path: root/doc/rfc/rfc8028.txt

Internet Engineering Task Force (IETF)                          F. Baker
Request for Comments: 8028
Updates: 4861                                               B. Carpenter
Category: Standards Track                              Univ. of Auckland
ISSN: 2070-1721                                            November 2016


     First-Hop Router Selection by Hosts in a Multi-Prefix Network

Abstract

   This document describes expected IPv6 host behavior in a scenario
   that has more than one prefix, each allocated by an upstream network
   that is assumed to implement BCP 38 ingress filtering, when the host
   has multiple routers to choose from.  It also applies to other
   scenarios such as the usage of stateful firewalls that effectively
   act as address-based filters.  Host behavior in choosing a first-hop
   router may interact with source address selection in a given
   implementation.  However, the selection of the source address for a
   packet is done before the first-hop router for that packet is chosen.
   Given that the network or host is, or appears to be, multihomed with
   multiple provider-allocated addresses, that the host has elected to
   use a source address in a given prefix, and that some but not all
   neighboring routers are advertising that prefix in their Router
   Advertisement Prefix Information Options, this document specifies to
   which router a host should present its transmission.  It updates RFC
   4861.

Status of This Memo

   This is an Internet Standards Track document.

   This document is a product of the Internet Engineering Task Force
   (IETF).  It represents the consensus of the IETF community.  It has
   received public review and has been approved for publication by the
   Internet Engineering Steering Group (IESG).  Further information on
   Internet Standards is available in Section 2 of RFC 7841.

   Information about the current status of this document, any errata,
   and how to provide feedback on it may be obtained at
   http://www.rfc-editor.org/info/rfc8028.










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Copyright Notice

   Copyright (c) 2016 IETF Trust and the persons identified as the
   document authors.  All rights reserved.

   This document is subject to BCP 78 and the IETF Trust's Legal
   Provisions Relating to IETF Documents
   (http://trustee.ietf.org/license-info) in effect on the date of
   publication of this document.  Please review these documents
   carefully, as they describe your rights and restrictions with respect
   to this document.  Code Components extracted from this document must
   include Simplified BSD License text as described in Section 4.e of
   the Trust Legal Provisions and are provided without warranty as
   described in the Simplified BSD License.

Table of Contents

   1.  Introduction and Applicability  . . . . . . . . . . . . . . .   3
     1.1.  Host Model  . . . . . . . . . . . . . . . . . . . . . . .   4
     1.2.  Requirements Language . . . . . . . . . . . . . . . . . .   5
   2.  Sending Context Expected by the Host  . . . . . . . . . . . .   5
     2.1.  Expectations the Host Has of the Network  . . . . . . . .   5
     2.2.  Expectations of Multihomed Networks . . . . . . . . . . .   7
   3.  Reasonable Expectations of the Host . . . . . . . . . . . . .   7
     3.1.  Interpreting Router Advertisements  . . . . . . . . . . .   7
     3.2.  Default Router Selection  . . . . . . . . . . . . . . . .   9
     3.3.  Source Address Selection  . . . . . . . . . . . . . . . .   9
     3.4.  Redirects . . . . . . . . . . . . . . . . . . . . . . . .   9
     3.5.  History . . . . . . . . . . . . . . . . . . . . . . . . .  10
   4.  Residual Issues . . . . . . . . . . . . . . . . . . . . . . .  10
   5.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .  10
   6.  Security Considerations . . . . . . . . . . . . . . . . . . .  11
   7.  References  . . . . . . . . . . . . . . . . . . . . . . . . .  11
     7.1.  Normative References  . . . . . . . . . . . . . . . . . .  11
     7.2.  Informative References  . . . . . . . . . . . . . . . . .  12
   Acknowledgements  . . . . . . . . . . . . . . . . . . . . . . . .  13
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .  13














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1.  Introduction and Applicability

   This document describes the expected behavior of an IPv6 [RFC2460]
   host in a network that has more than one prefix, each allocated by an
   upstream network that is assumed to implement BCP 38 [RFC2827]
   ingress filtering, and in which the host is presented with a choice
   of routers.  It expects that the network will implement some form of
   egress routing, so that packets sent to a host outside the local
   network from a given ISP's prefix will go to that ISP.  If the packet
   is sent to the wrong egress, it is liable to be discarded by the BCP
   38 filter.  However, the mechanics of egress routing once the packet
   leaves the host are out of scope.  The question here is how the host
   interacts with that network.

   Various aspects of this issue, and possible solution approaches, are
   discussed in "IPv6 Multihoming without Network Address Translation"
   [RFC7157].

   BCP 38 filtering by ISPs is not the only scenario where such behavior
   is valuable.  Implementations that combine existing recommendations,
   such as [RFC6092] and [RFC7084] can also result in such filtering.
   Another case is when the connections to the upstream networks include
   stateful firewalls, such that return packets in a stream will be
   discarded if they do not return via the firewall that created the
   state for the outgoing packets.  A similar cause of such discards is
   unicast reverse path forwarding (uRPF) [RFC3704].

   In this document, the term "filter" is used for simplicity to cover
   all such cases.  In any case, one cannot assume that the host is
   aware whether an ingress filter, a stateful firewall, or any other
   type of filter is in place.  Therefore, the only known consistent
   solution is to implement the features defined in this document.

   Note that, apart from ensuring that a message with a given source
   address is given to a first-hop router that appears to know about the
   prefix in question, this specification is consistent with [RFC4861].
   Nevertheless, implementers of Sections 6.2.3, 6.3.4, 6.3.6, and 8.1
   of RFC 4861 should extend their implementations accordingly.  This
   specification is fully consistent with [RFC6724] and depends on
   support for its Rule 5.5 (see Section 3.3).  Hosts that do not
   support these features may fail to communicate in the presence of
   filters as described above.









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1.1.  Host Model

   It could be argued that the proposal in this document, which is to
   send messages using a source address in a given prefix to the router
   that advertised the prefix in its Router Advertisement (RA), is a
   form of the Strong End System (ES, e.g., Host) model, discussed in
   Section 3.3.4.2 of [RFC1122].  In short, [RFC1122] identifies two
   basic models.  First, the "strong host" model describes the host as a
   set of hosts in one chassis, each of which uses a single address on a
   single interface and always both sends and receives on that
   interface.  Alternatively, the "weak host" model treats the host as
   one system with zero or more addresses on every interface and is
   capable of using any interface for any communication.  As noted
   there, neither model is completely satisfactory.  For example, a host
   with a link-local-only interface and a default route pointing to that
   interface will necessarily send packets using that interface but with
   a source address derived from some other interface, and will
   therefore be a de facto weak host.  If the router upstream from such
   a host implements BCP 38 Ingress Filtering [RFC2827], such as by
   implementing uRPF on each interface, the router might prevent
   communication by weak hosts.

                +-----------------+
                |                 |
                |     MIF Router  +---/--- Other interfaces
                |                 |
                +---+---------+---+
                    |         | Two interfaces with subnets
                    |         | from a common prefix
                  --+-+--   --+-+--
                      |         |
                   +--+---------+--+
                   |   MIF Host    |
                   +---------------+

                Figure 1: Hypothetical MIF Interconnection

   The proposal also differs slightly from the language in [RFC1122] for
   the Strong Host model.  The proposal is that the packet will go to a
   router that advertised a given prefix but that does not specify what
   interface that might happen on.  Hence, if the router is a multi-
   interface (MIF) router and it is using a common prefix spanning two
   or more LANs shared by the host (as in Figure 1), the host might use
   either of those LANs, according to this proposal.  The Strong Host
   model is not stated in those terms, but in terms of the interface
   used.  A strong host would treat such an MIF router as two separate
   routers when obeying the rules from RFC 1122 as they apply in the
   Strong case:



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   (A)  A host MUST silently discard an incoming datagram whose
        destination address does not correspond to the physical
        interface through which it is received.

   (B)  A host MUST restrict itself to sending (non-source-routed) IP
        datagrams only through the physical interface that corresponds
        to the IP source address of the datagrams.

   However, when comparing the presumptive route lookup mechanisms in
   each model, this proposal is indeed most similar to the Strong Host
   model, as is any source/destination routing paradigm.

   Strong:  route (src IP addr, dest IP addr, TOS) -> gateway

   Weak:  route (dest IP addr, TOS) -> gateway, interface

   In the hypothetical MIF model suggested in Figure 1, the address
   fails to identify a single interface, but it does identify a single
   gateway.

1.2.  Requirements Language

   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 [RFC2119].

2.  Sending Context Expected by the Host

2.1.  Expectations the Host Has of the Network

   A host receives prefixes in a Router Advertisement [RFC4861], which
   goes on to identify whether they are usable by Stateless Address
   Autoconfiguration (SLAAC) [RFC4862]  with any type of interface
   identifier [RFC4941] [RFC7217].  When no prefixes are usable for
   SLAAC, the Router Advertisement would normally signal the
   availability of DHCPv6 [RFC3315] and the host would use it to
   configure its addresses.  In the latter case (or if both SLAAC and
   DHCPv6 are used on the same link for some reason), the configured
   addresses generally match one of the prefixes advertised in a Router
   Advertisement that are supposed to be on-link for that link.

   The simplest multihomed network implementation in which a host makes
   choices among routers might be a LAN with one or more hosts on it and
   two or more routers, one for each upstream network, or a host that is
   served by disjoint networks on separate interfaces.  In such a
   network, especially the latter, there is not necessarily a routing
   protocol, and the two routers may not even know that the other is a
   router as opposed to a host, or may be configured to ignore its



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   presence.  One might expect that the routers may or may not receive
   each other's RAs and form an address in the other router's prefix
   (which is not per [RFC4862], but is implemented by some stub router
   implementations).  However, all hosts in such a network might be
   expected to create an address in each prefix so advertised.

          +---------+   +---------+    +---------+    +---------+
          |   ISP   |   |   ISP   |    |   ISP   |    |   ISP   |
          +----+----+   +----+----+    +----+----+    +----+----+
               |             |              |              |
               |             |              |              |
          +----+----+   +----+----+    +----+----+    +----+----+
          |  Router |   |  Router |    |  Router |    |  Router |
          +----+----+   +----+----+    +----+----+    +----+----+
               |             |              |              |
               +------+------+              |  +--------+  |
                      |                     +--+  Host  +--+
                 +----+----+                   +--------+
                 |  Host   |
                 +---------+
               Common LAN Case            Disjoint LAN Case
            (Multihomed Network)          (Multihomed Host)

                       Figure 2: Two Simple Networks

   If there is no routing protocol among those routers, there is no
   mechanism by which packets can be deterministically forwarded between
   the routers (as described in BCP 84 [RFC3704]) in order to avoid
   filters.  Even if there was routing, it would result in an indirect
   route, rather than a direct route originating with the host; this is
   not "wrong", but can be inefficient.  Therefore, the host would do
   well to select the appropriate router itself.

   Since the host derives fundamental default routing information from
   the Router Advertisement, this implies that, in any network with
   hosts using multiple prefixes, each prefix SHOULD be advertised via a
   Prefix Information Option (PIO) [RFC4861] by one of the attached
   routers, even if addresses are being assigned using DHCPv6.  A router
   that advertises a prefix indicates that it is able to appropriately
   route packets with source addresses within that prefix, regardless of
   the setting of the L and A flags in the PIO.

   In some circumstances, both L and A might be zero.  If SLAAC is not
   wanted (A=0) and there is no reason to announce an on-link prefix
   (L=0), a PIO SHOULD be sent to inform hosts that they should use the
   router in question as the first hop for packets with source addresses
   in the PIO prefix.  An example case is the MIF router in Figure 1,
   which could send PIOs with A=L=0 for the common prefix.  Although



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   this does not violate the existing standard [RFC4861], such a PIO has
   not previously been common, and it is possible that existing host
   implementations simply ignore such a PIO or that existing router
   implementations are not capable of sending such a PIO.  Newer
   implementations that support this mechanism should be updated
   accordingly:

   o  A host SHOULD NOT ignore a PIO simply because both L and A flags
      are cleared (extending Section 6.3.4 of [RFC4861]).

   o  A router SHOULD be able to send such a PIO (extending
      Section 6.2.3 of [RFC4861]).

2.2.  Expectations of Multihomed Networks

   Networking equipment needs to support source/destination routing for
   at least some of the routes in the Forwarding Information Base (FIB),
   such as default egress routes differentiated by source prefix.
   Installation of source/destination routes in the FIB might be
   accomplished using static routes, Software-Defined Networking (SDN)
   technologies, or dynamic routing protocols.

3.  Reasonable Expectations of the Host

3.1.  Interpreting Router Advertisements

   As described in [RFC4191] and [RFC4861], a Router Advertisement may
   contain zero or more Prefix Information Options (PIOs) or zero or
   more Route Information Options (RIOs).  In their original intent,
   these indicate general information to a host: "the router whose
   address is found in the source address field of this packet is one of
   your default routers", "you might create an address in this prefix",
   or "this router would be a good place to send traffic directed to a
   given destination prefix".  In a multi-prefix network with multiple
   exits, the host's characterization of each default router SHOULD
   include the prefixes it has announced (extending Section 6.3.4 of
   [RFC4861]).  In other words, the PIO is reinterpreted to also imply
   that the advertising router would be a reasonable first hop for any
   packet using a source address in any advertised prefix, regardless of
   Default Router Preference.











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                                                +---------+  |
                                    ( ISP A ) - +  Bob-A  +--+  +-----+
    +-------+                      /            +---------+  +--+     |
    |       |                     /                          |  |     |
    | Alice +--/--( The Internet )                              | Bob |
    |       |                     \                          |  |     |
    +-------+                      \            +---------+  +--+     |
                                    ( ISP B ) - +  Bob-B  +--+  +-----+
                                                +---------+  |

                 Figure 3: PIOs, RIOs, and Default Routes

   The implications bear consideration.  Imagine, Figure 3, that hosts
   Alice and Bob are in communication.  Bob's network consists of at
   least Bob (the computer), two routers (Bob-A and Bob-B), and the
   links between them; it may be much larger, for example, a campus or
   corporate network.  Bob's network is therefore multihomed, and Bob's
   first-hop routers are Bob-A (to the upstream ISP A advertising prefix
   PA) and Bob-B (to the upstream network B and advertising prefix PB).
   We assume that Bob is not applying Rule 5.5 of [RFC6724].  If Bob is
   responding to a message from Alice, his choice of source address is
   forced to be the address Alice used as a destination (which we may
   presume to have been in prefix PA).  Hence, Bob either created or was
   assigned an address in PA, and can only reasonably send traffic using
   it to Bob-A as a first-hop router.  If there are several routers in
   Bob's network advertising the prefix PA (referred to as "Bob-Ax"
   routers), then Bob should choose its first-hop router only from among
   those routers.  From among the multiple Bob-Ax routers, Bob should
   choose the first-hop router based on the criteria specified in
   Section 3 of [RFC4191].  If none of the Bob-Ax routers has advertised
   an RA with a non-zero Router Lifetime or an RIO with a non-zero Route
   Lifetime that includes Alice, but router Bob-B has, it is irrelevant.
   Bob is using the address allocated in PA and courts a BCP 38 discard
   if he doesn't send the packet to Bob-A.

   In the special case that Bob is initiating the conversation, an RIO
   might, however, influence source address choice.  Bob could
   presumably use any address allocated to him, in this case, his
   address in PA or PB.  If Bob-B has advertised an RIO for Alice's
   prefix and Bob-A has not, Bob MAY take that fact into account in
   address selection -- choosing an address that would allow him to make
   use of the RIO.









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3.2.  Default Router Selection

   Default Router Selection (Section 6.3.6 of [RFC4861]) is extended as
   follows: A host SHOULD select default routers for each prefix it is
   assigned an address in.  Routers that have advertised the prefix in
   their Router Advertisement message SHOULD be preferred over routers
   that do not advertise the prefix, regardless of Default Router
   Preference.  Note that this document does not change the way in which
   default router preferences are communicated [RFC4191].

   If no router has advertised the prefix in an RA, normal routing
   metrics will apply.  An example is a host connected to the Internet
   via one router, and at the same time connected by a VPN to a private
   domain that is also connected to the global Internet.

   As a result of this, when a host sends a packet using a source
   address in one of those prefixes and has no history directing it
   otherwise, it SHOULD send it to the indicated default router.  In the
   "simplest" network described in Section 2.1, that would get it to the
   only router that is directly capable of getting it to the right ISP.
   This will also apply in more complex networks, even when more than
   one physical or virtual interface is involved.

   In more complex cases, wherein routers advertise RAs for multiple
   prefixes whether or not they have direct or isolated upstream
   connectivity, the host is dependent on the routing system already.
   If the host gives the packet to a router advertising its source
   prefix, it should be able to depend on the router to do the right
   thing.

3.3.  Source Address Selection

   There is an interaction with Default Address Selection [RFC6724].  A
   host following the recommendation in the previous section will store
   information about which next hops advertised which prefixes.  Rule
   5.5 of RFC 6724 states that the source address used to send to a
   given destination address should, if possible, be chosen from a
   prefix known to be advertised by the next-hop router for that
   destination.  Therefore, this selection rule SHOULD be implemented in
   a host following the recommendation in the previous section.

3.4.  Redirects

   There is potential for adverse interaction with any off-link Redirect
   (Redirect for a destination that is not on-link) message sent by a
   router in accordance with Section 8 of [RFC4861].  Hosts SHOULD apply
   off-link redirects only for the specific pair of source and
   destination addresses concerned, so the host's Destination Cache



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   might need to contain appropriate source-specific entries.  This
   extends the validity check specified in Section 8.1 of [RFC4861].

3.5.  History

   Some modern hosts maintain history, in terms of what has previously
   worked or not worked for a given address or prefix and in some cases
   the effective window and Maximum Segment Size (MSS) values for TCP or
   other protocols.  This might include a next-hop address for use when
   a packet is sent to the indicated address.

   When such a host makes a successful exchange with a remote
   destination using a particular address pair, and the host has
   previously received a PIO that matches the source address, then the
   host SHOULD include the prefix in such history, whatever the setting
   of the L and A flags in the PIO.  On subsequent attempts to
   communicate with that destination, if it has an address in that
   prefix at that time, a host MAY use an address in the remembered
   prefix for the session.

4.  Residual Issues

   Consider a network where routers on a link run a routing protocol and
   are configured with the same information.  Thus, on each link, all
   routers advertise all prefixes on that link.  The assumption that
   packets will be forwarded to the appropriate egress by the local
   routing system might cause at least one extra hop in the local
   network (from the host to the wrong router, and from there to another
   router on the same link).

   In a slightly more complex situation such as the disjoint LAN case of
   Figure 2, for example, a home plus corporate home-office
   configuration, the two upstream routers might be on different LANs
   and therefore different subnets (e.g., the host is itself
   multihomed).  In that case, there is no way for the "wrong" router to
   detect the existence of the "right" router, or to route to it.

   In such a case, it is particularly important that hosts take the
   responsibility to memorize and select the best first hop as described
   in Section 3.

5.  IANA Considerations

   This document does not request any registry actions.







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6.  Security Considerations

   This document is intended to avoid connectivity issues in the
   presence of BCP 38 ingress filters or stateful firewalls combined
   with multihoming.  It does not, in itself, create any new security or
   privacy exposures.  However, since the solution is designed to ensure
   that routing occurs correctly in situations where it previously
   failed, this might result in unexpected exposure of networks that
   were previously unreachable.

   There might be a small privacy improvement: with the current
   practice, a multihomed host that sends packets with the wrong address
   to an upstream router or network discloses the prefix of one upstream
   to the other upstream network.  This practice reduces the probability
   of that occurrence.

7.  References

7.1.  Normative References

   [RFC2119]  Bradner, S., "Key words for use in RFCs to Indicate
              Requirement Levels", BCP 14, RFC 2119,
              DOI 10.17487/RFC2119, March 1997,
              <http://www.rfc-editor.org/info/rfc2119>.

   [RFC2460]  Deering, S. and R. Hinden, "Internet Protocol, Version 6
              (IPv6) Specification", RFC 2460, DOI 10.17487/RFC2460,
              December 1998, <http://www.rfc-editor.org/info/rfc2460>.

   [RFC4191]  Draves, R. and D. Thaler, "Default Router Preferences and
              More-Specific Routes", RFC 4191, DOI 10.17487/RFC4191,
              November 2005, <http://www.rfc-editor.org/info/rfc4191>.

   [RFC4861]  Narten, T., Nordmark, E., Simpson, W., and H. Soliman,
              "Neighbor Discovery for IP version 6 (IPv6)", RFC 4861,
              DOI 10.17487/RFC4861, September 2007,
              <http://www.rfc-editor.org/info/rfc4861>.

   [RFC6724]  Thaler, D., Ed., Draves, R., Matsumoto, A., and T. Chown,
              "Default Address Selection for Internet Protocol Version 6
              (IPv6)", RFC 6724, DOI 10.17487/RFC6724, September 2012,
              <http://www.rfc-editor.org/info/rfc6724>.









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7.2.  Informative References

   [RFC1122]  Braden, R., Ed., "Requirements for Internet Hosts -
              Communication Layers", STD 3, RFC 1122,
              DOI 10.17487/RFC1122, October 1989,
              <http://www.rfc-editor.org/info/rfc1122>.

   [RFC2827]  Ferguson, P. and D. Senie, "Network Ingress Filtering:
              Defeating Denial of Service Attacks which employ IP Source
              Address Spoofing", BCP 38, RFC 2827, DOI 10.17487/RFC2827,
              May 2000, <http://www.rfc-editor.org/info/rfc2827>.

   [RFC3315]  Droms, R., Ed., Bound, J., Volz, B., Lemon, T., Perkins,
              C., and M. Carney, "Dynamic Host Configuration Protocol
              for IPv6 (DHCPv6)", RFC 3315, DOI 10.17487/RFC3315, July
              2003, <http://www.rfc-editor.org/info/rfc3315>.

   [RFC3704]  Baker, F. and P. Savola, "Ingress Filtering for Multihomed
              Networks", BCP 84, RFC 3704, DOI 10.17487/RFC3704, March
              2004, <http://www.rfc-editor.org/info/rfc3704>.

   [RFC4862]  Thomson, S., Narten, T., and T. Jinmei, "IPv6 Stateless
              Address Autoconfiguration", RFC 4862,
              DOI 10.17487/RFC4862, September 2007,
              <http://www.rfc-editor.org/info/rfc4862>.

   [RFC4941]  Narten, T., Draves, R., and S. Krishnan, "Privacy
              Extensions for Stateless Address Autoconfiguration in
              IPv6", RFC 4941, DOI 10.17487/RFC4941, September 2007,
              <http://www.rfc-editor.org/info/rfc4941>.

   [RFC6092]  Woodyatt, J., Ed., "Recommended Simple Security
              Capabilities in Customer Premises Equipment (CPE) for
              Providing Residential IPv6 Internet Service", RFC 6092,
              DOI 10.17487/RFC6092, January 2011,
              <http://www.rfc-editor.org/info/rfc6092>.

   [RFC7084]  Singh, H., Beebee, W., Donley, C., and B. Stark, "Basic
              Requirements for IPv6 Customer Edge Routers", RFC 7084,
              DOI 10.17487/RFC7084, November 2013,
              <http://www.rfc-editor.org/info/rfc7084>.

   [RFC7157]  Troan, O., Ed., Miles, D., Matsushima, S., Okimoto, T.,
              and D. Wing, "IPv6 Multihoming without Network Address
              Translation", RFC 7157, DOI 10.17487/RFC7157, March 2014,
              <http://www.rfc-editor.org/info/rfc7157>.





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RFC 8028       Router Selection in a Multi-Prefix Network  November 2016


   [RFC7217]  Gont, F., "A Method for Generating Semantically Opaque
              Interface Identifiers with IPv6 Stateless Address
              Autoconfiguration (SLAAC)", RFC 7217,
              DOI 10.17487/RFC7217, April 2014,
              <http://www.rfc-editor.org/info/rfc7217>.

Acknowledgements

   Comments were received from Jinmei Tatuya and Ole Troan, who have
   suggested important text, plus Mikael Abrahamsson, Steven Barth,
   Carlos Bernardos Cano, Chris Bowers, Zhen Cao, Juliusz Chroboczek,
   Toerless Eckert, David Farmer, Bob Hinden, Ben Laurie, Dusan Mudric,
   Tadahisa Okimoto, Pierre Pfister, Behcet Sarikaya, Mark Smith, and
   James Woodyatt.

Authors' Addresses

   Fred Baker
   Santa Barbara, California  93117
   United States of America

   Email: FredBaker.IETF@gmail.com


   Brian Carpenter
   Department of Computer Science
   University of Auckland
   PB 92019
   Auckland  1142
   New Zealand

   Email: brian.e.carpenter@gmail.com



















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