
mapping table in AP, so that only the needed port
is used for transmission. Wireless routers are ac-
cess points with routing capability that typically
includes support for dynamic host control protocol
(DHCP) and network address translation (NAT).
To move the frames from one station to the other,
WKHVWDQGDUGGH¿QHVDZLUHOHVVPHGLXP
that supports two radio frequency (RF) physical
layers and one infrared physical layer. RF layers
are more popular now (Held, 2003, pp. 7-14).
Modes of Operation
IEEE802.11 WLAN can operate in two modes,
namely ad hoc (or peer-to-peer) and infrastructure
mode. These modes come under the basic service
set (BSS), which is a coverage area of commu-

nication that allows one station to communicate
to the other. Ad hoc mode has WLAN stations or
nodes communicating with one another without an
access point to form an independent basic service
set (IBSS). In contrast, infrastructure mode has
WLAN nodes communicating with a central AP
that is, in turn, linked to a wired LAN to form
a basic service set. Here, the AP acts as a relay
between wireless stations or between wired and
wireless stations. A combination of many BSS
with a backbone distribution system (normally
ethernet) forms an extended service set (ESS).
IEEE 802.11 Architecture and
Standards
802.11 is a member of IEEE 802 family, which
GH¿QHVWKHVSHFL¿FDWLRQVIRUORFDODUHDQHWZRUN
WHFKQRORJLHV,(((VSHFL¿FDWLRQVDUHFHQWHUHG
on the two lowest layers of OSI model, namely the
physical layer and the data link layer. The base
VSHFL¿FDWLRQLQFOXGHVWKH0$&OD\HU
and two physical layers namely, the frequency
hopping spread spectrum (FHSS) layer in the
2.4 GHz band, and the direct sequence spread
spectrum (DSSS) layer. Later revisions to 802.11
added additional physical layers like high-rate
direct-sequence layer (HR/DSSS) for 802.11b
and orthogonal frequency division multiplexing
(OFDM) layer for 802.11a.
The different extensions to the 802.11 standard
use the radio frequency band differently. Some

of the popular 802.11 extensions are as follows:
2157
Wireless LAN Setup and Security Loopholes
E ² VSHFL¿HV WKH XVH RI '666 DW  
5.5 and 11 Mbps. The 802.11 products are quite
popular with its voluminous production. 802.11a
VSHFL¿HVWKHXVHRIDIUHTXHQF\PXOWLSOH[LQJ
scheme called orthogonal frequency division
multiplexing (OFDM), and it uses a physical
layer standard that operates at data rates up to 54
Mbps. As high frequencies attenuate more, one
needs more 802.11a access points compared to
XVLQJEDFFHVVSRLQWVJVSHFL¿HVD
high-speed extension to 802.11b that operates in
2.4 GHz frequency band using OFDM to obtain
data rates up to 54 Mbps and as well as back-
ward compatible with 802.11b devices. 802.11i
recognizes the limitations of WEP and enhances
ZLUHOHVVVHFXULW\,WGH¿QHVWZRQHZHQFU\SWLRQ
methods as well as an authentication method. The
two encryption methods designed to replace WEP
include temporal key integrity protocol (TKIP)
and advanced encryption standard (AES). The
authentication is based on the port-based 802.1x
DSSURDFKGH¿QHGE\ D S U LRU,(((V W D QG D UG2W KH U
802.11 extensions include 802.11c (focuses on
MAC bridges), 802.11d (focuses on worldwide
use of WLAN with operation at different power
levels), 802.11e (focuses on quality of service),
802.11f (focuses on access point interoperability)

and 802.11h (focuses on addressing interference
problems when used with other communication
equipments) (Held, 2003, pp. 27-32).
Joining an Existing Cell
There are three stages that a station has to go
through to get connected to an existing cell,
namely scanning, authentication, and associa-
tion. When a station wants to access an existing
BSS (either after power up, sleep mode, or just
entering the BSS area), the station needs to get
synchronization information from the access
point (or from the other stations when in ad-hoc
mode). The station can get this information by
one of the two modes: passive scanning and active
scanning. In passive scanning mode, the station
just waits to receive a beacon frame from the
AP and records information from it. The beacon
frame is a periodic frame sent by the AP with
synchronization information. This mode can save
battery power, as it does not require transmitting.
In active scanning modeWKHVWDWLRQWULHVWR¿QG
an access point by transmitting probe request
frames, and waiting for probe response frames
from the AP. This is more assertive in nature. It
follows the simple process as follows. Firstly, it
moves to a channel to look for an incoming frame.
If incoming frame is detected, the channel can
be probed. Secondly, it tries to gain access to
the medium by sending a probe request frame.
7KLUGO\LWZDLWVIRUDSUHGH¿QHGWLPHWRORRNIRU

any probe response frame and if unsuccessful, to
move to the next channel.
The second stage is authentication. It is nec-
essary, when the stations try to communicate to
one another, to prove their identity. Two major
DSSURDFKHVWKDWDUHVSHFL¿HGLQDUHRSHQ
system authentication and shared-key authentica-
tion. In open system authentication, the access
point accepts the mobile station implicitly without
YHUL¿FDWLRQDQGLWLVHVVHQWLDOO\DWZRIUDPHH[-
change communication. In shared key authentica-
tion, WEP (wired equivalent privacy) encryption
has to be enabled. It requires that a shared key
be distributed to stations before attempting to
do authentication. The shared-key authentication
exchange consists of four management frame
exchanges that include a challenge-response
approach.
The third stage is association, and this is
restricted to infrastructure networks only. Once
the authentication is completed, stations can as-
sociate with an access point so that it can gain full
access to the network. Exchange of data can only
be performed after an association is established.
The association process is a two-step process
further involving three stages: unauthenticated-
unassociated stage, authenticated-unassociated
stage, and authenticated-associated stage.
2158
Wireless LAN Setup and Security Loopholes

All access points (AP) transmit a beacon man-
DJHPHQWIUDPHDW¿[HGLQWHUYDOV$ZLUHOHVVFOLHQW
that wants to associate with an access point and
join a BSS listens for beacon messages that con-
tain information regarding VHUYLFHVHWLGHQWL¿HU
(SSID) or network names to determine the access
points within range. After identifying which AP
to associate with, the client and AP will perform
mutual authentication by exchanging several
management frames as part of the process. After
getting authenticated, the client moves to second
stage and then to third stage. To get associated,
the client needs to send an association request
frame, and the AP needs to respond with an as-
sociation response frame (Arbaugh, Shankar, &
Wan, 2001).
Association helps to locate the position of the
mobile station, so that frames destined for that
station can be forwarded to the right access point.
Once the association is complete, the access point
would register the mobile station on the network.
This is done by sending gratuitous ARP (address
resolution protocol) packets, so that the mobile
station’s MAC address is mapped with the switch
port connected to the access point. Reassociation
is a procedure of moving the association from an
old access point to a new one. It is also used to
rejoin a network if the station leaves the cell and
returns later to the same access point.
WLAN Association Table on CISCO

Access Point
Figure 1 shows the details of a wireless node that
LVFRQQHFWHGLQDZLUHOHVV/$1FHOO7KH¿JXUH
shows the details of CISCO Aironet 320 series AP
and another client connected within the cell. This
is a very simple wireless connection between a
station and AP, with no encryption enabled and no
authentication enabled. The forthcoming section
shows how to make the setup more secure.
ENCRYPTION MECHANISMS IN
IEEE 802.11B AND 802.11I
As WLAN data signals are transmitted over the
air, it makes them vulnerable to eavesdropping.
Figure 1. CISCO access point association table screen
2159
Wireless LAN Setup and Security Loopholes
7KXV FRQ¿GHQWLDOLW\ RI WUDQVPLWWHG GDWD PXVW
be protected, at any cost, by means of encryp-
WLRQ7KH,(((EVWDQGDUGGH¿QHVVXFKD
mechanism, known as wired equivalent privacy,
which uses the RC4 encryption method. However,
various security researchers have found numerous
ÀDZVLQ:(3GHVLJQ7KHPRVWGHYDVWDWLQJQHZV
broke out in 2001, which explained that the WEP
encryption key can be recovered when enough
packets are captured. Since then, this attack has
EHHQYHUL¿HGE\VHYHUDORWKHUVDQGLQIDFWIUHH
software is available for download that allows
for capturing WEP packets and using those to
crack the key.

Wired Equivalent Privacy
Wired equivalent privacy is a standard encryp-
tion for wireless networking. It is a user authen-
tication and data encryption system from IEEE
802.11 that is used to overcome security threats.
Basically, WEP provides security to WLAN by
encrypting the information transmitted over the
air, so that only the receivers who have the correct
encryption key can decrypt the information. If a
user activates WEP, the network interface card
encrypts the payload (frame body and CRC) of
each 802.11 frame, before transmission, using
an RC4 stream cipher provided by RSA security.
The receiving station, such as an access point,
performs decryption upon arrival of the frame.
As a result, 802.11 WEP only encrypts data be-
tween 802.11 stations. Once the frame enters the
wired side of the network, such as between access
points, WEP no longer applies. As part of the
encryption process, WEP prepares a key schedule
³VHHG´E\FRQFDWHQDWLQJWKHVKDUHGVHFUHWNH\
supplied by the user of the sending station with
a randomly generated 24-bit initialization vector
(IV). The IV lengthens the life of the secret key
because the station can change the IV for each
frame transmission. WEP inputs the resulting
”seed” into a pseudorandom number generator
that produces a key stream equal to the length of
the frame’s payload plus a 32-bit integrity check
sum value (ICV). The ICV is a check sum that

the receiving station eventually recalculates and
compares with the one sent by the sending station
to determine whether the transmitted data under-
went any form of tampering while in transit. If
the receiving station calculates an ICV that does
not match the one found in the frame, then the
UHFHLYLQJVWDWLRQFDQUHMHFWWKHIUDPHRUÀDJWKH
user (Borisov, Goldberg, & Wagner, 2001). The
WEP encryption process is shown as follows:
1. Plaintext (P) = Message (M) + Integrity
Check Sum of Message (C(M))
2. Keystream = RC4(v, k), where v is the IV
and k is

he shared key
3. Ciphertext (C) = Plaintext (P) Keystream
4. Transmitted Data = v + Ciphertext
The decryption is done by using th

reverse
process as follows:
1. Ciphertext (C) Keystream
Æ Plaintext
(P)
What is Wrong with WEP?
WEP has been part of the 802.11 standard since
LQLWLDOUDWL¿FDWLRQLQ6HSWHPEHU$WWKDWWLPH
the 802.11 committee was aware of some WEP
limitations; however, WEP was the best choice
WRHQVXUHHI¿FLHQWLPSOHPHQWDWLRQVZRUOGZLGH

Nevertheless, WEP has undergone much scrutiny
and criticism over the past couple of years. WEP
is vulnerable because of relatively short IVs and
keys that remain static. The issues with WEP do
not really have much to do with the RC4 encryp-
t i o n a l g o r i t h m . W i t h o n l y 2 4 b i t s , W E P e v e n t u a l l y
uses the same IV for different data packets. For
a large busy network, this reoccurrence of IVs
can happen within an hour or so. This results in
the transmission of frames having key streams
that are too similar. If a hacker collects enough
frames based on the same IV, the individual
2160
Wireless LAN Setup and Security Loopholes
can determine the shared values among them;
for instance, the key stream or the shared secret
key. This leads to the hacker decrypting any of
the 802.11 frames. The static nature of the shared
secret keys emphasizes this problem. 802.11
does not provide any functions that support the
exchange of keys among stations. As a result,
system administrators and users generally use
the same keys for weeks, months, and even years.
This gives mischievous culprits plenty of time to
monitor and hack into WEP-enabled networks.
Some vendors deploy dynamic key distribution
VROXWLRQVEDVHGRQ[ZKLFKGH¿QLWHO\LP-
proves the security of wireless LANs (Giller &
Bulliard, 2004).
7KH PDMRU:(3GHVLJQÀDZVPD\EHVXP-

marized as follows (Gast, 2002, pp. 93-96):
• Manual key management is a big problem
with WEP. The secret key has to be manu-
ally distributed to the user community, and
widely distributed secrets tend to leak out
as time goes by.
• When key streams are reused, stream ciphers
are vulnerable to analysis. Two frames that
use the same IV are almost certain to use
the same secret key and key stream, and this
problem is aggravated by the fact that some
implementations do not even choose random
IVs. There are cases where, when the card
was inserted, the IV started off as zero,
and incremented by one for each frame. By
reusing initialization vectors, WEP enables
an attacker to decrypt the encrypted data
without ever learning the encryption key
or even resorting to high-tech techniques.
While often dismissed as too slow, a patient
attacker can compromise the encryption of
an entire network after only a few hours of
data collection.
• WEP provides no forgery protection. Even
without knowing the encryption key, an
adversary can change 802.11 packets in ar-
bitrary and undetectable ways, deliver data
to unauthorized parties, and masquerade as
an authorized user. Even worse, an adversary
can also learn more about an encryption

key with forgery attacks than with strictly
passive attacks.
• WEP offers no protection against replays.
An adversary can create forgeries, without
changing any data in an existing packet,
simply by recording WEP packets and then
retransmitting later. Replay, a special type
of forgery attack, can be used to derive
information about the encryption key and
the data it protects.
• WEP misuses the RC4 encryption algorithm
in a way that exposes the protocol to weak
key attacks and public domain hacker tools
like Aircrack, and many others exploit this
weakness. An attacker can utilize the WEP
IV to identify RC4 weak keys, and then use
k n o w n p l a i n t e x t f r o m e a c h p a c k e t t o r e c o ve r
the encryption key.
• Decryption dictionaries, which consist of a
large collection of frames encrypted with the
same key streams, can be built because of
infrequent rekeying. Since more frames with
the same IV come in, chances of decrypting
them are more, even if the key is not known
or recovered.
• WEP uses CRC for integrity check, en-
crypted using RC4 key stream. From a
cryptography view point, CRC is not secure
I U R P D Q D W W D F N RII U D PH P R G L ¿FD W L R Q  ZKH U H 
W KH D W W D F NH U PR G L ¿H VW K H I U D PH G D W D F R QW H Q W V 

as well as the CRC value.
In view of these WEP shortcomings, the
IEEE 802.11 Task Group i (TGi) is developing a
new set of WLAN security protocols to form the
future IEEE 802.11i standard. These include the
temporal key integrity protocol (TKIP) and the
counter mode with CBC-MAC protocol (CCMP).
The TKIP is a short-term solution that will adapt
existing WEP implementations to address the
:(3ÀDZVZKLOHZDLWLQJIRU&&03WREHIXOO\
2161
Wireless LAN Setup and Security Loopholes
deployed. CCMP is a long-term solution that
ZLOO QRW RQO\ DGGUHVV FXUUHQW :(3 ÀDZV EXW
will include a new design incorporating the new
advanced encryption standard (AES).
The New 802.11i Standard
The new security standard, 802.11i, which was
FRQ¿UPHGDQGUDWL¿HGLQ-XQHHOLPLQDWHV
all the weaknesses of WEP. It is divided into three
main categories (Strand, 2004):
1. Temporary key integrity protocol (TKIP):
This is, essentially, a short-term solution
WKDW¿[HVDOO:(3ZHDNQHVVHV,WZRXOGEH
compatible with old 802.11 devices, and it
SURYLGHVLQWHJULW\DQGFRQ¿GHQWLDOLW\
2. Counter mode with CBC-MAC protocol
(CCMP): This is a new protocol designed
with planning based on RFC 2610, which
u s e s A E S a s c r y p t o g r a p h i c a l g o r i t h m . S i n c e

this is more CPU intensive than RC4 (used in
WEP and TKIP), new and improved 802.11
hardware may be required. Some drivers can
implement CCMP in software. It provides
LQWHJULW\DQGFRQ¿GHQWLDOLW\
3. 802.1x port-based network access control:
Either when using TKIP or CCMP, 802.1x
is used as authentication.
TKIP and CCMP will be explained in the fol-
lowing sections. 802.1x is explained in detail in
the section titled Radius Server and Authentica-
tion Mechanisms.
Temporary Key Integrity Protocol
(TKIP)
TKIP is part of a draft standard from the IEEE
802.11i working group. TKIP is an enhancement to
WEP security. The TKIP algorithms are designed
explicitly for implementation on legacy hardware,
hopefully without unduly disrupting performance.
TKIP adds four new algorithms to WEP (Cam-
Winget, Housley, Wagner, & Walker, 2003):
• A cryptographic message integrity code,
called Michael, to defeat forgeries has
been added. Michael is an MIC algorithm
that calculates a keyed function of data at
the transmitter; sends the resulting value
as a CRC check or tag with the data to the
receiver, where it recalculates the tag value;
and compares the computed result with
the tag accompanying the data. If the two

values match, the receiver accepts the data
as authentic. Otherwise, the receiver rejects
the data as a forgery.
• A new IV sequencing discipline to remove
replay attacks has been added. TKIP
extends the current WEP format to use a
48-bit sequence number, and associates the
sequence number with the encryption key.
TKIP mixes the sequence number into the
encryption key and encrypts the MIC and
the WEP ICV. This design translates replay
attacks into ICV or MIC failures.
• A per-packet key mixing function, to decor-
relate the public IVs from weak keys is
added. TKIP introduces a new per-packet
encryption key construction, based on a
mixing function. The mixing function takes
the base key, transmitter MAC address,
and packet sequence number as inputs,
and outputs a new per-packet WEP key. To
minimize computational requirements, the
mixing function is split into two phases.
7KH¿UVWSKDVHXVHVDQRQOLQHDUVXEVWLWXWLRQ
table, or S-box, to combine the base key, the
transmitter MAC address, and the four most
VLJQL¿FDQW RFWHWV RI WKH SDFNHW VHTXHQFH
number to produce an intermediate value.
The second phase mixes the intermediate
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the packet sequence number, and produces

a per-packet key.
2162
Wireless LAN Setup and Security Loopholes
• A rekeying mechanism is added to provide
fresh encryption and integrity keys, undo-
ing the threat of attacks stemming from key
reuse. The IEEE 802.1x key management
scheme provides fresh keys (Cam-Winget
et al., 2003).
Counter Mode with CBC-MAC
Protocol (CCMP)
CCMP (counter mode with cipher block chain-
ing message authentication code protocol) is
the preferred encryption protocol in the 802.11i
standard. CCMP is based upon the CCM mode
of the AES encryption algorithm. CCMP utilizes
128-bit keys, with a 48-bit initialization vector
(IV) for replay detection. The counter mode (CM)
component of CCMP is the algorithm providing
data privacy. The cipher block chaining message
authentication code (CBC-MAC) component of
CCMP provides data integrity and authentica-
tion. CCMP is designed for IEEE 802.11i by D.
Whiting, N. Ferguson, and R. Housley.
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but without the restrictions of the already-deployed
hardware. The protocol using CCM has many
properties in common with TKIP. Freedom from
constraints associated with current hardware leads
to a more elegant solution. As with TKIP, CCMP

employs the 48-bit IV, ensuring the lifetime of the
AES key is longer than any possible association.
,QWKLVZD\NH\PDQDJHPHQWFDQEHFRQ¿QHGWR
the beginning of an association and ignored for its
lifetime. CCMP uses the 48-bit IV as a sequence
n u m b e r t o p r o v i d e r e p l a y d e t e c t i o n , j u s t l i k e T K I P.
AES eliminates any need for per-packet keys, so
CCMP has no per-packet key derivation function
(Cam-Winget et al., 2003).
Comparing WEP, TKIP, and CCMP
WEP, TKIP, and CCMP can be compared as in
the Table 1. As it is quite obvious from the previ-
Table 1. Summary of WEP, TKIP, and CCMP comparison (Cam-Winget et al., 2003)
WEP TKIP CCMP
Cipher
RC4 RC4 AES
Key Size
40 or 104 bits 128 bits encryption,
64 bits authentication
128 bits
Key Lifetime
24-bit IV, wrap 48-bit IV 48-bit IV
Packet Key Integrity
Concatenating IV to
base key
Mixing Function Not needed
Packet Data
CRC-32 Michael CCM
Packet Header
None Michael CCM

Replay Detection
None Use IV sequencing Use IV sequencing
Key Management
None EAP-based (802.1x) EAP-based (802.1x)
2163
Wireless LAN Setup and Security Loopholes
ous discussion, CCMP is the future choice, and
TKIP is only an interim solution.
RADIUS SERVER AND
AUTHENTICATION MECHANISMS
To address the shortcomings of WEP with respect
to authentication, a solution based on 802.1x
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IETF’s extensible authentication protocol (EAP)
as in RFC 2284. Its goal is to provide a foundation
of architecture for access control, authentication,
and key management for wireless LANs.
($3ZDVGHVLJQHGZLWKÀH[LELOLW\LQPLQG
and it is being used as a basis for various network
authentication protocols. :3$ ZL¿ SURWHFWHG
access) is proposed to enhance the security of
ZLUHOHVV QHWZRUNV WKURXJK VSHFL¿FDWLRQV RI
security enhancements that increase the level of
authentication, access control, replay prevention,
message integrity, message privacy, and key
distribution to existing WiFi systems. RFC 2284
states that, in general during EAP authentication,
after the link establishment phase is complete (i.e.,
after establishing connection), the authenticator
sends one or more requests to authenticate the

peer (client). Typically, the authenticator will send
an initial identity request, and that could be fol-
lowed by one or more requests for authentication
information. The client sends a response packet in
reply to each request made by authenticator. The
authentication phase is ended by the authenticator
with a success or failure packet. Figure 2 shows
a general EAP diagram.
Figure 2. Authenticated wireless node can only gain access to other LAN resources (Strand, 2004) (See
steps 1, 2, and 3 in the diagram)