Internet Engineering Task Force (IETF) M. Friedl
Request for Comments: 9941 OpenSSH
Category: Informational J. Mojzis
ISSN: 2070-1721 TinySSH
S. Josefsson
March 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
Provisions Relating to IETF Documents
(https://trustee.ietf.org/license-info) in effect on the date of
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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 SSH transport layer [RFC4253]
supports an extensible set of methods. Elliptic Curve Algorithms in
SSH [RFC5656] defines how elliptic curves are integrated into the
extensible SSH framework, and SSH KEX Using Curve25519 and Curve448
[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 Elliptic Curve Cryptography (ECC) in
SSH [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 of the SSH Protocol [RFC4251], ECC for
SSH [RFC5656], Elliptic Curves for Security [RFC7748], and SSH KEX
Using Curve25519 and Curve448 [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 curve25519-sha256
[RFC8731], the X25519 shared secret K is used bignum-encoded in that
document, and this raises the potential for a hash-processing time
side-channel 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 ]....01v.......O
0016: 97 a1 74 0e 6b 6f cf 1a d9 d9 99 8a 32 a5 61 e5 ..t.ko......2.a.
0032: 9e 4d 93 67 e2 66 18 f0 0a f5 54 f4 48 65 0c 60 .M.g.f....T.He.`
0048: d1 12 92 c2 aa a9 e4 7c ea 32 a3 f5 86 cb c4 c3 .......|.2......
0064: d5 c2 6f 34 5e 7f d3 57 51 d3 e3 d9 cc 1c e4 49 ..o4^..WQ......I
0080: bb ea 3e 2e 58 5e ac ba 0a b8 22 00 7c 77 a4 e0 ..>.X^....".|w..
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 ..8........v..>.
0128: 7c 74 1e 58 46 f6 81 f0 f2 f2 56 5b f3 be ce c9 |t.XF.....V[....
0144: c8 99 9f 03 88 81 db 17 75 1d fb f5 b1 e2 f3 5d ........u......]
0160: 32 ce 19 75 49 e7 e1 17 bf 35 0d 97 7c ac 0a cf 2..uI....5..|...
0176: 6c 8a 0f fc 07 4b a7 8b c5 93 f7 47 7c b6 d5 bf l....K.....G|...
0192: 02 f0 96 80 e8 dc f3 87 c9 f0 b2 91 e7 37 70 82 .............7p.
0208: 3e 47 b7 18 72 be 5a da b1 85 d3 6e 56 5d 8a a3 >G..r.Z....nV]..
0224: 62 fa 3e d0 ea 6e b9 fa 69 ec 96 86 94 81 2e 88 b.>..n..i.......
0240: 2b ba e5 af 70 1e ae ba 5f cb ea 82 e5 ba 67 0e +...p..._.....g.
0256: 4d f6 2a ec 13 a9 19 b4 08 9c b7 32 bb 40 de c3 M.*........2.@..
0272: e9 33 e1 c4 0d 5b 72 00 06 c4 3b 7f 57 d4 85 76 .3...[r...;.W..v
0288: 4c 4c 3d ab 8e 1b 00 00 ac d9 8c 05 b3 18 24 85 LL=...........$.
0304: 77 28 74 71 0d 68 8b 02 2c 59 55 a7 4d a4 6e 37 w(tq.h..,YU.M.n7
0320: 85 6c 77 68 f5 b7 a7 52 61 af 37 b4 09 07 34 68 .lwh...Ra.7...4h
0336: b6 83 ca f2 03 25 47 f9 09 e6 da bd 82 07 7e d1 .....%G.......~.
0352: 78 16 74 1a a5 4c 5b ac 78 d8 0f 1a 44 08 44 a7 x.t..L[.x...D.D.
0368: ef 85 00 43 19 c3 3e b4 54 e6 3f f1 ac 83 03 ce ...C..>.T.?.....
0384: 7c bd ef 3c fd eb 47 6f f7 f9 e0 1f 13 9f cb 77 |..<..Go.......w
0400: 52 40 9d 3a d7 8b ad bf cc f1 06 ec 93 32 48 be R@.:.........2H.
0416: 0a 53 99 5c dd 9e 96 3b 84 21 8f b2 b4 fd b8 97 .S.\...;.!......
0432: 8b 7a 8f 71 aa e6 af 4e 22 53 18 f0 a2 30 a0 53 .z.q...N"S...0.S
0448: 30 c9 d8 a9 d7 67 08 a5 ad 81 64 7b 3a 02 ae ff 0....g....d{:...
0464: e7 fa 41 68 d0 54 e3 42 86 da f7 f0 98 31 38 e5 ..Ah.T.B.....18.
0480: 8c fa 86 5c 5c f9 82 f8 a2 09 91 91 96 72 12 e5 ...\\........r..
0496: 8f 8b 8e 9b e8 5d bd 66 4b 6e ec a3 b3 03 c5 4e .....].fKn.....N
0512: 0f 7e a5 15 ef ab 01 8c 6d 02 52 77 bc 9a 02 f2 .~......m.Rw....
0528: 2e bf 03 40 fe 5a 80 5a c0 78 1e 95 21 10 9d dd ...@.Z.Z.x..!...
0544: 37 87 00 ae 13 c5 9d 9c 81 87 37 3e 7d e0 40 bc 7.........7>}.@.
0560: 83 76 69 4f 9f c4 08 fd aa a1 7e aa 88 0e 4c 56 .viO......~...LV
0576: a0 47 c5 d6 94 fb 52 67 f3 36 de b2 7e bf d1 33 .G....Rg.6..~..3
0592: 41 fd 05 20 66 60 f4 91 96 5f 19 33 2d 17 ec e0 A.. f`..._.3-...
0608: 3e 93 7a 66 3b b0 de f4 ad 51 90 a4 a1 94 f3 37 >.zf;....Q.....7
0624: 9a 77 11 02 67 45 6d 4d 19 80 33 58 56 2c b8 11 .w..gEmM..3XV,..
0640: 51 7b bc ec 43 fe 3d 96 ac f7 f0 8b 8d c6 2c 02 Q{..C.=.......,.
0656: 2f c0 67 21 56 49 ee bf 07 17 48 f9 30 0b 18 2c /.g!VI....H.0..,
0672: fa 7b 57 93 be f7 12 99 57 be 98 e7 55 84 da ed .{W.....W...U...
0688: 5c 94 71 fa 48 0f ed 97 ab e4 a5 d6 b6 26 3a e4 \.q.H........&:.
0704: cb fe f9 ed 07 4b 42 bf e5 a1 d1 34 4d 7b 67 b9 .....KB....4M{g.
0720: b7 06 7b d2 c7 ae 57 15 21 58 55 70 70 93 f1 87 ..{...W.!XUpp...
0736: 31 bf 85 74 fe 36 0d 08 c8 07 a2 14 fc d5 96 8b 1..t.6..........
0752: 59 62 97 30 43 75 c2 a9 4f ec f9 e9 33 a9 38 cb Yb.0Cu..O...3.8.
0768: ae ee 63 34 8c 65 54 e7 9d d4 23 a2 4f b9 00 ed ..c4.eT...#.O...
0784: b4 be 0b 1c df d4 97 c0 89 ab dd 5f 75 13 ce 37 ..........._u..7
0800: f3 d2 26 55 72 39 61 f0 d2 11 e8 e7 5f 93 5b 79 ..&Ur9a....._.[y
0816: e5 6c 28 f3 0a f9 5e 99 b8 a0 e6 4a 22 88 e5 28 .l(...^....J"..(
0832: 82 0c 6f 72 1d dd 80 84 57 04 72 f4 26 56 71 f3 ..or....W.r.&Vq.
0848: 92 23 ff 9e a9 fd 05 0b 51 99 72 32 98 a5 02 87 .#......Q.r2....
0864: fe bb 99 18 5a b3 ec ab f9 26 7b 97 79 da 5f 19 ....Z....&{.y._.
0880: 4e e7 7d a5 2d 53 40 2a 1f 1b 62 df 3b 11 82 e6 N.}.-S@*..b.;...
0896: 90 7f 0f 56 0c 75 14 03 e7 6f aa f0 0e 0a 17 13 ...V.u...o......
0912: 54 f5 ea d7 21 31 2c 7a c5 7f a3 ae 14 f3 05 42 T...!1,z.......B
0928: e9 c9 6c 6d d1 0a cb 19 35 7f 01 8a 8c e2 a1 09 ..lm....5.......
0944: b5 c6 e5 e8 2b 4f 1e a2 e9 ce 5b e4 76 f7 53 4f ....+O....[.v.SO
0960: 52 d4 75 22 4b aa 1e cd 42 0e be d7 dc 76 6f 94 R.u"K...B....vo.
0976: 0a 37 47 ca 44 bd e6 9e c1 2a 0d 57 f3 c2 47 40 .7G.D....*.W..G@
0992: 23 db a8 45 c7 9b 4a 96 13 6a 73 ad 6a a2 a8 e4 #..E..J..js.j...
1008: df 92 34 76 f9 47 8d b9 21 63 46 c2 d7 f2 64 e6 ..4v.G..!cF...d.
1024: 17 27 9f cf f3 ae cd 3a 7d ed 5e 46 7c 33 71 f6 .'.....:}.^F|3q.
1040: 71 c8 92 dc ae e6 a0 c8 05 0c e0 37 fb ea 15 ed q..........7....
1056: b0 78 a5 bf b1 48 8b 46 64 1e c8 81 00 55 82 89 .x...H.Fd....U..
1072: 25 f8 b1 8b 1c e4 96 54 f8 be 97 b1 d3 20 f3 a0 %......T..... ..
1088: b5 c1 dd d5 27 d0 61 d9 96 2a 74 76 a8 33 10 78 ....'.a..*tv.3.x
1104: ff b2 86 ee 4f 0b 78 73 dd 7f 7c b5 02 e9 12 35 ....O.xs..|....5
1120: d3 9e ab 81 cd 9b 61 fb 2b 33 72 ee c6 bb 8a bc ......a.+3r.....
1136: bd 4f e5 9b c2 55 8f a0 b1 e7 1a 6a c1 e3 f1 5c .O...U.....j...\
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 ..#y..N..U...>b.
0016: eb 9b 6a 6f ca de ed 90 04 db b1 30 f6 ff ef 4f ..jo.......0...O
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 qg.U.....|....}.
0016: 4f b6 22 5e 4d 77 81 73 4f 1d b9 82 79 ff e9 34 O."^Mw.sO...y..4
0032: 26 9f d2 2e 4e c6 a3 5f 79 9c 26 68 99 3a 0f 40 &...N.._y.&h.:.@
0048: 33 2a 7d dd fa 7a e7 6b 1e e7 9d 50 b7 48 0f aa 3*}..z.k...P.H..
0064: aa 97 ff e7 8c 6c ac 5d 10 df 2b e3 cc 93 ea dc .....l.]..+.....
0080: 18 17 b3 34 42 70 7a 27 85 58 2a ae c2 e6 b9 26 ...4Bpz'.X*....&
0096: 93 fd 23 a9 ae ac 4a 35 8b 57 c1 5c 95 cb 23 fb ..#...J5.W.\..#.
0112: e5 93 0f 7c f5 63 6b 5b a1 53 b5 55 d0 75 16 21 ...|.ck[.S.U.u.!
0128: 8a db 95 ff c8 58 ac f4 7e 46 69 0a 4c a9 c8 cc .....X..~Fi.L...
0144: eb e8 66 7c c4 fb fd 98 2c 0c 7f 41 8c 34 89 49 ..f|....,..A.4.I
0160: a0 25 59 eb 63 a1 e6 8f 37 bf bc b3 ce 0a da 53 .%Y.c...7......S
0176: 54 7f c2 41 52 eb 6c 9e 6e d0 ea af 6a 82 5d 17 T..AR.l.n...j.].
0192: 6f 17 8d 06 8a 86 55 60 28 31 12 4a 0c de 6b be o.....U`(1.J..k.
0208: eb fd 38 13 6c 56 69 ad 0e 72 c8 bd b4 69 9d 32 ..8.lVi..r...i.2
0224: b4 1c 8e 6f f4 25 e1 9b c5 6f 8b 02 77 52 ae 72 ...o.%...o..wR.r
0240: eb 9b 03 c8 9f de 15 bd f6 5a e8 9d 83 81 7b 48 .........Z....{H
0256: 7a 69 9a d0 91 41 aa 07 5a fa ad d6 e8 55 39 d9 zi...A..Z....U9.
0272: d1 0f d2 18 dc a0 9d 1c f1 e4 1c 0d f8 88 85 6b ...............k
0288: 6d 11 24 3e 61 de 48 95 5f 2a d1 c9 ad 3f b8 41 m.$>a.H._*...?.A
0304: 49 6d 9f 7c 3c bf 20 fe 37 7f 8c 8c 8f 72 ca f4 Im.|<. .7....r..
0320: 19 e4 cc a1 d8 08 cb 69 ec da 2b 88 e8 98 e9 1e .......i..+.....
0336: 29 af 86 6f 19 a8 67 56 ef b4 33 e4 2b b8 fe 61 )..o..gV..3.+..a
0352: ad 36 4c 42 f8 ec 04 38 09 62 02 66 b5 54 fc 69 .6LB...8.b.f.T.i
0368: 46 29 05 27 d8 32 fd 37 4c d4 62 55 e1 ae e9 62 F).'.2.7L.bU...b
0384: 66 a0 f4 cb 4b 01 af 6b ea 09 80 00 a2 2b ff 0e f...K..k.....+..
0400: 85 2c 92 b2 5c f9 f3 eb 44 a3 9a e8 55 bb e3 2f .,..\...D...U../
0416: 2d 20 5a 77 67 97 57 90 7f 4b b3 08 92 41 1a c0 - Zwg.W..K...A..
0432: f6 1b e9 a4 06 29 ea 31 eb 81 f0 94 96 aa 26 95 .....).1......&.
0448: 06 ed 4b f0 d3 9f aa 73 89 fa 6e f7 8f 4b f5 fa ..K....s..n..K..
0464: e4 5f 7c b6 08 e9 b2 18 77 99 9c ac 7b fb ec 41 ._|.....w...{..A
0480: 41 1e 29 c2 d0 a5 de bc 59 2f 14 45 6d af b1 e0 A.).....Y/.Em...
0496: 9c 77 73 0e ac 52 23 73 11 35 27 17 8c a3 ff 0e .ws..R#s.5'.....
0512: 52 5d b7 c8 06 c5 05 43 15 53 e8 fc 83 64 df 10 R].....C.S...d..
0528: 8b 9c 74 5c 0e d9 54 5e 9a 49 cf 13 e4 1d 86 35 ..t\..T^.I.....5
0544: 24 a3 27 75 d3 d6 b4 95 78 8f 0d 81 3b 80 6b 26 $.'u....x...;.k&
0560: 25 9f 14 b1 65 73 e8 ce fa 95 6d b1 15 0c 76 3c %...es....m...v<
0576: b1 75 a9 96 78 c8 4b 91 06 a9 94 bc ec fa 44 eb .u..x.K.......D.
0592: 39 77 4d ee df ae eb 0e 90 61 eb ab 6a 17 1b 24 9wM......a..j..$
0608: 3c 3a 6e c4 bb 6f 72 46 3d 9a b8 8c 6a e7 45 c7 <:n..orF=...j.E.
0624: 0f 81 db 19 6e ce 65 74 ca db 73 ec 1e ce 5f d7 ....n.et..s..._.
0640: 43 6b fe ff c0 e1 61 26 aa b7 6f e0 dc 7f d1 de Ck....a&..o.....
0656: 95 f0 28 fd 24 9c 73 1c cf ef 3e fe 21 a1 e5 4e ..(.$.s...>.!..N
0672: 77 da db 12 01 7a e4 2c b5 f3 9d 30 e6 49 99 d6 w....z.,...0.I..
0688: 21 58 cc 5b 5b d5 ff ca ea df 9a fd d6 73 be cd !X.[[........s..
0704: ae 7c 0d ea 78 e4 dd 74 f9 93 53 21 70 b7 cd 16 .|..x..t..S!p...
0720: ea c7 e9 5d 01 e0 e3 e6 53 46 7f fa a0 48 3e 5b ...]....SF...H>[
0736: af 64 46 ff 0f 0c b5 c9 92 48 e8 20 35 1d c8 ae .dF......H. 5...
0752: d8 c4 38 31 aa 2c b5 91 6b eb 86 ac 2b fa 86 f2 ..81.,..k...+...
0768: d1 bd 7d 51 4c be f3 bf 4b d0 f0 78 0e 20 d3 30 ..}QL...K..x. .0
0784: fc f8 00 53 2a 6a 9b d9 e4 0e 08 d1 ad 52 7a ca ...S*j.......Rz.
0800: f3 8b 0e a8 fb 45 3c 66 03 66 b4 54 a5 3d 8e df .....E<f.f.T.=..
0816: 4a 8f 66 f0 16 44 3b a9 f1 b3 db bb 7e d6 38 e5 J.f..D;.....~.8.
0832: 5f 62 27 bb ba 34 0a 6f 9b 78 dd ae 54 ab 54 53 _b'..4.o.x..T.TS
0848: 3a e1 d2 f1 d8 1e 8b 31 61 cd 69 8a 63 fb 7c 24 :......1a.i.c.|$
0864: 75 5f e6 6d 64 3d e4 12 cb 2d b3 6f 0f 5a 19 28 u_.md=...-.o.Z.(
0880: 1f d6 f6 9c ee 44 11 1a c5 84 d6 e3 a2 05 5d d4 .....D........].
0896: 85 db f1 8f e4 17 df bc 4c 78 98 d1 70 3b 63 d6 ........Lx..p;c.
0912: a4 91 db f1 9e 16 23 fa e0 54 f6 64 d1 0b d0 d6 ......#..T.d....
0928: a6 fd f1 66 72 8c 65 d8 17 af c9 33 49 c8 e9 4d ...fr.e....3I..M
0944: 1c 0a 77 2b 96 86 f2 16 55 3a e3 f6 00 bb b6 5a ..w+....U:.....Z
0960: 86 f6 fc 3f d6 f9 a4 1d fd 29 1d 5b 65 dc b3 14 ...?.....).[e...
0976: 96 10 3e c1 9a 90 23 e8 88 81 24 42 68 7a aa 25 ..>...#...$Bhz.%
0992: ba f3 50 bd b9 ae be dc b3 ff 39 81 44 89 00 9d ..P.......9.D...
1008: 4e 26 d6 ef df 7c e0 53 d3 ed 34 07 3d f2 1e 42 N&...|.S..4.=..B
1024: 28 af 1d 12 ce 98 c7 b0 7b 90 81 b5 ea f3 2c (.......{.....,
server public key c25519:
0000: 18 6c 55 03 db 1c 38 e3 40 d7 09 24 77 46 14 b8 .lU...8.@..$wF..
0016: 5e e4 7f 19 98 04 9b 90 1f f6 b9 7f b0 70 9e 32 ^............p.2
shared secret
0000: 9b 73 7d 41 d6 cf bb 12 56 c5 8c ad 0a 6a e2 c9 .s}A....V....j..
0016: bf 84 a9 0a 72 91 eb 52 e4 c1 81 c8 d2 44 7b 56 ....r..R.....D{V
client kem key:
0000: 2c 0c 5a 36 e6 77 70 b4 d8 ab 38 9a 92 96 3a cd ,.Z6.wp...8...:.
0016: 10 82 38 36 40 be 2d 66 08 02 b8 17 cf eb b9 be ..86@.-f........
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 ,.Z6.wp...8...:.
0016: 10 82 38 36 40 be 2d 66 08 02 b8 17 cf eb b9 be ..86@.-f........
0032: 9b 73 7d 41 d6 cf bb 12 56 c5 8c ad 0a 6a e2 c9 .s}A....V....j..
0048: bf 84 a9 0a 72 91 eb 52 e4 c1 81 c8 d2 44 7b 56 ....r..R.....D{V
encoded shared secret:
0000: 00 00 00 40 42 54 58 44 6f 22 75 63 04 de d7 5a ...@BTXDo"uc...Z
0016: 1f 23 fe f9 b1 8b 36 eb e0 e6 e2 60 c3 00 12 63 .#....6....`...c
0032: b0 18 3f 42 49 07 e6 d8 22 b3 b7 6c 6c 38 37 b5 ..?BI..."..ll87.
0048: b4 1f b0 d0 76 35 c7 57 e6 5e fb ef cb 5b c3 8a ....v5.W.^...[..
0064: 1a 15 a9 6d ...m
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/