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Versions: 00 01 02 03 draft-ietf-ntp-mac

Internet Engineering Task Force                              A. Malhotra
Internet-Draft                                               S. Goldberg
Intended status: Standards Track                       Boston University
Expires: April 28, 2017                                 October 25, 2016


       Message Authentication Codes for the Network Time Protocol
                       draft-aanchal4-ntp-mac-02

Abstract

   The Network Time Protocol (NTP) RFC 5905 [RFC5905] uses a message
   authentication code (MAC) to cryptographically authenticate its UDP
   packets.  Currently, NTP packets are authenticated by appending a
   128-bit key to the NTP data, and hashing the result with MD5 to
   obtain a 128-bit tag.  However, as discussed in [BCK] and [RFC6151],
   this is not a secure MAC.  As such, this draft considers different
   secure MAC algorithms for use with NTP, evaluates their performance,
   and recommends the use of CMAC-AES [RFC4493].  We also suggest
   deprecating the use of MD5 as defined in [RFC5905] for authenticating
   NTP packets.

Status of This Memo

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

   Internet-Drafts are working documents of the Internet Engineering
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   This Internet-Draft will expire on April 28, 2017.

Copyright Notice

   Copyright (c) 2016 IETF Trust and the persons identified as the
   document authors.  All rights reserved.

   This document is subject to BCP 78 and the IETF Trust's Legal
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   (http://trustee.ietf.org/license-info) in effect on the date of
   publication of this document.  Please review these documents



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   carefully, as they describe your rights and restrictions with respect
   to this document.  Code Components extracted from this document must
   include Simplified BSD License text as described in Section 4.e of
   the Trust Legal Provisions and are provided without warranty as
   described in the Simplified BSD License.

Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   2
     1.1.  Requirements Language . . . . . . . . . . . . . . . . . .   2
   2.  MAC Algorithms  . . . . . . . . . . . . . . . . . . . . . . .   3
   3.  Requirements  . . . . . . . . . . . . . . . . . . . . . . . .   3
     3.1.  Performance Requirements  . . . . . . . . . . . . . . . .   3
     3.2.  Security Requirements . . . . . . . . . . . . . . . . . .   4
   4.  Performance Results . . . . . . . . . . . . . . . . . . . . .   4
   5.  Other Hardware Platforms  . . . . . . . . . . . . . . . . . .   5
   6.  Security Considerations . . . . . . . . . . . . . . . . . . .   6
     6.1.  Why is GMAC not suitable for NTP? . . . . . . . . . . . .   7
   7.  Use HMAC or CMAC instead  . . . . . . . . . . . . . . . . . .   9
   8.  GMAC-SIV - Another Potential MAC Candidate  . . . . . . . . .   9
   9.  Recommendations . . . . . . . . . . . . . . . . . . . . . . .  10
   10. Acknowledgements  . . . . . . . . . . . . . . . . . . . . . .  10
   11. References  . . . . . . . . . . . . . . . . . . . . . . . . .  10
     11.1.  Normative References . . . . . . . . . . . . . . . . . .  10
     11.2.  Informative References . . . . . . . . . . . . . . . . .  11
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .  12

1.  Introduction

   NTP uses a message authentication code (MAC) to authenticate its
   packets.  Currently, NTP packets are authenticated by appending a
   128-bit key to the NTP data, and hashing the result with MD5 to
   obtain a 128-bit tag.  However, as discussed in [BCK] and [RFC6151],
   this not a secure MAC.  As such, this draft considers different
   secure MAC algorithms for use with NTP, evaluates their performance,
   and recommends the use of CMAC-AES [RFC4493].  We also suggest
   deprecating the use of MD5, as defined in [RFC5905], for
   authenticating NTP packets.

1.1.  Requirements Language

   The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
   "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this
   document are to be interpreted as described in RFC 2119 [RFC2119].







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2.  MAC Algorithms

   We consider five diverse MAC algorithms, which encompass hash-based
   HMAC-MD5 and HMAC-SHA224 [RFC2104], block cipher-based CMAC-AES
   [RFC4493], and universal hashing-based Galois MAC (GMAC) [RFC4543]
   and Poly1305(ChaCha20) as in section 2.6 of [RFC7539].  For
   completeness we also benchmark the legacy MD5(key||message) from
   [RFC5905].

   +--------------------+----------------------+-----------------------+
   | Algorithm          |     Input Key Length |     Output Tag Length |
   |                    |              (Bytes) |               (Bytes) |
   +--------------------+----------------------+-----------------------+
   | legacy MD5         |                   16 |                    16 |
   | HMAC-MD5           |                   16 |                    16 |
   | HMAC-SHA224        |                   16 |                    16 |
   | CMAC(AES)          |                   16 |                    16 |
   | GMAC(AES)          |                   16 |                    16 |
   | Poly1305(ChaCha20) |                   32 |                    16 |
   +--------------------+----------------------+-----------------------+

   The choice of algorithms evaluated here is motivated, in part, by
   standardization and availablity of their open source implementations.
   All algorithms we consider, other than the plain MD5, are
   standardized.  Four out of five algorithms are at least available in
   the OpenSSL library, while Poly1305(ChaCha20) is implemented in
   LibreSSL (a fork of OpenSSL) and also in BoringSSL (Google's
   implementation of OpenSSL).

   The output tag length for HMAC-SHA224 is 28 bytes, but we truncate it
   to 16 bytes as in section 4 of [RFC7630] to fit into the NTP packet.
   As noted in section 6 of [RFC2104] it is safe to truncate the output
   of MACs as long as the truncated length is greater than 80-bits and
   not less than half the length of the hash output.

3.  Requirements

3.1.  Performance Requirements

   In order to accurately compute the time, NTP ideally requires MAC
   algorithms to have a constant computational latency.  However, this
   is generally not possible, since latency depends on the CPU load,
   temperature, and other uncontrollable factors.  Instead, a MAC
   algorithm that requires fewer clock cycles for computation is
   prefered over one that requires more clock cycles, as this directly
   translates to a reduction in jitter (i.e., the variance of the
   latency for computing the MAC).




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   Throughput is another important consideration.  NTP servers may have
   to deal with thousands of client requests per second.  A study [NIST]
   on the usage analysis of NIST's NTP stratum 1 servers shows that
   these servers cater to 28,000 requests/second on an average, per
   server.

   Most of the Internet is served by stratum 2 and stratum 3 servers,
   some of which are a part of voluntary NTP pool.  These machines may
   be running old hardware.  Generally, while benchmarking MAC
   algorithms, several optimization techniques on custom specialized
   hardware are used to get the best results.  However, for the reason
   stated above we choose to benchmark performance on a range of
   software and hardware platforms with and without optimizations.

3.2.  Security Requirements

   There are several more constraints specific to NTP that need to be
   taken into account.

   1.  NTP servers are stateless, i.e. they do not keep per client
       state.

   2.  Per [RFC5905], NTP uses a pre-shared symmetric key.  This makes
       key management difficult because there is no in-band mechanism
       for distributing keys.  As such, to simplify key management, some
       deployments use the same pre-shared key at many servers
       (typically at the same stratum).  In other words, the same key is
       used for several client/server associations.

   3.  [RFC5905] also has no in-band mechanism to refresh keys.

4.  Performance Results

   The NTP header is 48 bytes long.  We therefore consider the latency
   and throughput for several secure MAC algorithms when computed over
   48-byte messages.

   We customize the in-built speed utility of OpenSSL-1.0.2g (03 May
   2016) version to compute the latency and throughput for each MAC as
   shown in the tables below.  OpenSSL, however, does not implement
   stream-cipher ChaCha20-based Poly1305 MAC algorithm.  To speed test
   this MAC, we use LibreSSL 2.3.1, a fork of OpenSSL implementation.
   OpenSSL and LibreSSL are the most widely used cryptographic libraries
   and are used by the current NTP implementations.

   Since the introduction of New Instruction (NI) set for hardware
   support in Intel chips, certain MACs like CMAC and GMAC have
   performance advantage on such machines.  Based on this, we perform



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   two different benchmarks: one with AES-NI enabled and the other with
   it disabled.  Benchmarks were taken on an x86_64, Intel(R) Xeon(R)
   CPU E5-2676 v3 @ 2.40GHz with one core CPU.

   This table shows throughput in terms of number of 48-byte NTP payload
   processed per second.

          +--------------------+-------------+-----------------+
          | Algorithm          | with AES-NI |  without AES-NI |
          +--------------------+-------------+-----------------+
          | legacy MD5         |       3118K |           3165K |
          | HMAC-MD5           |       2742K |           2749K |
          | HMAC-SHA224        |       1265K |           1267K |
          | CMAC(AES)          |       7567K |           4388K |
          | GMAC(AES)          |      16612K |           4627K |
          | Poly1305(ChaCha20) |       2598K |           2398K |
          +--------------------+-------------+-----------------+

   This table shows latency in terms of number of CPU cycles per byte
   (cpb) when processing a 48-byte NTP payload.

          +--------------------+-------------+-----------------+
          | Algorithm          | with AES-NI |  without AES-NI |
          +--------------------+-------------+-----------------+
          | legacy MD5         |        16.0 |            15.7 |
          | HMAC-MD5           |        18.2 |            18.1 |
          | HMAC-SHA224        |        39.4 |            39.0 |
          | CMAC(AES)          |         6.6 |            11.3 |
          | GMAC(AES)          |         3.0 |            10.8 |
          | Poly1305(ChaCha20) |        14.4 |            15.0 |
          +--------------------+-------------+-----------------+

5.  Other Hardware Platforms

   We also perform tests on the following ARM CPU cores and
   PowerPC(PPC)core with OpenSSL 1.0.2h released May 2016.  These cores
   are most commonly used in consumer products and Industrial Control
   Systems (ICS) components.  We select these cores to cover the ARM
   architecture versions 5/6 to 8.  The results vary depending on the
   availability of CPU specific optimizations.  For example the used
   Cortex-A9 and Cortex-A53 CPU have a NEON unit and OpenSSL can utilize
   it to accelerate AES.

   1.  Freescale/Apple PPC74xx 1.5GHz

   2.  NXP i.MX6 1GHz (dual core) ARM Cortex-A9

   3.  Broadcom BCM2837 1.2GHz (quad core) ARM Cortex-A53



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   4.  Marvell 88F6281 1.2GHz 88FR131 (ARMv5te compliant)

   The table below shows throughput in terms of number of 48-byte NTP
   payload processed per second.

   +--------------------+---------+------------+-------------+---------+
   | Algorithm          | PPC74xx |        ARM |  ARM Cortex | Marvell |
   |                    |         |  Cortex-A9 |        A-53 |         |
   +--------------------+---------+------------+-------------+---------+
   | legacy MD5         |    600K |       543K |        748K |    383k |
   | HMAC-MD5           |    463K |       415K |        864K |    438k |
   | HMAC-SHA224        |    276K |       245K |        357K |    150k |
   | CMAC(AES)          |    576K |       412K |        614K |    246k |
   | GMAC(AES)          |    681K |      1362K |       2193K |    453k |
   | Poly1305(ChaCha20) |    335K |       379K |        580K |    273k |
   +--------------------+---------+------------+-------------+---------+

   The table below shows latency in terms of number of CPU cycles per
   byte (cpb) when processing a 48-byte NTP payload.

   +--------------------+---------+------------+-------------+---------+
   | Algorithm          | PPC74xx |        ARM |  ARM Cortex | Marvell |
   |                    |         |  Cortex-A9 |        A-53 |         |
   +--------------------+---------+------------+-------------+---------+
   | legacy MD5         |    52.1 |       38.4 |        33.4 |    65.3 |
   | HMAC-MD5           |    67.4 |       50.3 |        29.0 |    57.1 |
   | HMAC-SHA224        |   113.3 |       85.2 |        70.1 |   166.5 |
   | CMAC(AES)          |    54.2 |       50.5 |        40.7 |   101.2 |
   | GMAC(AES)          |    50.0 |       15.3 |        11.4 |    55.1 |
   | Poly1305(ChaCha20) |    93.1 |       55.0 |        43.1 |    91.7 |
   +--------------------+---------+------------+-------------+---------+

6.  Security Considerations

   The MD5 (key||message) "message authentication code" specified in
   [RFC5905] is vulnerable to length extension attacks, and uses the
   insecure MD5 hash function, and therefore MUST be deprecated.

   Therefore, we consider hash-based MACs (HMAC-MD5, HMAC-SHA224), and
   cipher-based MACs (CMAC-AES, Poly1305 (ChaCha20)).  The upper bound
   on the security level provided by any MAC against brute-force attacks
   is min (key-length, tag-length).  The security of these MACs can be
   worse but not better than this bound.  All MAC algorithms we consider
   have comparable key-lengths and output tag-lengths.  So the advantage
   of an adversary that wishes to forge a MAC is lower-bounded by
   1/2^{128}.





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   Assume that an adversary can obtain a valid MAC for q distinct
   messages.  Then the table below describes the advantage of an
   adversary that wishes to forge a MAC in terms of number of queries
   (q) it launches.

       +--------------------------+-------------------------------+
       | Algorithm                |                     Advantage |
       +--------------------------+-------------------------------+
       | HMAC-MD5 [MB]            |                   q^2/2^{128} |
       | HMAC-SHA224 [BCK]        |                   q^2/2^{224} |
       | CMAC(AES)[IK]            |                   q^2/2^{128} |
       | GMAC(AES) [IOM]          |                   q^2/2^{128} |
       | Poly1305(ChaCha20) [DJB] | {e^{{q^2}/{2^{129}}}}/2^{103} |
       +--------------------------+-------------------------------+

   Poly1305 can easily handle up to q=2^{64} but security degrades
   pretty rapidly after that.

   However, the bounds in the table above are somewhat optimistic, for
   the following reasons.

   1.  GMAC has an initialization vector (IV) that [RFC4106] allows to
       be 1 <= len(IV) <= 2^{64}-1.  Per [RFC4106], implementations are
       optimized to handle a 12-octet IV.  With a 12-octet IV, the total
       number of message invocations is bound to 2^{48}. Moreover, if
       the IV is reused even once (for the same secret authentication
       key and different input messages), then [Joux]  shows that the
       secret authetication key can easily be recovered by the
       adversary.  Notice that this attack is even stronger than a
       message forgery because it recovers the authentication key.  This
       is known as nonce-reuse vulnerability.

   2.  The other three algorithms evaluated here do not suffer from
       nonce reuse vulnerabilities where an adversary can recover the
       authentication key if the nonce is reused just once.

   3.  The table above suggests that for CMAC, the total number of
       invocations of the MAC is limited to 2^{64}. However, [NIST-CMAC]
       recommends, to be on the safe side, that the total number of
       invocations of the block cipher algorithm during the lifetime of
       the key is limited to 2^{48}.

6.1.  Why is GMAC not suitable for NTP?

   [Joux] showed that for GMAC-AES, if the IV is repeated just once,
   then the authentication key can be fully recovered.  None of the
   other algorithms evaluated here have this vulnerability.  Thus, for




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   GMAC-AES to be secure, we need to make sure that IV is never
   repeated.

   [NIST-GMAC] recommends constructing the 12-byte IV used in GMAC by
   concatenating a fixed 4-byte salt value concatenate with a variable
   8-byte nonce i.e.  IV = ( salt|| nonce).  Here salt is an implicit
   value established when a session is established, remains fixed for
   all exchanges in a session (i.e. for all invocations that use the
   same authenication key) between the sender and the receiver.
   Meanwhile, the nonce is freshly generated for each authenticated
   message.

   Because NTP servers do not keep per-client state, the nonce can not
   be a sequential value.  Instead, this nonce must be randomly
   generated 8-bytes value chosen freshly for each authenticated
   message.  According to birthday bound, the nonce value will be
   repeated, with high probability, after 2^{32} messages sent in a
   given association.  This leads to a repeated IV value and to [Joux]'s
   attack.  Thus, to prevent repeated nonces, we would need to require
   the authentication key to be refreshed for the association after
   2^{32} messages.

   On one hand, 2^{32} is a lot of queries for an honest client,
   assuming that the client queries once per minute (which is NTP's
   minimum polling interval [RFC5905]).  On the other hand, a man-in-
   the-middle (MiTM) can quickly and easily exhaust this number by
   replaying old authenticated queries to the NTP server.

   The main problem here is that NTP lacks an explict in-band key
   refresh mechanism that can be invoked automatically (without operator
   intervention).  And a key refresh mechanism is unlikely to be adopted
   as it would allow denial-of-service (DoS) attacks.  The state less
   nature makes NTP resilient against DoS attacks.

   Even if there was a method by which key-refresh could be performed,
   there is an additional problem.  An NTP server does not keep per-
   client state.  Therefore, it cannot keep track of the number of
   messages it sent in a given association.  One idea is to have the
   client keep this state, and then send an authenicated request for a
   key refresh.  However, a man-in-the-middle could replay old
   authenticated queries to the NTP server, and then intercept the
   server's' response before they reach the legitimate client.  In this
   case, the client would never know when to ask for a key refresh.

   Alternatively, the server could maintain a global counter (since it
   can't afford to keep per client counter).  And after 2^{32} messages,
   it can refresh the keys with all its clients.  However, a man-in-the-




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   middle could exhaust this number quickly and the server will have to
   refresh keys with all the clients very frequently.

   Thus, we conclude that a scheme that requires refreshing the key
   after 2^{32} client queries is not a good idea at all.

   Even in the absence of a man-in-the-middle, there is also the problem
   of multiple servers using the same authentication key.  The salt
   could be used to distinguish IVs across different client/server
   associations that use the same authenication key.  However, this
   brings us back to the original key management problem.  One way to
   deal with this is to choose the 4-byte salt at random.  However, this
   gives rise to a birthday bound of 2^{16} = 65,000 unique IVs.  If we
   consider 20,000 stratum 3 clients synchronizing to three stratum 2
   servers each, all of which are in the same organization and share the
   same symmetric key, we get very close to the birthday bound.  This is
   another disadvantage of using GMAC with NTP.

7.  Use HMAC or CMAC instead

   1.  CMAC seems to be the next best choice.  Leaving out GMAC, it has
       the best performance with and without hardware support.  It is
       not vulnerable to nonce misuse issues.

   2.  HMACs are inherently slower because of their structure and also
       in some cases because of lack of built-in hardware support.

   3.  On the other hand, it is much easier to get the right
       implementation for HMAC compared to CMAC.

8.  GMAC-SIV - Another Potential MAC Candidate

   GMAC-SIV is another possible MAC candidate, which claims to be nonce-
   misuse resistant [SIV].  There is an IETF Internet draft for the
   standardization of GCM-SIV AEAD mode.

   In terms of security, GCM-SIV (AEAD) achieves usual notion of nonce-
   based security of an authenticated encryption mode as long as a
   unique nonce is used per authentication key per message.  If,
   however, the nonce is reused authenticity is still retained (unlike
   in GMAC).

   But there is not many implementations for GCM-SIV available except
   for the one from the authors.  We customized this code for
   authentication only mode GMAC-SIV and run it on an x86_64, Intel(R)
   Xeon(R) CPU E5-2676 v3 @ 2.40GHz with one core CPU with AES-NI
   enabled.  GMAC-SIV takes ~5.9 CPU cycles/byte to generate a tag of
   length 16 bytes on a 48-byte NTP payload.  The performance efficiency



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   is far less than GMAC, but is slightly better than CMAC.  CMAC, on
   the other hand is a standardized mode of operation and has several
   open source implementations.

9.  Recommendations

   From the tables we clearly see that GMAC(AES) has the best latency
   and throughput performance in both hardware and software
   implementations.  It is freely available, and there is a flexibilty
   of changing the underlying block-cipher.  However there are several
   security problems surrounding the use of this mode, as highlighted
   above, so it is not recommended.

   CMAC, on the other hand, is the next best choice in terms of
   performance and security.  So we recommend the use of CMAC (AES).

10.  Acknowledgements

   The authors wish to acknowledge useful discussions with Leen
   Alshenibr, Daniel Franke, Ethan Heilman, Kenny Paterson, Leonid
   Reyzin, Harlan Stenn, Mayank Varia.

11.  References

11.1.  Normative References

   [RFC2104]  Krawczyk, H., Bellare, M., and R. Canetti, "HMAC: Keyed-
              Hashing for Message Authentication", RFC 2104,
              DOI 10.17487/RFC2104, February 1997,
              <http://www.rfc-editor.org/info/rfc2104>.

   [RFC2119]  Bradner, S., "Key words for use in RFCs to Indicate
              Requirement Levels", BCP 14, RFC 2119,
              DOI 10.17487/RFC2119, March 1997,
              <http://www.rfc-editor.org/info/rfc2119>.

   [RFC4106]  Viega, J. and D. McGrew, "The Use of Galois/Counter Mode
              (GCM) in IPsec Encapsulating Security Payload (ESP)",
              RFC 4106, DOI 10.17487/RFC4106, June 2005,
              <http://www.rfc-editor.org/info/rfc4106>.

   [RFC4493]  Song, JH., Poovendran, R., Lee, J., and T. Iwata, "The
              AES-CMAC Algorithm", RFC 4493, DOI 10.17487/RFC4493, June
              2006, <http://www.rfc-editor.org/info/rfc4493>.







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   [RFC4543]  McGrew, D. and J. Viega, "The Use of Galois Message
              Authentication Code (GMAC) in IPsec ESP and AH", RFC 4543,
              DOI 10.17487/RFC4543, May 2006,
              <http://www.rfc-editor.org/info/rfc4543>.

   [RFC5905]  Mills, D., Martin, J., Ed., Burbank, J., and W. Kasch,
              "Network Time Protocol Version 4: Protocol and Algorithms
              Specification", RFC 5905, DOI 10.17487/RFC5905, June 2010,
              <http://www.rfc-editor.org/info/rfc5905>.

   [RFC6151]  Turner, S. and L. Chen, "Updated Security Considerations
              for the MD5 Message-Digest and the HMAC-MD5 Algorithms",
              RFC 6151, DOI 10.17487/RFC6151, March 2011,
              <http://www.rfc-editor.org/info/rfc6151>.

   [RFC7539]  Nir, Y. and A. Langley, "ChaCha20 and Poly1305 for IETF
              Protocols", RFC 7539, DOI 10.17487/RFC7539, May 2015,
              <http://www.rfc-editor.org/info/rfc7539>.

   [RFC7630]  Merkle, J., Ed. and M. Lochter, "HMAC-SHA-2 Authentication
              Protocols in the User-based Security Model (USM) for
              SNMPv3", RFC 7630, DOI 10.17487/RFC7630, October 2015,
              <http://www.rfc-editor.org/info/rfc7630>.

11.2.  Informative References

   [BCK]      Bellare, M., Canetti, R., and H. Krawczyk, "Keyed Hash
              Functions and Message Authentication", in Proceedings of
              Crypto'96, 1996.

   [DJB]      Bernstein, D., "The Poly1305-AES message-authentication
              code", in Fast Software Encryption, 2005.

   [GK]       Gueron, S. and V. Krasnov, "The fragility of AES-GCM
              authentication algorithm", in Proceedings of 11th
              International Conference on Information Technology: New
              Generations 2014, 2014.

   [IK]       Iwata, T. and K. Kurosawa, "Keyed Hash Functions and
              Message Authentication", in Progress in Cryptology-
              INDOCRYPT 2003, 2003.

   [IOM]      Iwata, T., Ohashi, K., and K. Minematsu, "Breaking and
              Repairing GCM Security Proofs", in Proceedings of CRYPTO
              2012, 2012.






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   [Joux]     Joux, A., "Authentication Failures in NIST version of
              GCM",
              <http://csrc.nist.gov/groups/ST/toolkit/BCM/documents/
              comments/800-38_Series-Drafts/GCM/Joux_comments.pdf>.

   [MB]       Bellare, M., "New Proofs for NMAC and HMAC:Security
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   [NIST]     Sherman, J. and J. Levine, "Usage Analysis of the NIST
              Internet Time Service", in Journal of Research of the
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   [NIST-CMAC]
              Dworkin, M., "Recommendation for Block Cipher Modes of
              Operation: The CMAC Mode for Authentication", in NIST
              Special Publication 800-38B, 2005.

   [NIST-GMAC]
              Dworkin, M., "Recommendation for Block Cipher Modes of
              Operation: Galois/Counter Mode (GCM) and GMAC", in NIST
              Special Publication 800-38D, 2007.

   [SIV]      Gueron, S., Langley, A., and Y. Lindell,
              "https://tools.ietf.org/html/draft-gueron-gcmsiv-00",
              in Work in Progress, 2016.

Authors' Addresses

   Aanchal Malhotra
   Boston University
   111 Cummington St
   Boston, MA  02215
   US

   Email: aanchal4@bu.edu


   Sharon Goldberg
   Boston University
   111 Cummington St
   Boston, MA  02215
   US

   Email: goldbe@cs.bu.edu






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