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HIP                                                         R. Moskowitz
Internet-Draft                                                     X. Xu
Intended status: Standards Track                                  B. Liu
Expires: December 24, 2018                                        Huawei
                                                           June 22, 2018


                      Hierarchical HITs for HIPv2
                draft-moskowitz-hierarchical-hip-06.txt

Abstract

   This document describes using a hierarchical HIT to facilitate large
   deployments in mobile networks.

Status of This Memo

   This Internet-Draft is submitted in full conformance with the
   provisions of BCP 78 and BCP 79.

   Internet-Drafts are working documents of the Internet Engineering
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   This Internet-Draft will expire on December 24, 2018.

Copyright Notice

   Copyright (c) 2018 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
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   the Trust Legal Provisions and are provided without warranty as
   described in the Simplified BSD License.





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Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   2
   2.  Terms and Definitions . . . . . . . . . . . . . . . . . . . .   3
     2.1.  Requirements Terminology  . . . . . . . . . . . . . . . .   3
     2.2.  Definitions . . . . . . . . . . . . . . . . . . . . . . .   3
   3.  Problem Space . . . . . . . . . . . . . . . . . . . . . . . .   3
     3.1.  Meeting the future of Mobile Networking . . . . . . . . .   3
     3.2.  Semi-permanency of Identities . . . . . . . . . . . . . .   4
     3.3.  Managing a large flat address space . . . . . . . . . . .   4
     3.4.  Defense against fraudulent HITs . . . . . . . . . . . . .   4
     3.5.  Desire for administrative control by RVS providers  . . .   4
   4.  The Hierarchical Host Identity Tag (HIT)  . . . . . . . . . .   5
     4.1.  The Hierarchy ID (HID)  . . . . . . . . . . . . . . . . .   5
       4.1.1.  The Registered Assigning Authority (RAA)  . . . . . .   5
       4.1.2.  The Hierarchical HIT Domain Authority (HDA) . . . . .   5
       4.1.3.  Example of the HID DNS  . . . . . . . . . . . . . . .   6
       4.1.4.  Changes to ORCHIDv2 to support Hierarchical HITs  . .   6
       4.1.5.  Collision risks with Hierarchical HITs  . . . . . . .   7
   5.  HIP Parameters  . . . . . . . . . . . . . . . . . . . . . . .   7
     5.1.  HIT_SUITE_LIST  . . . . . . . . . . . . . . . . . . . . .   7
     5.2.  CLIENT_INFO . . . . . . . . . . . . . . . . . . . . . . .   8
   6.  HHIT Registry services to support hierarchical HITs . . . . .   8
     6.1.  Hierarchical HIT Registration using X.509 Certificates  .   8
     6.2.  Hierarchical HIT Registration using a PSK . . . . . . . .   9
     6.3.  Hierarchical HIT Registration Type  . . . . . . . . . . .   9
     6.4.  Hierarchical HIT Registration Failure Type  . . . . . . .   9
     6.5.  Registration failure behavior . . . . . . . . . . . . . .   9
       6.5.1.  Example of a simple HDA policy  . . . . . . . . . . .  10
   7.  Using hierarchical HITs . . . . . . . . . . . . . . . . . . .  10
     7.1.  Contacting a HIP client . . . . . . . . . . . . . . . . .  10
     7.2.  Defense against fraudulent HITs . . . . . . . . . . . . .  11
   8.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .  11
   9.  RAA Management Organization Considerations  . . . . . . . . .  11
   10. Security Considerations . . . . . . . . . . . . . . . . . . .  11
     10.1.  Privacy Concerns . . . . . . . . . . . . . . . . . . . .  12
   11. Acknowledgments . . . . . . . . . . . . . . . . . . . . . . .  12
   12. References  . . . . . . . . . . . . . . . . . . . . . . . . .  13
     12.1.  Normative References . . . . . . . . . . . . . . . . . .  13
     12.2.  Informative References . . . . . . . . . . . . . . . . .  13
   Appendix A.  Calculating Collision Probabilities  . . . . . . . .  14
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .  14

1.  Introduction

   This document expands on HIPv2 [RFC7401] to describe the structure of
   a hierarchical HIT, the Registry services to support this hierarchy,
   and given a hierarchical HIT, how a device is found in the network.



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   Separate documents will further expand on the registry service and
   how a device can advertise its availability and services provided.

2.  Terms and Definitions

2.1.  Requirements Terminology

   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 RFC 2119 [RFC2119].

2.2.  Definitions

   HDA (Hierarchical HIT Domain Authority):  The 14 bit field
      identifying the HIT Domain Authority under a RAA.

   HID (Hierarchy ID):  The 32 bit field providing the HIT Hierarchy ID.

   RAA (Registered Assigning Authority):  The 18 bit field identifying
      the Hierarchical HIT Assigning Authority.

3.  Problem Space

3.1.  Meeting the future of Mobile Networking

   The evolution of mobile networking to greater bandwidth and faster
   mobility will favor IP mobility technologies that optimize shortest
   routing paths for both mobile-to-stationary and mobile-to-mobile
   applications.  For this, devices will need to use the IP address
   which provide the shortest path for where they are physically in the
   mobile network.  The mobile device will need services that will
   discover the IP addresses for their peer mobile devices and keep them
   connected to those peers even when both devices move in the network
   at the same time (the double-jump problem).  In order to support
   these services, there needs to be billable services to support the
   infrastructure.  In some area close tracking of mobile devices will
   be mandatory.  In other device obfuscation to protect privacy and/or
   safety will be the only life-enabling approach.

   These conflicting requirements can be met with the Host Identity
   Protocol (HIP), provided its Rendezvous Server service is scaleable
   and manageable.  Providers of RVS will need both a viable and
   scaleable business model.








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3.2.  Semi-permanency of Identities

   A device Identity has some degree of permanency.  A device creates
   its identity and registers it to some 3rd-party that will assert a
   level of trust for that identity.  A device may have multiple
   identities to use in different contexts, and it may deprecate an
   identity for any number of reasons.  The asserting 3rd-party may
   withdraw its assertion of an identity for any number of reasons.  An
   identity system needs to facilitate all of this.

3.3.  Managing a large flat address space

   For HIP to be successfully used in large mobile networks, it must
   support an Identity per device, or at least 10 billion Identities.
   Perhaps a Distributed Hash Table [I-D.irtf-hiprg-dht] can scale this
   large.  There is still the operational challenges in establishing
   such a world-wide DHT implementation and how RVS [RFC8004] works with
   such a large population.  There is also the challenge of how to turn
   this into a viable business for the Mobile Network Providers.

   Even though the probability of collisions with 7B HITs (one HIT per
   person) in a 96 bit flat address space is 3.9E-10, it is still real.
   How are collisions managed?  It is also possible that weak key
   uniqueness, as has been shown in deployed TLS certificates, results
   in a much greater probability of collisions.  Thus resolution of
   collisions needs to be a feature in a globally mobile network.

3.4.  Defense against fraudulent HITs

   How can a host protect against a fraudulent HIT?  That is, a second
   pre-image attack on the HI hash that produces the HIT.  A strong
   defense would require every HIT/HI registered and openly verifiable.
   This would best be done as part of the R1 and I2 validation.

3.5.  Desire for administrative control by RVS providers

   An RVS provider may only be willing to provide discovery (RVS)
   services to HIP devices it knows and trusts.  A flat HIT space does
   not provide any intrinsic functionality to support this.  A
   hierarchical HIT space can be mapped to the RVS provider.  DNS can
   effectively be used to provide the HIT to IP mapping without DHT.

   A hierarchical HIT space also creates a type of a business labeling
   for the RVS provider.  "These are my customers."







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4.  The Hierarchical Host Identity Tag (HIT)

   The Hierarchical HIT is a small but important enhancement over the
   flat HIT space.  It represents the HI in only a 64 bit hash and uses
   the other 32 bits to create a hierarchical administration
   organization for HIT domains.  Hierarchical HITs are ORCHIDs
   [RFC7343].  The change in construction rules are in Section 4.1.4.

   A Hierarchical HIT is built from the following fields:

   o  28 bit IANA prefix

   o  4 bit HIT Suite ID

   o  32 bit Hierarchy ID (HID)

   o  64 bit ORCHID hash

4.1.  The Hierarchy ID (HID)

   The Hierarchy ID (HID) provides the structure to organize HITs into
   administrative domains.  HIDs are further divided into 2 fields:

   o  14 bit Registered Assigning Authority (RAA)

   o  18 bit Hierarchical HIT Domain Authority (HDA)

4.1.1.  The Registered Assigning Authority (RAA)

   An RAA is a business that manages a registry of HDAs.

   The RAA is a 14 bit field (16,384 RAAs) assigned sequentially by a
   numbers management organization, perhaps ICANN's IANA service.  An
   RAA must provide a set of services to allocate HDAs to organizations.
   It must have a public policy on what is necessary to obtain an HDA.
   The RAA need not maintain any HIP related services.  It must maintain
   a DNS zone for discovering HID RVS servers.

   This DNS zone may be a reverse PTR for its RAA.  Assume that the RAA
   is 100.  The PTR record is constructed at a 2 bit grouping:

   0.1.2.1.0.0.0.hhit.arpa   IN PTR      raa.bar.com.

4.1.2.  The Hierarchical HIT Domain Authority (HDA)

   An HDA may be an ISP or any third party that takes on the business to
   provide RVS and other needed services for HIP enabled devices.




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   The HDA is an 18 bit field (262,144 HDAs per RAA) assigned
   sequentially by an RAA.  An HDA should maintain a set of RVS servers
   that its client HIP-enabled customers use.  How this is done and
   scales to the potentially millions of customers is outside the scope
   of this document.  This service should be discoverable through the
   DNS zone maintained by the HDA's RAA.

   An RAA may assign a block of values to an individual organization.
   This is completely up to the individual RAA's published policy for
   delegation.

4.1.3.  Example of the HID DNS

   HID related services should be discoverable via DNS.  For example the
   RVS for a HID could be found via the following.  Assume that the RAA
   is 100 and the HDA is 50.  The PTR record is constructed at a 2 bit
   grouping:

   2.0.3.0.0.0.0.0.0.1.3.1.0.0.0.0.hhit.arpa   IN PTR      rvs.foo.com.

   The RAA is running its zone, 1.3.1.0.0.0.0.hhit.arpa under the
   hhit.arpa zone.

4.1.4.  Changes to ORCHIDv2 to support Hierarchical HITs

   ORCHIDv2 [RFC7343] has a number of inputs including a context, some
   header bits, the hash algorithm, and the public key.  The output is a
   96 bit value.  Hierarchical HIT makes the following changes.  The HID
   is added as part of the header bits and the output is a 64 bit value,
   derived the same way as the 96 bit hash.

           Input      :=  HID | HOST_ID
           OGA ID     :=  4-bit Orchid Generation Algorithm identifier
                                   The HIT Suite ID = 0x40
           Hash Input :=  Context ID | Input
                                   Same Context ID as HIPv2
           Prefix     :=  HIPv2 Prefix
           HID        :=  Hierarchy ID
           Hash       :=  Hash_function( Hash Input )
           Encode_64  :=  Same as Encode_96, but only 64 bits
           ORCHID     :=  Prefix | OGA ID | HID | Encode_64( Hash )

   Hierarchical HIT uses the same context as all other HIPv2 HIT Suites
   as they are clearly separated by the distinct HIT Suite ID.







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4.1.5.  Collision risks with Hierarchical HITs

   The 64 bit hash size does have an increased risk of collisions over
   the 96 bit hash size used for the other HIT Suites.  There is a 0.01%
   probability of a collision in a population of 66 million.  The
   probability goes up to 1% for a population of 663 million.  See
   Appendix A for the collision probability formula.

   However, this risk of collision is within a single HDA.  Further, all
   HDAs are expected to provide a registration process for reverse
   lookup validation.  This registration process would reject a
   collision, forcing the client to generate a new HI and thus
   hierarchical HIT and reapplying to the registration process.

5.  HIP Parameters

   The HIP parameters carry information that is necessary for
   establishing and maintaining a HIP association.  For example, the
   device's public keys as well as the signaling for negotiating ciphers
   and payload handling are encapsulated in HIP parameters.  Additional
   information, meaningful for end hosts or middleboxes, may also be
   included in HIP parameters.  The specification of the HIP parameters
   and their mapping to HIP packets and packet types is flexible to
   allow HIP extensions to define new parameters and new protocol
   behavior.

5.1.  HIT_SUITE_LIST

   The HIT_SUITE_LIST parameter contains a list of the supported HIT
   suite IDs of the Responder.  Based on the HIT_SUITE_LIST, the
   Initiator can determine which source HIT Suite IDs are supported by
   the Responder.  The HIT_SUITE_LIST parameter is defined in
   Section 5.2.10 of [RFC7401].

   The following HIT Suite IDs are defined for Hierarchical HITs, and
   the relationship between the four-bit ID value used in the OGA ID
   field and the eight-bit encoding within the HIT_SUITE_LIST ID field
   is clarified:

   HIT Suite              Four-bit ID    Eight-bit encoding

   ECDSA/hier/SHA-256           4             0x40

   Note that the Hierarchical HIP HIT Suite ID allows the devices to use
   the hierarchical RVS discovery and authentication services to
   validate the peer and discover available services.  The Responder
   SHOULD respond with a HIP hierarchical HIT suite ID when the HIT of
   the Initiator is a HIP hierarchical HIT.



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5.2.  CLIENT_INFO

      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              |             Length            |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     /                      Client Information                       /
     /                                                               /
     /                               +-------------------------------+
     /                               |            Padding            |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+

     Type           [TBD-IANA]
     Length         length in octets, excluding Type, Length, and
                    Padding
     Client         The information required by the HDA in the format
     Information    required by the HDA.

   This parameter contains client information to include in the HIT
   registration.  The specific content and format is set by the HDA.

6.  HHIT Registry services to support hierarchical HITs

   Hierarchical HIT registration SHOULD be performed using the HIP
   Registration Extension [RFC8003].  The client either uses an X.509
   certificate [RFC8002], or use a PSK, as defined in Appendix A of HIP-
   DEX [I-D.ietf-hip-dex], to validate the registration.

   The Registration should include additional client information.  This
   information may be contained within the X.509 certificate and/or is
   carried in the CLIENT_INFO parameter, see Section 5.2.  The Registrar
   can include its requirements in the R1 packet, and the client provide
   its information in the I2 packet.  This parameter may be encrypted
   within the ENCRYPTED parameter.  If the CLIENT_INFO contains Personal
   Identifying Information (PII), then it MUST be placed into the
   ENCRYPTED parameter.

   The content and internal format of the CLIENT_INFO parameter is set
   by the HDA's policy and is outside the scope of this document.
   Examples of client information can by phone number, IMEI, and ICCID.

6.1.  Hierarchical HIT Registration using X.509 Certificates

   This requires the HIP client to possess a client certificate trusted
   by the HDA/Registrar.  Registration will either succeed or fail.





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6.2.  Hierarchical HIT Registration using a PSK

   This requires the HIP client and the HDA/Registrar to share a PSK.
   The PSK may already exist prior to starting the registration and just
   be used within the registration.  A PSK out-of-band exchange may be
   triggered by performing the registration without any authentication.

   If no client authentication is included in the I2 packet, the
   registration fails with "No Authentication provided".  If the I2
   packet included the proper HDA required client information, the HDA
   can use it to set up a side channel for an out-of-band delivery of a
   PSK.  And example of this would be to send an SMS message with the
   PSK.  Once the client possesses the PSK, it can rerun the
   registration at which point the HI and HIT duplicate checks are
   performed.

6.3.  Hierarchical HIT Registration Type

   The Registration Type used in the REG_REQUEST is:

   Number   Registration Type
   ------   -----------------
   2        HIT Registration

6.4.  Hierarchical HIT Registration Failure Type

   The Registration may fail.  In fact, with PSK, this may be the
   response to expect an SMS message with the PSK to use in a second
   registration request.  Failure Types used in the REG_FAIL are:

Failure Type      Reason
------------      -----------------------
[TBD-IANA]        Hierarchical HIT Already Registered
[TBD-IANA]        HI Already Registered
[TBD-IANA]        Previously Registered HI with different device information
[TBD-IANA]        No Authentication provided
[TBD-IANA]        Invalid Authentication
[TBD-IANA]        Invalid Authentication, new PSK sent via SMS

6.5.  Registration failure behavior

   If the failure type is "Hierarchical HIT Already Registered", the
   client's HI is hashing to an existing HIT and must generate a new HI
   and hierarchical HIT and reregister.  If the failure is "HI Already
   Registered", the client should assume it is registered.  If the
   failure is "Previously Registered HI with different device
   information", either the client managed to generate a duplicate HI,
   probably indicating a weak key generation algorithm, or the client



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   was previously registered on a different device.  Resolving this
   conflict will be left to the HDA's policy.

6.5.1.  Example of a simple HDA policy

   A simple HDA policy would be to require the device to generate a new
   HI and thus HHIT and try registration again.  The HDA policy may also
   provide a URL for "Previous Registration Resolution".  This contact
   is primarily to assist a device that was registered, but had some
   local failure resulting in a new registration attempt.

7.  Using hierarchical HITs

   All HIP clients with hierarchical HITs maintain an RVS connection
   with their HDA's RVS server(s).  How the HDA scales this service up
   to a potential population in the millions is out of scope of this
   document.  Lifetime management of these connections is also out of
   scope.

   One approach an HDA can use to address the scaling challenge is to
   add an internal level of hierarchy to assign a set number of devices
   per RVS server.

   Peering agreements between HDAs would allow for geographically close
   RVS to a device.  This may reduce the latency for use of a device's
   current RVS.  This is a subject of another document.

7.1.  Contacting a HIP client

   A service Initiator uses some service to discover the HIT of the
   service Responder.  The Initiator uses the hierarchical information
   in the HIT to find the Responder's RVS.  A trusted RVS discover
   method could use the DNS PTR to RVS as shown in Section 4.1.3.  An I1
   is sent to that RVS which forwards it to the Responder.

   The potential Responder uses the HIT in the I1 to query the
   Initiator's RVS about the Initiator.  The nature of information, and
   method of communication are determined by the Initiator's HDA and the
   Responder's (and or HDA's) relationship with it.  Based on the
   Responder's local policy, this information will be used to determine
   if the contact is to be accepted.  If accepted, the Responder may
   proceed sending an R1 to the Initiator.  It may alternatively
   initiate some non-HIP process.

   It should be noted that this R1 may contain a REG_INFO list for the
   Initiator to validate that the Responder does offer the desired
   service.




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7.2.  Defense against fraudulent HITs

   Both the Initiator and Responder MAY validate a peer host as a
   defense against a second pre-image attack on the HHIT.  This may
   occur via a CERT [RFC8002] in R1 or I2.  It may be through a back end
   process associated with the R1 or I2 validation to look up the HHIT
   and retrieve the registered HI.

8.  IANA Considerations

   IANA will need to make the following changes to the "Host Identity
   Protocol (HIP) Parameters" registries:

   HIT Suite ID:  This document defines the new HIT Suite "Hierarchy
      with ECDSA/SHA256" (see Section 5.1).

   CLIENT_INFO:  This document defines the new CLIENT_INFO parameter
      (see Section 5.2).  The parameter value will be assigned by IANA.

   Reg Type:  This document defines the new Registration Type for the
      REG_REQUEST parameter "HIT Registration" (see Section 6.3).

   Reg Fail:  This document defines the new Failure Types for the
      REG_FAIL parameter (see Section 6.4).

9.  RAA Management Organization Considerations

   Introducing the RAA management organization may be the largest hurdle
   for hierarchical HITs.  Thus it would be best if this were adopted by
   an organization already in the business of allocating numbers within
   either the Internet or the Mobile, cellular, infrastructure.

   One consideration would be to reserve the first N RAA values to map
   to the existing DNS TLDs.  For example, these TLDs can be organized
   in an ascending order and numbered accordingly.  Thus the 2 character
   TLDs will be a lower number than the 3 character TLDs.  After that,
   it could be a first come, first numbered assignment process.

10.  Security Considerations

   There are potential risks with the hierarchical HIT, the Registry
   service, and the discovery of potential peer hosts using its
   hierarchical HIT.

   A 64 bit hash space presents a real risk of second pre-image attacks.
   The HHIT Registry services effectively block attempts to "take over"
   a HHIT.  It does not stop a rogue attempting to impersonate a known
   HHIT.  This attack can be mitigated by the Responder using DNS to



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   find the HI for the HHIT or the RVS for the HHIT that then provides
   the registered HI.

   The two risks with hierarchical HITs are the use of an invalid HID
   and forced HIT collisions.  The use of the "hhit.arpa."  DNS zone is
   a strong protection against invalid HIDs.  Querying an HDA's RVS for
   a HIT under the HDA protects against talking to unregistered clients.
   The Registry service has direct protection against forced or
   accidental HIT hash collisions.

   By using the HIP Registration Extension, the Registry service is
   protected from direct attacks.  This service does rely on either the
   integrity of a PKI service or an out-of-band PSK delivery process.
   Thus the risk to the Registry service is highly related to the trust
   in these authentication setup services.  Further, the duplicate HI
   resolution process may require human interaction with related social
   engineering risks.

   Finally the peer host discovery process relies on trusting the
   finding the proper HDA for the host and its forwarding the I1 to the
   proper Responder.  A rogue RVS, impersonating the RVS for the HIT,
   could redirect the I1 to a client that has forced a collision with
   the HIT and the Initiator would be none the wiser.  The only defense
   against this is if the Initiator has some other source for the
   Responder HI and validate the HI in the R1.

10.1.  Privacy Concerns

   Mobile-privacy-attack [I-D.moskowitz-mobile-privacy-attack] details
   how Eve can follow a communication between two mobile peers using the
   session Identifiers and deep knowledge about those Identifiers gained
   by hacking servers that log PII related to the Identifiers.

   Hierarchical HITs not only does not mitigate this attack, it can
   actually aggravate it by supplying the HDA where the HHIT is
   registered.

   A HIP Privacy Enhanced Base Exchange, to be defined in a separate
   draft, along with a Privacy Enhanced ESP tunnel, can be used to hide
   all the HIP and ESP Identifiers from Eve.

11.  Acknowledgments

   Sue Hares of Huawei contributed to the clarity in this document.







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12.  References

12.1.  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,
              <https://www.rfc-editor.org/info/rfc2119>.

12.2.  Informative References

   [I-D.ietf-hip-dex]
              Moskowitz, R. and R. Hummen, "HIP Diet EXchange (DEX)",
              draft-ietf-hip-dex-06 (work in progress), December 2017.

   [I-D.irtf-hiprg-dht]
              Ahrenholz, J., "Host Identity Protocol Distributed Hash
              Table Interface", draft-irtf-hiprg-dht-05 (work in
              progress), December 2011.

   [I-D.moskowitz-mobile-privacy-attack]
              Moskowitz, R., "An Attack on Privacy in Mobile Devices",
              draft-moskowitz-mobile-privacy-attack-01 (work in
              progress), November 2017.

   [RFC7343]  Laganier, J. and F. Dupont, "An IPv6 Prefix for Overlay
              Routable Cryptographic Hash Identifiers Version 2
              (ORCHIDv2)", RFC 7343, DOI 10.17487/RFC7343, September
              2014, <https://www.rfc-editor.org/info/rfc7343>.

   [RFC7401]  Moskowitz, R., Ed., Heer, T., Jokela, P., and T.
              Henderson, "Host Identity Protocol Version 2 (HIPv2)",
              RFC 7401, DOI 10.17487/RFC7401, April 2015,
              <https://www.rfc-editor.org/info/rfc7401>.

   [RFC8002]  Heer, T. and S. Varjonen, "Host Identity Protocol
              Certificates", RFC 8002, DOI 10.17487/RFC8002, October
              2016, <https://www.rfc-editor.org/info/rfc8002>.

   [RFC8003]  Laganier, J. and L. Eggert, "Host Identity Protocol (HIP)
              Registration Extension", RFC 8003, DOI 10.17487/RFC8003,
              October 2016, <https://www.rfc-editor.org/info/rfc8003>.

   [RFC8004]  Laganier, J. and L. Eggert, "Host Identity Protocol (HIP)
              Rendezvous Extension", RFC 8004, DOI 10.17487/RFC8004,
              October 2016, <https://www.rfc-editor.org/info/rfc8004>.





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Internet-Draft              Hierarchical HITs                  June 2018


Appendix A.  Calculating Collision Probabilities

   The accepted formula for calculating the probability of a collision
   is:


           p = 1 - e^{-k^2/(2n)}


           P       Collision Probability
           n       Total possible population
           k       Actual population



Authors' Addresses

   Robert Moskowitz
   Huawei
   Oak Park, MI  48237
   USA

   Email: rgm@labs.htt-consult.com


   Xiaohu Xu
   Huawei
   Huawei Bld, No.156 Beiqing Rd.
   Beijing, Hai-Dian District  100095
   China

   Email: xuxiaohu@huawei.com


   Bingyang Liu
   Huawei
   Huawei Bld, No.156 Beiqing Rd.
   Beijing, Hai-Dian District  100095
   China

   Email: liubingyang@huawei.com










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