draft-kampanakis-ssh-pq-ke.txt

CURDLE                                                     P. Kampanakis
Internet-Draft                                                       AWS
Intended status: Experimental                                 D. Stebila
Expires: 11 November 2024                         University of Waterloo
                                                               T. Hansen
                                                                     AWS
                                                             10 May 2024


                    PQ/T Hybrid Key Exchange in SSH
                  draft-kampanakis-curdle-ssh-pq-ke-02

Abstract

   This document defines Post-Quantum Traditional (PQ/T) Hybrid key
   exchange methods based on traditional ECDH key exchange and post-
   quantum key encapsulation schemes.  These methods are defined for use
   in the SSH Transport Layer Protocol.

Status of This Memo

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   provisions of BCP 78 and BCP 79.

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   This Internet-Draft will expire on 11 November 2024.

Copyright Notice

   Copyright (c) 2024 IETF Trust and the persons identified as the
   document authors.  All rights reserved.











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   This document is subject to BCP 78 and the IETF Trust's Legal
   Provisions Relating to IETF Documents (https://trustee.ietf.org/
   license-info) in effect on the date of publication of this document.
   Please review these documents carefully, as they describe your rights
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Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   2
     1.1.  Requirements Language . . . . . . . . . . . . . . . . . .   4
   2.  PQ/T Hybrid Key Exchange  . . . . . . . . . . . . . . . . . .   4
     2.1.  PQ/T Hybrid Key Exchange Method Abstraction . . . . . . .   4
     2.2.  PQ/T Hybrid Key Exchange Message Numbers  . . . . . . . .   5
     2.3.  PQ/T Hybrid Key Exchange Method Names . . . . . . . . . .   5
       2.3.1.  mlkem768nistp256-sha256 . . . . . . . . . . . . . . .   5
       2.3.2.  mlkem1024nistp384-sha384  . . . . . . . . . . . . . .   6
       2.3.3.  mlkem768x25519-sha256 . . . . . . . . . . . . . . . .   6
     2.4.  Shared Secret K . . . . . . . . . . . . . . . . . . . . .   7
     2.5.  Key Derivation  . . . . . . . . . . . . . . . . . . . . .   7
   3.  Message Size  . . . . . . . . . . . . . . . . . . . . . . . .   8
   4.  Acknowledgements  . . . . . . . . . . . . . . . . . . . . . .   8
   5.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .   8
   6.  Security Considerations . . . . . . . . . . . . . . . . . . .   9
   7.  References  . . . . . . . . . . . . . . . . . . . . . . . . .  10
     7.1.  Normative References  . . . . . . . . . . . . . . . . . .  10
     7.2.  Informative References  . . . . . . . . . . . . . . . . .  10
   Appendix A.  Other Combiners  . . . . . . . . . . . . . . . . . .  13
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .  14

1.  Introduction

   Secure Shell (SSH) [RFC4251] performs key establishment using key
   exchange methods based on (Elliptic Curve) Diffie-Hellman style
   schemes defined in [RFC5656] and [RFC8731].  The cryptographic
   security of these key exchanges relies on certain instances of the
   discrete logarithm problem being computationally infeasible to solve
   for adversaries.











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   However, if sufficiently large quantum computers become available,
   these instances would no longer be computationally infeasible
   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 could record the encrypted communication
   sent between the client and server in an SSH session and later
   decrypt it when sufficiently large quantum computers become
   available.  This kind of attack is known as a "harvest-now-decrypt-
   later" attack.

   This document addresses the problem by extending the SSH Transport
   Layer Protocol [RFC4253] key exchange with Post-Quantum Traditional
   (PQ/T) Hybrid [I-D.ietf-pquip-pqt-hybrid-terminology] key exchange
   methods.  The security provided by each individual key exchange
   scheme in a PQ/T Hybrid key exchange method is independent.  This
   means that the PQ/T Hybrid key exchange method will always be at
   least as secure as the most secure key exchange scheme executed as
   part of the exchange.  [PQ-PROOF] [PQ-PROOF2] contain proofs of
   security for such PQ/T Hybrid key exchange schemes.

   In the context of the [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'.

   *  '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.





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   The post-quantum KEM used in the document is ML-KEM.  ML-KEM was
   standardized in 2024 [FIPS203]. [ EDNOTE: Reference normatively the
   ratified version [I-D.draft-cfrg-schwabe-kyber-04] if it is ever
   ratified.  Otherwise keep a normative reference of [FIPS203].  And
   remove the reference to [FIPS203-ipd]. ]

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 [RFC2119].

2.  PQ/T Hybrid Key Exchange

2.1.  PQ/T Hybrid Key Exchange Method Abstraction

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

   In a PQ/T Hybrid key exchange, instead of SSH_MSG_KEXDH_INIT
   [RFC4253] or SSH_MSG_KEX_ECDH_INIT [RFC5656], the client sends

          byte     SSH_MSG_KEX_HYBRID_INIT
          string   C_INIT

   where C_INIT is the concatenation of C_PK2 and C_PK1.  C_PK1 and
   C_PK2 represent the ephemeral client public keys used for each key
   exchange of the PQ/T Hybrid mechanism.  Typically, C_PK1 represents a
   traditional / classical (i.e., ECDH) key exchange public key.  C_PK2
   represents the 'pk' output of the corresponding post-quantum KEM's
   'KeyGen' at the client.

   Instead of SSH_MSG_KEXDH_REPLY [RFC4253] or SSH_MSG_KEX_ECDH_REPLY
   [RFC5656], the server sends

          byte     SSH_MSG_KEX_HYBRID_REPLY
          string   K_S, server's public host key
          string   S_REPLY
          string   the signature on the exchange hash

   where S_REPLY is the concatenation of S_CT2 and S_PK1.  Typically,
   S_PK1 represents the ephemeral (EC)DH server public key.  S_CT2
   represents the ciphertext 'ct' output of the corresponding KEM's
   'Encaps' algorithm generated by the server which encapsulates a
   secret to the client public key C_PK2.




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   C_PK1, S_PK1, C_PK2, S_CT2 are used to establish two shared secrets,
   K_CL and K_PQ.  K_CL is the output from the classical ECDH exchange
   using C_PK1 and S_PK1.  K_PQ is the post-quantum shared secret
   decapsulated from S_CT2.  K_CL and K_PQ are used together to generate
   the shared secret K according to Section 2.4.

2.2.  PQ/T Hybrid Key Exchange Message Numbers

   The message numbers 30-49 are key-exchange-specific and in a private
   namespace defined in [RFC4250] that may be redefined by any key
   exchange method [RFC4253] without requiring an IANA registration
   process.

   The following private namespace message numbers are defined in this
   document:

         #define SSH_MSG_KEX_HYBRID_INIT               30
         #define SSH_MSG_KEX_HYBRID_REPLY              31

2.3.  PQ/T Hybrid Key Exchange Method Names

   The PQ/T Hybrid key exchange method names defined in this document
   (to be used in SSH_MSG_KEXINIT [RFC4253]) are

         mlkem768nistp256-sha256
         mlkem1024nistp384-sha384
         mlkem768x25519-sha256

   These instantiate the abstract PQ/T Hybrid key exchanges defined in
   Section 2.1.

2.3.1.  mlkem768nistp256-sha256

   mlkem768nistp256-sha256 defines that the traditional client and
   server public keys C_PK1, S_PK1 belong to the NIST P-256 curve
   [nist-sp800-186].  The private and public keys are generated as
   described therein.  The public keys are defined as octet strings for
   NIST P-256 as per [RFC5656]; point compression may be used.  The K_CL
   shared secret is generated from the exchanged C_PK1 and S_PK1 public
   keys as defined in [RFC5656] (key agreement method ecdh-
   sha2-nistp256).










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   The post-quantum C_PK2 and S_CT2 represent ML-KEM-768 public key and
   ciphertext from the client and server respectively which are encoded
   as octet strings.  The K_PQ shared secret is decapsulated from the
   ciphertext S_CT2 using the client post-quantum KEM private key as
   defined in [FIPS203]. [ EDNOTE: Reference normatively the ratified
   version [I-D.draft-cfrg-schwabe-kyber-04] if it is ever ratified.
   Otherwise keep a normative reference of [FIPS203].  And remove the
   reference to [FIPS203-ipd]. ]

   The HASH function used in the key exchange [RFC4253] is SHA-256
   [nist-sha2] [RFC6234].

2.3.2.  mlkem1024nistp384-sha384

   mlkem1024nistp384-sha384 defines that the classical client and server
   public keys C_PK1, S_PK1 belong to the NIST P-384 curve
   [nist-sp800-186].  The private and public keys are generated as
   described therein.  The public keys are defined as octet strings for
   NIST P-384 as per [RFC5656]; point compression may be used.  The K_CL
   shared secret is generated from the exchanged C_PK1 and S_PK1 public
   keys as defined in [RFC5656] (key agreement method ecdh-
   sha2-nistp384).

   The post-quantum C_PK2 and S_CT2 represent ML-KEM-1024 public key and
   ciphertext from the client and server respectively which are encoded
   as octet strings.  The K_PQ shared secret is decapsulated from the
   ciphertext S_CT2 using the client post-quantum KEM private key as
   defined in [FIPS203]. [ EDNOTE: Reference normatively the ratified
   version [I-D.draft-cfrg-schwabe-kyber-04] if it is ever ratified.
   Otherwise keep a normative reference of [FIPS203].  And remove the
   reference to [FIPS203-ipd]. ].

   The HASH function used in the key exchange [RFC4253] is SHA-384
   [nist-sha2] [RFC6234].

   This method is compliant with CNSA 2.0 requirements [CNSA2] until
   2033.  CNSA 2.0 requires support for ML-KEM-1024 in 2025 and makes it
   mandatory without any classical algorithm in the key exchange in
   2033.

2.3.3.  mlkem768x25519-sha256

   mlkem768x25519-sha256 defines that the traditional client and server
   public keys C_PK1, S_PK1 belong to the Curve25519 curve [RFC7748].
   Private and public keys are generated as described therein.  The
   public keys are defined as strings of 32 bytes as per [RFC8731].  The
   K_CL shared secret is generated from the exchanged C_PK1 and S_PK1
   public keys as defined in [RFC8731] (key agreement method



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   curve25519-sha256).

   The post-quantum C_PK2 and S_CT2 represent ML-KEM-768 public key and
   ciphertext from the client and server respectively which are encoded
   as octet strings.  The K_PQ shared secret is decapsulated from the
   ciphertext S_CT2 using the client post-quantum KEM private key as
   defined in [FIPS203]. [ EDNOTE: Reference normatively the ratified
   version [I-D.draft-cfrg-schwabe-kyber-04] if it is ever ratified.
   Otherwise keep a normative reference of [FIPS203].  And remove the
   reference to [FIPS203-ipd]. ].

   The HASH function used in the key exchange [RFC4253] is SHA-256
   [nist-sha2] [RFC6234].

2.4.  Shared Secret K

   The PQ/T Hybrid key exchange establishes K_CL and K_PQ from the ECDH
   and ML-KEM key exchanges respectively.  The shared secret, K, is the
   HASH output of the concatenation of the two shared secrets K_CL and
   K_PQ as

           K = HASH(K_PQ || K_CL)

   This is similar, but not the same (for efficiency), logic as in TLS
   1.3 [I-D.ietf-tls-hybrid-design].  In [I-D.ietf-tls-hybrid-design],
   the classical and post-quantum exchanged secrets are concatenated and
   used in the key schedule whereas in this document they are
   concatenated and hashed before being used in SSH's key derivation
   methodology.

   The ECDH shared secret was traditionally encoded as an integer as per
   [RFC4253], [RFC5656], and [RFC8731] and used in deriving the key.  In
   this specification, the two shared secrets, K_PQ and K_CL, are fed
   into the hash function to derive K.  Thus, K_PQ and K_CL are encoded
   as fixed-length byte arrays, not as integers.  Byte arrays are
   defined in Section 5 of [RFC4251].

2.5.  Key Derivation

   The derivation of encryption keys MUST be done from the shared secret
   K according to Section 7.2 in [RFC4253] with a modification on the
   exchange hash H.

   The PQ/T Hybrid key exchange hash H is the result of computing the
   HASH, where HASH is the hash algorithm specified in the named PQ/T
   Hybrid key exchange method name, over the concatenation of the
   following




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         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 K_S, server's public host key
         string C_INIT, client message octet string
         string S_REPLY, server message octet string
         string K, SSH shared secret

   K, the shared secret used in H, was traditionally encoded as an
   integer (mpint) as per [RFC4253], [RFC5656], and [RFC8731].  In this
   specification, K is the hash output of the two concatenated byte
   arrays (Section 2.4) which is not an integer.  Thus, K is encoded as
   a string using the process described in Section 5 of [RFC4251] and is
   then fed along with other data in H to the key exchange method's HASH
   function to generate encryption keys.

3.  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 method names (Section 2.3) that cause any PQ/T Hybrid
   key exchange method related packets to exceed the minimally supported
   packet length.  This document does not define behavior in cases where
   a PQ/T Hybrid key exchange message cause a packet to exceed the
   minimally supported packet length.

4.  Acknowledgements

   The authors want to thank Gerado Ravago from AWS for implementing the
   draft and finding issues.  We also want to thank Damien Miller and
   Markus Friedl for their feedback and for bringing some of the SSH key
   exchange methods in this document in OpenSSH.

5.  IANA Considerations

   This memo includes requests of IANA to register new method names
   "mlkem768nistp256-sha256", "mlkem1024nistp384-sha384", and
   "mlkem768x25519-sha256" to be registered by IANA in the "Key Exchange
   Method Names" registry for SSH [IANA-SSH].




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6.  Security Considerations

   The security considerations given in [RFC5656] and [RFC8731] also
   apply to the ECDH part of the P/T Hybrid key exchange schemes defined
   in this document.

   The way a derived binary secret string is encoded (i.e., adding or
   removing zero bytes for encoding) before it is hashed may lead to a
   variable-length secret which raises the potential for a side-channel
   attack.  In broad terms, when the secret is longer, the hash function
   may need to process more blocks internally which could determine the
   length of what is hashed.  This could leak the most significant bit
   of the derived secret and/or allow detection of when the most
   significant bytes are zero.  In some unfortunate circumstances, this
   has led to timing attacks, e.g. the Lucky Thirteen [LUCKY13] and
   Raccoon [RACCOON] attacks.  In [RFC8731] and [RFC5656], the ECDH
   shared secrets were mpint and fixed-length integer encoded
   respectively which raised a potential for such side-channel attacks.
   This problem is addressed in this document by encoding K_PQ and K_CL
   as fixed-length byte arrays and K as a string.  Implementations MUST
   use these encodings for K_PQ, K_CL, and K.

   [NIST-SP-800-56C] and [NIST-SP-800-135] gives NIST recommendations
   for key derivation methods in key exchange protocols.  Some PQ/T
   Hybrid combinations may combine the shared secret from a NIST-
   approved algorithm (e.g., ECDH using the nistp256/secp256r1 curve or
   ML-KEM) with a shared secret from a non-approved algorithm (e.g.,
   X25519).  [NIST-SP-800-56C] lists simple concatenation as an approved
   method for generation of a PQ/T Hybrid shared secret in which one of
   the constituent shared secret is from an approved method.  Thus, the
   combination of the two shared secrets in this document is FIPS-
   approved assuming the ECDH curve and ML-KEM negotiated parameters are
   FIPS approved.  [NIST-SP-800-135] also approves the key derivation
   used in SSH.  This method is the same used in this document to derive
   keys from the quantum-resistant shared secret for use in SSH.  Thus,
   the keys derived from the PQ/T Hybrid key exchange in this document
   are FIPS approved.

   [PQ-PROOF] [PQ-PROOF2] contain proofs of security for PQ/T Hybrid key
   exchange schemes.  [PQ-PROOF2] discusses how the key combination to
   derive K and the derivation of SSH symmetric keys in this document
   can be proven IND-CPA and IND-CCA2 secure with some assumptions.
   IND-CPA is achieved if we assume the HASH calls perform as a KDF
   which is a reasonable assumption.  IND-CCA2 security is achieved by
   assuming the HASH is a random oracle which is a stronger assumption
   especially for hash functions like SHA-2 which permit length
   extension concerns.  To leverage a HASH which is more suitable as a
   random oracle, we could use SHAKE256 or introduce HMAC-SHA-256 as



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   proposed in options (2b) and (2c) in Appendix A.  This document uses
   SHA2 which is ubiquitous although it makes an IND-CCA2 proof need
   stronger assumptions because even SSH's traditional key derivation
   has not been proven to be IND-CCA2.  As with (EC)DH keys today,
   generating an ephemeral key exchange keypair for ECDH and ML-KEM is
   still REQUIRED per connection by this specification (IND-CPA
   security).  Implementations also MUST NOT reuse randomness in the
   generation of KEM ciphertexts.

7.  References

7.1.  Normative References

   [FIPS203]  "*** BROKEN REFERENCE ***".

   [FIPS203-ipd]
              National Institute of Standards and Technology (NIST),
              "Module-Lattice-based Key-Encapsulation Mechanism
              Standard", NIST Federal Information Processing Standards,
              24 August 2023, <https://nvlpubs.nist.gov/nistpubs/FIPS/
              NIST.FIPS.203.ipd.pdf>.

   [I-D.draft-cfrg-schwabe-kyber-04]
              Schwabe, P. and B. Westerbaan, "Kyber Post-Quantum KEM",
              Work in Progress, Internet-Draft, draft-cfrg-schwabe-
              kyber-04, 2 January 2024,
              <https://datatracker.ietf.org/doc/html/draft-cfrg-schwabe-
              kyber-04>.

   [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>.

   [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>.

7.2.  Informative References








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   [CNSA2]    National Security Agency (NSA), "Announcing the Commercial
              National Security Algorithm Suite 2.0", April 2024,
              <https://www.nsa.gov/Press-Room/News-
              Highlights/Article/Article/3148990/nsa-releases-future-
              quantum-resistant-qr-algorithm-requirements-for-national-
              se/>.

   [I-D.connolly-cfrg-xwing-kem]
              Connolly, D., Schwabe, P., and B. Westerbaan, "X-Wing:
              general-purpose hybrid post-quantum KEM", Work in
              Progress, Internet-Draft, draft-connolly-cfrg-xwing-kem-
              02, 26 March 2024, <https://datatracker.ietf.org/doc/html/
              draft-connolly-cfrg-xwing-kem-02>.

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

   [I-D.ietf-pquip-pqt-hybrid-terminology]
              D, F. and M. P, "Terminology for Post-Quantum Traditional
              Hybrid Schemes", Work in Progress, Internet-Draft, draft-
              ietf-pquip-pqt-hybrid-terminology-03, 9 May 2024,
              <https://datatracker.ietf.org/doc/html/draft-ietf-pquip-
              pqt-hybrid-terminology-03>.

   [I-D.ietf-tls-hybrid-design]
              Stebila, D., Fluhrer, S., and S. Gueron, "Hybrid key
              exchange in TLS 1.3", Work in Progress, Internet-Draft,
              draft-ietf-tls-hybrid-design-10, 5 April 2024,
              <https://datatracker.ietf.org/doc/html/draft-ietf-tls-
              hybrid-design-10>.

   [I-D.josefsson-chempat]
              Josefsson, S., "Chempat: Generic Instantiated PQ/T Hybrid
              Key Encapsulation Mechanisms", Work in Progress, Internet-
              Draft, draft-josefsson-chempat-01, 14 April 2024,
              <https://datatracker.ietf.org/doc/html/draft-josefsson-
              chempat-01>.

   [IANA-SSH] IANA, "Secure Shell (SSH) Protocol Parameters", 2021,
              <https://www.iana.org/assignments/ssh-parameters/ssh-
              parameters.xhtml>.






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   [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>.

   [PQ-PROOF] Campagna, M. and A. Petcher, "Security of Hybrid Key
              Encapsulation", 2020, <https://eprint.iacr.org/2020/1364>.

   [PQ-PROOF2]
              Petcher, A. and M. Campagna, "Security of Hybrid Key
              Establishment using Concatenation", 2023,
              <https://eprint.iacr.org/2023/972>.

   [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/>.

   [RFC4250]  Lehtinen, S. and C. Lonvick, Ed., "The Secure Shell (SSH)
              Protocol Assigned Numbers", RFC 4250,
              DOI 10.17487/RFC4250, January 2006,
              <https://www.rfc-editor.org/info/rfc4250>.



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   [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>.

   [RFC6234]  Eastlake 3rd, D. and T. Hansen, "US Secure Hash Algorithms
              (SHA and SHA-based HMAC and HKDF)", RFC 6234,
              DOI 10.17487/RFC6234, May 2011,
              <https://www.rfc-editor.org/info/rfc6234>.

   [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>.

   [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>.

Appendix A.  Other Combiners

   Other combiners to derive K and the SSH keys were considered while
   working on this document.  These include

   (1)  K = K_PQ || K_CL.  All SSH keys are derived from K as defined in
        Section 7.2 in [RFC4253].

   (2)  All SSH keys are derived from K as defined in Section 7.2 in
        [RFC4253].

        (a)  K = HASH(K_PQ, K_CL).  This is the option adopted in this
             specification.

        (b)  K = HMAC-HASH(K_PQ, K_CL)

        (c)  K = HMAC-HASH(0, K_PQ || K_CL)

   (3)  K = HKDF-HASH_Extract(0, K_PQ || K_CL).  SSH keys are now
        derived from K using HKDF-HASH(K, H || session_id,
        6*sizeof(HASH)).

   Option (3) follows the Extract-and-Expand logic described in
   [NIST-SP-800-56C].  It deviates from existing SSH key derivation
   significantly and might be viewed as too far from the current SSH
   design.  It probably would be a good approach for SSH to move from
   basic hashing everywhere to use proper KDFs with extract/expand, but
   that should be a separate effort.




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   We also considered combiners like the ones proposed in
   [I-D.josefsson-chempat] and [I-D.connolly-cfrg-xwing-kem].
   [I-D.connolly-cfrg-xwing-kem] has a separate IND-CCA2 security proof.
   Although such combiners may be proven IND-CCA2 secure, to be IND-
   CCA2, the SSH key derivation would still require the assumptions laid
   out in [PQ-PROOF2] and discussed in Section 6.

Authors' Addresses

   Panos Kampanakis
   AWS
   Email: kpanos@amazon.com


   Douglas Stebila
   University of Waterloo
   Email: dstebila@uwaterloo.ca


   Torben Hansen
   AWS
   Email: htorben@amazon.com





























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