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RFC 2894 - Router Renumbering for IPv6


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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.

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,

   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

   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.

   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.

   +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
   |                                                               |
   /                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.

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 |
                                  +-+-+-+-+-+-+-+-+

              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;

                  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

               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.

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

               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.

    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].

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

   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.

   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.

   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.

      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.

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].

   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.

   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.

   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.

   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

   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.

   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)

   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)

   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.

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.

12.  Author's Address

   Matt Crawford
   Fermilab MS 368
   PO Box 500
   Batavia, IL 60510
   USA

   Phone: +1 630 840 3461
   EMail: crawdad@fnal.gov

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)

   and the confidence estimate of Section 8.2 is the h -> 1 limit of
   this expression.

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