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Router Renumbering for IPv6
draft-ietf-ipngwg-router-renum-10

The information below is for an old version of the document that is already published as an RFC.
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This is an older version of an Internet-Draft that was ultimately published as RFC 2894.
Author Dr. Matt Crawford
Last updated 2013-03-02 (Latest revision 2000-03-16)
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Intended RFC status Proposed Standard
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IESG IESG state Became RFC 2894 (Proposed Standard)
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draft-ietf-ipngwg-router-renum-10
IPng Working Group                                         Matt Crawford
Internet Draft                                                  Fermilab
                                                          March 10, 2000

                        Router Renumbering for IPv6
                  <draft-ietf-ipngwg-router-renum-10.txt>

Status of this Memo

    This document is an Internet-Draft and is in full conformance with
    all provisions of Section 10 of RFC 2026.  Internet-Drafts are
    working documents of the Internet Engineering Task Force (IETF), its
    areas, and its working groups.  Note that other groups may also
    distribute working documents as Internet-Drafts.

    Internet-Drafts are draft documents valid for a maximum of six
    months and may be updated, replaced, or obsoleted by other documents
    at any time.  It is inappropriate to use Internet- Drafts as
    reference material or to cite them other than as "work in progress."

     The list of current Internet-Drafts can be accessed at
     http://www.ietf.org/ietf/1id-abstracts.txt

     The list of Internet-Draft Shadow Directories can be accessed at
     http://www.ietf.org/shadow.html.

1.  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.

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Status of this Memo ...............................................    1

1.  Abstract ......................................................    1

2.  Functional Overview ...........................................    3

3.  Definitions ...................................................    4
    3.1.  Terminology .............................................    4
    3.2.  Requirements ............................................    5

4.  Message Format ................................................    5
    4.1.  Router Renumbering Header ...............................    7
    4.2.  Message Body -- Command Message .........................    9
        4.2.1.  Prefix Control Operation ..........................    9
            4.2.1.1.  Match-Prefix Part ...........................    9
            4.2.1.2.  Use-Prefix Part .............................   11
    4.3.  Message Body -- Result Message ..........................   12

5.  Message Processing ............................................   14
    5.1.  Header Check ............................................   14
    5.2.  Bounds Check ............................................   15
    5.3.  Execution ...............................................   16
    5.4.  Summary of Effects ......................................   18

6.  Sequence Number Reset .........................................   18

7.  IANA Considerations ...........................................   19

8.  Security Considerations .......................................   19
    8.1.  Security Policy and Association Database Entries ........   19

9.  Implementation and Usage Advice for Reliability ...............   20
    9.1.  Outline and Definitions .................................   21
    9.2.  Computations ............................................   23
    9.3.  Additional Assurance Methods ............................   25

10.  Usage Examples ...............................................   25
    10.1.  Maintaining Global-Scope Prefixes ......................   25
    10.2.  Renumbering a Subnet ...................................   26

11.  Acknowledgments ..............................................   28

12.  References ...................................................   28

13.  Author's Address .............................................   29

Appendix -- Derivation of Reliability Estimates ...................   30

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2.  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.

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    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.

3.  Definitions

3.1.  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.

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    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.

3.2.  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].

4.  Message Format

    There are two types of Router Renumbering messages: Commands, which
    are sent to routers, and Results, which are sent by routers.  A

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    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
    8, "Security Considerations".

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    The use of authentication for Router Renumbering Result messages is
    RECOMMENDED.

4.1.  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 6.

    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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                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

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                      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.

4.2.  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.

4.2.1.  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.

4.2.1.1.  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:

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                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.

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4.2.1.2.  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

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                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].

4.3.  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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      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 5.3.

    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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5.  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.

5.1.  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

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    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.

5.2.  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 6.

    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

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    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.

5.3.  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 3.1) 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

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    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.

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5.4.  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.

6.  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.

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    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 5.

    The invalidation of authentication keys caused by a valid SNR
    message will cause retransmitted copies of that message to be
    ignored.

7.  IANA Considerations

    Following the policies outlined in [IANACON], new values of the Code
    field in the Router Renumbering Header (section 4.1) and the OpCode
    field of the Match-Prefix Part (section 4.2.1.1) are to be allocated
    by IETF consensus only.

8.  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.

8.1.  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

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    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.

9.  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

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    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.

9.1.  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:

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         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 4.1) 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

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    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.)

9.2.  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

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    [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

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    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.

9.3.  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.

10.  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.

10.1.  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

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    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.

10.2.  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

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    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.

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11.  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.

12.  References

    [AARCH] Hinden, R. and S. Deering, "IP Version 6 Addressing
        Architecture", RFC 2373.

    [AH] Kent, S. and R. Atkinson, "IP Authentication Header", RFC 2402.

    [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.

    [IANACON] Narten, T. and H. T. Alvestrand, "Guidelines for Writing
        an IANA Considerations Section in RFCs", RFC 2434.

    [ICMPV6] Conta, A. and S. Deering, "Internet Control Message
        Protocol (ICMPv6) for the Internet Protocol Version 6 (IPv6)",
        RFC 2460.

    [IPSEC] Kent, S. and R. Atkinson, "Security Architecture for the
        Internet Protocol", RFC 2401.

    [IPV6] Deering, S. and R. Hinden, "Internet Protocol, Version 6
        (IPv6) Specification", RFC 2460.

    [IPV6MIB] Haskin, D. and S. Onishi, "Management Information Base for
        IP Version 6: Textual Conventions and General Group", RFC 2466.

    [KWORD] Bradner, S., "Key words for use in RFCs to Indicate
        Requirement Levels," RFC 2119.

    [ND] Narten, T., Nordmark, E. and W. Simpson, "Neighbor Discovery
        for IP Version 6 (IPv6)", RFC 2461.

    [OSPFMIB] Baker, F. and R. Coltun, "OSPF Version 2 Management

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        Information Base", RFC 1850.

13.  Author's Address

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

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

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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 9.2.

    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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    and the confidence estimate of Section 9.2 is the h -> 1 limit of
    this expression.

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