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Versions: 00 01 rfc2627                                                 
Network Working Group                                 Debby M. Wallner
Category: Informational                               Eric J. Harder
                                                      Ryan C. Agee
                                                      National Security Agency
                                                      July 1, 1997
                                                      Expire in six months




              Key Management for Multicast: Issues and Architectures
                        <draft-wallner-key-arch-00.txt>




Status of this memo

   This document is being submitted as an Informational RFC (Request for
   Comment) to the Internet Engineering Task Force (IETF) for consideration
   as a method for the establishment of multicast communication sessions.
   Comments and suggestions for improvements are requested and should be
   addressed to the authors.  The views expressed in this paper are those of
   the authors and do not necessarily reflect the views of the U.S. Department
   of Defense or any of its agencies.  Distribution of this document is
   unlimited.




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

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                         Key Management for Multicast                  July 1997

   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 the Department of Defense as well as the 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 multicast
   communication being that multiple receivers simultaneously get the same
   transmission.  Thus the problem is to enable 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.

   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

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   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, Multicast Backbone (MBONE), 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, wargaming and MBONE.

   The wargaming scenario deals with the Defense Department's need to simulate
   a wartime 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.  Wargaming could be more
   demanding from a key management perspective than an actual wartime scenario
   for several reasons.  First, the nodes of the simulation net may be
   dispersed throughout the country.  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 the ones
   listed.  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 wargaming

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   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 MBONE 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 MBONE 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:

      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.



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   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:

      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.







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      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.

         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.

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   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 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 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

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   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 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

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   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.

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

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   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.

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).










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                          --------------------------
                         |                          |
                         |        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.



   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


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   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 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





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   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, 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 to
 of users    (k)         (d+1)          rekey remaining      rekey remaining
                                        participants of      participants of
                                        multicast group -    multicast group -
                                        one key per message  multiple keys per
                                           (kd-1)            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.

   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

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   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 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.

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   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 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

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   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 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

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   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.

   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.






























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7.0  REFERENCES

        1. Harney, Hugh; Muckenhirn, Carl; and Rivers, Thomas; "Group Key
           Management Protocol Architecture," dtd September 1994, Sparta, Inc.

        2. Harney, Hugh; Muckenhirn, Carl; and Rivers, Thomas; "Group Key
           Management Protocol Specification," dtd September 1994, Sparta, Inc.

        3. Maughan, Douglas; Schertler, Mark; Schneider, Mark; and
           Turner, Jeff;  "Internet Security Association and Key Management
           Protocol, Version 7" dtd. 21 February 1997.

        4. Ballardie, A.; "Scalable Multicast Key Distribution," dtd May 1996.



Address of Authors

The authors are with:

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

1.  Debby M. Wallner
Phone: 301-688-0331
E-mail: dmwalln@orion.ncsc.mil

2.  Eric J. Harder
Phone: 301-688-0850
E-mail: ejh@tycho.ncsc.mil

3.  Ryan C. Agee