Secure Shell (SSH) Key Exchange Method Using Hybrid Streamlined NTRU Prime sntrup761 and X25519 with SHA-512: sntrup761x25519-sha512

Internet Engineering Task Force (IETF)                         M. Friedl
Request for Comments: 9941                                       OpenSSH
Category: Informational                                        J. Mojzis
ISSN: 2070-1721                                                  TinySSH
                                                            S. Josefsson
                                                              April 2026


  Secure Shell (SSH) Key Exchange Method Using Hybrid Streamlined NTRU
    Prime sntrup761 and X25519 with SHA-512: sntrup761x25519-sha512

Abstract

   This document describes a widely deployed hybrid key exchange method
   in the Secure Shell (SSH) protocol that is based on Streamlined NTRU
   Prime sntrup761 and X25519 with SHA-512.

Status of This Memo

   This document is not an Internet Standards Track specification; it is
   published for informational purposes.

   This document is a product of the Internet Engineering Task Force
   (IETF).  It represents the consensus of the IETF community.  It has
   received public review and has been approved for publication by the
   Internet Engineering Steering Group (IESG).  Not all documents
   approved by the IESG are candidates for any level of Internet
   Standard; see Section 2 of RFC 7841.

   Information about the current status of this document, any errata,
   and how to provide feedback on it may be obtained at
   https://www.rfc-editor.org/info/rfc9941.

Copyright Notice

   Copyright (c) 2026 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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   in the Revised BSD License.

Table of Contents

   1.  Introduction
   2.  Requirements Language
   3.  Key Exchange Method: sntrup761x25519-sha512
   4.  Security Considerations
   5.  IANA Considerations
   6.  References
     6.1.  Normative References
     6.2.  Informative References
   Appendix A.  Test Vectors
   Acknowledgements
   Authors' Addresses

1.  Introduction

   Secure Shell (SSH) [RFC4251] is a secure remote login protocol.  The
   key exchange protocol described in [RFC4253] supports an extensible
   set of methods.  [RFC5656] defines how elliptic curves are integrated
   into the extensible SSH framework, and [RFC8731] adds
   curve25519-sha256 to support the pre-quantum Elliptic Curve Diffie-
   Hellman (ECDH) X25519 function [RFC7748].

   Streamlined NTRU Prime [NTRUPrimePQCS] [NTRUPrime] [NTRUPrimeWeb]
   provides post-quantum small lattice-based key-encapsulation
   mechanisms.  The sntrup761 instance has been implemented widely.

   This document specifies a hybrid construction using both sntrup761
   and X25519, in the intention that a hybrid would be secure if either
   algorithms is secure.

   This document also describes how to implement key exchange based on a
   hybrid between Streamlined NTRU Prime sntrup761 and X25519 with
   SHA-512 [RFC6234] in SSH.

   This document was derived from SSH KEX Using Curve25519 and Curve448
   [RFC8731].

2.  Requirements Language

   The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
   "SHOULD", "SHOULD NOT", "RECOMMENDED", "NOT RECOMMENDED", "MAY", and
   "OPTIONAL" in this document are to be interpreted as described in
   BCP 14 [RFC2119] [RFC8174] when, and only when, they appear in all
   capitals, as shown here.

3.  Key Exchange Method: sntrup761x25519-sha512

   The key agreement is done by the X25519 Diffie-Hellman protocol as
   described in Section 3 ("Key Exchange Methods") of [RFC8731] and by
   the key encapsulation method described in [NTRUPrimePQCS].

   The key exchange procedure reuses the ECDH key exchange defined in
   Sections 4 ("ECDH Key Exchange") and 7.1 ("ECDH Message Numbers") of
   [RFC5656].

   The protocol flow and the SSH_MSG_KEX_ECDH_INIT and
   SSH_MSG_KEX_ECDH_REPLY messages are identical, except that we use
   different ephemeral public values Q_C and Q_S and shared secret K as
   described below.

   Implementations MAY use the name SSH_MSG_KEX_HYBRID_INIT where
   SSH_MSG_KEX_ECDH_INIT is used and the name SSH_MSG_KEX_HYBRID_REPLY
   where SSH_MSG_KEX_ECDH_REPLY is used, as long as the encoding on the
   wire is identical.  These symbolic names do not appear on the wire;
   they are merely used in specifications to refer to particular byte
   values.  For consistency with [RFC5656], which defines the packet
   syntax, we use those names in the rest of this document.

   The SSH_MSG_KEX_ECDH_INIT's value Q_C that holds the client's
   ephemeral public key MUST be constructed by concatenating the
   1158-byte public key output from the key generator of sntrup761 with
   the 32-byte K_A = X25519(a, 9) as described in [NTRUPrimePQCS] and
   [RFC8731].  The Q_C value is thus 1190 bytes.

   The SSH_MSG_KEX_ECDH_REPLY's value Q_S that holds the server's
   ephemeral public key MUST be constructed by concatenating the
   1039-byte ciphertext output from the key encapsulation mechanism of
   sntrup761 with the 32-byte K_B = X25519(b, 9) as described in
   [NTRUPrimePQCS] and [RFC8731].  The Q_S value is thus 1071 bytes.

   Clients and servers MUST abort if the length of the received public
   keys Q_C or Q_S are not the expected lengths.  An abort for these
   purposes is defined as a disconnect (SSH_MSG_DISCONNECT) of the
   session and SHOULD use the SSH_DISCONNECT_KEY_EXCHANGE_FAILED reason
   for the message; see Section 11.1 ("Disconnection Message") of
   [RFC4253].  No further validation is required beyond what is
   described in [RFC7748], [RFC8731], and [NTRUPrimePQCS].

   The SSH_MSG_KEX_ECDH_REPLY's signature value is computed as described
   in ECC for SSH [RFC5656] with the following changes.  Instead of
   encoding the shared secret K as "mpint", it MUST be encoded as
   "string".  The shared secret K value MUST be the 64-byte output octet
   string of the SHA-512 hash computed with the input as the 32-byte
   octet string key output from the key encapsulation mechanism of
   sntrup761 concatenated with the 32-byte octet string of X25519(a,
   X25519(b, 9)) = X25519(b, X25519(a, 9)).

   Some earlier implementations may implement this protocol only through
   the name sntrup761x25519-sha512@openssh.com; therefore, it is
   RECOMMENDED to announce and accept that name as an alias of this
   protocol to increase chances for successfully negotiating the
   protocol.

4.  Security Considerations

   The security considerations in [RFC4251], [RFC5656], [RFC7748], and
   [RFC8731] are inherited.

   Streamlined NTRU Prime sntrup761 aims for the standard goal of IND-
   CCA2 security, is widely implemented with good performance on a wide
   range of architectures, and has been studied by researchers for
   several years.  However, new cryptographic primitives should be
   introduced and trusted conservatively, and new research findings may
   be published at any time that may warrant implementation
   reconsideration.  The method described here to combine Curve25519
   with sntrup761 (i.e., SHA-512 hashing the concatenated outputs) is
   also available for the same kind of cryptographic scrutiny.

   The increase in communication size and computational requirements may
   be a concern for restricted computational devices, which would then
   not be able to take advantage of the improved security properties
   offered by this work.

   Since sntrup761x25519-sha512 is expected to offer no reduction of
   security compared to curve25519-sha256, it is recommended that it is
   used and preferred whenever curve25519-sha256 is used today, if the
   extra communication size and computational requirements are
   acceptable.

   As discussed in the security considerations of [RFC8731], the X25519
   shared secret K is bignum-encoded in that document, and this raises
   the potential for a side-channel attack that could leak one bit of
   the secret due to the different length of the bignum sign pad.  This
   document resolves that problem by using string encoding instead of
   bignum encoding.

   The security properties of the protocol in this document, SSH itself,
   and the cryptographic algorithms used (including Streamlined NTRU
   Prime) depend on the availability and proper use of cryptographically
   secure random data.

5.  IANA Considerations

   IANA has added the following entry to the "Key Exchange Method Names"
   registry within the "Secure Shell (SSH) Protocol Parameters" registry
   group [IANA-KEX]:

         +========================+===========+=================+
         | Method Name            | Reference | OK to Implement |
         +========================+===========+=================+
         | sntrup761x25519-sha512 | RFC 9941  | SHOULD          |
         +------------------------+-----------+-----------------+

                                 Table 1

6.  References

6.1.  Normative References

   [NTRUPrimePQCS]
              Bernstein, D.J., Brumley, B. B., Chen, M.,
              Chuengsatiansup, C., Lange, T., Marotzke, A., Peng, B.,
              Tuveri, N., Vredendaal, C. V., and B. Yang, "NTRU Prime:
              round 3", DOI 10.5281/zenodo.13983972, October 2020,
              <https://doi.org/10.5281/zenodo.13983972>.
              <https://ntruprime.cr.yp.to/nist/ntruprime-20201007.pdf>.

   [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>.

   [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>.

   [RFC8174]  Leiba, B., "Ambiguity of Uppercase vs Lowercase in RFC
              2119 Key Words", BCP 14, RFC 8174, DOI 10.17487/RFC8174,
              May 2017, <https://www.rfc-editor.org/info/rfc8174>.

   [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>.

6.2.  Informative References

   [IANA-KEX] IANA, "Key Exchange Method Names",
              <https://www.iana.org/assignments/ssh-parameters>.

   [NTRUPrime]
              Bernstein, D.J., Chuengsatiansup, C., Lange, T., and C.
              van Vredendaal, "NTRU Prime: reducing attack surface at
              low cost", August 2017,
              <https://ntruprime.cr.yp.to/ntruprime-20170816.pdf>.

   [NTRUPrimeWeb]
              NTRU Prime, "NTRU Prime", <https://ntruprime.cr.yp.to/>.

   [OpenSSH]  OpenSSH, "OpenSSH", <https://www.openssh.com/>.

   [TinySSH]  TinySSH, "TinySSH", <https://tinyssh.org/>.

Appendix A.  Test Vectors

   SSH2_MSG_KEX_ECDH_INIT

   client public key sntrup761:
   0000: 5d b3 a9 d3 93 30 31 76 0e 8a f5 87 f7 b2 8c 4f
   0016: 97 a1 74 0e 6b 6f cf 1a d9 d9 99 8a 32 a5 61 e5
   0032: 9e 4d 93 67 e2 66 18 f0 0a f5 54 f4 48 65 0c 60
   0048: d1 12 92 c2 aa a9 e4 7c ea 32 a3 f5 86 cb c4 c3
   0064: d5 c2 6f 34 5e 7f d3 57 51 d3 e3 d9 cc 1c e4 49
   0080: bb ea 3e 2e 58 5e ac ba 0a b8 22 00 7c 77 a4 e0
   0096: bd 16 5c 3a f7 b3 25 08 c1 81 fd 0d 9f 99 a3 be
   0112: ae e3 38 84 13 ff f0 b4 0f cb ab 76 1e 95 3e 1e
   0128: 7c 74 1e 58 46 f6 81 f0 f2 f2 56 5b f3 be ce c9
   0144: c8 99 9f 03 88 81 db 17 75 1d fb f5 b1 e2 f3 5d
   0160: 32 ce 19 75 49 e7 e1 17 bf 35 0d 97 7c ac 0a cf
   0176: 6c 8a 0f fc 07 4b a7 8b c5 93 f7 47 7c b6 d5 bf
   0192: 02 f0 96 80 e8 dc f3 87 c9 f0 b2 91 e7 37 70 82
   0208: 3e 47 b7 18 72 be 5a da b1 85 d3 6e 56 5d 8a a3
   0224: 62 fa 3e d0 ea 6e b9 fa 69 ec 96 86 94 81 2e 88
   0240: 2b ba e5 af 70 1e ae ba 5f cb ea 82 e5 ba 67 0e
   0256: 4d f6 2a ec 13 a9 19 b4 08 9c b7 32 bb 40 de c3
   0272: e9 33 e1 c4 0d 5b 72 00 06 c4 3b 7f 57 d4 85 76
   0288: 4c 4c 3d ab 8e 1b 00 00 ac d9 8c 05 b3 18 24 85
   0304: 77 28 74 71 0d 68 8b 02 2c 59 55 a7 4d a4 6e 37
   0320: 85 6c 77 68 f5 b7 a7 52 61 af 37 b4 09 07 34 68
   0336: b6 83 ca f2 03 25 47 f9 09 e6 da bd 82 07 7e d1
   0352: 78 16 74 1a a5 4c 5b ac 78 d8 0f 1a 44 08 44 a7
   0368: ef 85 00 43 19 c3 3e b4 54 e6 3f f1 ac 83 03 ce
   0384: 7c bd ef 3c fd eb 47 6f f7 f9 e0 1f 13 9f cb 77
   0400: 52 40 9d 3a d7 8b ad bf cc f1 06 ec 93 32 48 be
   0416: 0a 53 99 5c dd 9e 96 3b 84 21 8f b2 b4 fd b8 97
   0432: 8b 7a 8f 71 aa e6 af 4e 22 53 18 f0 a2 30 a0 53
   0448: 30 c9 d8 a9 d7 67 08 a5 ad 81 64 7b 3a 02 ae ff
   0464: e7 fa 41 68 d0 54 e3 42 86 da f7 f0 98 31 38 e5
   0480: 8c fa 86 5c 5c f9 82 f8 a2 09 91 91 96 72 12 e5
   0496: 8f 8b 8e 9b e8 5d bd 66 4b 6e ec a3 b3 03 c5 4e
   0512: 0f 7e a5 15 ef ab 01 8c 6d 02 52 77 bc 9a 02 f2
   0528: 2e bf 03 40 fe 5a 80 5a c0 78 1e 95 21 10 9d dd
   0544: 37 87 00 ae 13 c5 9d 9c 81 87 37 3e 7d e0 40 bc
   0560: 83 76 69 4f 9f c4 08 fd aa a1 7e aa 88 0e 4c 56
   0576: a0 47 c5 d6 94 fb 52 67 f3 36 de b2 7e bf d1 33
   0592: 41 fd 05 20 66 60 f4 91 96 5f 19 33 2d 17 ec e0
   0608: 3e 93 7a 66 3b b0 de f4 ad 51 90 a4 a1 94 f3 37
   0624: 9a 77 11 02 67 45 6d 4d 19 80 33 58 56 2c b8 11
   0640: 51 7b bc ec 43 fe 3d 96 ac f7 f0 8b 8d c6 2c 02
   0656: 2f c0 67 21 56 49 ee bf 07 17 48 f9 30 0b 18 2c
   0672: fa 7b 57 93 be f7 12 99 57 be 98 e7 55 84 da ed
   0688: 5c 94 71 fa 48 0f ed 97 ab e4 a5 d6 b6 26 3a e4
   0704: cb fe f9 ed 07 4b 42 bf e5 a1 d1 34 4d 7b 67 b9
   0720: b7 06 7b d2 c7 ae 57 15 21 58 55 70 70 93 f1 87
   0736: 31 bf 85 74 fe 36 0d 08 c8 07 a2 14 fc d5 96 8b
   0752: 59 62 97 30 43 75 c2 a9 4f ec f9 e9 33 a9 38 cb
   0768: ae ee 63 34 8c 65 54 e7 9d d4 23 a2 4f b9 00 ed
   0784: b4 be 0b 1c df d4 97 c0 89 ab dd 5f 75 13 ce 37
   0800: f3 d2 26 55 72 39 61 f0 d2 11 e8 e7 5f 93 5b 79
   0816: e5 6c 28 f3 0a f9 5e 99 b8 a0 e6 4a 22 88 e5 28
   0832: 82 0c 6f 72 1d dd 80 84 57 04 72 f4 26 56 71 f3
   0848: 92 23 ff 9e a9 fd 05 0b 51 99 72 32 98 a5 02 87
   0864: fe bb 99 18 5a b3 ec ab f9 26 7b 97 79 da 5f 19
   0880: 4e e7 7d a5 2d 53 40 2a 1f 1b 62 df 3b 11 82 e6
   0896: 90 7f 0f 56 0c 75 14 03 e7 6f aa f0 0e 0a 17 13
   0912: 54 f5 ea d7 21 31 2c 7a c5 7f a3 ae 14 f3 05 42
   0928: e9 c9 6c 6d d1 0a cb 19 35 7f 01 8a 8c e2 a1 09
   0944: b5 c6 e5 e8 2b 4f 1e a2 e9 ce 5b e4 76 f7 53 4f
   0960: 52 d4 75 22 4b aa 1e cd 42 0e be d7 dc 76 6f 94
   0976: 0a 37 47 ca 44 bd e6 9e c1 2a 0d 57 f3 c2 47 40
   0992: 23 db a8 45 c7 9b 4a 96 13 6a 73 ad 6a a2 a8 e4
   1008: df 92 34 76 f9 47 8d b9 21 63 46 c2 d7 f2 64 e6
   1024: 17 27 9f cf f3 ae cd 3a 7d ed 5e 46 7c 33 71 f6
   1040: 71 c8 92 dc ae e6 a0 c8 05 0c e0 37 fb ea 15 ed
   1056: b0 78 a5 bf b1 48 8b 46 64 1e c8 81 00 55 82 89
   1072: 25 f8 b1 8b 1c e4 96 54 f8 be 97 b1 d3 20 f3 a0
   1088: b5 c1 dd d5 27 d0 61 d9 96 2a 74 76 a8 33 10 78
   1104: ff b2 86 ee 4f 0b 78 73 dd 7f 7c b5 02 e9 12 35
   1120: d3 9e ab 81 cd 9b 61 fb 2b 33 72 ee c6 bb 8a bc
   1136: bd 4f e5 9b c2 55 8f a0 b1 e7 1a 6a c1 e3 f1 5c
   1152: 83 8f f0 9c 5b 04

   client public key c25519:
   0000: be f9 23 79 d7 fd 4e 8a 10 55 9b dc e5 3e 62 13
   0016: eb 9b 6a 6f ca de ed 90 04 db b1 30 f6 ff ef 4f

   SSH2_MSG_KEX_ECDH_REPLY

   server cipher text:
   0000: 71 67 00 55 f8 ac 87 1a af 7c ef cf 1c b4 7d b9
   0016: 4f b6 22 5e 4d 77 81 73 4f 1d b9 82 79 ff e9 34
   0032: 26 9f d2 2e 4e c6 a3 5f 79 9c 26 68 99 3a 0f 40
   0048: 33 2a 7d dd fa 7a e7 6b 1e e7 9d 50 b7 48 0f aa
   0064: aa 97 ff e7 8c 6c ac 5d 10 df 2b e3 cc 93 ea dc
   0080: 18 17 b3 34 42 70 7a 27 85 58 2a ae c2 e6 b9 26
   0096: 93 fd 23 a9 ae ac 4a 35 8b 57 c1 5c 95 cb 23 fb
   0112: e5 93 0f 7c f5 63 6b 5b a1 53 b5 55 d0 75 16 21
   0128: 8a db 95 ff c8 58 ac f4 7e 46 69 0a 4c a9 c8 cc
   0144: eb e8 66 7c c4 fb fd 98 2c 0c 7f 41 8c 34 89 49
   0160: a0 25 59 eb 63 a1 e6 8f 37 bf bc b3 ce 0a da 53
   0176: 54 7f c2 41 52 eb 6c 9e 6e d0 ea af 6a 82 5d 17
   0192: 6f 17 8d 06 8a 86 55 60 28 31 12 4a 0c de 6b be
   0208: eb fd 38 13 6c 56 69 ad 0e 72 c8 bd b4 69 9d 32
   0224: b4 1c 8e 6f f4 25 e1 9b c5 6f 8b 02 77 52 ae 72
   0240: eb 9b 03 c8 9f de 15 bd f6 5a e8 9d 83 81 7b 48
   0256: 7a 69 9a d0 91 41 aa 07 5a fa ad d6 e8 55 39 d9
   0272: d1 0f d2 18 dc a0 9d 1c f1 e4 1c 0d f8 88 85 6b
   0288: 6d 11 24 3e 61 de 48 95 5f 2a d1 c9 ad 3f b8 41
   0304: 49 6d 9f 7c 3c bf 20 fe 37 7f 8c 8c 8f 72 ca f4
   0320: 19 e4 cc a1 d8 08 cb 69 ec da 2b 88 e8 98 e9 1e
   0336: 29 af 86 6f 19 a8 67 56 ef b4 33 e4 2b b8 fe 61
   0352: ad 36 4c 42 f8 ec 04 38 09 62 02 66 b5 54 fc 69
   0368: 46 29 05 27 d8 32 fd 37 4c d4 62 55 e1 ae e9 62
   0384: 66 a0 f4 cb 4b 01 af 6b ea 09 80 00 a2 2b ff 0e
   0400: 85 2c 92 b2 5c f9 f3 eb 44 a3 9a e8 55 bb e3 2f
   0416: 2d 20 5a 77 67 97 57 90 7f 4b b3 08 92 41 1a c0
   0432: f6 1b e9 a4 06 29 ea 31 eb 81 f0 94 96 aa 26 95
   0448: 06 ed 4b f0 d3 9f aa 73 89 fa 6e f7 8f 4b f5 fa
   0464: e4 5f 7c b6 08 e9 b2 18 77 99 9c ac 7b fb ec 41
   0480: 41 1e 29 c2 d0 a5 de bc 59 2f 14 45 6d af b1 e0
   0496: 9c 77 73 0e ac 52 23 73 11 35 27 17 8c a3 ff 0e
   0512: 52 5d b7 c8 06 c5 05 43 15 53 e8 fc 83 64 df 10
   0528: 8b 9c 74 5c 0e d9 54 5e 9a 49 cf 13 e4 1d 86 35
   0544: 24 a3 27 75 d3 d6 b4 95 78 8f 0d 81 3b 80 6b 26
   0560: 25 9f 14 b1 65 73 e8 ce fa 95 6d b1 15 0c 76 3c
   0576: b1 75 a9 96 78 c8 4b 91 06 a9 94 bc ec fa 44 eb
   0592: 39 77 4d ee df ae eb 0e 90 61 eb ab 6a 17 1b 24
   0608: 3c 3a 6e c4 bb 6f 72 46 3d 9a b8 8c 6a e7 45 c7
   0624: 0f 81 db 19 6e ce 65 74 ca db 73 ec 1e ce 5f d7
   0640: 43 6b fe ff c0 e1 61 26 aa b7 6f e0 dc 7f d1 de
   0656: 95 f0 28 fd 24 9c 73 1c cf ef 3e fe 21 a1 e5 4e
   0672: 77 da db 12 01 7a e4 2c b5 f3 9d 30 e6 49 99 d6
   0688: 21 58 cc 5b 5b d5 ff ca ea df 9a fd d6 73 be cd
   0704: ae 7c 0d ea 78 e4 dd 74 f9 93 53 21 70 b7 cd 16
   0720: ea c7 e9 5d 01 e0 e3 e6 53 46 7f fa a0 48 3e 5b
   0736: af 64 46 ff 0f 0c b5 c9 92 48 e8 20 35 1d c8 ae
   0752: d8 c4 38 31 aa 2c b5 91 6b eb 86 ac 2b fa 86 f2
   0768: d1 bd 7d 51 4c be f3 bf 4b d0 f0 78 0e 20 d3 30
   0784: fc f8 00 53 2a 6a 9b d9 e4 0e 08 d1 ad 52 7a ca
   0800: f3 8b 0e a8 fb 45 3c 66 03 66 b4 54 a5 3d 8e df
   0816: 4a 8f 66 f0 16 44 3b a9 f1 b3 db bb 7e d6 38 e5
   0832: 5f 62 27 bb ba 34 0a 6f 9b 78 dd ae 54 ab 54 53
   0848: 3a e1 d2 f1 d8 1e 8b 31 61 cd 69 8a 63 fb 7c 24
   0864: 75 5f e6 6d 64 3d e4 12 cb 2d b3 6f 0f 5a 19 28
   0880: 1f d6 f6 9c ee 44 11 1a c5 84 d6 e3 a2 05 5d d4
   0896: 85 db f1 8f e4 17 df bc 4c 78 98 d1 70 3b 63 d6
   0912: a4 91 db f1 9e 16 23 fa e0 54 f6 64 d1 0b d0 d6
   0928: a6 fd f1 66 72 8c 65 d8 17 af c9 33 49 c8 e9 4d
   0944: 1c 0a 77 2b 96 86 f2 16 55 3a e3 f6 00 bb b6 5a
   0960: 86 f6 fc 3f d6 f9 a4 1d fd 29 1d 5b 65 dc b3 14
   0976: 96 10 3e c1 9a 90 23 e8 88 81 24 42 68 7a aa 25
   0992: ba f3 50 bd b9 ae be dc b3 ff 39 81 44 89 00 9d
   1008: 4e 26 d6 ef df 7c e0 53 d3 ed 34 07 3d f2 1e 42
   1024: 28 af 1d 12 ce 98 c7 b0 7b 90 81 b5 ea f3 2c

   server public key c25519:
   0000: 18 6c 55 03 db 1c 38 e3 40 d7 09 24 77 46 14 b8
   0016: 5e e4 7f 19 98 04 9b 90 1f f6 b9 7f b0 70 9e 32

   shared secret
   0000: 9b 73 7d 41 d6 cf bb 12 56 c5 8c ad 0a 6a e2 c9
   0016: bf 84 a9 0a 72 91 eb 52 e4 c1 81 c8 d2 44 7b 56

   client kem key:
   0000: 2c 0c 5a 36 e6 77 70 b4 d8 ab 38 9a 92 96 3a cd
   0016: 10 82 38 36 40 be 2d 66 08 02 b8 17 cf eb b9 be

   concatenation of KEM key and ECDH shared key:
   0000: 2c 0c 5a 36 e6 77 70 b4 d8 ab 38 9a 92 96 3a cd
   0016: 10 82 38 36 40 be 2d 66 08 02 b8 17 cf eb b9 be
   0032: 9b 73 7d 41 d6 cf bb 12 56 c5 8c ad 0a 6a e2 c9
   0048: bf 84 a9 0a 72 91 eb 52 e4 c1 81 c8 d2 44 7b 56

   encoded shared secret:
   0000: 00 00 00 40 42 54 58 44 6f 22 75 63 04 de d7 5a
   0016: 1f 23 fe f9 b1 8b 36 eb e0 e6 e2 60 c3 00 12 63
   0032: b0 18 3f 42 49 07 e6 d8 22 b3 b7 6c 6c 38 37 b5
   0048: b4 1f b0 d0 76 35 c7 57 e6 5e fb ef cb 5b c3 8a
   0064: 1a 15 a9 6d

                                  Figure 1

Acknowledgements

   Jan Mojzis added "sntrup4591761x25519-sha512@tinyssh.org" to TinySSH
   [TinySSH] in 2018, and Markus Friedl implemented it for OpenSSH
   [OpenSSH] in 2019.  In 2020, Damien Miller replaced sntrup4591761
   with sntrup761 in OpenSSH to create
   "sntrup761x25519-sha512@openssh.com".  TinySSH added support for it
   in 2021.  It became the default key exchange algorithm in OpenSSH in
   2022.  That is identical to the "sntrup761x25519-sha512" mechanism
   described in this document.

   Thanks to the following people for review and comments: Roman
   Danyliw, Loganaden Velvindron, Panos Kampanakis, Mark Baushke, Theo
   de Raadt, Tero Kivinen, Deb Cooley, Paul Wouters, Damien Miller, Mike
   Bishop, Éric Vyncke, D. J. Bernstein, and Gorry Fairhurst.

Authors' Addresses

   Markus Friedl
   OpenSSH
   Email: markus@openbsd.org


   Jan Mojzis
   TinySSH
   Email: jan.mojzis@gmail.com


   Simon Josefsson
   Email: simon@josefsson.org
   URI:   https://blog.josefsson.org/