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Network Working Group                                          A. PerrigRequest for Comments: 4082                                       D. SongCategory: Informational                       Carnegie Mellon University                                                              R. Canetti                                                                     IBM                                                             J. D. Tygar                                      University of California, Berkeley                                                              B. Briscoe                                                                      BT                                                               June 2005Timed Efficient Stream Loss-Tolerant Authentication (TESLA):Multicast Source Authentication Transform IntroductionStatus 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.Perrig, et al.               Informational                      [Page 1]

RFC 4082                   TESLA Introduction                  June 2005Table of Contents1. Introduction ....................................................21.1. Notation ...................................................32. Functionality ...................................................42.1. Threat Model and Security Guarantee ........................52.2. Assumptions ................................................53. The Basic TESLA Protocol ........................................63.1. Protocol Sketch ............................................63.2. Sender Setup ...............................................73.3. Bootstrapping Receivers ....................................83.3.1. Time Synchronization ................................93.4. Broadcasting Authenticated Messages .......................103.5. Authentication at Receiver ................................113.6. Determining the Key Disclosure Delay ......................123.7. Denial of Service Protection ..............................133.7.1. Additional Group Authentication ....................143.7.2. Not Re-using Keys ..................................153.7.3. Sender Buffering ...................................173.8. Some Extensions ...........................................174. Layer Placement ................................................175. Security Considerations ........................................186. Acknowledgements ...............................................197. Informative References .........................................191.  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 thatPerrig, et al.               Informational                      [Page 2]

RFC 4082                   TESLA Introduction                  June 2005   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 inSection 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).Perrig, et al.               Informational                      [Page 3]

RFC 4082                   TESLA Introduction                  June 20052.  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.Perrig, et al.               Informational                      [Page 4]

RFC 4082                   TESLA Introduction                  June 20052.1.  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 (seeSection 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 inPerrig, et al.               Informational                      [Page 5]

RFC 4082                   TESLA Introduction                  June 2005          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 inSection3.4.   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 orPerrig, et al.               Informational                      [Page 6]

RFC 4082                   TESLA Introduction                  June 2005        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 isPerrig, et al.               Informational                      [Page 7]

RFC 4082                   TESLA Introduction                  June 2005   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 (seeSection 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 inSection 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 inSection 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.)Perrig, et al.               Informational                      [Page 8]

RFC 4082                   TESLA Introduction                  June 2005      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.Perrig, et al.               Informational                      [Page 9]

RFC 4082                   TESLA Introduction                  June 2005   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').Perrig, et al.               Informational                     [Page 10]

RFC 4082                   TESLA Introduction                  June 20053.5.  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.Perrig, et al.               Informational                     [Page 11]

RFC 4082                   TESLA Introduction                  June 2005      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, aPerrig, et al.               Informational                     [Page 12]

RFC 4082                   TESLA Introduction                  June 2005   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 inSection 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.Perrig, et al.               Informational                     [Page 13]

RFC 4082                   TESLA Introduction                  June 2005        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 (seeSection3.2 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 inSection 3.4.Perrig, et al.               Informational                     [Page 14]

RFC 4082                   TESLA Introduction                  June 2005   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 inSection 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 inSection3.6.Perrig, et al.               Informational                     [Page 15]

RFC 4082                   TESLA Introduction                  June 2005   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 inSection 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:Perrig, et al.               Informational                     [Page 16]

RFC 4082                   TESLA Introduction                  June 2005      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 denialPerrig, et al.               Informational                     [Page 17]

RFC 4082                   TESLA Introduction                  June 2005        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.Perrig, et al.               Informational                     [Page 18]

RFC 4082                   TESLA Introduction                  June 20056.  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",RFC2246, 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.Perrig, et al.               Informational                     [Page 19]

RFC 4082                   TESLA Introduction                  June 2005   [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.Perrig, et al.               Informational                     [Page 20]

RFC 4082                   TESLA Introduction                  June 2005Authors' 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.comPerrig, et al.               Informational                     [Page 21]

RFC 4082                   TESLA Introduction                  June 2005Full Copyright Statement   Copyright (C) The Internet Society (2005).   This document is subject to the rights, licenses and restrictions   contained inBCP 78, and except as set forth therein, the authors   retain all their rights.   This document and the information contained herein are provided on an   "AS IS" basis and THE CONTRIBUTOR, THE ORGANIZATION HE/SHE REPRESENTS   OR IS SPONSORED BY (IF ANY), THE INTERNET SOCIETY AND THE INTERNET   ENGINEERING TASK FORCE DISCLAIM ALL WARRANTIES, EXPRESS OR IMPLIED,   INCLUDING BUT NOT LIMITED TO ANY WARRANTY THAT THE USE OF THE   INFORMATION HEREIN WILL NOT INFRINGE ANY RIGHTS OR ANY IMPLIED   WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE.Intellectual Property   The IETF takes no position regarding the validity or scope of any   Intellectual Property Rights or other rights that might be claimed to   pertain to the implementation or use of the technology described in   this document or the extent to which any license under such rights   might or might not be available; nor does it represent that it has   made any independent effort to identify any such rights.  Information   on the procedures with respect to rights in RFC documents can be   found inBCP 78 andBCP 79.   Copies of IPR disclosures made to the IETF Secretariat and any   assurances of licenses to be made available, or the result of an   attempt made to obtain a general license or permission for the use of   such proprietary rights by implementers or users of this   specification can be obtained from the IETF on-line IPR repository athttp://www.ietf.org/ipr.   The IETF invites any interested party to bring to its attention any   copyrights, patents or patent applications, or other proprietary   rights that may cover technology that may be required to implement   this standard.  Please address the information to the IETF at ietf-   ipr@ietf.org.Acknowledgement   Funding for the RFC Editor function is currently provided by the   Internet Society.Perrig, et al.               Informational                     [Page 22]