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Network Working Group B. Aboba
Request for Comments: 4436 Microsoft Corporation
Category: Standards Track J. Carlson
Sun Microsystems
S. Cheshire
Apple Computer
March 2006
Detecting Network Attachment in IPv4 (DNAv4)
Status of This Memo
This document specifies an Internet standards track protocol for the
Internet community, and requests discussion and suggestions for
improvements. Please refer to the current edition of the "Internet
Official Protocol Standards" (STD 1) for the standardization state
and status of this protocol. Distribution of this memo is unlimited.
Copyright Notice
Copyright (C) The Internet Society (2006).
Abstract
The time required to detect movement between networks and to obtain
(or to continue to use) an IPv4 configuration may be significant as a
fraction of the total handover latency in moving between points of
attachment. This document synthesizes, from experience in the
deployment of hosts supporting ARP, DHCP, and IPv4 Link-Local
addresses, a set of steps known as Detecting Network Attachment for
IPv4 (DNAv4), in order to decrease the handover latency in moving
between points of attachment.
Aboba, et al. Standards Track [Page 1]
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Table of Contents
1. Introduction ....................................................2
1.1. Applicability ..............................................2
1.2. Requirements ...............................................5
1.3. Terminology ................................................5
2. Overview ........................................................6
2.1. Reachability Test ..........................................8
2.1.1. Packet Format .......................................9
2.2. IPv4 Address Acquisition ..................................10
2.3. IPv4 Link-Local Addresses .................................11
2.4. Manually Assigned Addresses ...............................12
3. Security Considerations ........................................12
4. References .....................................................13
4.1. Normative References ......................................13
4.2. Informative References ....................................13
5. Acknowledgements ...............................................14
1. Introduction
The time required to detect movement between networks and to obtain
(or to continue to use) an operable IPv4 configuration may be
significant as a fraction of the total handover latency in moving
between points of attachment.
This document synthesizes, from experience in the deployment of hosts
supporting ARP [RFC826], DHCP [RFC2131], and IPv4 Link-Local
addresses [RFC3927], a set of steps known as Detecting Network
Attachment for IPv4 (DNAv4). DNAv4 optimizes the (common) case of
re-attachment to a network that one has been connected to previously
by attempting to re-use a previous (but still valid) configuration,
reducing the re-attachment time on LANs to a few milliseconds. Since
this procedure is dependent on the ARP protocol, it is not suitable
for use on media that do not support ARP.
1.1. Applicability
DHCP is an effective and widely adopted mechanism for a host to
obtain an IP address for use on a particular network link, or to
re-validate a previously obtained address via DHCP's INIT-REBOOT
mechanism [RFC2131].
When obtaining a new address, DHCP specifies that the client SHOULD
use ARP to verify that the offered address is not already in use.
The process of address conflict detection [ACD] can take as much as
seven seconds. In principle, this time interval could be shortened,
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with the obvious trade-off: the less time a host spends waiting to
see if another host is already using its intended address, the
greater the risk of inadvertent address conflicts.
Where the client successfully re-validates a previously obtained
address using the INIT-REBOOT mechanism, the DHCP specification does
not require the client to perform address conflict detection, so this
seven-second delay does not apply. However, the DHCP server may be
slow to respond or may be down and not responding at all, so hosts
could benefit from having an alternative way to quickly determine
that a previously obtained address is valid for use on this
particular link.
When the client moves between networks, the address re-validation
attempt may be unsuccessful; a DHCPNAK may be received in response to
a DHCPREQUEST, causing the client to restart the configuration
process by moving to the INIT state. If an address previously
obtained on the new network is still operable, DNAv4 enables the host
to confirm the new configuration quickly, bypassing restart of the
configuration process and conflict detection.
The alternative mechanism specified by this document applies when a
host has a previously allocated DHCP address, which was not returned
to the DHCP server via a DHCPRELEASE message, and which still has
time remaining on its lease. In this case, the host may determine
whether it has re-attached to the logical link where this address is
valid for use, by sending a unicast ARP Request packet to a router
previously known for that link (or, in the case of a link with more
than one router, by sending one or more unicast ARP Request packets
to one or more of those routers).
The use of unicast ARP has a number of benefits. One benefit is that
unicast packets impose less burden on the network than broadcast
packets, particularly on 802.11 networks where broadcast packets may
be sent at rates as low as 1 Mb/sec. Another benefit is that if the
host is not on the link it hoped to find itself on, a broadcast ARP
Request could pollute the ARP caches of peers on that link. When
using private addresses [RFC1918], another device could be
legitimately using the same address, and a broadcast ARP Request
could disrupt its communications, causing TCP connections to be
broken, and similar problems. Also, using a unicast ARP packet
addressed to the MAC address of the router the host is expecting to
find means that if the host is not on the expected link there will be
no device with that MAC address, and the ARP packet will harmlessly
disappear into the void without doing any damage.
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These issues that define the applicability of DNAv4 lead us to a
number of conclusions:
o DNAv4 is a performance optimization. Its purpose is to speed
up a process that may require as much as a few hundred
milliseconds (DHCP INIT-REBOOT), as well as to reduce multi-
second conflict detection delays when a host changes networks.
o As a performance optimization, it must not sacrifice
correctness. In other words, false positives are not
acceptable. DNAv4 must not conclude that a host has returned
to a previously visited link where it has an operable IP
address if this is not in fact the case.
o As a performance optimization, false negatives are acceptable.
It is not an absolute requirement that this optimization
correctly recognize a previously visited link in all possible
cases. For example, if a router ignores unicast ARP Requests,
then DNAv4 will not be able to detect that it has returned to
the same link in the future. This is acceptable because the
host still operates correctly as it did without DNAv4, just
without the performance benefit. Users and network operators
who desire the performance improvement offered by DNAv4 can
upgrade their routers to support DNAv4.
o As a performance optimization, where DNAv4 fails to provide a
benefit, it should add little or no delay compared to today's
DHCP processing. In practice, this implies that DHCP
processing needs to proceed in parallel. Waiting for DNAv4 to
fail before beginning DHCP processing can greatly increase
total processing time, the opposite of the desired effect.
o Trials are inexpensive. DNAv4 performs its checks using small
unicast packets. An IPv4 ARP packet on Ethernet is just 42
octets, including the Ethernet header. This means that the
cost of an unsuccessful attempt is small, whereas the cost of a
missed opportunity (having the right address available as a
candidate and choosing not to try it for some reason) is large.
As a result, the best strategy is often to try all available
candidate configurations, rather than try to determine which
candidates, if any, may be correct for this link, based on
heuristics or hints. For a heuristic to offer the prospect of
being a potentially useful way to eliminate inappropriate
configurations from the candidate list, that heuristic has to
(a) be fast and inexpensive to compute, as compared to sending
a 42-octet unicast packet, and (b) have high probability of not
falsely eliminating a candidate configuration that could be
found to be the correct one.
Aboba, et al. Standards Track [Page 4]
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o Time is limited. If DNAv4 is to be effective in enabling low
latency handoffs, it needs to complete in less than 10 ms.
This implies that any heuristic used to eliminate candidate
configurations needs to take at most a few milliseconds to
compute. This does not leave much room for heuristics based on
observation of link-layer or Internet-layer traffic.
1.2. Requirements
In this document, several words are used to signify the requirements
of the specification. The key words "MUST", "MUST NOT", "REQUIRED",
"SHALL", "SHALL NOT", "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY",
and "OPTIONAL" in this document are to be interpreted as described in
"Key words for use in RFCs to Indicate Requirement Levels" [RFC2119].
1.3. Terminology
This document uses the following terms:
ar$sha
ARP packet field: Sender Hardware Address [RFC826]. The hardware
(MAC) address of the originator of an ARP packet.
ar$spa
ARP packet field: Sender Protocol Address [RFC826]. For IP
Address Resolution, this is the IPv4 address of the sender of the
ARP packet.
ar$tha
ARP packet field: Target Hardware Address [RFC826]. The hardware
(MAC) address of the target of an ARP packet.
ar$tpa
ARP packet field: Target Protocol Address [RFC826]. For IPv4
Address Resolution, the IPv4 address for which one desires to know
the hardware address.
DHCP client
A DHCP client or "client" is an Internet host using the Dynamic
Host Configuration Protocol (DHCP) [RFC2131] to obtain
configuration parameters, such as a network address.
DHCP server
A DHCP server or "server" is an Internet host that returns
configuration parameters to DHCP clients.
Aboba, et al. Standards Track [Page 5]
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Link
A communication facility or medium over which network nodes can
communicate. Each link is associated with a minimum of two
endpoints. Each link endpoint has a unique link-layer identifier.
Link Down
An event provided by the link layer that signifies a state change
associated with the interface's no longer being capable of
communicating data frames; transient periods of high frame loss
are not sufficient. DNAv4 does not utilize "Link Down"
indications.
Link Layer
Conceptual layer of control or processing logic that is
responsible for maintaining control of the data link. The data
link layer functions provide an interface between the higher-layer
logic and the data link. The link layer is the layer immediately
below IP.
Link Up
An event provided by the link layer that signifies a state change
associated with the interface's becoming capable of communicating
data frames.
Point of Attachment
The link endpoint on the link to which the host is currently
connected.
Routable address
In this specification, the term "routable address" refers to any
unicast IPv4 address other than an IPv4 Link-Local address. This
includes private addresses as specified in "Address Allocation for
Private Internets" [RFC1918].
Operable address
In this specification, the term "operable address" refers either
to a static IPv4 address, or an address assigned via DHCPv4 that
has not been returned to the DHCP server via a DHCP RELEASE
message, and whose lease has not yet expired.
2. Overview
On connecting to a new point of attachment, the host responds to a
"Link Up" indication from the link layer by carrying out the DNAv4
procedure.
For each network that it connects to, it is assumed that the host
saves the following parameters to stable storage:
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[1] The IPv4 and MAC address of one or more test nodes on the
network.
[2] The IPv4 configuration parameters, including the DHCP client
identifier, assigned address, and lease expiration time.
From the set of networks that have operable IPv4 addresses associated
with them, the host selects a subset and attempts to confirm the
configuration for each network, using the reachability test described
in Section 2.1.
For a particular network, the host SHOULD use the addresses of local
routers (preferably default gateways) as its test nodes. If more
than one address is known, those addresses may be tested in parallel.
In order to ensure configuration validity, the host SHOULD only
configure routes for which the next hop address passes the
reachability test. Other routes SHOULD be re-learned.
DNAv4 does not significantly increase the likelihood of an address
conflict. The reachability test is only carried out for a network
when the host has previously completed conflict detection as
recommended in Section 2.2 of the DHCP specification [RFC2131] and
obtained an operable IPv4 configuration on that network.
Restrictions on sending ARP Requests and Responses are described in
Section 2.1.1.
One case where DNAv4 does increase the likelihood of an address
conflict is when:
o a DHCP server hands out an address lease,
o the host with that lease leaves the network,
o the DHCP server is power-cycled or crashes and is rebooted,
o the DHCP server, having failed to save leases to stable
storage, assigns that same address to another host, and
o the first host returns and, having a still-valid lease with
time remaining, proceeds to use its assigned address,
conflicting with the new host that is now using that same
address.
While Section 4 of the DHCP specification [RFC2131] assumes that DHCP
servers save their leases in persistent storage, almost no consumer-
grade NAT gateway does so. Short DHCP lease lifetimes can mitigate
this risk, though this also limits the operable candidate
configurations available for DNAv4 to try.
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2.1. Reachability Test
The host skips the reachability test for a network if any of the
following conditions are true:
[a] The host does not have an operable routable IPv4 address on that
network. In this case, the reachability test cannot confirm that
the host has an operable routable IPv4 address, so completing the
reachability test would serve no purpose.
[b] The host does not know the addresses of any test nodes on that
network. In this case, insufficient information is available to
carry out the reachability test.
[c] If DHCP authentication [RFC3118] is configured. The reachability
test utilizes ARP, which is insecure. Hosts that have been
configured to attempt DHCP authentication SHOULD NOT utilize the
reachability test. Security issues are discussed in Section 4.
[d] The contents of the DHCP Client Identifier option that the client
used to obtain the candidate configuration is different from the
DHCP Client Identifier option the client intends to present on
the interface in question. In this case, it is anticipated that
a DHCP server would NAK any request made by the client to acquire
or extend the candidate configuration, since the two interfaces
are presenting differing identities.
If the reachability test is successful, the host SHOULD continue to
use the operable routable IPv4 address associated with the confirmed
network, without needing to re-acquire it. Once a valid reachability
test response is received, validation is complete, and additional
responses should be discarded.
If a DHCPv4 client is operational, it is RECOMMENDED that the host
attempt to obtain IPv4 configuration via DHCPv4 in parallel with the
reachability tests, with the host using the first answer returned.
This ensures that the DNAv4 procedure will not result in additional
delay in the case where reachability tests fail, or where sending a
DHCPREQUEST from the INIT-REBOOT state, as described in Section 3.2
and 4.3.2 of the DHCP specification [RFC2131], completes more quickly
than the reachability tests.
In situations where both DNAv4 and DHCP are used on the same link, it
is possible that the reachability test will complete successfully,
and then DHCP will complete later with a different result. If this
happens, the implementation SHOULD abandon the reachability test
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results and use the DHCP result instead, unless the address confirmed
via the reachability test has been manually assigned (see Section
2.4).
Where the reachability test does not return an answer, this is
typically because the host is not attached to the network whose
configuration is being tested. In such circumstances, there is
typically little value in aggressively retransmitting reachability
tests that do not elicit a response.
Where DNAv4 and DHCP are tried in parallel, one strategy is to
forsake reachability test retransmissions and to allow only the DHCP
client to retransmit. In order to reduce competition between DNAv4
and DHCP retransmissions, a DNAv4 implementation that retransmits may
utilize the retransmission strategy described in Section 4.1 of the
DHCP specification [RFC2131], scheduling DNAv4 retransmissions
between DHCP retransmissions.
If a response is received to any reachability test or DHCP message,
pending retransmissions are canceled. It is RECOMMENDED that a DNAv4
implementation retransmit no more than twice. To provide damping in
the case of spurious "Link Up" indications, it is RECOMMENDED that
the DNAv4 procedure be carried out no more than once a second.
2.1.1. Packet Format
The reachability test is performed by sending a unicast ARP Request.
The host MUST set the target protocol address (ar$tpa) to the IPv4
address of the node being tested, and the sender protocol address
field (ar$spa) to its own candidate IPv4 address. The ARP Request
MUST use the host MAC address as the source, and the test node MAC
address as the destination. The host includes its MAC address in the
sender hardware address field (ar$sha) and sets the target hardware
address field (ar$tha) to 0.
If a valid ARP Reply is received, the MAC address in the sender
hardware address field (ar$sha) in the ARP Reply is matched against
the target hardware address field (ar$tpa) in the ARP Request, and
the IPv4 address in the sender protocol address field (ar$spa) of the
ARP Reply is matched against the target protocol address field
(ar$tpa) in the ARP Request. If a match is found, then the host
continues to use that IPv4 address, subject to the lease re-
acquisition and expiration behavior described in Section 4.4.5 of the
DHCP specification [RFC2131].
The risk of an address conflict is greatest when the host moves
between private networks, since in this case the completion of
conflict detection on the former network does not provide assurance
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against an address conflict on the new network. Until a host has
confirmed the operability of its IPv4 configuration by receipt of a
response to the reachability test, it SHOULD NOT respond to ARP
Requests and SHOULD NOT broadcast ARP Requests containing its address
within the sender protocol address field (ar$spa).
Sending an ICMP Echo Request [RFC792] would not be an acceptable way
of testing a candidate configuration, since sending any IP packet
generally requires an ARP Request/Reply exchange and, as explained
above, ARP packets may not be broadcast safely until after the
candidate configuration has been confirmed. Also, where a host moves
from one private network to another, an ICMP Echo Request can result
in an ICMP Echo Response even when the MAC address has changed, as
long as the IPv4 address remains the same. This can occur, for
example, where a host moves from one home network using prefix
192.168/16 to another one. In addition, if the ping is sent with TTL
> 1, then an ICMP Echo Response can be received from an off-link
router. As a result, if the MAC address of the test node is not
checked, the host can mistakenly confirm attachment, potentially
resulting in an address conflict. As a result, sending an ICMP Echo
Request SHOULD NOT be used as a substitute for the reachability test.
2.2. IPv4 Address Acquisition
If the host has an operable routable IPv4 address on one or more
networks, and if DHCPv4 is enabled on the interface, the host SHOULD
attempt to acquire an IPv4 configuration using DHCPv4, in parallel
with one or more reachability tests. This is accomplished by
entering the INIT-REBOOT state and sending a DHCPREQUEST to the
broadcast address, as specified in Section 4.4.2 of the DHCP
specification [RFC2131].
If the host does not have an operable routable IPv4 address on any
network, the host enters the INIT state and sends a DHCPDISCOVER
packet to the broadcast address, as described in Section 4.4.1 of the
DHCP specification [RFC2131]. If the host supports the Rapid Commit
Option [RFC4039], it is possible that the exchange can be shortened
from a 4-message exchange to a 2-message exchange.
If the host does not receive a response to a DHCPREQUEST or
DHCPDISCOVER, then it retransmits as specified in Section 4.1 of the
DHCP specification [RFC2131].
As discussed in Section 4.4.4 of the DHCP specification [RFC2131], a
host in INIT or REBOOTING state that knows the address of a DHCP
server may use that address in the DHCPDISCOVER or DHCPREQUEST rather
than the IPv4 broadcast address. In the INIT-REBOOT state, a
DHCPREQUEST is sent to the broadcast address so that the host will
Aboba, et al. Standards Track [Page 10]
RFC 4436 DNAv4 March 2006
receive a response regardless of whether the previously configured
IPv4 address is correct for the network to which it has connected.
Sending a DHCPREQUEST to the unicast address in INIT-REBOOT state is
not appropriate, since if the DHCP client has moved to another
subnet, a DHCP server response cannot be routed back to the client
since the DHCPREQUEST will bypass the DHCP relay and will contain an
invalid source address.
2.3. IPv4 Link-Local Addresses
DNAv4 applies only to previously configured addresses that had some
lease lifetime associated with them, during which lifetime the
address may be legitimately regarded as being reserved for exclusive
use by the assigned host. DHCP-assigned addresses fit this
description, but IPv4 Link-Local address [RFC3927] do not, since IPv4
Link-Local addresses are not handed out by an authoritative server
and do not come with any guaranteed usable lifetime.
A host's claim on an IPv4 Link-Local address is valid only as long as
that host remains connected to the link, actively defending against
probes for its chosen address. As soon as a host shuts down, sleeps,
or otherwise disconnects from a link, it immediately relinquishes any
claim it may have had on any IPv4 Link-Local address on that link. A
host wishing to reclaim a previously used IPv4 Link-Local address
MUST perform the full probing and announcement process required by
"Dynamic Configuration of IPv4 Link-Local Addresses" [RFC3927] and
MUST NOT attempt to use DNAv4 as a shortcut to bypass that process.
Where the host does not have an operable routable IPv4 address on any
network, the host MAY configure an IPv4 Link-Local address prior to
entering the INIT state and sending a DHCPDISCOVER packet, as
described in Section 2.3 of the DHCP specification [RFC2131]. Where
a host can confirm that it remains connected to a network on which it
possesses an operable routable IPv4 address, that address should be
used, and the IPv4 Link-Local address is deprecated, as noted in
Section 1.9 of the IPv4 Link-Local specification [RFC3927].
Where a host has an operable routable IPv4 address on one or more
networks but the reachability test cannot confirm the configuration
and the DHCPv4 client does not receive a response after employing the
retransmission algorithm, Section 3.2 of the DHCP specification
[RFC2131] states that the client MAY choose to use the previously
allocated network address and configuration parameters for the
remainder of the unexpired lease.
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2.4. Manually Assigned Addresses
An implementation may use DNAv4 to confirm the configuration of
manually assigned addresses. However, special consideration is
required for this to produce reliable results, so it SHOULD NOT be
enabled by default.
For the purposes of DNAv4, manually assigned addresses may be treated
as equivalent to DHCP-assigned addresses with an infinite lifetime.
This does not significantly increase the probability of an address
conflict as long as the manually assigned address is reserved by the
DHCP server or is outside the scope of addresses assigned by a DHCP
server. However, where the manually assigned address is within an
address scope utilized by a DHCP server, it is possible that the host
will be unavailable when the DHCP server checks for a conflict prior
to assigning the conflicting address. In this case, a host utilizing
DNAv4 could confirm an address that had been assigned to another
host.
Typically, an address is manually assigned on a network because a
dynamically assigned address was not suitable for some reason.
Therefore, where DNAv4 and DHCP are run in parallel and DNAv4
confirms a manual configuration, it may be undesirable to allow this
configuration to be overridden by DHCP, as described in Section 2.1.
However, packet loss may cause the reachability test to fail while
DHCP completes successfully, resulting in the host obtaining a
dynamic address where a static address is desired. In order to
provide for reliable reconfirmation of manually assigned addresses,
reachability tests for manual configurations require a more
aggressive retransmission strategy than that detailed in Section 4.1
of the DHCP specification [RFC2131]. For example, shorter
retransmission intervals and more persistent retransmissions may be
required.
3. Security Considerations
Detecting Network Attachment for IPv4 (DNAv4) is based on ARP and
DHCP and inherits the security vulnerabilities of these two
protocols.
ARP [RFC826] traffic is not secured, so an attacker gaining access to
the network can spoof a response to the reachability test described
in Section 2.1, leading the querier to conclude falsely that it is
attached to a network that it is not connected to.
Similarly, where DHCPv4 traffic is not secured, an attacker could
masquerade as a DHCPv4 server, in order to convince the host that it
was attached to a particular network. This and other threats
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relating to DHCPv4 are described in "Authentication for DHCP
Messages" [RFC3118].
The effect of these attacks will typically be limited to denial of
service, unless the host utilizes its IP configuration for other
purposes, such as security configuration or location determination.
For example, a host that disables its personal firewall based on
evidence that it had attached to a home network could be compromised
by spoofing of the DNAv4 reachability test. In general, adjustment
of the security configuration based on DNAv4 is NOT RECOMMENDED.
Hosts that depend on secure IP configuration SHOULD NOT use DNAv4 but
SHOULD instead utilize DHCP authentication [RFC3118], possibly in
combination with the Rapid Commit Option [RFC4039].
4. References
4.1. Normative References
[RFC826] Plummer, D., "Ethernet Address Resolution Protocol: Or
converting network protocol addresses to 48.bit Ethernet
address for transmission on Ethernet hardware", STD 37, RFC
826, November 1982.
[RFC2119] Bradner, S., "Key words for use in RFCs to Indicate
Requirement Levels", BCP 14, RFC 2119, March 1997.
[RFC2131] Droms, R., "Dynamic Host Configuration Protocol", RFC 2131,
March 1997.
4.2. Informative References
[ACD] Cheshire, S., "IPv4 Address Conflict Detection", Work in
Progress, July 2005.
[RFC792] Postel, J., "Internet Control Message Protocol", STD 5, RFC
792, September 1981.
[RFC1918] Rekhter, Y., Moskowitz, B., Karrenberg, D., de Groot, G.,
and E. Lear, "Address Allocation for Private Internets",
BCP 5, RFC 1918, February 1996.
[RFC3118] Droms, R. and W. Arbaugh, "Authentication for DHCP
Messages", RFC 3118, June 2001.
[RFC3927] Cheshire, S., Aboba, B., and E. Guttman, "Dynamic
Configuration of IPv4 Link-Local Addresses", RFC 3927, May
2005.
Aboba, et al. Standards Track [Page 13]
RFC 4436 DNAv4 March 2006
[RFC4039] Park, S., Kim, P., and B. Volz, "Rapid Commit Option for
the Dynamic Host Configuration Protocol version 4
(DHCPv4)", RFC 4039, March 2005.
5. Acknowledgements
The authors would like to acknowledge Greg Daley of Monash
University, Erik Guttman and Erik Nordmark of Sun Microsystems, Ralph
Droms of Cisco Systems, Ted Lemon of Nominum, John Loughney of Nokia,
Thomas Narten of IBM and David Hankins of ISC for contributions to
this document.
Authors' Addresses
Bernard Aboba
Microsoft Corporation
One Microsoft Way
Redmond, WA 98052
Phone: +1 425 818 4011
Fax: +1 425 936 7329
EMail: bernarda@microsoft.com
James Carlson
Sun Microsystems, Inc
1 Network Drive
Burlington, MA 01803-2757
USA
Phone: +1 781 442 2084
Fax: +1 781 442 1677
EMail: james.d.carlson@sun.com
Stuart Cheshire
Apple Computer, Inc.
1 Infinite Loop
Cupertino, California 95014, USA
Phone: +1 408 974 3207
EMail: rfc@stuartcheshire.org
Aboba, et al. Standards Track [Page 14]
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Aboba, et al. Standards Track [Page 15]