Network Working Group M. Crawford
Request for Comments: 2894 Fermilab
Category: Standards Track August 2000
Router Renumbering for IPv6
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 (2000). All Rights Reserved.
IESG Note:
This document defines mechanisms for informing a set of routers of
renumbering operations they are to perform, including a mode of
operation in environments in which the exact number of routers is
unknown. Reliably informing all routers when the actual number of
routers is unknown is a difficult problem. Implementation and
operational experience will be needed to fully understand the
applicabilty and scalability aspects of the mechanisms defined in
this document when the number of routers is unknown.
Abstract
IPv6 Neighbor Discovery and Address Autoconfiguration conveniently
make initial assignments of address prefixes to hosts. Aside from
the problem of connection survival across a renumbering event, these
two mechanisms also simplify the reconfiguration of hosts when the
set of valid prefixes changes.
This document defines a mechanism called Router Renumbering ("RR")
which allows address prefixes on routers to be configured and
reconfigured almost as easily as the combination of Neighbor
Discovery and Address Autoconfiguration works for hosts. It provides
a means for a network manager to make updates to the prefixes used by
and advertised by IPv6 routers throughout a site.
Crawford Standards Track [Page 1]
RFC 2894 Router Renumbering for IPv6 August 2000
Table of Contents
1. Functional Overview ....................................... 2
2. Definitions ............................................... 4
2.1. Terminology ......................................... 4
2.2. Requirements ........................................ 5
3. Message Format ............................................ 5
3.1. Router Renumbering Header ........................... 7
3.2. Message Body -- Command Message ..................... 9
3.2.1. Prefix Control Operation ...................... 9
3.2.1.1. Match-Prefix Part ....................... 9
3.2.1.2. Use-Prefix Part ......................... 11
3.3. Message Body -- Result Message ...................... 12
4. Message Processing ........................................ 14
4.1. Header Check ........................................ 14
4.2. Bounds Check ........................................ 15
4.3. Execution ........................................... 16
4.4. Summary of Effects .................................. 17
5. Sequence Number Reset ..................................... 18
6. IANA Considerations ....................................... 19
7. Security Considerations ................................... 19
7.1. Security Policy and Association Database Entries .... 19
8. Implementation and Usage Advice for Reliability ........... 20
8.1. Outline and Definitions ............................. 21
8.2. Computations ........................................ 23
8.3. Additional Assurance Methods ........................ 24
9. Usage Examples ............................................ 25
9.1. Maintaining Global-Scope Prefixes ................... 25
9.2. Renumbering a Subnet ................................ 26
10. Acknowledgments .......................................... 27
11. References ............................................... 28
12. Author's Address ......................................... 29
Appendix -- Derivation of Reliability Estimates ............... 30
Full Copyright Statement ...................................... 32
1. Functional Overview
Router Renumbering Command packets contain a sequence of Prefix
Control Operations (PCOs). Each PCO specifies an operation, a
Match-Prefix, and zero or more Use-Prefixes. A router processes each
PCO in sequence, checking each of its interfaces for an address or
prefix which matches the Match-Prefix. For every interface on which
a match is found, the operation is applied. The operation is one of
ADD, CHANGE, or SET-GLOBAL to instruct the router to respectively add
the Use-Prefixes to the set of configured prefixes, remove the prefix
which matched the Match-Prefix and replace it with the Use-Prefixes,
Crawford Standards Track [Page 2]
RFC 2894 Router Renumbering for IPv6 August 2000
or replace all global-scope prefixes with the Use-Prefixes. If the
set of Use-Prefixes in the PCO is empty, the ADD operation does
nothing and the other two reduce to deletions.
Additional information for each Use-Prefix is included in the Prefix
Control Operation: the valid and preferred lifetimes to be included
in Router Advertisement Prefix Information Options [ND], and either
the L and A flags for the same option, or an indication that they are
to be copied from the prefix that matched the Match-Prefix.
It is possible to instruct routers to create new prefixes by
combining the Use-Prefixes in a PCO with some portion of the existing
prefix which matched the Match-Prefix. This simplifies certain
operations which are expected to be among the most common. For every
Use-Prefix, the PCO specifies a number of bits which should be copied
from the existing address or prefix which matched the Match-Prefix
and appended to the use-prefix prior to configuring the new prefix on
the interface. The copied bits are zero or more bits from the
positions immediately after the length of the Use- Prefix. If
subnetting information is in the same portion of the old and new
prefixes, this synthesis allows a single Prefix Control Operation to
define a new global prefix on every router in a site, while
preserving the subnetting structure.
Because of the power of the Router Renumbering mechanism, each RR
message includes a sequence number to guard against replays, and is
required to be authenticated and integrity-checked. Each single
Prefix Control Operation is idempotent and so could be retransmitted
for improved reliability, as long as the sequence number is current,
without concern about multiple processing. However, non-idempotent
combinations of PCOs can easily be constructed and messages
containing such combinations could not be safely reprocessed.
Therefore, all routers are required to guard against processing an RR
message more than once. To allow reliable verification that Commands
have been received and processed by routers, a mechanism for
duplicate-command notification to the management station is included.
Possibly a network manager will want to perform more renumbering, or
exercise more detailed control, than can be expressed in a single
Router Renumbering packet on the available media. The RR mechanism
is most powerful when RR packets are multicast, so IP fragmentation
is undesirable. For these reasons, each RR packet contains a
"Segment Number". All RR packets which have a Sequence Number
greater than or equal to the highest value seen are valid and must be
processed. However, a router must keep track of the Segment Numbers
of RR messages already processed and avoid reprocessing a message
Crawford Standards Track [Page 3]
RFC 2894 Router Renumbering for IPv6 August 2000
whose Sequence Number and Segment Number match a previously processed
message. (This list of processed segment numbers is reset when a new
highest Sequence Number is seen.)
The Segment Number does not impose an ordering on packet processing.
If a specific sequence of operations is desired, it may be achieved
by ordering the PCOs in a single RR Command message or through the
Sequence Number field.
There is a "Test" flag which indicates that all routers should
simulate processing of the RR message and not perform any actual
reconfiguration. A separate "Report" flag instructs routers to send
a Router Renumbering Result message back to the source of the RR
Command message indicating the actual or simulated result of the
operations in the RR Command message.
The effect or simulated effect of an RR Command message may also be
reported to network management by means outside the scope of this
document, regardless of the value of the "Report" flag.
2. Definitions
2.1. Terminology
Address
This term always refers to a 128-bit IPv6 address [AARCH]. When
referring to bits within an address, they are numbered from 0 to
127, with bit 0 being the first bit of the Format Prefix.
Prefix
A prefix can be understood as an address plus a length, the latter
being an integer in the range 0 to 128 indicating how many leading
bits are significant. When referring to bits within a prefix,
they are numbered in the same way as the bits of an address. For
example, the significant bits of a prefix whose length is L are
the bits numbered 0 through L-1, inclusive.
Match
An address A "matches" a prefix P whose length is L if the first L
bits of A are identical with the first L bits of P. (Every
address matches a prefix of length 0.) A prefix P1 with length L1
matches a prefix P2 of length L2 if L1 >= L2 and the first L2 bits
of P1 and P2 are identical.
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RFC 2894 Router Renumbering for IPv6 August 2000
Prefix Control Operation
This is the smallest individual unit of Router Renumbering
operation. A Router Renumbering Command packet includes zero or
more of these, each comprising one matching condition, called a
Match-Prefix Part, and zero or more substitution specifications,
called Use-Prefix Parts.
Match-Prefix
This is a Prefix against which a router compares the addresses and
prefixes configured on its interfaces.
Use-Prefix
The prefix and associated information which is to be configured on
a router interface when certain conditions are met.
Matched Prefix
The existing prefix or address which matched a Match-Prefix.
New Prefix
A prefix constructed from a Use-Prefix, possibly including some of
the Matched Prefix.
Recorded Sequence Number
The highest sequence number found in a valid message MUST be
recorded in non-volatile storage.
Note that "matches" is a transitive relation but not symmetric.
If two prefixes match each other, they are identical.
2.2. Requirements
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 [KWORD].
3. Message Format
There are two types of Router Renumbering messages: Commands, which
are sent to routers, and Results, which are sent by routers. A third
message type is used to synchronize a reset of the Recorded Sequence
Number with the cancellation of cryptographic keys. The three types
of messages are distinguished the ICMPv6 "Code" field and differ in
the contents of the "Message Body" field.
Crawford Standards Track [Page 5]
RFC 2894 Router Renumbering for IPv6 August 2000
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| |
/ IPv6 header, extension headers /
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| |
/ ICMPv6 & RR Header (16 octets) /
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| |
/ RR Message Body /
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Router Renumbering Message Format
Router Renumbering messages are carried in ICMPv6 packets with Type =
138. The RR message comprises an RR Header, containing the ICMPv6
header, the sequence and segment numbers and other information, and
the RR Message Body, of variable length.
All fields marked "reserved" or "res" MUST be set to zero on
generation of an RR message, and ignored on receipt.
All implementations which generate Router Renumbering Command
messages MUST support sending them to the All Routers multicast
address with link and site scopes, and to unicast addresses of link-
local and site-local formats. All routers MUST be capable of
receiving RR Commands sent to those multicast addresses and to any of
their link local and site local unicast addresses. Implementations
SHOULD support sending and receiving RR messages addressed to other
unicast addresses. An implementation which is both a sender and
receiver of RR commands SHOULD support use of the All Routers
multicast address with node scope.
Data authentication and message integrity MUST be provided for all
Router Renumbering Command messages by appropriate IP Security
[IPSEC] means. The integrity assurance must include the IPv6
destination address and the RR Header and Message Body. See section
7, "Security Considerations".
The use of authentication for Router Renumbering Result messages is
RECOMMENDED.
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RFC 2894 Router Renumbering for IPv6 August 2000
3.1. Router Renumbering Header
0 1 2 3
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Type | Code | Checksum |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| SequenceNumber |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| SegmentNumber | Flags | MaxDelay |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| reserved |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Fields:
Type 138 (decimal), the ICMPv6 type value assigned to Router
Renumbering
Code 0 for a Router Renumbering Command
1 for a Router Renumbering Result
255 for a Sequence Number Reset.
The Sequence Number Reset is described in section 5.
Checksum The ICMPv6 checksum, as specified in [ICMPV6]. The
checksum covers the IPv6 pseudo-header and all fields of
the RR message from the Type field onward.
SequenceNumber
An unsigned 32-bit sequence number. The sequence number
MUST be non-decreasing between Sequence Number Resets.
SegmentNumber
An unsigned 8-bit field which enumerates different valid
RR messages having the same SequenceNumber. No ordering
among RR messages is imposed by the SegmentNumber.
Flags A combination of one-bit flags. Five are defined and
three bits are reserved.
+-+-+-+-+-+-+-+-+
|T|R|A|S|P| res |
+-+-+-+-+-+-+-+-+
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RFC 2894 Router Renumbering for IPv6 August 2000
The flags T, R, A and S have defined meanings in an RR
Command message. In a Result message they MUST be
copied from the corresponding Command. The P flag is
meaningful only in a Result message and MUST be zero in
a transmitted Command and ignored in a received Command.
T Test command --
0 indicates that the router configuration is to be
modified;
1 indicates a "Test" message: processing is to be
simulated and no configuration changes are to be
made.
R Result requested --
0 indicates that a Result message MUST NOT be sent
(but other forms of logging are not precluded);
1 indicates that the router MUST send a Result
message upon completion of processing the Command
message;
A All interfaces --
0 indicates that the Command MUST NOT be applied to
interfaces which are administratively shut down;
1 indicates that the Command MUST be applied to all
interfaces regardless of administrative shutdown
status.
S Site-specific -- This flag MUST be ignored unless
the router treats interfaces as belonging to
different "sites".
0 indicates that the Command MUST be applied to
interfaces regardless of which site they belong
to;
1 indicates that the Command MUST be applied only to
interfaces which belong to the same site as the
interface to which the Command is addressed. If
the destination address is appropriate for
interfaces belonging to more than one site, then
the Command MUST be applied only to interfaces
belonging to the same site as the interface on
which the Command was received.
P Processed previously --
0 indicates that the Result message contains the
complete report of processing the Command;
Crawford Standards Track [Page 8]
RFC 2894 Router Renumbering for IPv6 August 2000
1 indicates that the Command message was previously
processed (and is not a Test) and the responding
router is not processing it again. This Result
message MAY have an empty body.
MaxDelay An unsigned 16-bit field specifying the maximum time, in
milliseconds, by which a router MUST delay sending any
reply to this Command. Implementations MAY generate the
random delay between 0 and MaxDelay milliseconds with a
finer granularity than 1ms.
3.2. Message Body -- Command Message
The body of an RR Command message is a sequence of zero or more
Prefix Control Operations, each of variable length. The end of the
sequence MAY be inferred from the IPv6 length and the lengths of
extension headers which precede the ICMPv6 header.
3.2.1. Prefix Control Operation
A Prefix Control Operation has one Match-Prefix Part of 24 octets,
followed by zero or more Use-Prefix Parts of 32 octets each.
3.2.1.1. Match-Prefix Part
0 1 2 3
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| OpCode | OpLength | Ordinal | MatchLen |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| MinLen | MaxLen | reserved |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| |
+- -+
| |
+- MatchPrefix -+
| |
+- -+
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Fields:
OpCode An unsigned 8-bit field specifying the operation to be
performed when the associated MatchPrefix matches an
interface's prefix or address. Values are:
1 the ADD operation
Crawford Standards Track [Page 9]
RFC 2894 Router Renumbering for IPv6 August 2000
2 the CHANGE operation
3 the SET-GLOBAL operation
OpLength The total length of this Prefix Control Operation, in
units of 8 octets. A valid OpLength will always be of
the form 4N+3, with N equal to the number of UsePrefix
parts (possibly zero).
Ordinal An 8-bit field which MUST have a different value in each
Prefix Control Operation contained in a given RR Command
message. The value is otherwise unconstrained.
MatchLen An 8-bit unsigned integer between 0 and 128 inclusive
specifying the number of initial bits of MatchPrefix
which are significant in matching.
MinLen An 8-bit unsigned integer specifying the minimum length
which any configured prefix must have in order to be
eligible for testing against the MatchPrefix.
MaxLen An 8-bit unsigned integer specifying the maximum length
which any configured prefix may have in order to be
eligible for testing against the MatchPrefix.
MatchPrefix The 128-bit prefix to be compared with each interface's
prefix or address.
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RFC 2894 Router Renumbering for IPv6 August 2000
3.2.1.2. Use-Prefix Part
0 1 2 3
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| UseLen | KeepLen | FlagMask | RAFlags |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Valid Lifetime |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| Preferred Lifetime |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
|V|P| reserved |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| |
+- -+
| |
+- UsePrefix -+
| |
+- -+
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Fields:
UseLen An 8-bit unsigned integer less than or equal to 128
specifying the number of initial bits of UsePrefix to
use in creating a new prefix for an interface.
KeepLen An 8-bit unsigned integer less than or equal to (128-
UseLen) specifying the number of bits of the prefix or
address which matched the associated Match-Prefix which
should be retained in the new prefix. The retained bits
are those at positions UseLen through (UseLen+KeepLen-1)
in the matched address or prefix, and they are copied to
the same positions in the New Prefix.
FlagMask An 8-bit mask. A 1 bit in any position means that the
corresponding flag bit in a Router Advertisement (RA)
Prefix Information Option for the New Prefix should be
set from the RAFlags field in this Use-Prefix Part. A 0
bit in the FlagMask means that the RA flag bit for the
New Prefix should be copied from the corresponding RA
flag bit of the Matched Prefix.
RAFlags An 8 bit field which, under control of the FlagMask
field, may be used to initialize the flags in Router
Advertisement Prefix Information Options [ND] which
advertise the New Prefix. Note that only two flags have
Crawford Standards Track [Page 11]
RFC 2894 Router Renumbering for IPv6 August 2000
defined meanings to date: the L (on-link) and A
(autonomous configuration) flags. These flags occupy
the two leftmost bit positions in the RAFlags field,
corresponding to their position in the Prefix
Information Option.
Valid Lifetime
A 32-bit unsigned integer which is the number of seconds
for which the New Prefix will be valid [ND, SAA].
Preferred Lifetime
A 32-bit unsigned integer which is the number of seconds
for which the New Prefix will be preferred [ND, SAA].
V A 1-bit flag indicating that the valid lifetime of the
New Prefix MUST be effectively decremented in real time.
P A 1-bit flag indicating that the preferred lifetime of
the New Prefix MUST be effectively decremented in real
time.
UsePrefix The 128-bit Use-prefix which either becomes or is used
in forming (if KeepLen is nonzero) the New Prefix. It
MUST NOT have the form of a multicast or link-local
address [AARCH].
3.3. Message Body -- Result Message
The body of an RR Result message is a sequence of zero or more Match
Reports of 24 octets. An RR Command message with the "R" flag set
will elicit an RR Result message containing one Match Report for each
Prefix Control Operation, for each different prefix it matches on
each interface. The Match Report has the following format.
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RFC 2894 Router Renumbering for IPv6 August 2000
0 1 2 3
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| reserved |B|F| Ordinal | MatchedLen |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| InterfaceIndex |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
| |
+- -+
| |
+- MatchedPrefix -+
| |
+- -+
| |
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Fields:
B A one-bit flag which, when set, indicates that one or
more fields in the associated PCO were out of bounds.
The bounds check is described in section 4.2.
F A one-bit flag which, when set, indicates that one or
more Use-Prefix parts from the associated PCO were not
honored by the router because of attempted formation of
a forbidden prefix format, such as a multicast or
loopback address.
Ordinal Copied from the Prefix Control Operation whose
MatchPrefix matched the MatchedPrefix on the interface
indicated by InterfaceIndex.
MatchedLen The length of the Matched Prefix.
InterfaceIndex
The router's numeric designation of the interface on
which the MatchedPrefix was configured. This MUST be
the same as the value of ipv6IfIndex which designates
that index in the SNMP IPv6 MIB General Group [IPV6MIB].
It is possible for a Result message to be larger than the Command
message which elicited it. Such a Result message may have to be
fragmented for transmission. If so, it SHOULD be fragmented to the
IPv6 minimum required MTU [IPV6].
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RFC 2894 Router Renumbering for IPv6 August 2000
4. Message Processing
Processing of received Router Renumbering Result messages is entirely
implementation-defined. Implementation of Command message processing
may vary in detail from the procedure set forth below, so long as the
result is not affected.
Processing of received Router Renumbering Command messages consists
of three conceptual parts: header check, bounds check, and execution.
4.1. Header Check
The ICMPv6 checksum and type are presumed to have been checked before
a Router Renumbering module receives a Command to process. In an
implementation environment where this may not be the case, those
checks MUST be made at this point in the processing.
If the ICMPv6 length derived from the IPv6 length is less than 16
octets, the message MUST be discarded and SHOULD be logged to network
management.
If the ICMPv6 Code field indicates a Result message, a router which
is not a source of RR Command messages MUST discard the message and
SHOULD NOT log it to network management.
If the IPv6 destination address is neither an All Routers multicast
address [AARCH] nor one of the receiving router's unicast addresses,
the message MUST be discarded and SHOULD be logged to network
management.
Next, the SequenceNumber is compared to the Recorded Sequence Number.
(If no RR messages have been received and accepted since system
initialization, the Recorded Sequence Number is zero.) This
comparison is done with the two numbers considered as unsigned
integers, not as DNS-style serial numbers. If the SequenceNumber is
less than the Recorded Sequence Number, the message MUST be discarded
and SHOULD be logged to network management.
Finally, if the SequenceNumber in the message is greater than the
Recorded Sequence Number or the T flag is set, skip to the bounds
check. Otherwise the SegmentNumber MUST now be checked. If a
correctly authenticated message with the same SequenceNumber and
SegmentNumber has not already been processed, skip to the bounds
check. Otherwise, this Command is a duplicate and not a Test
Command. If the R flag is not set, the duplicate message MUST be
discarded and SHOULD NOT be logged to network management. If R is
set, an RR Result message with the P flag set MUST be scheduled for
transmission to the source address of the Command after a random time
Crawford Standards Track [Page 14]
RFC 2894 Router Renumbering for IPv6 August 2000
uniformly distributed between 0 and MaxDelay milliseconds. The body
of that Result message MUST either be empty or be a saved copy of the
Result message body generated by processing of the previous message
with the same SequenceNumber and SegmentNumber. After scheduling the
Result message, the Command MUST be discarded without further
processing.
4.2. Bounds Check
If the SequenceNumber is greater than the Recorded Sequence Number,
then the list of processed SegmentNumbers and the set of saved Result
messages, if any, MUST be cleared and the Recorded Sequence Number
MUST be updated to the value used in the current message, regardless
of subsequent processing errors.
Next, if the ICMPv6 Code field indicates a Sequence Number Reset,
skip to section 5.
At this point, if T is set in the RR header and R is not set, the
message MAY be discarded without further processing.
If the R flag is set, begin constructing an RR Result message. The
RR header of the Result message is completely determined at this time
except for the Checksum.
The values of the following fields of a PCO MUST be checked to ensure
that they are within the appropriate bounds.
OpCode must be a defined value.
OpLength must be of the form 4N+3 and consistent the the length
of the Command packet and the PCO's offset within the
packet.
MatchLen must be between 0 and 128 inclusive
UseLen, KeepLen
in each Use-Prefix Part must be between 0 and 128
inclusive, as must the sum of the two.
If any of these fields are out of range in a PCO, the entire PCO MUST
NOT be performed on any interface. If the R flag is set in the RR
header then add to the RR Result message a Match Report with the B
flag set, the F flag clear, the Ordinal copied from the PCO, and all
other fields zero. This Match Report MUST be included only once, not
once per interface.
Crawford Standards Track [Page 15]
RFC 2894 Router Renumbering for IPv6 August 2000
Note that MinLen and MaxLen need not be explicitly bounds checked,
even though certain combinations of values will make any matches
impossible.
4.3. Execution
For each applicable router interface, as determined by the A and S
flags, the Prefix Control Operations in an RR Command message must be
carried out in order of appearance. The relative order of PCO
processing among different interfaces is not specified.
If the T flag is set, create a copy of each interface's configuration
on which to operate, because the results of processing a PCO may
affect the processing of subsequent PCOs. Note that if all
operations are performed on one interface before proceeding to
another interface, only one interface-configuration copy will be
required at a time.
For each interface and for each Prefix Control Operation, each prefix
configured on that interface with a length between the MinLen and
MaxLen values in the PCO is tested to determine whether it matches
(as defined in section 2.1) the MatchPrefix of the PCO. The
configured prefixes are tested in an arbitrary order. Any new prefix
configured on an interface by the effect of a given PCO MUST NOT be
tested against that PCO, but MUST be tested against all subsequent
PCOs in the same RR Command message.
Under a certain condition the addresses on an interface are also
tested to see whether any of them matches the MatchPrefix. If and
only if a configured prefix "P" does have a length between MinLen and
MaxLen inclusive, does not match the MatchPrefix "M", but M does
match P (this can happen only if M is longer than P), then those
addresses on that interface which match P MUST be tested to determine
whether any of them matches M. If any such address does match M,
process the PCO as if P matched M, but when forming New Prefixes, if
KeepLen is non-zero, bits are copied from the address. This special
case allows a PCO to be easily targeted to a single specific
interface in a network.
If P does not match M, processing is finished for this combination of
PCO, interface and prefix. Continue with another prefix on the same
interface if there are any more prefixes which have not been tested
against this PCO and were not created by the action of this PCO. If
no such prefixes remain on the current interface, continue processing
with the next PCO on the same interface, or with another interface.
Crawford Standards Track [Page 16]
RFC 2894 Router Renumbering for IPv6 August 2000
If P does match M, either directly or because a configured address
which matches P also matches M, then P is the Matched Prefix.
Perform the following steps.
If the Command has the R flag set, add a Match Report to the
Result message being constructed.
If the OpCode is CHANGE, mark P for deletion from the current
interface.
If the OpCode is SET-GLOBAL, mark all global-scope prefixes on the
current interface for deletion.
If there are any Use-Prefix parts in the current PCO, form the New
Prefixes. Discard any New Prefix which has a forbidden format,
and if the R flag is set in the command, set the F flag in the
Match Report for this PCO and interface. Forbidden prefix formats
include, at a minimum, multicast, unspecified and loopback
addresses. [AARCH] Any implementation MAY forbid, or allow the
network manager to forbid other formats as well.
For each New Prefix which is already configured on the current
interface, unmark that prefix for deletion and update the
lifetimes and RA flags. For each New Prefix which is not already
configured, add the prefix and, if appropriate, configure an
address with that prefix.
Delete any prefixes which are still marked for deletion, together
with any addresses which match those prefixes but do not match any
prefix which is not marked for deletion.
After processing all the Prefix Control Operations on all the
interfaces, an implementation MUST record the SegmentNumber of the
packet in a list associated with the SequenceNumber.
If the Command has the R flag set, compute the Checksum and
schedule the Result message for transmission after a random time
interval uniformly distributed between 0 and MaxDelay
milliseconds. This interval SHOULD begin at the conclusion of
processing, not the beginning. A copy of the Result message MAY
be saved to be retransmitted in response to a duplicate Command.
4.4. Summary of Effects
The only Neighbor Discovery [ND] parameters which can be affected by
Router Renumbering are the following.
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A router's addresses and advertised prefixes, including the prefix
lengths.
The flag bits (L and A, and any which may be defined in the
future) and the valid and preferred lifetimes which appear in a
Router Advertisement Prefix Information Option.
That unnamed property of the lifetimes which specifies whether
they are fixed values or decrementing in real time.
Other internal router information, such as the time until the next
unsolicited Router Advertisement or MIB variables MAY be affected as
needed.
All configuration changes resulting from Router Renumbering SHOULD be
saved to non-volatile storage where this facility exists. The
problem of properly restoring prefix lifetimes from non-volatile
storage exists independently of Router Renumbering and deserves
careful attention, but is outside the scope of this document.
5. Sequence Number Reset
It may prove necessary in practice to reset a router's Recorded
Sequence Number. This is a safe operation only when all
cryptographic keys previously used to authenticate RR Commands have
expired or been revoked. For this reason, the Sequence Number Reset
message is defined to accomplish both functions.
When a Sequence Number Reset (SNR) has been authenticated and has
passed the header check, the router MUST invalidate all keys which
have been used to authenticate previous RR Commands, including the
key which authenticated the SNR itself. Then it MUST discard any
saved RR Result messages, clear the list of recorded SegmentNumbers
and reset the Recorded Sequence Number to zero.
If the router has no other, unused authentication keys already
available for Router Renumbering use it SHOULD establish one or more
new valid keys. The details of this process will depend on whether
manual keying or a key management protocol is used. In either case,
if no keys are available, no new Commands can be processed.
A SNR message SHOULD contain no PCOs, since they will be ignored. If
and only if the R flag is set in the SNR message, a router MUST
respond with a Result Message containing no Match Reports. The
header and transmission of the Result are as described in section 3.
The invalidation of authentication keys caused by a valid SNR message
will cause retransmitted copies of that message to be ignored.
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6. IANA Considerations
Following the policies outlined in [IANACON], new values of the Code
field in the Router Renumbering Header (section 3.1) and the OpCode
field of the Match-Prefix Part (section 3.2.1.1) are to be allocated
by IETF consensus only.
7. Security Considerations
The Router Renumbering mechanism proposed here is very powerful and
prevention of spoofing it is important. Replay of old messages must,
in general, be prevented (even though a narrow class of messages
exists for which replay would be harmless). What constitutes a
sufficiently strong authentication algorithm may change from time to
time, but algorithms should be chosen which are strong against
current key-recovery and forgery attacks.
Authentication keys must be as well protected as any other access
method that allows reconfiguration of a site's routers. Distribution
of keys must not expose them or permit alteration, and key validity
must be limited in terms of time and number of messages
authenticated.
Note that although a reset of the Recorded Sequence Number requires
the cancellation of previously-used authentication keys, introduction
of new keys and expiration of old keys does not require resetting the
Recorded Sequence Number.
7.1. Security Policy and Association Database Entries
The Security Policy Database (SPD) [IPSEC] of a router implementing
this specification MUST cause incoming Router Renumbering Command
packets to either be discarded or have IPsec applied. (The
determination of "discard" or "apply" MAY be based on the source
address.) The resulting Security Association Database (SAD) entries
MUST ensure authentication and integrity of the destination address
and the RR Header and Message Body, and the body length implied by
the IPv6 length and intervening extension headers. These
requirements are met by the use of the Authentication Header [AH] in
transport or tunnel mode, or the Encapsulating Security Payload [ESP]
in tunnel mode with non-NULL authentication. The mandatory-to-
implement IPsec authentication algorithms (other than NULL) seem
strong enough for Router Renumbering at the time of this writing.
Note that for the SPD to distinguish Router Renumbering from other
ICMP packets requires the use of the ICMP Type field as a selector.
This is consistent with, although not mentioned by, the Security
Architecture specification [IPSEC].
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At the time of this writing, there exists no multicast key management
protocol for IPsec and none is on the horizon. Manually configured
Security Associations will therefore be common. The occurrence of
"from traffic" in the table below would therefore more realistically
be a wildcard or a fixed range. Use of a small set of shared keys
per management station suffices, so long as key distribution and
storage are sufficiently safeguarded.
A sufficient set of SPD entries for incoming traffic could select
Field SPD Entry SAD Entry
------- --------- ---------
Source wildcard from traffic
Destination wildcard from SPD
Transport ICMPv6 from SPD
ICMP Type Rtr. Renum. from SPD
Action Apply IPsec
SA Spec AH/Transport Mode
or there might be an entry for each management station and/or for
each of the router's unicast addresses and for each of the defined
All-Routers multicast addresses, and a final wildcard entry to
discard all other incoming RR messages.
The SPD and SAD are conceptually per-interface databases. This fact
may be exploited to permit shared management of a border router, for
example, or to discard all Router Renumbering traffic arriving over
tunnels.
8. Implementation and Usage Advice for Reliability
Users of Router Renumbering will want to be sure that every non-
trivial message reaches every intended router. Well-considered
exploitation of Router Renumbering's retransmission and response-
directing features should make that goal achievable with high
confidence even in a minimally reliable network.
In one set of cases, probably the majority, the network management
station will know the complete set of routers under its control.
Commands can be retransmitted, with the "R" (Reply-requested) flag
set in the RR header, until Results have been collected from all
routers. If unicast Security Associations (or the means for creating
them) are available, the management station may switch from multicast
to unicast transmission when the number of routers still unheard-from
is suitably small.
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To maintain a list of managed routers, the management station can
employ any of several automatic methods which may be more convenient
than manual entry in a large network. Multicast RR "Test" commands
can be sent periodically and the results archived, or the management
station can use SNMP to "peek" into a link-state routing protocol
such as OSPF [OSPFMIB]. (In the case of OSPF, roughly one router per
area would need to be examined to build a complete list of routers.)
In a large dynamic network where the set of managed routers is not
known but reliable execution is desired, a scalable method for
achieving confidence in delivery is described here. Nothing in this
section affects the format or content of Router Renumbering messages,
nor their processing by routers.
A management station implementing these reliability mechanisms MUST
alert an operator who attempts to commence a set of Router
Renumbering Commands when retransmission of a previous set is not yet
completed, but SHOULD allow the operator to override the warning.
8.1. Outline and Definitions
The set of routers being managed with Router Renumbering is
considered as a set of populations, each population having a
characteristic probability of successful round-trip delivery of a
Command/Result pair. The goal is to estimate a lower bound, P, on
the round-trip probability for the whole set. With this estimate and
other data about the responses to retransmissions of the Command, a
confidence level can be computed for hypothesis that all routers have
been heard from.
If the true probability of successful round-trip communication with a
managed router were a constant, p, for all managed routers then an
estimate P of p could be derived from either of these statistics:
The expected ratio of the number of routers first heard from after
transmission (N + 1) to the number first heard from after N is
(1 - p).
When N different routers have been heard from after M
transmissions of a Command, the expected total number of Result
messages received is pNM. If R is the number of Results actually
received, then P = R/MN.
The two methods are not equivalent. The first suffers numerical
problems when the number of routers still to be heard from gets
small, so the P = R/MN estimate should be used.
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Since the round-trip probability is not expected to be uniform in the
real world, and the less-reliable units are more important to a
lower-bound estimate but more likely to be missed in sampling, the
sample from which P is computed is biased toward the less-reliable
routers. After the Nth transmission interval, N > 2, neglect all
routers heard from in intervals 1 through F from the reliability
estimate, where F is the greatest integer less than one-half of N.
For example, after five intervals, only routers first heard from in
the third through fifth intervals will be counted.
A management station implementing the methods of this section should
allow the user to specify the following parameters, and default them
to the indicated values.
Ct The target delivery confidence, default 0.999.
Pp A presumptive, pessimistic initial estimate of the lower
bound of the round-trip probability, P, to prevent early
termination. (See below.) Default 0.75.
Ti The initial time between Command retransmissions. Default 4
seconds. MaxDelay milliseconds (see section 3.1) must be
added to the retransmission timer. Knowledge of the
routers' processing time for RR Commands may influence the
setting of Ti. Ti+MaxDelay is also the minimum time the
management station must wait for Results after each
transmission before computing a new confidence level. The
phrase "end of the Nth interval" means a time Ti+MaxDelay
after the Nth transmission of a Command.
Tu The upper bound on the period between Command
retransmissions. Default 512 seconds.
The following variables, some a function of the retransmission
counter N, are used in the next section.
T(N) The time between Command transmissions N and N+1 is V*T(N) +
MaxDelay, where V is random and roughly uniform in the range
[0.75, 1.0]. T(1) = Ti and for N > 1, T(N) = min(2*T(N-1),
Tu).
M(N) The cumulative number of distinct routers from which replies
have been received to any of the first N transmissions of
the Command.
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RFC 2894 Router Renumbering for IPv6 August 2000
F=F(N) FLOOR((N-1)/2). All routers from which responses were
received in the first F intervals will be effectively
omitted from the estimate of the round-trip probability
computed at the Nth interval.
R(N,F) The total number of RR Result messages, including
duplicates, received by the end of the Nth interval from
those routers which were NOT heard from in any of the first
F intervals.
p(N) The estimate of the worst-case round-trip delivery
probability.
c(N) The computed confidence level.
An asterisk (*) is used to denote multiplication and a caret (^)
denotes exponentiation.
If the difference in reliability between the "good" and "bad" parts
of a managed network is very great, early c(N) values will be too
high. Retransmissions should continue for at least Nmin = log(1-
Ct)/log(1-Pp) intervals, regardless of the current confidence
estimate. (In fact, there's no need to compute p(N) and c(N) until
after Nmin intervals.)
8.2. Computations
Letting A = N*(M(N)-M(F))/R(N,F) for brevity, the estimate of the
round-trip delivery probability is p(N) = 1-Q, where Q is that root
of the equation
Q^N - A*Q + (A-1) = 0
which lies between 0 and 1. (Q = 1 is always a root. If N is odd
there is also a negative root.) This may be solved numerically, for
example with Newton's method (see any standard text, for example
[ANM]). The first-order approximation
Q1 = 1 - 1/A
may be used as a starting point for iteration. But Q1 should NOT be
used as an approximate solution as it always underestimates Q, and
hence overestimates p(N), which would cause an overestimate of the
confidence level.
If necessary, the spurious root Q = 1 can be divided out, leaving
Q^(N-1) + Q^(N-2) + ... + Q - (A-1) = 0
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RFC 2894 Router Renumbering for IPv6 August 2000
as the equation to solve. Depending on the numerical method used,
this could be desirable as it's just possible (but very unlikely)
that A=N and so Q=1 was a double root of the earlier equation.
After N > 2 (or N >= Nmin) intervals have been completed, Compute the
lower-bound reliability estimate
p(N) = R(N,F)/((N-F)*(M(N) - M(F))).
Compute the confidence estimate
c(N) = (1 - (1-p(N))^N)^(M(N) - M(F) + 1).
which is the Bayesian probability that M(N) is the number of routers
present given the number of responses which were collected, as
opposed to M(N)+1 or any greater number. It is assumed that the a
priori probability of there being K routers was no greater than that
of K-1 routers, for all K > M(N).
When c(N) >= Ct and N >= Nmin, retransmissions of the Command may
cease. Otherwise another transmission should be scheduled at a time
V*T(N) + MaxDelay after the previous (Nth) transmission, or V*T(N)
after the conclusion of processing responses to the Nth transmission,
whichever is later.
One corner case needs consideration. Divide-by-zero may occur when
computing p. This can happen only when no new routers have been
heard from in the last N-F intervals. Generally, the confidence
estimate c(N) will be close to unity by then, but in a pathological
case such as a large number of routers with reliable communication
and a much smaller number with very poor communication, the
confidence estimate may still be less than Ct when p's denominator
vanishes. The implementation may continue, and should continue if
the minimum number of transmissions given in the previous paragraph
have not yet been made. If new routers are heard from, p(N) will
again be non-singular.
Of course no limited retransmission scheme can fully address the
possibility of long-term problems, such as a partitioned network.
The network manager is expected to be aware of such conditions when
they exist.
8.3. Additional Assurance Methods
As a final means to detect routers which become reachable after
missing renumbering commands during an extended network split, a
management station MAY adopt the following strategy. When performing
each new operation, increment the SequenceNumber by more than one.
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After the operation is believed complete, periodically send some
"no-op" RR Command with the R (Result Requested) flag set and a
SequenceNumber one less than the highest used. Any responses to such
a command can only come from router that missed the last operation.
An example of a suitable "no-op" command would be an ADD operation
with MatchLen = 0, MinLen = 0, MaxLen = 128, and no Use-Prefix Parts.
If old authentication keys are saved by the management station, even
the reappearance of routers which missed a Sequence Number Reset can
be detected by the transmission of no-op commands with the invalid
key and a SequenceNumber higher than any used before the key was
invalidated. Since there is no other way for a management station to
distinguish a router's failure to receive an entire sequence of
repeated SNR messages from the loss of that router's single SNR
Result Message, this is the RECOMMENDED way to test for universal
reception of a SNR Command.
9. Usage Examples
This section sketches some sample applications of Router Renumbering.
Extension headers, including required IPsec headers, between the IPv6
header and the ICMPv6 header are not shown in the examples.
9.1. Maintaining Global-Scope Prefixes
A simple use of the Router Renumbering mechanism, and one which is
expected to to be common, is the maintenance of a set of global
prefixes with a subnet structure that matches that of the site's
site-local address assignments. In the steady state this would serve
to keep the Preferred and Valid lifetimes set to their desired
values. During a renumbering transition, similar Command messages
can add new prefixes and/or delete old ones. An outline of a
suitable Command message follows. Fields not listed are presumed set
to suitable values. This Command assumes all router interfaces to be
maintained already have site-local [AARCH] addresses.
IPv6 Header
Next Header = 58 (ICMPv6)
Source Address = (Management Station)
Destination Address = FF05::2 (All Routers, site-local scope)
ICMPv6/RR Header
Type = 138 (Router Renumbering), Code = 0 (Command)
Flags = 60 hex (R, A)
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First (and only) PCO:
Match-Prefix Part
OpCode = 3 (SET-GLOBAL)
OpLength = 4 N + 3 (assuming N global prefixes)
Ordinal = 0 (arbitrary)
MatchLen = 10
MatchPrefix = FEC0::0
First Use-Prefix Part
UseLen = 48 (Length of TLA ID + RES + NLA ID [AARCH])
KeepLen = 16 (Length of SLA (subnet) ID [AARCH])
FlagMask, RAFlags, Lifetimes, V & P flags -- as desired
UsePrefix = First global /48 prefix
. . .
Nth Use-Prefix Part
UseLen = 48
KeepLen = 16
FlagMask, RAFlags, Lifetimes, V & P flags -- as desired
UsePrefix = Last global /48 prefix
This will cause N global prefixes to be set (or updated) on each
applicable interface. On each interface, the SLA ID (subnet) field
of each global prefix will be copied from the existing site-local
prefix.
9.2. Renumbering a Subnet
A subnet can be gracefully renumbered by setting the valid and
preferred timers on the old prefix to a short value and having them
run down, while concurrently adding adding the new prefix. Later,
the expired prefix is deleted. The first step is described by the
following RR Command.
IPv6 Header
Next Header = 58 (ICMPv6)
Source Address = (Management Station)
Destination Address = FF05::2 (All Routers, site-local scope)
ICMPv6/RR Header
Type = 138 (Router Renumbering), Code = 0 (Command)
Flags = 60 hex (R, A)
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RFC 2894 Router Renumbering for IPv6 August 2000
First (and only) PCO:
Match-Prefix Part
OpCode = 2 (CHANGE)
OpLength = 11 (reflects 2 Use-Prefix Parts)
Ordinal = 0 (arbitrary)
MatchLen = 64
MatchPrefix = Old /64 prefix
First Use-Prefix Part
UseLen = 0
KeepLen = 64 (this retains the old prefix value intact)
FlagMask = 0, RAFlags = 0
Valid Lifetime = 28800 seconds (8 hours)
Preferred Lifetime = 7200 seconds (2 hours)
V flag = 1, P flag = 1
UsePrefix = 0::0
Second Use-Prefix Part
UseLen = 64
KeepLen = 0
FlagMask = 0, RAFlags = 0
Lifetimes, V & P flags -- as desired
UsePrefix = New /64 prefix
The second step, deletion of the old prefix, can be done by an RR
Command with the same Match-Prefix Part (except for an OpLength
reduced from 11 to 3) and no Use-Prefix Parts. Any temptation to set
KeepLen = 64 in the second Use-Prefix Part above should be resisted,
as it would instruct the router to sidestep address configuration.
10. Acknowledgments
This protocol was designed by Matt Crawford based on an idea of
Robert Hinden and Geert Jan de Groot. Many members of the IPNG
Working Group contributed useful comments, in particular members of
the DIGITAL UNIX IPv6 team. Bill Sommerfeld provided helpful IPsec
expertise. Relentless browbeating by various IESG members may have
improved the final quality of this specification.
Crawford Standards Track [Page 27]
RFC 2894 Router Renumbering for IPv6 August 2000
11. References
[AARCH] Hinden, R. and S. Deering, "IP Version 6 Addressing
Architecture", RFC 2373, July 1998.
[AH] Kent, S. and R. Atkinson, "IP Authentication Header", RFC
2402, November 1998.
[ANM] Isaacson, E. and H. B. Keller, "Analysis of Numerical
Methods", John Wiley & Sons, New York, 1966.
[ESP] Kent, S. and R. Atkinson, "IP Encapsulating Security
Payload (ESP)", RFC 2406, November 1998.
[IANACON] Narten, T. and H. Alvestrand, "Guidelines for Writing an
IANA Considerations Section in RFCs", BCP 26, RFC 2434,
October 1998.
[ICMPV6] Conta, A. and S. Deering, "Internet Control Message
Protocol (ICMPv6) for the Internet Protocol Version 6
(IPv6)", RFC 2463, December 1998.
[IPSEC] Kent, S. and R. Atkinson, "Security Architecture for the
Internet Protocol", RFC 2401, November 1998.
[IPV6] Deering, S. and R. Hinden, "Internet Protocol, Version 6
(IPv6) Specification", RFC 2460, December 1998.
[IPV6MIB] Haskin, D. and S. Onishi, "Management Information Base for
IP Version 6: Textual Conventions and General Group", RFC
2466, December 1998.
[KWORD] Bradner, S., "Key words for use in RFCs to Indicate
Requirement Levels", BCP 14, RFC 2119, March 1997.
[ND] Narten, T., Nordmark, E. and W. Simpson, "Neighbor
Discovery for IP Version 6 (IPv6)", RFC 2461, December
1998.
[OSPFMIB] Baker, F. and R. Coltun, "OSPF Version 2 Management
Information Base", RFC 1850, November 1995.
Crawford Standards Track [Page 28]
RFC 2894 Router Renumbering for IPv6 August 2000
12. Author's Address
Matt Crawford
Fermilab MS 368
PO Box 500
Batavia, IL 60510
USA
Phone: +1 630 840 3461
EMail:
[email protected]
Crawford Standards Track [Page 29]
RFC 2894 Router Renumbering for IPv6 August 2000
Appendix -- Derivation of Reliability Estimates
If a population S of size k is repeatedly sampled with an efficiency
p, the expected number of members of S first discovered on the nth
sampling is
m = [1 - (1-p)^n] * k
The expected total number of members of S found in samples, including
duplicates, is
r = n * p * k
Taking the ratio of m to r cancels the unknown factor k and yields an
equation
[1 - (1-p)^n] / p = nm/r
which may be solved for p, which is then an estimator of the sampling
efficiency. (The statistical properties of the estimator will not be
examined here.) Under the substitution p = 1-q, this becomes the
first equation of Section 8.2.
With the estimator p in hand, and a count m of members of S
discovered after n samplings, we can compute the a posteriori
probability that the true size of S is m+j, for j >= 0. Let Hj
denote the hypothesis that the true size of S is m+j, and let R
denote the result that m members have been found in n samplings.
Then
P{R | Hj} = [(m+j)!/m!j!] * [1-(1-p)^n]^m * [(1-p)^n]^j
We are interested in P{H0 | R}, but to find it we need to assign a
priori values to P{Hj}. Let the size of S be exponentially
distributed
P{Hj} / P{H0} = h^(-j)
for arbitrary h in (0, 1). The value of h will be eliminated from
the result.
The Bayesian method yields
P{Hj | R} / P{H0 | R} = [(m+j)!/m!j!] * [h*(1-p)^n]^j
The reciprocal of the sum over j >= 0 of these ratios is
P{H0 | R} = [1-h*(1-p)^n] ^ (m+1)
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RFC 2894 Router Renumbering for IPv6 August 2000
and the confidence estimate of Section 8.2 is the h -> 1 limit of
this expression.
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RFC 2894 Router Renumbering for IPv6 August 2000
Full Copyright Statement
Copyright (C) The Internet Society (2000). All Rights Reserved.
This document and translations of it may be copied and furnished to
others, and derivative works that comment on or otherwise explain it
or assist in its implementation may be prepared, copied, published
and distributed, in whole or in part, without restriction of any
kind, provided that the above copyright notice and this paragraph are
included on all such copies and derivative works. However, this
document itself may not be modified in any way, such as by removing
the copyright notice or references to the Internet Society or other
Internet organizations, except as needed for the purpose of
developing Internet standards in which case the procedures for
copyrights defined in the Internet Standards process must be
followed, or as required to translate it into languages other than
English.
The limited permissions granted above are perpetual and will not be
revoked by the Internet Society or its successors or assigns.
This document and the information contained herein is provided on an
"AS IS" basis and THE INTERNET SOCIETY AND THE INTERNET ENGINEERING
TASK FORCE DISCLAIMS ALL WARRANTIES, EXPRESS OR IMPLIED, INCLUDING
BUT NOT LIMITED TO ANY WARRANTY THAT THE USE OF THE INFORMATION
HEREIN WILL NOT INFRINGE ANY RIGHTS OR ANY IMPLIED WARRANTIES OF
MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE.
Acknowledgement
Funding for the RFC Editor function is currently provided by the
Internet Society.
Crawford Standards Track [Page 32]
