





Network Working Group                                       D. Wallner
Request for Comments: 2627                                   E. Harder
Category: Informational                                        R. Agee
                                              National Security Agency
                                                             June 1999


         Key Management for Multicast: Issues and Architectures

Status of this Memo

   This memo provides information for the Internet community.  It does
   not specify an Internet standard of any kind.  Distribution of this
   memo is unlimited.

Copyright Notice

   Copyright (C) The Internet Society (1999).  All Rights Reserved.

Abstract

   This report contains a discussion of the difficult problem of key
   management for multicast communication sessions.  It focuses on two
   main areas of concern with respect to key management, which are,
   initializing the multicast group with a common net key and rekeying
   the multicast group.  A rekey may be necessary upon the compromise of
   a user or for other reasons (e.g., periodic rekey).  In particular,
   this report identifies a technique which allows for secure compromise
   recovery, while also being robust against collusion of excluded
   users.  This is one important feature of multicast key management
   which has not been addressed in detail by most other multicast key
   management proposals [1,2,4].  The benefits of this proposed
   technique are that it minimizes the number of transmissions required
   to rekey the multicast group and it imposes minimal storage
   requirements on the multicast group.

1.0  MOTIVATION

   It is recognized that future networks will have requirements that
   will strain the capabilities of current key management architectures.
   One of these requirements will be the secure multicast requirement.
   The need for high bandwidth, very dynamic secure multicast
   communications is increasingly evident in a wide variety of
   commercial, government, and Internet communities.  Specifically, the
   secure multicast requirement is the necessity for multiple users who
   share the same security attributes and communication requirements to
   securely communicate with every other member of the multicast group
   using a common multicast group net key.  The largest benefit of the



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   multicast communication being that multiple receivers simultaneously
   get the same transmission.  Thus the problem is enabling each user to
   determine/obtain the same net key without permitting unauthorized
   parties to do likewise (initializing the multicast group) and
   securely rekeying the users of the multicast group when necessary.
   At first glance, this may not appear to be any different than current
   key management scenarios.  This paper will show, however, that future
   multicast scenarios will have very divergent and dynamically changing
   requirements which will make it very challenging from a key
   management perspective to address.

2.0  INTRODUCTION

   The networks of the future will be able to support gigabit bandwidths
   for individual users, to large groups of users.  These users will
   possess various quality of service options and multimedia
   applications that include video, voice, and data, all on the same
   network backbone.  The desire to create small groups of users all
   interconnected and capable of communicating with each other, but who
   are securely isolated from all other users on the network is being
   expressed strongly by users in a variety of communities.

   The key management infrastructure must support bandwidths ranging
   from kilobits/second to gigabits/second, handle a range of multicast
   group sizes, and be flexible enough for example to handle such
   communications environments as wireless and mobile technologies.  In
   addition to these performance and communications requirements, the
   security requirements of different scenarios are also wide ranging.
   It is required that users can be added and removed securely and
   efficiently, both individually and in bulk.  The system must be
   resistant to compromise, insofar as users who have been dropped
   should not be able to read any subsequent traffic, even if they share
   their secret information.  The costs we seek to minimize are time
   required for setup, storage space for each end user, and total number
   of transmissions required for setup, rekey and maintenance.  It is
   also envisioned that any proposed multicast security mechanisms will
   be implemented no lower than any layer with the characteristics of
   the network layer of the protocol stack.  Bandwidth efficiency for
   any key management system must also be considered.  The trade-off
   between security and performance of the entire multicast session
   establishment will be discussed in further detail later in this
   document.









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   The following section will explain several potential scenarios where
   multicast capabilities may be needed, and quantify their requirements
   from both a performance and security perspective.  It will be
   followed in Section 4.0 by a list of factors one must consider when
   designing a potential solution.  While there are several security
   services that will be covered at some point in this document, much of
   the focus of this document has been on the generation and
   distribution of multicast group net keys.  It is assumed that all
   potential multicast participants either through some manual or
   automated, centralized or decentralized mechanism have received
   initialization keying material (e.g. certificates).  This document
   does not address the initialization key distribution issue.  Section
   5 will then detail several potential multicast key management
   architectures, manual (symmetric) and public key based (asymmetric),
   and highlight their relative advantages and disadvantages (Note:The
   list of advantages and disadvantages is by no means all inclusive.).
   In particular, this section emphasizes our technique which allows for
   secure compromise recovery.

3.0  MULTICAST SCENARIOS

   There are a variety of potential scenarios that may stress the key
   management infrastructure.  These scenarios include, but are not
   limited to, wargaming, law enforcement, teleconferencing, command and
   control conferencing, disaster relief, and distributed computing.
   Potential performance and security requirements, particularly in
   terms of multicast groups that may be formed by these users for each
   scenario, consists of the potential multicast group sizes,
   initialization requirements (how fast do users need to be brought
   on-line), add/drop requirements (how fast a user needs to be added or
   deleted from the multicast group subsequent to initialization), size
   dynamics (the relative number of people joining/leaving these groups
   per given unit of time), top level security requirements, and
   miscellaneous special issues for each scenario.  While some scenarios
   describe future secure multicast requirements, others have immediate
   security needs.

   As examples, let us consider two scenarios, distributed gaming and
   teleconferencing.

   Distributed gaming deals with the government's need to simulate a
   conflict scenario for the purposes of training and evaluation.  In
   addition to actual communications equipment being used, this concept
   would include a massive interconnection of computer simulations
   containing, for example, video conferencing and image processing.
   Distributed gaming could be more demanding from a key management
   perspective than an actual scenario for several reasons.  First, the
   nodes of the simulation net may be dispersed throughout the country.



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   Second, very large bandwidth communications, which enable the
   possibility for real time simulation capabilities, will drive the
   need to drop users in and out of the simulation quickly.  This is
   potentially the most demanding scenario of any considered.

   This scenario may involve group sizes of potentially 1000 or more
   participants, some of which may be collected in smaller subgroups.
   These groups must be initialized very rapidly, for example, in a ten
   second total initialization time.  This scenario is also very
   demanding in that users may be required to be added or dropped from
   the group within one second.  From a size dynamics perspective, we
   estimate that approximately ten percent of the group members may
   change over a one minute time period.  Data rate requirements are
   broad, ranging from kilobits per second (simulating tactical users)
   to gigabits per second (multicast video). The distributed gaming
   scenario has a fairly thorough set of security requirements covering
   access control, user to user authentication, data confidentiality,
   and data integrity.  It also must be "robust" which implies the need
   to handle noisy operating environments that are typical for some
   tactical devices.  Finally, the notion of availability is applied to
   this scenario which implies that the communications network supplying
   the multicast capability must be up and functioning a specified
   percentage of the time.

   The teleconference scenario may involve group sizes of potentially
   1000 or more participants.  These groups may take up to minutes to be
   initialized.  This scenario is less demanding in that users may be
   required to be added or dropped from the group within seconds.  From
   a size dynamics perspective, we estimate that approximately ten
   percent of the group members may change over a period of minutes.
   Data rate requirements are broad, ranging from kilobits per second to
   100's of Mb per second.  The teleconference scenario also has a
   fairly thorough set of security requirements covering access control,
   user to user authentication, data confidentiality, data integrity,
   and non-repudiation.  The notion of availability is also applicable
   to this scenario.  The time frame for when this scenario must be
   provided is now.

4.0   ARCHITECTURAL ISSUES

   There are many factors that must be taken into account when
   developing the desired key management architecture.  Important issues
   for key management architectures include level (strength) of
   security, cost, initializing the system, policy concerns, access
   control procedures, performance requirements and support mechanisms.
   In addition, issues particular to multicast groups include:





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      1. What are the security requirements of the group members? Most
         likely there will be some group controller, or controllers.  Do
         the other members possess the same security requirements as the
         controller(s)?

      2. Interdomain issues - When crossing from one "group domain" to
         another domain with a potentially different security policy,
         which policy is enforced?  An example would be two users
         wishing to communicate, but having different cryptoperiods
         and/or key length policies.

      3. How does the formation of the multicast group occur?  Will the
         group controller initiate the user joining process, or will the
         users initiate when they join the formation of the multicast
         group?

      4. How does one handle the case where certain group members have
         inferior processing capabilities which could delay the
         formation of the net key?  Do these users delay the formation
         of the whole multicast group, or do they come on-line later
         enabling the remaining participants to be brought up more
         quickly?

      5. One must minimize the number of bits required for multicast
         group net key distribution.  This greatly impacts bandwidth
         limited equipments.

   All of these and other issues need to be taken into account, along
   with the communication protocols that will be used which support the
   desired multicast capability.  The next section addresses some of
   these issues and presents some candidate architectures that could be
   used to tackle the key management problem for multicasting.

5.0  CANDIDATE ARCHITECTURES

   There are several basic functions that must be performed in order for
   a secure multicast session to occur.  The order in which these
   functions will be performed, and the efficiency of the overall
   solution results from making trade-offs of the various factors listed
   above.  Before looking at specific architectures, these basic
   functions will be outlined, along with some definition of terms that
   will be used in the representative architectures. These definitions
   and functions are as follows:








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      1. Someone determines the need for a multicast session, sets the
         security attributes for that particular session (e.g.,
         classification levels of traffic, algorithms to be used, key
         variable bit lengths, etc.), and creates the group access
         control list which we will call the initial multicast group
         participant list.  The entity which performs these functions
         will be called the INITIATOR.  At this point, the multicast
         group participant list is strictly a list of users who the
         initiator wants to be in the multicast group.

      2. The initiator determines who will control the multicast group.
         This controller will be called the ROOT (or equivalently the
         SERVER). Often, the initiator will become the root, but the
         possibility exists where this control may be passed off to
         someone other than the initiator. (Some key management
         architectures employ multiple roots, see [4].) The root's job
         is to perform the addition and deletion of group participants,
         perform user access control against the security attributes of
         that session, and distribute the traffic encryption key for the
         session which we will call the multicast group NET KEY.  After
         initialization, the entity with the authority to accept or
         reject the addition of future group participants, or delete
         current group participants is called the LIST CONTROLLER.

         This may or may not be the initiator. The list controller has
         been distinguished from the root for reasons which will become
         clear later.  In short, it may be desirable for someone to have
         the authority to accept or reject new members, while another
         party (the root) would actually perform the function.

      3. Every participant in the multicast session will be referred to
         as a GROUP PARTICIPANT.  Specific group participants other than
         the root or list controller will be referred to as LEAVES.

      4. After the root checks the security attributes of the
         participants listed on the multicast group participant list to
         make sure that they all support the required security
         attributes, the root will then pass the multicast group list to
         all other participants and create and distribute the Net Key.
         If a participant on the multicast group list did not meet the
         required security attributes, the leaf must be deleted from the
         list.

         Multiple issues can be raised with the distribution of the
         multicast group list and Net Key.






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          a.  An issue exists with the time ordering of these functions.
              The multicast group list could be distributed before or
              after the link is secured (i.e. the Net Key is
              distributed).

          b.  An issue exists when a leaf refuses to join the session.
              If a leaf refuses to join a session, we can send out a
              modified list before sending out the Net Key, however
              sending out modified lists, potentially multiple times,
              would be inefficient.  Instead, the root could continue
              on, and would not send the Net Key to those participants
              on the list who rejected the session.

          For the scenario architectures which follow, we assume the
          multicast group list will be distributed to the group
          participants once before the Net Key is distributed.  Unlike
          the scheme described in [4], we recommend that the multicast
          group participant list be provided to all leaves.  By
          distributing this list to the leaves, it allows them to
          determine upfront whether they desire to participate in the
          multicast group or not, thus saving potentially unnecessary
          key exchanges.

   Four potential key management architectures to distribute keying
   material for multicast sessions are presented.  Recall that the
   features that are highly desirable for the architecture to possess
   include the time required to setup the multicast group should be
   minimized, the number of transmissions should be minimized, and
   memory/storage requirements should be minimized. As will be seen, the
   first three proposals each fall short in a different aspect of these
   desired qualities, whereas the fourth proposal appears to strike a
   balance in the features desired.  Thus, the fourth proposal is the
   one recommended for general implementation and use.

   Please note that these approaches also address securely eliminating
   users from the multicast group, but don't specifically address adding
   new users to the multicast group following initial setup because this
   is viewed as evident as to how it would be performed.

5.1  MANUAL KEY DISTRIBUTION

   Through manual key distribution, symmetric key is delivered without
   the use of public key exchanges.  To set up a multicast group Net Key
   utilizing manual key distribution would require a sequence of events
   where Net Key and spare Net Keys would be ordered by the root of the
   multicast session group. Alternate (supersession) Net Keys are
   ordered (by the root) to be used in case of a compromise of a group
   participant(s). The Net Keys would be distributed to each individual



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   group participant, often through some centralized physical
   intermediate location. At some predetermined time, all group
   participants would switch to the new Net Key.  Group participants use
   this Net Key until a predetermined time when they need another new
   Net Key. If the Net Key is compromised during this time, the
   alternate Net Key is used. Group participants switch to the alternate
   Net Key as soon as they receive it, or upon notification from the
   root that everyone has the new Net Key and thus the switch over
   should take place. This procedure is repeated for each cryptoperiod.

   A scheme like this may be attractive because the methods exist today
   and are understood by users.  Unfortunately, this type of scheme can
   be time consuming to set up the multicast group based on time
   necessary to order keying material and having it delivered.  For most
   real time scenarios, this method is much too slow.

5.2  N Root/Leaf Pairwise Keys Approach

   This approach is a brute force method to provide a common multicast
   group Net Key to the group participants. In this scheme, the
   initiator sets the security attributes for a particular session,
   generates a list of desired group participants and transmits the list
   to all group participants.  The leaves then respond with an initial
   acceptance or rejection of participation.  By sending the list up
   front, time can be saved by not performing key exchanges with people
   who rejected participation in the session.  The root (who for this
   and future examples is assumed to be the initiator) generates a
   pairwise key with one of the participants (leaves) in the multicast
   group using some standard public key exchange technique (e.g., a
   Diffie-Hellman public key exchange.)  The root will then provide the
   security association parameters of the multicast (which may be
   different from the parameters of the initial pairwise key) to this
   first leaf.  Parameters may include items such as classification and
   policy.  Some negotiation (through the use of a Security Association
   Management Protocol, or SAMP) of the parameters may be necessary.
   The possibility exists for the leaf to reject the connection to the
   multicast group based on the above parameters and  multicast group
   list.  If the leaf rejects this session, the root will repeat this
   process with another leaf.

   Once a leaf accepts participation in the multicast session, these two
   then choose a Net Key to be used by the multicast group.  The Net Key
   could be generated through another public key exchange between the
   two entities, or simply chosen by the root, depending upon the policy
   which is in place for the multicast group ( i.e. this policy decision
   will not be a real time choice).  The issue here is the level of
   trust that the leaf has in the root.  If the initial pairwise key
   exchange provides some level of user authentication, then it seems



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   adequate to just have the root select the Net Key at this stage.
   Another issue is the level of trust in the strength of the security
   of the generated key.  Through a cooperative process, both entities
   (leaf and root) will be providing information to be used in the
   formation of the Net Key.

   The root then performs a pairwise key exchange with another leaf and
   optionally performs the negotiation discussed earlier.  Upon
   acceptance by the leaf to join the multicast group, the root sends
   the leaf the Net Key.

   This pairwise key exchange and Net Key distribution continues for all
   N users of the multicast group.

   Root/leaves cache pairwise keys for future use.  These keys serve as
   Key Encryption Keys (KEKs) used for rekeying leaves in the net at a
   later time.  Only the root will cache all of the leaves' pairwise
   keys.  Each individual leaf will cache only its own unique pairwise
   Key Encryption Key.

   There are two cases to consider when caching the KEKs.  The first
   case is when the Net key and KEK are per session keys. In this case,
   if one wants to exclude a group participant from the multicast
   session (and rekey the remaining participants with a new Net Key),
   the root would distribute a new Net key encrypted with each
   individual KEK to every legitimate remaining participant.  These KEKs
   are deleted once the multicast session is completed.

   The second case to consider is when the KEKs are valid for more than
   one session.  In this case, the Net Key may also be valid for
   multiple sessions, or the Net Key may still only be valid for one
   session as in the above case.  Whether the Net Key is valid for one
   session or more than one session, the KEK will be cached.  If the Net
   Key is only valid per session, the KEKs will be used to encrypt new
   Net Keys for subsequent multicast sessions.  The deleting of group
   participants occurs as in the previous case described above,
   regardless of whether the Net Key is per session or to be used for
   multiple sessions.

   A scheme like this may be attractive to a user because it is a
   straightforward extension of certifiable public key exchange
   techniques. It may also be attractive because it does not involve
   third parties.  Only the participants who are part of the multicast
   session participate in the keying mechanism.  What makes this scheme
   so undesirable is that it will be transmission intensive as we scale






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   up in numbers, even for the most computationally efficient
   participants, not to mention those with less capable hardware
   (tactical, wireless, etc.).  Every time the need arises to drop an
   "unauthorized" participant, a new Net Key must be distributed.

   This distribution requires a transmission from the Root to each
   remaining participant, whereby the new Net Key will be encrypted
   under the cover of each participant's unique pairwise Key Encryption
   Key (KEK).

   Note: This approach is essentially the same as one proposal to the
   Internet Engineering Task Force (IETF) Security Subworking Group [Ref
   1,2].

   Also note that there exist multiple twists to an approach like this.
   For example, instead of having the root do all N key exchanges, the
   root could pass some of this functionality (and control) to a number
   of leaves beneath him.  For example, the multicast group list could
   be split in half and the root tells one leaf to take half of the
   users and perform a key exchange with them (and then distribute the
   Net key) while the root will take care of the other half of the list.
   (The chosen leaves are thus functioning as a root and we can call
   them "subroots."  These subroots will have leaves beneath them, and
   the subroots will maintain the KEK of each leaf beneath it.)  This
   scales better than original approach as N becomes large.
   Specifically, it will require less time to set up (or rekey) the
   multicast net because the singular responsibility of performing
   pairwise key exchanges and distributing Net Key will be shared among
   multiple group participants and can be performed in parallel, as
   opposed to the root only distributing the Net Key to all of the
   participants.

   This scheme is not without its own security concerns.  This scheme
   pushes trust down to each subgroup controller - the root assumes that
   these "subroot" controllers are acting in a trustworthy way.  Every
   control element (root and subroots) must remain in the system
   throughout the multicast.  This effectively makes removing someone
   from the net (especially the subroots) harder and slower due to the
   distributed control.  When removing a participant from the multicast
   group which has functioned on behalf of the root, as a subroot, to
   distribute Net Key, additional steps will be necessary.  A new
   subroot must be delegated by the root to replace the removed subroot.
   A key exchange (to generate a new pairwise KEK) must occur between
   the new subroot and each leaf the removed subroot was responsible
   for.  A new Net Key will now be distributed from the root, to the
   subroots, and to the leaves.  Note that this last step would have
   been the only step required if the removed party was a leaf with no
   controlling responsibilities.



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5.3   COMPLEMENTARY VARIABLE APPROACH

   Let us suppose we have N leaves.  The Root performs a public key
   exchange with each leaf i (i= 1,2, ..., N).  The Root will cache each
   pairwise KEK. Each leaf stores their own KEK.  The root would provide
   the multicast group list of participants and attributes to all users.
   Participants would accept or reject participation in the multicast
   session as described in previous sections.  The root encrypts the Net
   Key for the Multicast group to each leaf, using their own unique
   KEK(i).  (The Root either generated this Net Key himself, or
   cooperatively generated with one of the leaves as was discussed
   earlier).  In addition to the encrypted Net Key, the root will also
   encrypt something called complementary variables and send them to the
   leaves.

   A leaf will NOT receive his own complementary variable, but he will
   receive the other N-1 leaf complementary variables.  The root sends
   the Net Key and complementary variables j, where j=1,2,...,N and j
   not equal to i, encrypted by KEK(i) to each leaf. Thus, every leaf
   receives and stores N variables which are the Net key, and N-1
   complementary variables.

   Thus to cut a user from the multicast group and get the remaining
   participants back up again on a new Net Key would involve the
   following. Basically, to cut leaf number 20 out of the net, one
   message is sent out that says "cut leaf 20 from the net." All of the
   other leaves (and Root) generate a new Net Key based on the current
   Net Key and Complementary variable 20.  [Thus some type of
   deterministic key variable generation process will be necessary for
   all participants of the multicast group]. This newly generated
   variable will be used as the new Net Key by all remaining
   participants of the multicast group.  Everyone except leaf 20 is able
   to generate the new Net Key, because they have complementary variable
   20, but leaf 20 does not.

   A scheme like this seems very desirable from the viewpoint of
   transmission savings since a rekey message encrypted with each
   individual KEK to every leaf does not have to be sent to delete
   someone from the net.  In other words, there will be one plaintext
   message to the multicast group versus N encrypted rekey messages.
   There exists two major drawbacks with this scheme.  First are the
   storage requirements necessary for the (N-1) complementary variables.
   Secondly, when deleting multiple users from the multicast group,
   collusion will be a concern.  What this means is that these deleted
   users could work together and share their individual complementary
   variables to regain access to the multicast session.





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5.4  HIERARCHICAL TREE APPROACH

   The Hierarchical Tree Approach is our recommended approach to address
   the multicast key management problem.  This approach provides for the
   following requisite features:

      1. Provides for the secure removal of a compromised user from the
         multicast group

      2. Provides for transmission efficiency

      3. Provides for storage efficiency

   This approach balances the costs of time, storage and number of
   required message transmissions, using a hierarchical system of
   auxiliary keys to facilitate distribution of new Net Key. The result
   is that the storage requirement for each user and the transmissions
   required for key replacement are both logarithmic in the number of
   users, with no background transmissions required. This approach is
   robust against collusion of excluded users. Moreover, while the
   scheme is hierarchical in nature, no infrastructure is needed beyond
   a server (e.g., a root), though the presence of such elements could
   be used to advantage (See Figure 1).

                        --------------------------
                       |                          |
                       |        S E R V E R       |
                       |                          |
                        --------------------------
                        |    |                   |
                        |    |     .  .  .  .    |
                        -    -                   -
                       |1|  |2|                 |n|
                        -    -                   -


                  Figure 1: Assumed Communication Architecture

   The scheme, advantages and disadvantages are enumerated in more
   detail below.  Consider Figure 2 below.  This figure illustrates the
   logical key distribution architecture, where keys exist only at the
   server and at the users.  Thus, the server in this architecture would
   hold Keys A through O, and the KEKs of each user.  User 11 in this
   architecture would hold its own unique KEK, and Keys F, K, N, and O.







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  net key                         Key O
                   -------------------------------------
  intermediate    |                                     |
  keys            |                                     |
              Key M                                 Key N
        -----------------                   --------------------
       |                 |                 |                    |
       |                 |                 |                    |
     Key I             Key J             Key K               Key L
   --------          --------         ---------           ----------
  |        |        |        |       |         |         |          |
  |        |        |        |       |         |         |          |
 Key A   Key B   Key C    Key D    Key E     Key F     Key G     Key H
  ---     ---     ---      ---      ---       ----      ----      ----
 |   |   |   |   |   |    |   |    |   |     |    |    |    |    |    |
 -   -   -   -   -   -    -   -   -   --    --   --   --   --   --   --
|1| |2| |3| |4| |5| |6|  |7| |8| |9| |10|  |11| |12| |13| |14| |15| |16|
 -   -   -   -   -   -    -   -   -   --    --   --   --   --   --   --
                               users



               Figure 2: Logical Key Distribution Architecture

   We now describe the organization of the key hierarchy and the setup
   process.  It will be clear from the description how to add users
   after the hierarchy is in place; we will also describe the removal of
   a user.  Note: The passing of the multicast group list and any
   negotiation protocols is not included in this discussion for
   simplicity purposes.

   We construct a rooted tree (from the bottom up) with one leaf
   corresponding to each user, as in Figure 2. (Though we have drawn a
   balanced binary tree for convenience, there is no need for the tree
   to be either balanced or binary - some preliminary analysis on tree
   shaping has been performed.) Each user establishes a unique pairwise
   key with the server. For users with transmission capability, this can
   be done using the public key exchange protocol. The situation is more
   complicated for receive-only users; it is easiest to assume these
   users have pre-placed key.

   Once each user has a pairwise key known to the server, the server
   generates (according to the security policy in place for that
   session) a key for each remaining node in the tree.  The keys
   themselves should be generated by a robust process.  We will also
   assume users have no information about keys they don't need.  (Note:
   There are no users at these remaining nodes, (i.e., they are logical
   nodes) and the key for each node need only be generated by the server



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   via secure means.)  Starting with those nodes all of whose children
   are leaves and proceeding towards the root, the server transmits the
   key for each node, encrypted using the keys for each of that node's
   children.  At the end of the process, each user can determine the
   keys corresponding to those nodes above her leaf.  In particular, all
   users hold the root key, which serves as the common Net Key for the
   group.  The storage requirement for a user at depth d is d+1 keys
   (Thus for the example in Figure 2, a user at depth d=4 would hold
   five keys.  That is, the unique Key Encryption Key generated as a
   result of the pairwise key exchange, three intermediate node keys -
   each separately encrypted and transmitted, and the common Net Key for
   the multicast group which is also separately encrypted.)

   It is also possible to transmit all of the intermediate node keys and
   root node key in one message, where the node keys would all be
   encrypted with the unique pairwise key of the individual leaf.  In
   this manner, only one transmission (of a larger message) is required
   per user to receive all of the node keys (as compared to d
   transmissions).  It is noted for this method, that the leaf would
   require some means to determine which key corresponds to which node
   level.

   It is important to note that this approach requires additional
   processing capabilities at the server where other alternative
   approaches may not.  In the worst case, a server will be responsible
   for generating the intermediate keys required in the architecture.

5.4.1 The Exclusion Principle

   Suppose that User 11 (marked on Figure 2 in black) needs to be
   deleted from the multicast group. Then all of the keys held by User
   11 (bolded Keys F, K, N, O) must be changed and distributed to the
   users who need them, without permitting User 11 or anyone else from
   obtaining them. To do this, we must replace the bolded keys held by
   User 11, proceeding from the bottom up.  The server chooses a new key
   for the lowest node, then transmits it encrypted with the appropriate
   daughter keys (These transmissions are represented by the dotted
   lines).  Thus for this example, the first key replaced is Key F, and
   this new key will be sent encrypted with User 12's unique pairwise
   key.

   Since we are proceeding from the bottom up, each of the replacement
   keys will have been replaced before it is used to encrypt another
   key. (Thus, for the replacement of Key K, this new key will be sent
   encrypted in the newly replaced Key F (for User 12) and will also be
   sent as one multicast transmission encrypted in the node key shared
   by Users 9 and 10 (Key E). For the replacement of Key N, this new key
   will be sent encrypted in the newly replaced Key K (for Users 9, 10,



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   and 12) and will also be encrypted in the node key shared by Users
   13, 14, 15, and 16 (Key L).  For the replacement of Key O, this new
   key will be sent encrypted in the newly replaced Key N (for Users 9,
   10, 12, 13, 14, 15, and 16) and will also be encrypted in the node
   key shared by Users 1, 2 , 3, 4, 5, 6, 7, and 8 (Key M).)  The number
   of transmissions required is the sum of the degrees of the replaced
   nodes. In a k-ary tree in which a sits at depth d, this comes to at
   most kd-1 transmissions.  Thus in this example, seven transmissions
   will be required to exclude User 11 from the multicast group and to
   get the other 15 users back onto a new multicast group Net Key that
   User 11 does not have access to.  It is easy to see that the system
   is robust against collusion, in that no set of users together can
   read any message unless one of them could have read it individually.

   If the same strategy is taken as in the previous section to send
   multiple keys in one message, the number of transmissions required
   can be reduced even further to four transmissions.  Note once again
   that the messages will be larger in the number of bits being
   transmitted.  Additionally, there must exist a means for each leaf to
   determine which key in the message corresponds to which node of the
   hierarchy.  Thus, in this example, for the replacement of keys F, K,
   N, and O to User 12, the four keys will be encrypted in one message
   under User 12's unique pairwise key.  To replace keys K, N, and O for
   Users 9 and 10, the three keys will be encrypted in one message under
   the node key shared by Users 9 and 10 (Key E).  To replace keys N and
   O for Users  13, 14, 15, 16, the two keys will be encrypted in one
   message under the node key shared by Users 13, 14, 15, and 16 (Key
   L). Finally, to replace key O for Users 1, 2 , 3, 4, 5, 6, 7, and 8,
   key O will be encrypted under the node key shared by Users 1, 2 , 3,
   4, 5, 6, 7, and 8 (Key M).  Thus the number of transmission required
   is at most (k-1)d.

   The following table demonstrates the removal of a user, and how the
   storage and transmission requirements grow with the number of users.

















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Table 1: Storage and Transmission Costs

Number    Degree   Storage per user  Transmissions to    Transmissions
of users   (k)        (d+1)          rekey remaining     to rekey
                                     participants of     remaining
                                     multicast group-    participants of
                                     one key per message multicast
                                         (kd-1)          group -
                                                         multiple keys
                                                         per message
                                                            (k-1)d
     8       2            4                 5                 3
     9       3            3                 5                 4
    16       2            5                 7                 4
  2048       2           12                21                11
  2187       3            8                20                14
131072       2           18                33                17
177147       3           12                32                22

The benefits of a scheme such as this are:

      1. The costs of user storage and rekey transmissions are balanced
         and scalable as the number of users increases.  This is not the
         case for [1], [2], or [4].

      2. The auxiliary keys can be used to transmit not only other keys,
         but also messages. Thus the hierarchy can be designed to place
         subgroups that wish to communicate securely (i.e. without
         transmitting to the rest of the large multicast group) under
         particular nodes, eliminating the need for maintenance of
         separate Net Keys for these subgroups. This works best if the
         users operate in a hierarchy to begin with (e.g., military
         operations), which can be reflected by the key hierarchy.

      3. The hierarchy can be designed to reflect network architecture,
         increasing efficiency (each user receives fewer irrelevant
         messages). Also, server responsibilities can be divided up
         among subroots (all of which must be secure).

      4. The security risk associated with receive-only users can be
         minimized by collecting such users in a particular area of the
         tree.

      5. This approach is resistant to collusion among arbitrarily many
         users.






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   As noted earlier, in the rekeying process after one user is
   compromised, in the case of one key per message, each replaced key
   must be decrypted successfully before the next key can be replaced
   (unless users can cache the rekey messages).  This bottleneck could
   be a problem on a noisy or slow network. (If multiple users are being
   removed, this can be parallelized, so the expected time to rekey is
   roughly independent of the number of users removed.)

   By increasing the valences and decreasing the depth of the tree, one
   can reduce the storage requirements for users at the price of
   increased transmissions.  For example, in the one key per message
   case, if n users are arranged in a k-ary tree, each user will need
   storage. Rekeying after one user is removed now requires
   transmissions.  As k approaches n, this approaches the pairwise key
   scheme described earlier in the paper.

5.4.2 Hierarchical Tree Approach Options

5.4.2.1  Distributed Hierarchical Tree Approach

   The Hierarchical Tree Approach outlined in this section could be
   distributed as indicated in Section 5.2 to more closely resemble the
   proposal put forth in [4].  Subroots could exist at each of the nodes
   to handle any joining or rekeying that is necessary for any of the
   subordinate users.  This could be particularly attractive to users
   which do not have a direct connection back to the Root.  Recall as
   indicated in Section 5.2, that the trust placed in these subroots to
   act with the authority and security of a Root, is a potentially
   dangerous proposition.  This thought is also echoed in [4].

   Some practical recommendations that might be made for these subroots
   include the following.  The subroots should not be allowed to change
   the multicast group participant list that has been provided to them
   from the Root.  One method to accomplish this, would be for the Root
   to sign the list before providing it to the subroots.  Authorized
   subroots could though be allowed to set up new multicast groups for
   users below them in the hierarchy.

   It is important to note that although this distribution may appear to
   provide some benefits with respect to the time required to initialize
   the multicast group (as compared to the time required to initialize
   the group as described in Section 5.4) and for periodic rekeying, it
   does not appear to provide any benefit in rekeying the multicast
   group when a user has been compromised.

   It is also noted that whatever the key management scheme is
   (hierarchical tree, distributed hierarchical tree, core based tree,
   GKMP, etc.), there will be a "hit" incurred to initialize the



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   multicast group with the first multicast group net key.  Thus, the
   hierarchical tree approach does not suffer from additional complexity
   with comparison to the other schemes with respect to initialization.

5.4.2.2  Multicast Group Formation

   Although this paper has presented the formation of the multicast
   group as being Root initiated, the hierarchical approach is
   consistent with user initiated joining.  User initiated joining is
   the method of multicast group formation presented in [4].  User
   initiated joining may be desirable when some core subset of users in
   the multicast group need to be brought up on-line and communicating
   more quickly.  Other participants in the multicast group can then be
   brought in when they wish.  In this type of approach though, there
   does not exist a finite period of time by when it can be ensured all
   participants will be a part of the multicast group.

   For example, in the case of a single root, the hierarchy is set up
   once, in the beginnning, by the initiator (also usually the root) who
   also generates the group participant list. The group of keys for each
   participant can then be individually requested (pulled) as soon as,
   but not until, each participant wishes to join the session.

5.4.2.3  Sender Specific Authentication

   In the multicast environment, the possibility exists that
   participants of the group at times may want to uniquely identify
   which participant is the sender of a multicast group message.  In the
   multicast key distribution system described by Ballardie [4], the
   notion of "sender specific keys" is presented.

   Another option to allow participants of a multicast group to uniquely
   determine the sender of a message is through the use of a signature
   process.  When a member of the multicast group signs a message with
   their own private signature key, the recipients of that signed
   message in the multicast group can use the sender's public
   verification key to determine if indeed the message is from who it is
   claimed to be from.

   Another related idea to this is the case when two users of a
   multicast group want to communicate strictly with each other, and
   want no one else to listen in on the communication.  If this
   communication relationship is known when the multicast group is
   originally set up, then these two participants could simply be placed
   adjacent to one another at the lowest level of the hierarchy (below a
   binary node).  Thus, they would naturally share a secret pairwise
   key.  Otherwise, a simple way to accomplish this is to perform a
   public key based pairwise key exchange between the two users to



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   generate a traffic encryption key for their private unicast
   communications.  Through this process, not only will the encrypted
   transmissions between them be readable only by them, but unique
   sender authentication can be accomplished via the public key based
   pairwise exchange.

5.4.2.4  Rekeying the Multicast Group and the Use of Group Key
         Encryption Keys

   Reference [4] makes use of a Group Key Encryption Key that can be
   shared by the multicast group for use in periodic rekeys of the
   multicast group. Aside from the potential security drawbacks of
   implementing a shared key for encrypting future keys, the use of a
   Group Key Encryption Key is of no benefit to a multicast group if a
   rekey is necessary due to the known compromise of one of the members.
   The strategy for rekeying the multicast group presented in Section
   5.4.1 specifically addresses this critical problem and offers a means
   to accomplish this task with minimal message transmissions and
   storage requirements.

   The question though can now be asked as to whether the rekey of a
   multicast group will be necessary in a non-compromise scenario.  For
   example, if a user decides they do not want to participate in the
   group any longer, and requests the list controller to remove them
   from the multicast group participant list, will a rekey of the
   multicast group be necessary?  If the security policy of the
   multicast group mandates that deleted users can no longer receive
   transmissions, than a rekey of a new net key will be required.  If
   the multicast group security policy does not care that the deleted
   person can still decrypt any transmissions (encrypted in the group
   net key that they might still hold), but does care that they can not
   encrypt and transmit messages, a rekey will once again be necessary.
   The only alternative to rekeying the multicast group under this
   scenario would require a recipient to check every received message
   sender, against the group participant list.  Thus rejecting any
   message sent by a user not on the list.  This is not a practical
   option.  Thus it is recommended to always rekey the multicast group
   when someone is deleted, whether it is because of compromise reasons
   or not.

5.4.2.5  Bulk Removal of Participants

   As indicated in Section 2, the need may arise to remove users in
   bulk.  If the users are setup as discussed in Section 5.4.1 into
   subgroups that wish to communicate securely all being under the same
   node, bulk user removal can be done quite simply if the whole node is
   to be removed.  The same technique as described in Section 5.4.1 is
   performed to rekey any shared node key that the remaining



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   participants hold in common with the removed node.

   The problem of bulk removal becomes more difficult when the
   participants to be removed are dispersed throughout the tree.
   Depending on how many participants are to be removed, and where they
   are located within the hierarchy, the number of transmissions
   required to rekey the multicast group could be equivalent to brute
   force rekeying of the remaining participants. Also the question can
   be raised as to at what point the remaining users are restructured
   into a new hierarchical tree, or should a new multicast group be
   formed.  Restructuring of the hierarchical tree would most likely be
   the preferred option, because it would not necessitate the need to
   perform pairwise key exchanges again to form the new user unique
   KEKs.

5.4.2.6  ISAKMP Compatibility

   Thus far this document has had a major focus on the architectural
   trade-offs involved in the generation, distribution, and maintenance
   of traffic encryption keys (Net Keys) for multicast groups.  There
   are other elements involved in the establishment of a secure
   connection among the multicast participants that have not been
   discussed in any detail.  For example, the concept of being able to
   "pick and choose" and negotiating the capabilities of the key
   exchange mechanism and various other elements is a very important and
   necessary aspect.

   The NSA proposal to the Internet Engineering Task Force (IETF)
   Security Subworking Group [Ref. 3] entitled "Internet Security
   Association and Key Management Protocol (ISAKMP)" has attempted to
   identify the various functional elements required for the
   establishment of a secure connection for the largest current network,
   the Internet.  While the proposal has currently focused on the
   problem of point to point connections, the functional elements should
   be the same for multicast connections, with appropriate changes to
   the techniques chosen to implement the individual functional
   elements.  Thus the implementation of ISAKMP is compatible with the
   use of the hierarchical tree approach.

6.0  SUMMARY

   As discussed in this report, there are two main areas of concern when
   addressing solutions for the multicast key management problem.  They
   are the secure initialization and rekeying of the multicast group
   with a common net key.  At the present time, there are multiple
   papers which address the initialization of a multicast group, but
   they do not adequately address how to efficiently and securely remove
   a compromised user from the multicast group.



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   This paper proposed a hierarchical tree approach to meet this
   difficult problem.  It is robust against collusion, while at the same
   time, balancing the number of transmissions required and storage
   required to rekey the multicast group in a time of compromise.

   It is also important to note that the proposal recommended in this
   paper is consistent with other multicast key management solutions
   [4], and allows for multiple options for its implementation.

7.0 Security Considerations

   Security concerns are discussed throughout this memo.

8.0  REFERENCES

   1. Harney, H., Muckenhirn, C. and T. Rivers, "Group Key Management
      Protocol Architecture", RFC 2094, September 1994.

   2. Harney, H., Muckenhirn, C. and T. Rivers, "Group Key Management
      Protocol Specification", RFC 2093,  September 1994.

   3. Maughan, D., Schertler, M. Schneider, M. and J.Turner, "Internet
      Security Association and Key Management Protocol, Version 7",
      February 1997.

   4. Ballardie, T., "Scalable Multicast Key Distribution", RFC 1949,
      May 1996.

   5. Wong, C., Gouda, M. and S. Lam, "Secure Group Communications Using
      Key Graphs", Technical Report TR 97-23, Department of Computer
      Sciences, The University of Texas at Austin, July 1997.




















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Authors' Addresses

   Debby M. Wallner
   National Security Agency
   Attn: R2
   9800 Savage Road  STE 6451
   Ft. Meade, MD.  20755-6451

   Phone: 301-688-0331
   EMail: dmwalln@orion.ncsc.mil


   Eric J. Harder
   National Security Agency
   Attn: R2
   9800 Savage Road  STE 6451
   Ft. Meade, MD.  20755-6451

   Phone: 301-688-0850
   EMail: ejh@tycho.ncsc.mil


   Ryan C. Agee
   National Security Agency
   Attn: R2
   9800 Savage Road  STE 6451
   Ft. Meade, MD.  20755-6451
























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Full Copyright Statement

   Copyright (C) The Internet Society (1999).  All Rights Reserved.

   This document and translations of it may be copied and furnished to
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Acknowledgement

   Funding for the RFC Editor function is currently provided by the
   Internet Society.



















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