Post-quantum public key algorithms for the Secure Shell (SSH) protocol
draft-kampanakis-curdle-pq-ssh-00

Document Type Active Internet-Draft (individual)
Authors Panos Kampanakis  , Douglas Steblia  , Markus Friedl  , Torben Hansen  , Dimitrios Sikeridis 
Last updated 2020-10-21
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CURDLE                                                     P. Kampanakis
Internet-Draft                                             Cisco Systems
Intended status: Experimental                                 D. Stebila
Expires: 24 April 2021                            University of Waterloo
                                                               M. Friedl
                                                                 OpenSSH
                                                               T. Hansen
                                                                     AWS
                                                            D. Sikeridis
                                                University of New Mexico
                                                         21 October 2020

 Post-quantum public key algorithms for the Secure Shell (SSH) protocol
                   draft-kampanakis-curdle-pq-ssh-00

Abstract

   This document defines hybrid key exchange methods based on classical
   ECDH key exchange and post-quantum key encapsulation schemes.  These
   methods are defined for use in the SSH Transport Layer Protocol.  It
   also defines post-quantum public key authentication methods based on
   post-quantum signature schemes.  These methods are defined for use in
   the SSH Authentication Protocol.

Note

   EDNOTE: The goal of this draft is to start the standardization of PQ
   algorithms in SSH early to mitigate the potential record-and-harvest
   later with a quantum computer attacks.  This draft is not expected to
   be finalized before the NIST PQ Project has standardized PQ
   algorithms.  After NIST has standardized then this document will
   replace TBD1, TBD3 with the appropriate algorithms and parameters
   before proceeding to ratification.

   EDNOTE: Discussion of this work is encouraged to happen on the IETF
   WG Mailing List or in the GitHub repository which contains the draft:
   https://github.com/csosto-pk/pq-ssh/issues .

   *Change Log* [EDNOTE: Remove befor publicaton].

   draft-kampanakis-curdle-pq-ssh-00
      *  Initial draft

Status of This Memo

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

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Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   3
     1.1.  Requirements Language . . . . . . . . . . . . . . . . . .   4
   2.  Hybrid Key Exchange . . . . . . . . . . . . . . . . . . . . .   5
     2.1.  Hybrid Key Exchange Method Abstraction  . . . . . . . . .   5
     2.2.  Key Derivation  . . . . . . . . . . . . . . . . . . . . .   6
     2.3.  HASH  . . . . . . . . . . . . . . . . . . . . . . . . . .   6
     2.4.  Hybrid Key Exchange Method Names  . . . . . . . . . . . .   6
       2.4.1.  ecdh-nistp256-TBD1-sha256 . . . . . . . . . . . . . .   7
       2.4.2.  x25519-TBD1-sha256  . . . . . . . . . . . . . . . . .   7
   3.  Key Authentication  . . . . . . . . . . . . . . . . . . . . .   8
     3.1.  Public Key Format . . . . . . . . . . . . . . . . . . . .   8
     3.2.  Signature Format  . . . . . . . . . . . . . . . . . . . .   8
     3.3.  Signing and Verification  . . . . . . . . . . . . . . . .   8
   4.  Message Size  . . . . . . . . . . . . . . . . . . . . . . . .   9
   5.  Acknowledgements  . . . . . . . . . . . . . . . . . . . . . .   9
   6.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .   9
   7.  Security Considerations . . . . . . . . . . . . . . . . . . .   9
   8.  References  . . . . . . . . . . . . . . . . . . . . . . . . .  10
     8.1.  Normative References  . . . . . . . . . . . . . . . . . .  10
     8.2.  Informative References  . . . . . . . . . . . . . . . . .  10

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   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .  12

1.  Introduction

   Secure Shell (SSH) [RFC4251] performs key establishment using key
   exchange methods based exclusively on (Elliptic Curve) Diffie-Hellman
   style schemes.  SSH [RFC4252], [RFC8332], [RFC5656], [RFC8709] also
   defines public key authentication methods based on RSA or ECDSA/EdDSA
   signature schemes.  The cryptographic security of these key exchange
   and signature schemes relies on certain instances of the discrete
   logarithm and integer factorization problems being computationally
   infeasable to solve for adversaries.

   However, when sufficiently large quantum computers become available
   these instances would no longer be computationally infeasable
   rendering the current key exchange and authentication methods in SSH
   insecure [I-D.hoffman-c2pq].  While large quantum computers are not
   available today an adversary can record the encrypted communication
   sent between the client and server in an SSH session and then later
   decrypt the communication when sufficiently large quantum computers
   become available.  This kind of attack is known as a "record-and-
   harvest" attack.  Record-and-harvest attacks do not apply
   retroactively to authentication but a quantum computer could threaten
   SSH authentication by impersonating as a legitimate client or server.

   This document proposes to address the problem by extending the SSH
   Transport Layer Protocol [RFC4253] with hybrid key exchange methods
   and the SSH Authentication Protocol [RFC4252] with public key methods
   based on post-quantum signature schemes.  A hybrid key exchange
   method maintains the same level of security provided by current key
   exchange methods, but also adds quantum resistance.  The security
   provided by the individual key exchange scheme in a hybrid key
   exchange method is independent.  This means that the hybrid key
   exchange method will always be at least as secure as the most secure
   key exchange scheme executed as part of the hybrid key exchange
   method.

   In the context of the NIST Post-Quantum Cryptography Standardization
   Project [NIST_PQ], key exchange algorithms are formulated as key
   encapsulation mechanisms (KEMs), which consist of three algorithms:

   *  'KeyGen() -> (pk, sk)': A probabilistic key generation algorithm,
      which generates a public key 'pk' and a secret key 'sk'.

   *  'Encaps(pk) -> (ct, ss)': A probabilistic encapsulation algorithm,
      which takes as input a public key 'pk' and outputs a ciphertext
      'ct' and shared secret 'ss'.

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   *  'Decaps(sk, ct) -> ss': A decapsulation algorithm, which takes as
      input a secret key 'sk' and ciphertext 'ct' and outputs a shared
      secret 'ss', or in some cases a distinguished error value.

   The main security property for KEMs is indistinguishability under
   adaptive chosen ciphertext attack (IND-CCA2), which means that shared
   secret values should be indistinguishable from random strings even
   given the ability to have arbitrary ciphertexts decapsulated.  IND-
   CCA2 corresponds to security against an active attacker, and the
   public key / secret key pair can be treated as a long-term key or
   reused.  A weaker security notion is indistinguishability under
   chosen plaintext attack (IND-CPA), which means that the shared secret
   values should be indistinguishable from random strings given a copy
   of the public key.  IND-CPA roughly corresponds to security against a
   passive attacker, and sometimes corresponds to one-time key exchange.

   The corresponding post-quantum signature algorithms defined in the
   NIST Post-Quantum Cryptography Standardization Project [NIST_PQ] are

   *  'KeyGen() -> (pk, sk)': A probabilistic key generation algorithm,
      which generates a public key 'pk' and a secret key 'sk'.

   *  'Sign(m, sk) -> sig': A deterministic signing algorithm, which
      takes as input a message 'm' and a private key 'sk' and outputs a
      signature 'sig'.

   *  'Verify(m, pk, sigma) -> pass/fail': A verification algorithm,
      which takes as input a message 'm', a public key 'pk' and a
      signature 'sig' and outputs a verification pass or failure of the
      signature on the message.

   The post-quantum KEMs used for hybrid key exchange in the document
   are TBD1.  The post-quantum signature algorithm used for key based
   authentication is TBD3.  [EDNOTE: Placeholder.  Algorithms will be
   identified after NIST Round 3 concludes.]  The post-quantum
   algorithms are defined in NIST Post-quantum Project
   [NIST_PQ].[EDNOTE: Update link.  Algorithms can change based on
   NIST's Round 3 standardization].

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.  Hybrid Key Exchange

2.1.  Hybrid Key Exchange Method Abstraction

   This section defines the abstract structure of a hybrid key exchange
   method.  The structure must be instantiated with two key exchange
   schemes.  The byte, string and mpint are to be interpreted in this
   document as described in [RFC4251].

   The client sends

          byte SSH_MSG_HBR_INIT
          string C_INIT

   where C_INIT would be the concatenation of C_PQ and C_CL.

   The server sends

          byte SSH_MSG_HBR_REPLY
          string S_REPLY

   where S_REPLY would be the concatenation of S_PQ and S_CL.

   [EDNOTE: Initially we were using S_CL, S_PQ, C_CL, C_PQ which were
   encoding the server and client client and server classical and post-
   quantum public key/ciphertext as its own string.  We since switched
   to an encoding method which concatenates them together as a single
   string in the C_INIT, S_REPLY message.  This method concatenates the
   raw values rather than the length of each value plus the value.  The
   total length of the concatenation is still known, but the relative
   lengths of the individual values that were concatenated is no longer
   part of the representation.  If that is the WG consensus we need to
   put a note of this in the Appendix for historical reference and
   expand on the concatenated string here in this section.]

   C_PQ represents the 'pk' output of the corresponding KEMs' 'KeyGen'
   at the client.  S_PQ represents the ciphertext 'ct' output of the
   corresponding KEMs' 'Encaps' algorithm generated by the server to the
   client's public key.  The client decapsulates the ciphertext by using
   its private key which leads to K_PQ, a post-quantum shared secret for
   SSH.

   C_CL and S_CL represent the ephemeral public key of the client and
   server respectively used for the classical (EC)DH key exchange which
   leads to K_CL, a classical shared secret for SSH.

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2.2.  Key Derivation

   The shared secrets K_CL and K_PQ are the output from the two key
   exchange schemes X and Y, respectively, that instantiates an abstract
   hybrid key exchange method Section 2.1.  The SSH shared secret K is
   derived as the hash algorithm specified in the named hybrid key
   exchange method name over the concatenation of K_PQ and K_CL:

           K = HASH(K_PQ, K_CL)

   The resulting bytes are fed as to the key exchange method's hash
   function to generate encryption keys.

   *FIPS-compliance of shared secret concatenation.* [NIST-SP-800-56C]
   or [NIST-SP-800-135] give NIST recommendations for key derivation
   methods in key exchange protocols.  Some hybrid combinations may
   combine the shared secret from a NIST-approved algorithm (e.g., ECDH
   using the nistp256/secp256r1 curve) with a shared secret from a non-
   approved algorithm (e.g., post-quantum).  [NIST-SP-800-56C] lists
   simple concatenation as an approved method for generation of a hybrid
   shared secret in which one of the constituent shared secret is from
   an approved method.

2.3.  HASH

   The derivation of encryption keys MUST be done according to
   Section 7.2 in [RFC4253] with a modification on the exchange hash H.
   The hybrid key exchange hash H is the result of computing the HASH,
   where HASH is the hash algorithm specified in the named hybrid key
   exchange method name, over the concatenation of the following

         string V_C, client identification string (CR and LF excluded)
         string V_S, server identification string (CR and LF excluded)
         string I_C, payload of the client's SSH_MSG_KEXINIT
         string I_S, payload of the server's SSH_MSG_KEXINIT
         string C_INIT, client message octet string
         string S_REPLY, server message octet string
         string K, SSH shared secret

   The HASH functions used for the definitions in this specification are
   SHA-256 [nist-sha2] [RFC4634][EDNOTE: Update here if necessary].

2.4.  Hybrid Key Exchange Method Names

   The hybrid key exchange method names defined in this document are

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         ecdh-nistp256-TBD1-sha256
         x25519-TBD1-sha256
         sntrup4591761x25519-sha512@tinyssh.org (currently implemented)

   [EDNOTE: Placeholder.  Algorithms will be identified after NIST Round
   3 concludes.]

2.4.1.  ecdh-nistp256-TBD1-sha256

   ecdh-nistp256-TBD1-sha256 defines that the classical C_CL or S_CL
   from the client or server NIST P-256 curve public key as defined in
   [nist-sp800-186].  Private and public keys are generated as described
   therein.  Public keys are defined as strings of 32 bytes for NIST
   P-256.  The K_CL shared secret is generated from the exchanged C_CL
   and S_CL public keys as defined in [RFC5656] (key agreement method
   ecdh-sha2-nistp256) with SHA-256 [nist-sha2] [RFC4634] .

   The post-quantum C_PQ or S_PQ string from the client and server are
   TBD1.  The K_PQ shared secret is decapsulated from the ciphertext
   S_PQ using the client private key [EDNOTE: Placeholder.  Update based
   on the algorithm identified after NIST Round 3 concludes.]

2.4.2.  x25519-TBD1-sha256

   x25519-TBD1-sha256 defines that the classical C_CL or S_CL from the
   client or server is Curve25519 public key as defined in [RFC7748].
   Private and public keys are generated as described therein.  Public
   keys are defined as strings of 32 bytes for Curve25519.  The K_CL
   shared secret is generated from the exchanged C_CL and S_CL public
   keys as defined in [RFC8731] (key agreement method curve25519-sha256)
   with SHA-256 [nist-sha2] [RFC4634] .

   The post-quantum C_PQ or S_PQ string from the client and server are
   TBD1.  The K_PQ shared secret is decapsulated from the ciphertext
   S_PQ using the client private key as defined in [EDNOTE: Placeholder.
   Update based on the algorithm identified after NIST Round 3
   concludes.]

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3.  Key Authentication

   [EDNOTE: Discuss if hybrid auth keys which combine classical and PQ
   signatures are necessary.  Since authentication cannot be broken
   retroactively, even if the PQ signature algorithms got broken, we
   could switch to a classical algorithm to at least keep the classical
   security.  On the other hand, that would take time to deploy while
   these entities would be vulnerabile to impersonation attacks.  Hybrid
   signatures add some overhead, but could provide the peace of mind of
   remaining secure with the classical algorithm without scrambling to
   deploy a change even if the PQ algorithms got broken. ]

3.1.  Public Key Format

         string    "ssh-TBD3"
         string    key

   Here, 'key' is the x-octet public key described in the TBD3
   specification.

   [EDNOTE: Placeholder.  Algorithms will be identified after NIST Round
   3 concludes.]

3.2.  Signature Format

          string  "ssh-TBD3"
          string  signature

   Here, 'signature' is the x-octet signature produced in accordance
   with the TBD3 specification.

   [EDNOTE: Placeholder.  Algorithms will be identified after NIST Round
   3 concludes.]

3.3.  Signing and Verification

   Signatures are generated according to the procedure in TBD3
   specification

   Signatures are verified according to the procedure in TBD3
   specification

   [EDNOTE: Placeholder.  Algorithms will be identified after NIST Round
   3 concludes.]

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4.  Message Size

   An implementation adhering to [RFC4253] must be able to support
   packets with an uncompressed payload length of 32768 bytes or less
   and a total packet size of 35000 bytes or less (including
   'packet_length', 'padding_length', 'payload', 'random padding', and
   'mac').  These numbers represent what must be 'minimally supported'
   by implementations.  This can present a problem when using post-
   quantum key exchange schemes because some post-quantum schemes can
   produce much larger messages than what is normally produced by
   existing key exchange methods defined for SSH.  This document does
   not define any named domain parameters (see Section 7) that cause any
   hybrid key exchange method related packets to exceed the minimally
   supported packet length.  This document does not define behaviour in
   cases where a hybrid key exchange message cause a packet to exceed
   the minimally supported packet length.

5.  Acknowledgements

6.  IANA Considerations

   This memo includes requests of IANA for SSH_MSG_HBR_INIT,
   SSH_MSG_HBR_REPLY, ecdh-nistp256-TBD1-sha256, x25519-TBD1-sha256, and
   ssh-TBD3.

7.  Security Considerations

   [EDNOTE: The security considerations given in [RFC5656] therefore
   also applies to the ECDH key exchange scheme defined in this
   document.  Similarly for the X25519 document.  PQ Algorithms are
   newer and standardized by NIST.  And more.  Should include something
   about the combination method for the KEM shared secrets. ]

   [EDNOTE: Discussion on whether an IND-CCA KEM is required or whether
   IND-CPA suffices.]  Any KEM used in the manner described in this
   document MUST explicitly be designed to be secure in the event that
   the public key is re-used, such as achieving IND-CCA2 security or
   having a transform like the Fujisaki-Okamoto transform [FO][HHK]
   applied.  While it is recommended that implementations avoid reuse of
   KEM public keys, implementations that do reuse KEM public keys MUST
   ensure that the number of reuses of a KEM public key abides by any
   bounds in the specification of the KEM or subsequent security
   analyses.  Implementations MUST NOT reuse randomness in the
   generation of KEM ciphertexts.

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   *Public keys, ciphertexts, and secrets should be constant length.*
   This document assumes that the length of each public key, ciphertext,
   and shared secret is fixed once the algorithm is fixed.  This is the
   case for all Round 3 finalists and alternate candidates.

   Note that variable-length secrets are, generally speaking, dangerous.
   In particular, when using key material of variable length and
   processing it using hash functions, a timing side channel may arise.
   In broad terms, when the secret is longer, the hash function may need
   to process more blocks internally.  In some unfortunate
   circumstances, this has led to timing attacks, e.g. the Lucky
   Thirteen [LUCKY13] and Raccoon [RACCOON] attacks.

   Therefore, this specification MUST only be used with algorithms which
   have fixed-length shared secrets (after the variant has been fixed by
   the algorithm identifier in the Method Names negotiation in
   Section 2.4).

8.  References

8.1.  Normative References

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

   [RFC4251]  Ylonen, T. and C. Lonvick, Ed., "The Secure Shell (SSH)
              Protocol Architecture", RFC 4251, DOI 10.17487/RFC4251,
              January 2006, <https://www.rfc-editor.org/info/rfc4251>.

   [RFC4252]  Ylonen, T. and C. Lonvick, Ed., "The Secure Shell (SSH)
              Authentication Protocol", RFC 4252, DOI 10.17487/RFC4252,
              January 2006, <https://www.rfc-editor.org/info/rfc4252>.

   [RFC4253]  Ylonen, T. and C. Lonvick, Ed., "The Secure Shell (SSH)
              Transport Layer Protocol", RFC 4253, DOI 10.17487/RFC4253,
              January 2006, <https://www.rfc-editor.org/info/rfc4253>.

8.2.  Informative References

   [FO]       Fujisaki, E. and T. Okamoto, "Secure Integration of
              Asymmetric and Symmetric Encryption Schemes",
              DOI 10.1007/s00145-011-9114-1, Journal of Cryptology Vol.
              26, pp. 80-101, December 2011,
              <https://doi.org/10.1007/s00145-011-9114-1>.

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   [HHK]      Hofheinz, D., Hövelmanns, K., and E. Kiltz, "A Modular
              Analysis of the Fujisaki-Okamoto Transformation",
              DOI 10.1007/978-3-319-70500-2_12, Theory of
              Cryptography pp. 341-371, 2017,
              <https://doi.org/10.1007/978-3-319-70500-2_12>.

   [I-D.hoffman-c2pq]
              Hoffman, P., "The Transition from Classical to Post-
              Quantum Cryptography", Work in Progress, Internet-Draft,
              draft-hoffman-c2pq-07, 26 May 2020,
              <https://tools.ietf.org/html/draft-hoffman-c2pq-07>.

   [LUCKY13]  Al Fardan, N.J. and K.G. Paterson, "Lucky Thirteen:
              Breaking the TLS and DTLS record protocols", 2013,
              <https://ieeexplore.ieee.org/
              iel7/6547086/6547088/06547131.pdf>.

   [nist-sha2]
              NIST, "FIPS PUB 180-4", 2015,
              <https://nvlpubs.nist.gov/nistpubs/FIPS/
              NIST.FIPS.180-4.pdf>.

   [NIST-SP-800-135]
              National Institute of Standards and Technology (NIST),
              "Recommendation for Existing Application-Specific Key
              Derivation Functions", December 2011,
              <https://doi.org/10.6028/NIST.SP.800-135r1>.

   [NIST-SP-800-56C]
              National Institute of Standards and Technology (NIST),
              "Recommendation for Key-Derivation Methods in Key-
              Establishment Schemes", August 2020,
              <https://doi.org/10.6028/NIST.SP.800-56Cr2>.

   [nist-sp800-186]
              NIST, "SP 800-186", 2019,
              <https://nvlpubs.nist.gov/nistpubs/SpecialPublications/
              NIST.SP.800-186-draft.pdf>.

   [NIST_PQ]  NIST, "Post-Quantum Cryptography", 2020,
              <https://csrc.nist.gov/projects/post-quantum-
              cryptography>.

   [RACCOON]  Merget, R., Brinkmann, M., Aviram, N., Somorovsky, J.,
              Mittmann, J., and J. Schwenk, "Raccoon Attack: Finding and
              Exploiting Most-Significant-Bit-Oracles in TLS-DH(E)",
              September 2020, <https://raccoon-attack.com/>.

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   [RFC4634]  Eastlake 3rd, D. and T. Hansen, "US Secure Hash Algorithms
              (SHA and HMAC-SHA)", RFC 4634, DOI 10.17487/RFC4634, July
              2006, <https://www.rfc-editor.org/info/rfc4634>.

   [RFC5656]  Stebila, D. and J. Green, "Elliptic Curve Algorithm
              Integration in the Secure Shell Transport Layer",
              RFC 5656, DOI 10.17487/RFC5656, December 2009,
              <https://www.rfc-editor.org/info/rfc5656>.

   [RFC7748]  Langley, A., Hamburg, M., and S. Turner, "Elliptic Curves
              for Security", RFC 7748, DOI 10.17487/RFC7748, January
              2016, <https://www.rfc-editor.org/info/rfc7748>.

   [RFC8332]  Bider, D., "Use of RSA Keys with SHA-256 and SHA-512 in
              the Secure Shell (SSH) Protocol", RFC 8332,
              DOI 10.17487/RFC8332, March 2018,
              <https://www.rfc-editor.org/info/rfc8332>.

   [RFC8709]  Harris, B. and L. Velvindron, "Ed25519 and Ed448 Public
              Key Algorithms for the Secure Shell (SSH) Protocol",
              RFC 8709, DOI 10.17487/RFC8709, February 2020,
              <https://www.rfc-editor.org/info/rfc8709>.

   [RFC8731]  Adamantiadis, A., Josefsson, S., and M. Baushke, "Secure
              Shell (SSH) Key Exchange Method Using Curve25519 and
              Curve448", RFC 8731, DOI 10.17487/RFC8731, February 2020,
              <https://www.rfc-editor.org/info/rfc8731>.

Authors' Addresses

   Panos Kampanakis
   Cisco Systems

   Email: pkampana@cisco.com

   Douglas Stebila
   University of Waterloo

   Email: dstebila@uwaterloo.ca

   Markus Friedl
   OpenSSH

   Email: markus@openbsd.org

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   Torben Hansen
   AWS

   Email: htorben@amazon.com

   Dimitrios Sikeridis
   University of New Mexico

   Email: dsike@unm.edu

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