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INFORMATIONAL

Network Working Group                                          A. Perrig
Request for Comments: 4082                                       D. Song
Category: Informational                       Carnegie Mellon University
                                                              R. Canetti
                                                                     IBM
                                                             J. D. Tygar
                                      University of California, Berkeley
                                                              B. Briscoe
                                                                      BT
                                                               June 2005


     Timed Efficient Stream Loss-Tolerant Authentication (TESLA):
         Multicast Source Authentication Transform Introduction

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 (2005).

Abstract

   This document introduces Timed Efficient Stream Loss-tolerant
   Authentication (TESLA).  TESLA allows all receivers to check the
   integrity and authenticate the source of each packet in multicast or
   broadcast data streams.  TESLA requires no trust between receivers,
   uses low-cost operations per packet at both sender and receiver, can
   tolerate any level of loss without retransmissions, and requires no
   per-receiver state at the sender.  TESLA can protect receivers
   against denial of service attacks in certain circumstances.  Each
   receiver must be loosely time-synchronized with the source in order
   to verify messages, but otherwise receivers do not have to send any
   messages.  TESLA alone cannot support non-repudiation of the data
   source to third parties.

   This informational document is intended to assist in writing
   standardizable and secure specifications for protocols based on TESLA
   in different contexts.








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Table of Contents

   1. Introduction ....................................................2
      1.1. Notation ...................................................3
   2. Functionality ...................................................4
      2.1. Threat Model and Security Guarantee ........................5
      2.2. Assumptions ................................................5
   3. The Basic TESLA Protocol ........................................6
      3.1. Protocol Sketch ............................................6
      3.2. Sender Setup ...............................................7
      3.3. Bootstrapping Receivers ....................................8
           3.3.1. Time Synchronization ................................9
      3.4. Broadcasting Authenticated Messages .......................10
      3.5. Authentication at Receiver ................................11
      3.6. Determining the Key Disclosure Delay ......................12
      3.7. Denial of Service Protection ..............................13
           3.7.1. Additional Group Authentication ....................14
           3.7.2. Not Re-using Keys ..................................15
           3.7.3. Sender Buffering ...................................17
      3.8. Some Extensions ...........................................17
   4. Layer Placement ................................................17
   5. Security Considerations ........................................18
   6. Acknowledgements ...............................................19
   7. Informative References .........................................19

1.  Introduction

   In multicast, a single packet can reach millions of receivers.
   Unfortunately, this introduces the danger that an attacker can
   potentially also reach millions of receivers with a malicious packet.
   Through source authentication, receivers can ensure that a received
   multicast packet originates from the correct source.  In these
   respects, a multicast is equivalent to a broadcast to a superset of
   the multicast receivers.

   In unicast communication, we can achieve data authentication through
   a simple mechanism: the sender and the receiver share a secret key to
   compute a message authentication code (MAC) of all communicated data.
   When a message with a correct MAC arrives, the receiver is assured
   that the sender generated that message.  Standard mechanisms achieve
   unicast authentication this way; for example, TLS or IPsec [1,2].

   Symmetric MAC authentication is not secure in a broadcast setting.
   Consider a sender that broadcasts authentic data to mutually
   mistrusting receivers.  The symmetric MAC is not secure: every
   receiver knows the MAC key and therefore could impersonate the sender
   and forge messages to other receivers.  Intuitively, we need an
   asymmetric mechanism to achieve authenticated broadcast, such that



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   every receiver can verify the authenticity of messages it receives,
   without being able to generate authentic messages.  Achieving this in
   an efficient way is a challenging problem [3].

   The standard approach to achieving such asymmetry for authentication
   is to use asymmetric cryptography; e.g., a digital signature.
   Digital signatures have the required asymmetric property: the sender
   generates the signature with its private key, and all receivers can
   verify the signature with the sender's public key, but a receiver
   with the public key alone cannot generate a digital signature for a
   new message.  A digital signature provides non-repudiation, a
   stronger property than authentication.  However, digital signatures
   have a high cost: they have a high computation overhead for both the
   sender and the receiver, and most signatures also have a high-
   bandwidth overhead.  Since we assume broadcast settings for which the
   sender does not retransmit lost packets, and the receiver still wants
   to authenticate each packet it receives immediately, we would need to
   attach a digital signature to each message.  Because of the high
   overhead of asymmetric cryptography, this approach would restrict us
   to low-rate streams, and to senders and receivers with powerful
   workstations.  We can try to amortize one digital signature over
   multiple messages.  However, this approach is still expensive in
   contrast to symmetric cryptography, since symmetric cryptography is
   in general 3 to 5 orders of magnitude more efficient than asymmetric
   cryptography.  In addition, the straight-forward amortization of one
   digital signature over multiple packets requires reliability, as the
   receiver needs to receive all packets to verify the signature.  A
   number of schemes that follow this approach are [4,5,6,7].  See [8]
   for more details.

   This document presents the Timed Efficient Stream Loss-tolerant
   Authentication protocol (TESLA).  TESLA uses mainly symmetric
   cryptography, and uses time-delayed key disclosure to achieve the
   required asymmetry property.  However, TESLA requires loosely
   synchronized clocks between the sender and the receivers.  See more
   details in Section 3.3.1.  Schemes that follow a similar approach to
   TESLA are [9,10,11].

1.1.  Notation

   To denote the subscript or an index of a variable, we use the
   underscore between the variable name and the index; e.g., the key K
   with index i is K_i, and the key K with index i+d is K_{i+d}.  To
   write a superscript, we use the caret; e.g., function F with the
   argument x executed i times is F^i(x).






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2.  Functionality

   TESLA provides delayed per-packet data authentication and integrity
   checking.  The key idea to providing both efficiency and security is
   a delayed disclosure of keys.  The delayed key disclosure results in
   an authentication delay.  In practice, the delay is on the order of
   one RTT (round-trip-time).

   TESLA has the following properties:

      o Low computation overhead for generation and verification of
        authentication information.

      o Low communication overhead.

      o Limited buffering required for the sender and the receiver, and
        therefore timely authentication for each individual packet.

      o Strong robustness to packet loss.

      o Scales to a large number of receivers.

      o Protects receivers from denial of service attacks in certain
        circumstances if configured appropriately.

      o Each receiver cannot verify message authenticity unless it is
        loosely time-synchronized with the source, where synchronization
        can take place at session setup.  Once the session is in
        progress, receivers need not send any messages or
        acknowledgements.

      o Non-repudiation is not supported; each receiver can know that a
        stream is from an authentic source, but cannot prove this to a
        third party.

   TESLA can be used in the network layer, in the transport layer, or in
   the application layer.  Delayed authentication, however, requires
   buffering of packets until authentication is completed.  Certain
   applications intolerant of delay may be willing to process packets in
   parallel to being buffered while awaiting authentication, as long as
   roll-back is possible if packets are later found to be
   unauthenticated.  For instance, an interactive video may play out
   packets still awaiting authentication, but if they are later found to
   be unauthenticated, it could stop further play-out and warn the
   viewer that the last x msec were unauthenticated and should be
   ignored.  However, in the remainder of this document, for brevity, we
   will assume that packets are not processed in parallel to buffering.




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2.1.  Threat Model and Security Guarantee

   We design TESLA to be secure against a powerful adversary with the
   following capabilities:

      o Full control over the network.  The adversary can eavesdrop,
        capture, drop, re-send, delay, and alter packets.

      o Access to a fast network with negligible delay.

      o The adversary's computational resources may be very large, but
        not unbounded.  In particular, this means that the adversary can
        perform efficient computations, such as computing a reasonable
        number of pseudo-random function applications and MACs with
        negligible delay.  Nonetheless, the adversary cannot find the
        key of a pseudo-random function (or distinguish it from a random
        function) with non-negligible probability.

   The security property of TESLA guarantees that the receiver never
   accepts M_i as an authentic message unless the sender really sent
   M_i.  A scheme that provides this guarantee is called a secure
   broadcast authentication scheme.

   Because TESLA expects the receiver to buffer packets before
   authentication, the receiver needs to protect itself from a potential
   denial of service (DoS) attack due to a flood of bogus packets (see
   Section 3.8).

2.2.  Assumptions

   TESLA makes the following assumptions in order to provide security:

      1.  The sender and the receiver must be loosely time-synchronized.
          Specifically, each receiver must be able to compute an upper
          bound on the lag of the receiver clock relative to the sender
          clock.  We denote this quantity with D_t.  (That is, D_t =
          sender time - receiver time).  We note that an upper bound on
          D_t can easily be obtained via a simple two-message exchange.
          (Such an exchange can be piggybacked on any secure session
          initiation protocol.  Alternatively, standard protocols such
          as NTP [15] can be used.

      2.  TESLA MUST be bootstrapped at session setup through a regular
          data authentication system.  One option is to use a digital
          signature algorithm for this purpose, in which case the
          receiver is required to have an authentic copy of either the
          sender's public key certificate or a root key certificate in




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          case of a PKI (public-key infrastructure).  Alternatively,
          this initialization step can be done using any secure session
          initiation protocol.

      3.  TESLA uses cryptographic MAC and PRF (pseudo-random
          functions).  These MUST be cryptographically secure.  Further
          details on the instantiation of the MAC and PRF are in Section
          3.4.

   We would like to emphasize that the security of TESLA does NOT rely
   on any assumptions about network propagation delay.

3.  The Basic TESLA Protocol

   TESLA is described in several academic publications: A book on
   broadcast security [12], a journal paper [13], and two conference
   papers [7,14].  Please refer to these publications for in-depth
   proofs of security, experimental results, etc.

   We first outline the main ideas behind TESLA.

3.1.  Protocol Sketch

   As we argue in the introduction, broadcast authentication requires a
   source of asymmetry.  TESLA uses time for asymmetry.  We first make
   sure that the sender and receivers are loosely time-synchronized as
   described above.  Next, the sender forms a one-way chain of keys, in
   which each key in the chain is associated with a time interval (say,
   a second).  Here is the basic approach:

      o The sender attaches a MAC to each packet.  The MAC is computed
        over the contents of the packet.  For each packet, the sender
        uses the current key from the one-way chain as a cryptographic
        key to compute the MAC.

      o The sender discloses a key from the one-way chain after some
        pre-defined time delay (e.g., the key used in time interval i is
        disclosed at time interval i+3).

      o Each receiver receives the packet.  Each receiver knows the
        schedule for disclosing keys and, since it has an upper bound on
        the local time at the sender, it can check that the key used to
        compute the MAC was not yet disclosed by the sender.  If it was
        not, then the receiver buffers the packet.  Otherwise the packet
        is dropped due to inability to authenticate.  Note that we do
        not know for sure whether a "late packet" is a bogus one or





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        simply a delayed packet.  We drop the packet because we are
        unable to authenticate it.  (Of course, an implementation may
        choose not to drop packets and to use them unauthenticated.)

      o Each receiver checks that the disclosed key belongs to the
        hash-chain (by checking against previously released keys in the
        chain) and then checks the correctness of the MAC.  If the MAC
        is correct, the receiver accepts the packet.

   Note that one-way chains have the property that if intermediate
   values of the one-way chain are lost, they can be recomputed using
   subsequent values in the chain.  Even if some key disclosures are
   lost, a receiver can recover the corresponding keys and check the
   correctness of earlier packets.

   We now describe the stages of the basic TESLA protocol in this order:
   sender setup, receiver bootstrap, sender transmission of
   authenticated broadcast messages, and receiver authentication of
   broadcast messages.

3.2.  Sender Setup

   The sender divides the time into uniform intervals of duration T_int.
   The sender assigns one key from the one-way chain to each time
   interval in sequence.

   The sender determines the length N of the one-way chain K_0,
   K_1, ..., K_N, and this length limits the maximum transmission
   duration before a new one-way chain must be created.  The sender
   picks a random value for K_N.  Using a pseudo-random function (PRF),
   f, the sender constructs the one-way function F: F(k) = f_k(0).  The
   rest of the chain is computed recursively using K_i = F(K_{i+1}).
   Note that this gives us K_i = F^{N-i}(K_N), so the receiver can
   compute any value in the key chain from K_N, even if it does not have
   intermediate values.  The key K_i will be used to authenticate
   packets sent in time interval i.

   Jakobsson [20] and Coppersmith and Jakobsson [21] present a storage-
   and computation-efficient mechanism for one-way chains.  For a chain
   of length N, storage is about log(N) elements, and the computation
   overhead to reconstruct each element is also about log(N).

   The sender determines the duration of a time interval, T_int, and the
   key disclosure delay, d.  (T_int is measured in time units, say
   milliseconds, and d is measured in number of time intervals.  That
   is, a key that is used for time interval i will be disclosed in time
   interval i+d.) It is stressed that the scheme remains secure for any
   values of T_int and d>0.  Still, correct choice of T_int and d is



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   crucial for the usability of the scheme.  The choice is influenced by
   the estimated network delay, the length of the transmission, and the
   tolerable delay at the receiver.  A T_int that is too short will
   cause the keys to run out too soon.  A T_int that is too long will
   cause excessive delay in authentication for some of the packets
   (those that were sent at the beginning of a time period).  A delay d
   that is too short will cause too many packets to be unverifiable by
   the receiver.  A delay d that is too long will cause excessive delay
   in authentication.

   The sender estimates a reasonable upper bound on the network delay
   between the sender and any receiver as m milliseconds.  This includes
   any delay expected in the stack (see Section 4, on layer placement).
   If the sender expects to send a packet every n milliseconds, then a
   reasonable value for T_int is max(n,m).  Based on T_int, a rule of
   thumb for determining the key disclosure delay, d, is given in
   Section 3.6.

   The above value for T_int is neither an upper or a lower bound; it is
   merely the value that reduces key change processing to a minimum
   without causing authentication delay to be higher than necessary.  If
   the application can tolerate higher authentication delay, then T_int
   can be made appropriately larger.  Also, if m (or n) increases during
   the session, perhaps due to congestion or a late joiner on a high
   delay path, T_int need not be revised.

   Finally, the sender needs to allow each receiver to synchronize its
   time with the sender.  See more details on how this can be done in
   Section 3.3.1.  (It is stressed that estimating the network delay is
   a separate task from the time synchronization between the sender and
   the receivers.)

3.3.  Bootstrapping Receivers

   Before a receiver can authenticate messages with TESLA, it needs to
   have the following:

      o An upper bound, D_t, on the lag of its own clock with respect to
        the clock of the sender.  (That is, if the local time reading is
        t, the current time reading at the sender is at most t+D_t.).

      o One authenticated key of the one-way key chain.  (Typically,
        this will be the last key in the chain; i.e., K_0.  This key
        will be signed by the sender, and all receivers will verify the
        signature with the public key of the signer.)






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      o The disclosure schedule of the following keys:

           - T_int, the interval duration.
           - T_0, the start time of interval 0.
           - N, the length of the one-way key chain.
           - d, the key disclosure delay d (in number of intervals).

   The receiver can perform the time synchronization and get the
   authenticated TESLA parameters in a two-round message exchange, as
   described below.  We stress again that time synchronization can be
   performed as part of the registration protocol between any receiver
   (including late joiners) and the sender, or between any receiver and
   a group controller.

3.3.1.  Time Synchronization

   Various approaches exist for time synchronization [15,16,17,18].
   TESLA only requires the receiver to know an upper bound on the delay
   of its local clock with respect to the sender's clock, so a simple
   algorithm is sufficient.  TESLA can be used with direct, indirect,
   and delayed synchronization as three default options.  The specific
   synchronization method will be part of each instantiation of TESLA.

   For completeness, we sketch a simple method for direct
   synchronization between the sender and a receiver:

      o The receiver sends a (sync t_r) message to the sender and
        records its local time, t_r, at the moment of sending.

      o Upon receipt of the (sync t_r) message, the sender records its
        local time, t_s, and sends (synch, t_r,t_s) to the receiver.

      o Upon receiving (synch,t_r,t_s), the receiver sets D_t = t_s -
        t_r + S, where S is an estimated bound on the clock drift
        throughout the duration of the session.

   Note:

      o Assuming that the messages are authentic (i.e., the message
        received by the receiver was actually sent by the sender), and
        assuming that the clock drift is at most S, then at any point
        throughout the session T_s < T_r + D_t, where T_s is the current
        time at the sender and T_r is the current time at the receiver.

      o The exchange of sync messages needs to be authenticated.  This
        can be done in a number of ways; for instance, with a secure NTP
        protocol or in conjunction with a session set-up protocol.




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   For indirect time synchronization (e.g., synchronization via a group
   controller), the sender and the controller engage in a protocol for
   finding the value D^0_t between them.  Next, each receiver, R,
   interacts with the group controller (say, when registering to the
   group) and finds the value D^R_t between the group controller and R.
   The overall value of D_t within R is set to the sum D_t = D^R_t +
   D^0_t.

3.4.  Broadcasting Authenticated Messages

   Each key in the one-way key chain corresponds to a time interval.
   Every time a sender broadcasts a message, it appends a MAC to the
   message, using the key corresponding to the current time interval.
   The key remains secret for the next d-1 intervals, so messages that a
   sender broadcasts in interval j effectively disclose key K_j-d.  We
   call d the key disclosure delay.

   We do not want to use the same key multiple times in different
   cryptographic operations; that is, using key K_j to derive the
   previous key of the one-way key chain K_{j-1}, and using the same key
   K_j as the key to compute the MACs in time interval j may potentially
   lead to a cryptographic weakness.  Using a pseudo-random function
   (PRF), f', we construct the one-way function F': F'(k) = f'_k(1).  We
   use F' to derive the key to compute the MAC of messages in each
   interval.  The sender derives the MAC key as follows: K'_i = F'(K_i).
   Figure 1 depicts the one-way key chain construction and MAC key
   derivation.  To broadcast message M_j in interval i the sender
   constructs the packet

                   P_j = {M_j || i || MAC(K'_i,M_j) || K_{i-d}}

      where || denotes concatenation.


                       F(K_i)     F(K_{i+1})      F(K_{i+2})
             K_{i-1} <------- K_i <------- K_{i+1} <------- K_{i+2}

                 |             |              |
                 | F'(K_{i-1}) | F'(K_i)      | F'(K_{i+1})
                 |             |              |
                 V             V              V

                K'_{i-1}      K'_i          K'_{i+1}

   Figure 1: At the top of the figure, we see the one-way key chain
   (derived using the one-way function F), and the derived MAC keys
   (derived using the one-way function F').




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3.5.  Authentication at Receiver

   Once a sender discloses a key, we must assume that all parties might
   have access to that key.  An adversary could create a bogus message
   and forge a MAC using the disclosed key.  So whenever a packet
   arrives, the receiver must verify that the MAC is based on a safe
   key; a safe key is one that is still secret (known only by the
   sender).  We define a safe packet or safe message as one with a MAC
   that is computed with a safe key.

   If a packet proves safe, it will be buffered, only to be released
   when its own key, disclosed in a later packet, proves its
   authenticity.  Although a newly arriving packet cannot immediately be
   authenticated, it may disclose a new key so that earlier, buffered
   packets can be authenticated.  Any newly disclosed key must be
   checked to determine whether it is genuine; then authentication of
   buffered packets that have been waiting for it can proceed.

   We now describe TESLA authentication at the receiver with more
   detail, listing all of these steps in the exact order they should be
   carried out:

      1.  Safe packet test: When the receiver receives packet P_j, which
          carries an interval index i, and a disclosed key K_{i-d}, it
          first records local time T at which the packet arrived.  The
          receiver then computes an upper bound t_j on the sender's
          clock at the time when the packet arrived: t_j = T + D_t.  To
          test whether the packet is safe, the receiver then computes
          the highest interval x the sender could possibly be in; namely
          x = floor((t_j - T_0) / T_int).  The receiver verifies that x
          < i + d (where i is the interval index), which implies that
          the sender is not yet in the interval during which it
          discloses the key K_i.

          Even if the packet is safe, the receiver cannot yet verify the
          authenticity of this packet sent in interval i without key
          K_i, which will be disclosed later.  Instead, it adds the
          triplet ( i, M_j, MAC( K'_i, M_j) ) to a buffer and verifies
          the authenticity after it learns K'_i.

          If the packet is unsafe, then the receiver considers the
          packet unauthenticated.  It should discard unsafe packets,
          but, at its own risk it may choose to use them unverified.

      2.  New key index test: Next the receiver checks whether a key K_v
          has already been disclosed with the same index v as the
          current disclosed key K_{i-d}, or with a later one; that is,
          with v >= i-d.



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      3.  Key verification test: If the disclosed key index is new, the
          receiver checks the legitimacy of K_{i-d} by verifying, for
          some earlier disclosed key K_v (v<i-d), that K_v = F^{i-d-
          v}(K_{i-d}).

          If key verification fails, the newly arrived packet P_j should
          be discarded.

      4.  Message verification tests: If the disclosed key is
          legitimate, the receiver then verifies the authenticity of any
          earlier safe, buffered packets of interval i-d.  To
          authenticate one of the buffered packets P_h containing
          message M_h protected with a MAC that used key index i-d, the
          receiver will compute K'_{i-d} = F'(K_{i-d}) from which it can
          compute MAC( K'_{i-d}, M_h).

          If this MAC equals the MAC stored in the buffer, the packet is
          authenticated and can be released from the buffer.  If the
          MACs do not agree, the buffered packet P_h should be
          discarded.

          The receiver continues to verify and release (or not) any
          remaining buffered packets that depend on the newly disclosed
          key K_{i-d}.

   Using a disclosed key, we can calculate all previous disclosed keys,
   so even if packets are lost, we will still be able to verify
   buffered, safe packets from earlier time intervals.  Thus, if i-d-
   v>1, the receiver can also verify the authenticity of the stored
   packets of intervals v+1 ... i-d-1.

3.6.  Determining the Key Disclosure Delay

   An important TESLA parameter is the key disclosure delay d.  Although
   the choice of the disclosure delay does not affect the security of
   the system, it is an important performance factor.  A short
   disclosure delay will cause packets to lose their safety property, so
   receivers will not be able to authenticate them; but a long
   disclosure delay leads to a long authentication delay for receivers.
   We recommend determining the disclosure delay as follows: In direct
   time synchronization, let the RTT, 2m, be a reasonable upper bound on
   the round trip time between the sender and any receiver including
   worst-case congestion delay and worst-case buffering delay in host
   stacks.  Then choose d = ceil( 2m / T_int) + 1.  Note that rounding
   up the quotient ensures that d >= 2.  Also note that a disclosure
   delay of one time interval (d=1) does not work.  Consider packets
   sent close to the boundary of the time interval: After the network
   propagation delay and the receiver time synchronization error, a



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   receiver will not be able to authenticate the packet, because the
   sender will already be in the next time interval when it discloses
   the corresponding key.

   Measuring the delay to each receiver before determining m will still
   not adequately predict the upper bound on delay to late joiners, or
   where congestion delay rises later in the session.  It may be
   adequate to use a hard-coded historic estimate of worst-case delay
   (e.g., round trip delays to any host on the intra-planetary Internet
   rarely exceed 500msec if routing remains stable).

   We stress that the security of TESLA does not rely on any assumptions
   about network propagation delay: If the delay is longer than
   expected, then authentic packets may be considered unauthenticated.
   Still, no inauthentic packet will be accepted as authentic.

3.7.  Denial of Service Protection

   Because TESLA authentication is delayed, receivers seem vulnerable to
   flooding attacks that cause them to buffer excess packets, even
   though they may eventually prove to be inauthentic.  When TESLA is
   deployed in an environment with a threat of flooding attacks, the
   receiver can take a number of extra precautions.

   First, we list simple DoS mitigation precautions that can and should
   be taken by any receiver independently of others, thus requiring no
   changes to the protocol or sender behaviour.  We precisely specify
   where these extra steps interleave with the receiver authentication
   steps already given in Section 3.5.

      o Session validity test: Before the safe packet test (Step 1),
        check that arriving packets have a valid source IP address and
        port number for the session, that they do not replay a message
        already received in the session, and that they are not
        significantly larger than the packet sizes expected in the
        session.

      o Reasonable misordering test: Before the key verification test
        (Step 3), check whether the disclosed key index i-d of the
        arriving packet is within g of the previous highest disclosed
        key index v; thus, for example, i-d-v <= g.  g sets the
        threshold beyond which an out-of-order key index is assumed to
        be malicious rather than just misordered.  Without this test, an
        attacker could exploit the iterated test in Step 3 to make
        receivers consume inordinate CPU time checking along the hash
        chain for what appear to be extremely misordered packets.





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        Each receiver can independently adapt g to prevailing attack
        conditions; for instance, by using the following algorithm.
        Initially, g should be set to g_max (say, 16).  But whenever an
        arriving packet fails the reasonable misordering test above or
        the key verification test (Step 3), g should be dropped to g_min
        (>0 and typically 1).  At each successful key verification (Step
        3), g should be incremented by 1 unless it is already g_max.
        These precautions will guarantee that sustained attack packets
        cannot cause the receiver to execute more than an average of
        g_min hashes each, unless they are paced against genuine
        packets.  In the latter case, attacks are limited to
        g_max/(g_max-g_min) hashes per each genuine packet.

        When choosing g_max and g_min, note that they limit the average
        gap in a packet sequence to g.max(n,m)/n packets (see Section
        3.2 for definitions of n and m).  So with g=1, m=100msec RTT,
        and n=4msec inter-packet period, reordering would be limited to
        gaps of 25 packets on average.  Bigger naturally occurring gaps
        would have to be written off as if they were losses.

   Stronger DoS protection requires that both senders and receivers
   arrange additional constraints on the protocol.  Below, we outline
   three alternative extensions to basic TESLA; the first adding group
   authentication, the second not re-using keys during a time interval,
   and the third moving buffering to the sender.

   It is important to understand the applicability of each scheme, as
   the first two schemes use slightly more (but bounded) resources in
   order to prevent attackers from consuming unbounded resources.
   Adding group authentication requires larger per-packet overhead.
   Never re-using a key requires both ends to process two hashes per
   packet (rather than per time interval), and the sender must store or
   re-generate a longer hash chain.  The merits of each scheme,
   summarised after each is described below, must be weighed against
   these additional costs.

3.7.1.  Additional Group Authentication

   This scheme simply involves addition of a group MAC to every packet.
   That is, a shared key K_g common to the whole group is communicated
   as an additional step during receiver bootstrap (Section 3.3).  Then,
   during broadcast of message M_j (Section 3.4), the sender computes
   the group MAC of each packet MAC(K_g, P_j), which it appends to the
   packet header.  Note that the group MAC covers the whole packet P_j;
   that is, the concatenation of the message M_j and the additional
   TESLA authentication material, using the formula in Section 3.4.





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   Immediately upon packet arrival, each receiver can check that each
   packet came from a group member, by recomputing and comparing the
   group MAC.

   Note that TESLA source authentication is only necessary when other
   group members cannot be trusted to refrain from spoofing the source;
   otherwise, simpler group authentication would be sufficient.
   Therefore, additional group authentication will only make sense in
   scenarios where other group members are trusted to refrain from
   flooding the group, but where they are still not trusted to refrain
   from spoofing the source.

3.7.2.  Not Re-using Keys

   In TESLA as described so far, each MAC key was used repeatedly for
   all the packets sent in a time interval.  If instead the sender were
   to guarantee never to use a MAC key more than once, each disclosed
   key could assume an additional purpose on top of authenticating a
   previously buffered packet.  Each key would also immediately show
   each receiver that the sender of each arriving packet knew the next
   key back along the hash chain, which is now only disclosed once,
   similar to S/KEY [22].  Therefore a reasonable receiver strategy
   would be to discard any arriving packets that disclosed a key seen
   already.  The fill rate of the receiver's buffer would then be
   clocked by each packet revealed by the genuine sender, preventing
   memory flooding attacks.

   An attacker with control of a network element or of a faster bypass
   network could intercept messages and overtake or replace them with
   different messages but with the same keys.  However, as long as
   packets are only buffered if they also pass the delay safety test,
   these bogus packets will fail TESLA verification after the disclosure
   delay.  Admittedly, receivers could be fooled into discarding genuine
   messages that had been overtaken by bogus ones.  But it is hard to
   overtake messages without compromising a network element, and any
   attacker that can compromise a network element can discard genuine
   messages anyway.  We will now describe this scheme in more detail.

   For the sender, the scheme is hardly different from TESLA.  It merely
   uses an interval duration short enough to ensure a new key back along
   the hash chain for each packet.  So the rule of thumb given in
   Section 3.2 for an efficient re-keying interval T_int no longer
   applies.  Instead, T_int is simply n, the inter-arrival time between
   packets in milliseconds.  The rule of thumb for calculating d, the
   key disclosure delay, remains unchanged from that given in Section
   3.6.





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   If the packet rate is likely to vary, for safety n should be taken as
   the minimum inter-departure time between any two packets.  (In fact,
   n need not be so strict; it can be the minimum average packet inter-
   departure time over any burst of d packets expected throughout the
   session.)

   Note that if the packet rate slows down, whenever no packets are sent
   in a key change interval, the key index must increment along the hash
   chain once for each missed interval.  (During a burst, if the less
   strict definition of n above has been used, packets may need to
   depart before their key change interval.  The sender can safely
   continue changing the key for each packet, using keys from future key
   intervals, because if n has been chosen as defined above, such bursts
   will never sustain long enough to cause the associated key to be
   disclosed in a period less than the disclosure delay later.)

   To be absolutely clear, the precise guarantees that the sender keeps
   to by following the above guidance are:

      o not to re-use a MAC key,

      o not to use a MAC key K_i after its time interval i, and

      o not to disclose key K_i sooner than the disclosure delay d *
        T_int following the packet it protects.

   Sender setup, receiver bootstrapping, and broadcasting authenticated
   messages are otherwise all identical to the descriptions in Sections
   3.2, 3.3, and 3.4, respectively.  However, the following step must be
   added to the receiver authentication steps in Section 3.5:

      o After Step 2, if a packet arrives carrying a key index i-d that
        has already been received, it should not be buffered.

   This simple scheme would suffice against DoS, were it not for the
   fact that a network sometimes misorders packets without being
   compromised.  Even without control of a network element, an attacker
   can opportunistically exploit such openings to fool a receiver into
   buffering a bogus packet and discarding a later genuine one.  A
   receiver can choose to set aside a fixed size cache and can manage it
   to minimise the chances of discarding a genuine packet.  However,
   given such vulnerabilities are rare and unpredictable, it is simpler
   to count these events as additions to the network loss rate.  As
   always, TESLA authentication will still uncover any bogus packets
   after the disclosure delay.

   To summarise, avoiding re-using keys has the following properties,
   even under extreme flooding attacks:



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      o After delayed TESLA authentication, packets arriving within the
        disclosure delay will always be identified as authentic if they
        are and as inauthentic if they are not authentic.

      o The fill rate of the receiver's buffer is clocked by each packet
        revealed by the genuine sender, preventing memory flooding
        attacks.

      o An attacker with control of a network element can cause any loss
        rate it chooses (but that's always true anyway).

      o Where attackers do not have control of any network elements, the
        effective loss rate is bounded by the sum of the network's
        actual loss rate and its re-ordering rate.

3.7.3.  Sender Buffering

   Buffering of packets can be moved to the sender side; then receivers
   can authenticate packets immediately upon receipt.  This method is
   described in [14].

3.8.  Some Extensions

   Let us mention two salient extensions of the basic TESLA scheme.  A
   first extension allows having multiple TESLA authentication chains
   for a single stream, where each chain uses a different delay for
   disclosing the keys.  This extension is typically used to deal with
   heterogeneous network delays within a single multicast transmission.
   A second extension allows having most of the buffering of packets at
   the sender side (rather than at the receiver side).  Both extensions
   are described in [14].

   TESLA's requirement that a key be received in a later packet for
   authentication prevents a receiver from authenticating the last part
   of a message.  Thus, to enable authentication of the last part of a
   message or of the last message before a transmission suspension, the
   sender needs to send an empty message with the key.

4.  Layer Placement

   TESLA authentication can be performed at any layer in the networking
   stack.  Three natural places are the network, transport, or
   application layer.  We list some considerations regarding the choice
   of layer:

      o Performing TESLA in the network layer has the advantage that the
        transport or application layer only receives authenticated data,
        potentially aiding a reliability protocol and mitigating denial



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        of service attacks.  (Indeed, reliable multicast tools based on
        forward error correction are highly susceptible to denial of
        service due to bogus packets.)

      o Performing TESLA in either the transport or the application
        layer has the advantage that the network layer remains
        unchanged, but it has the potential drawback that packets are
        obtained by the application layer only after being processed by
        the transport layer.  Consequently, if buffering is used in the
        transport, then this may introduce additional and unpredictable
        delays on top of the unavoidable network delays.

      o Note that because TESLA relies upon timing of packets, deploying
        TESLA on top of a protocol or layer that aggressively buffers
        packets and hides the true packet arrival time will
        significantly reduce TESLA's performance.

5.  Security Considerations

   See the academic publications on TESLA [7,13,19] for several security
   analyses.  Regarding the security of implementations, by far the most
   delicate point is the verification of the timing conditions.  Care
   should be taken to make sure that (a) the value bound D_t on the
   clock skew is calculated according to the spec at session setup and
   that (b) the receiver records the arrival time of the packet as soon
   as possible after the packet's arrival, and computes the safety
   condition correctly.

   It should be noted that a change to the key disclosure schedule for a
   message stream should never be declared within the message stream
   itself.  This would introduce a vulnerability, because a receiver
   that did not receive the notification of the change would still
   believe in the old key disclosure schedule.

   Finally, in common with all authentication schemes, if verification
   is located separately from the ultimate destination application
   (e.g., an IPSec tunnel end point), a trusted channel must be present
   between verification and the application.  For instance, the
   interface between the verifier and the application might simply
   assume that packets received by the application must have been
   verified by the verifier (because otherwise they would have been
   dropped).  The application is then vulnerable to reception of packets
   that have managed to bypass the verifier.








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6.  Acknowledgements

   We would like to thank the following for their feedback and support:
   Mike Luby, Mark Baugher, Mats Naslund, Dave McGrew, Ross Finlayson,
   Sylvie Laniepce, Lakshminath Dondeti, Russ Housley, and the IESG
   reviewers.

7.  Informative References

   [1]  Dierks, T. and C. Allen, "The TLS Protocol Version 1.0", RFC
        2246, January 1999.

   [2]  IPsec, "IP Security Protocol, IETF working group"
        http://www.ietf.org/html.charters/OLD/ipsec-charter.html.

   [3]  D. Boneh, G. Durfee, and M. Franklin, "Lower bounds for
        multicast message authentication," in Advances in Cryptology --
        EUROCRYPT 2001 (B. Pfitzmann, ed.), Vol. 2045 of Lecture Notes
        in Computer Science, (Innsbruck, Austria), p. 434-450,
        Springer-Verlag, Berlin Germany, 2001.

   [4]  R. Gennaro and P. Rohatgi, "How to Sign Digital Streams", tech.
        rep., IBM T.J.Watson Research Center, 1997.

   [5]  P. Rohatgi, "A compact and fast hybrid signature scheme for
        multicast packet authentication", 6th ACM Conference on Computer
        and Communications Security , November 1999.

   [6]  C. K. Wong and S. S. Lam, "Digital signatures for flows and
        multicasts," in Proc. IEEE ICNP `98, 1998.

   [7]  A. Perrig, R. Canetti, J. Tygar, and D. X. Song, "Efficient
        authentication and signing of multicast streams over lossy
        channels", IEEE Symposium on Security and Privacy, May 2000.

   [8]  R. Canetti, J. Garay, G. Itkis, D. Micciancio, M. Naor, and B.
        Pinkas, "Multicast security: A taxonomy and some efficient
        constructions", Infocom '99, 1999.

   [9] S. Cheung, "An efficient message authentication scheme for link
        state routing", 13th Annual Computer Security Applications
        Conference, 1997.

   [10] F. Bergadano, D. Cavagnino, and B. Crispo, "Chained stream
        authentication," in Selected Areas in Cryptography 2000,
        (Waterloo, Canada), August 2000. A talk describing this scheme
        was given at IBM Watson in August 1998.




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   [11] F. Bergadano, D. Cavalino, and B. Crispo, "Individual single
        source authentication on the mbone", ICME 2000, August 2000. A
        talk containing this work was given at IBM Watson, August 1998.

   [12] A. Perrig and J. D. Tygar, Secure Broadcast Communication in
        Wired and Wireless Networks Kluwer Academic Publishers, October
        2002.  ISBN 0792376501.

   [13] A. Perrig, R. Canetti, J. D. Tygar, and D. Song, "The tesla
        broadcast authentication protocol," RSA CryptoBytes, Volume 5,
        No. 2 Summer/Fall 2002.

   [14] A. Perrig, R. Canetti, D. Song, and J. D. Tygar, "Efficient and
        secure source authentication for multicast", Network and
        Distributed System Security Symposium, NDSS '01, p. 35-46,
        February 2001.

   [15] Mills, D., "Network Time Protocol (Version 3) Specification,
        Implementation and Analysis", RFC 1305, March 1992.

   [16] B. Simons, J. Lundelius-Welch, and N. Lynch, "An overview of
        clock synchronization", Fault-Tolerant Distributed Computing (B.
        Simons and A. Spector, eds.), No. 448 in LNCS, p. 84-96,
        Springer-Verlag, Berlin Germany, 1990.

   [17] D. Mills, "Improved algorithms for synchronizing computer
        network clocks", Proceedings of the conference on Communications
        architectures, protocols and applications, SIGCOMM 94, (London,
        England), p. 317-327, 1994.

   [18] L. Lamport and P. Melliar-Smith, "Synchronizing clocks in the
        presence of faults", J. ACM, Volume 32, No. 1, p. 52-78, 1985.

   [19] P. Broadfoot and G. Lowe, "Analysing a Stream Authentication
        Protocol using Model Checking", Proceedings of the 7th European
        Symposium on Research in Computer Security (ESORICS), 2002.

   [20] M. Jakobsson, "Fractal hash sequence representation and
        traversal", Cryptology ePrint Archive,
        http://eprint.iacr.org/2002/001/, January 2002.

   [21] D. Coppersmith and M. Jakobsson, "Almost optimal hash sequence
        traversal", Proceedings of the Sixth International Financial
        Cryptography Conference (FC '02), March 2002.

   [22] Haller, N., "The S/KEY One-Time Password System", RFC 1760,
        February 1995.




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Authors' Addresses

   Adrian Perrig
   ECE Department
   Carnegie Mellon University
   Pittsburgh, PA 15218
   US

   EMail: perrig@cmu.edu


   Ran Canetti
   IBM Research
   30 Saw Mill River Rd
   Hawthorne, NY 10532
   US

   EMail: canetti@watson.ibm.com


   Dawn Song
   ECE Department
   Carnegie Mellon University
   Pittsburgh, PA 15218
   US

   EMail: dawnsong@cmu.edu


   J. D. Tygar
   UC Berkeley - EECS & SIMS
   102 South Hall 4600
   Berkeley, CA  94720-4600
   US

   EMail: doug.tygar@gmail.com


   Bob Briscoe
   BT Research
   B54/77, BT Labs
   Martlesham Heath
   Ipswich, IP5 3RE
   UK

   EMail: bob.briscoe@bt.com





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Full Copyright Statement

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