RFC 9941 | NTRUPrime and X25519 for SSH | April 2026
Friedl, et al. | Informational | [Page]

Stream:
  Internet Engineering Task Force (IETF)
RFC:
  9941
Category:
  Informational
Published:
  April 2026
ISSN:
  2070-1721
Authors:
  M. Friedl
  OpenSSH
  J. Mojzis
  TinySSH
  S. Josefsson

# RFC 9941

# 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 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 and restrictions with respect to this document. Code Components extracted from this document must include Revised BSD License text as described in Section 4.e of the Trust Legal Provisions and are provided without warranty as described in the Revised BSD License.¶

## 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]:¶

Table 1
Method Name | Reference | OK to Implement
--- | --- | ---
sntrup761x25519-sha512 | RFC 9941 | SHOULD

## 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