SSH Curve25519/448: Secure Shell (SSH) Key Exchange Method Using Curve25519 and Curve448
Two elliptic curve key exchange methods for SSH, built on Curve25519 and Curve448.
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>.
@misc{rfc8731,
series = {Request for Comments},
number = 8731,
howpublished = {RFC 8731},
publisher = {RFC Editor},
doi = {10.17487/RFC8731},
url = {https://www.rfc-editor.org/info/rfc8731},
author = {A. Adamantiadis and S. Josefsson and M. Baushke},
title = {{Secure Shell (SSH) Key Exchange Method Using Curve25519 and Curve448}},
pagetotal = 6,
year = 2020,
month = feb,
} RFC text
Contents
Internet Engineering Task Force (IETF) A. Adamantiadis
Request for Comments: 8731 libssh
Category: Standards Track S. Josefsson
ISSN: 2070-1721 SJD AB
M. Baushke
Juniper Networks, Inc.
February 2020
Secure Shell (SSH) Key Exchange Method Using Curve25519 and Curve448
Abstract
This document describes the specification for using Curve25519 and
Curve448 key exchange methods in the Secure Shell (SSH) protocol.
Status of This Memo
This is an Internet Standards Track document.
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). Further information on
Internet Standards is available in 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/rfc8731.
Copyright Notice
Copyright (c) 2020 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 Simplified BSD License text as described in Section 4.e of
the Trust Legal Provisions and are provided without warranty as
described in the Simplified BSD License.
Table of Contents
1. Introduction
2. Requirements Language
3. Key Exchange Methods
3.1. Shared Secret Encoding
4. Security Considerations
5. IANA Considerations
6. References
6.1. Normative References
6.2. Informative References
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 this extensible SSH framework, and this document reuses the
Elliptic Curve Diffie-Hellman (ECDH) key exchange protocol messages
defined in Section 7.1 (ECDH Message Numbers) of [RFC5656]. Other
parts of [RFC5656], such as Elliptic Curve Menezes-Qu-Vanstone
(ECMQV) key agreement and Elliptic Curve Digital Signature Algorithm
(ECDSA), are not considered in this document.
This document describes how to implement key exchange based on
Curve25519 and Curve448 [RFC7748] in SSH. For Curve25519 with
SHA-256 [RFC6234][SHS], the algorithm described is equivalent to the
privately defined algorithm "curve25519-sha256@libssh.org", which at
the time of publication was implemented and widely deployed in libssh
[libssh] and OpenSSH [OpenSSH]. The Curve448 key exchange method is
similar but uses SHA-512 [RFC6234][SHS].
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 Methods
The key exchange procedure is similar to the ECDH method described in
Section 4 of [RFC5656], though with a different wire encoding used
for public values and the final shared secret. Public ephemeral keys
are encoded for transmission as standard SSH strings.
The protocol flow, the SSH_MSG_KEX_ECDH_INIT and
SSH_MSG_KEX_ECDH_REPLY messages, and the structure of the exchange
hash are identical to Section 4 of [RFC5656].
The method names registered by this document are "curve25519-sha256"
and "curve448-sha512".
The methods are based on Curve25519 and Curve448 scalar
multiplication, as described in [RFC7748]. Private and public keys
are generated as described therein. Public keys are defined as
strings of 32 bytes for Curve25519 and 56 bytes for Curve448.
The key-agreement schemes "curve25519-sha256" and "curve448-sha512"
perform the Diffie-Hellman protocol using the functions X25519 and
X448, respectively. Implementations SHOULD compute these functions
using the algorithms described in [RFC7748]. When they do so,
implementations MUST check whether the computed Diffie-Hellman shared
secret is the all-zero value and abort if so, as described in
Section 6 of [RFC7748]. Alternative implementations of these
functions SHOULD abort when either the client or the server input
forces the shared secret to one of a small set of values, as
described in Sections 6 and 7 of [RFC7748]. Clients and servers MUST
also abort if the length of the received public keys 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
[IANA-REASON]. No further validation is required beyond what is
described in [RFC7748]. The derived shared secret is 32 bytes when
"curve25519-sha256" is used and 56 bytes when "curve448-sha512" is
used. The encodings of all values are defined in [RFC7748]. The
hash used is SHA-256 for "curve25519-sha256" and SHA-512 for
"curve448-sha512".
3.1. Shared Secret Encoding
The following step differs from [RFC5656], which uses a different
conversion. This is not intended to modify that text generally, but
only to be applicable to the scope of the mechanism described in this
document.
The shared secret, K, is defined in [RFC4253] and [RFC5656] as an
integer encoded as a multiple precision integer (mpint).
Curve25519/448 outputs a binary string X, which is the 32- or 56-byte
point obtained by scalar multiplication of the other side's public
key and the local private key scalar. The 32 or 56 bytes of X are
converted into K by interpreting the octets as an unsigned fixed-
length integer encoded in network byte order.
The mpint K is then encoded using the process described in Section 5
of [RFC4251], and the resulting bytes are fed as described in
[RFC4253] to the key exchange method's hash function to generate
encryption keys.
When performing the X25519 or X448 operations, the integer values
there will be encoded into byte strings by doing a fixed-length
unsigned little-endian conversion, per [RFC7748]. It is only later
when these byte strings are then passed to the ECDH function in SSH
that the bytes are reinterpreted as a fixed-length unsigned big-
endian integer value K, and then later that K value is encoded as a
variable-length signed "mpint" before being fed to the hash algorithm
used for key generation. The mpint K is then fed along with other
data to the key exchange method's hash function to generate
encryption keys.
4. Security Considerations
The security considerations of [RFC4251], [RFC5656], and [RFC7748]
are inherited.
Curve25519 with SHA-256 provides strong (~128 bits) security, is
efficient on a wide range of architectures, and has characteristics
that allow for better implementation properties compared to
traditional elliptic curves. Curve448 with SHA-512 provides stronger
(~224 bits) security with similar implementation properties; however,
it has not received the same cryptographic review as Curve25519. It
is also slower (larger key material and larger secure hash
algorithm), but it is provided as a hedge to combat unforeseen
analytical advances against Curve25519 and SHA-256 due to the larger
number of security bits.
The way the derived mpint binary secret string is encoded before it
is hashed (i.e., adding or removing zero bytes for encoding) raises
the potential for a side-channel attack, which could determine the
length of what is hashed. This would leak the most significant bit
of the derived secret and/or allow detection of when the most
significant bytes are zero. For backwards-compatibility reasons, it
was decided not to address this potential problem.
This document provides "curve25519-sha256" as the preferred choice
but suggests that the "curve448-sha512" be implemented to provide
more than 128 bits of security strength should that become a
requirement.
5. IANA Considerations
IANA has added "curve25519-sha256" and "curve448-sha512" to the "Key
Exchange Method Names" registry for SSH [IANA-KEX] that was created
in Section 4.10 of [RFC4250].
6. References
6.1. Normative References
[RFC2119] Bradner, S., "Key words for use in RFCs to Indicate
Requirement Levels", BCP 14, RFC 2119,
DOI 10.17487/RFC2119, March 1997,
<https://www.rfc-editor.org/info/rfc2119>.
[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>.
[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>.
[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>.
[SHS] National Institute of Standards and Technology, "Secure
Hash Standard (SHS)", FIPS PUB 180-4,
DOI 10.6028/NIST.FIPS.180-4, August 2015,
<https://nvlpubs.nist.gov/nistpubs/FIPS/
NIST.FIPS.180-4.pdf>.
6.2. Informative References
[IANA-KEX] IANA, "Secure Shell (SSH) Protocol Parameters: Key
Exchange Method Names",
<https://www.iana.org/assignments/ssh-parameters/>.
[IANA-REASON]
IANA, "Secure Shell (SSH) Protocol Parameters:
Disconnection Messages Reason Codes and Descriptions",
<https://www.iana.org/assignments/ssh-parameters/>.
[libssh] libssh, "The SSH Library", <https://www.libssh.org/>.
[OpenSSH] OpenSSH group of OpenBSD, "The OpenSSH Project",
<https://www.openssh.com/>.
[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>.
Acknowledgements
The "curve25519-sha256" key exchange method is identical to the
"curve25519-sha256@libssh.org" key exchange method created by Aris
Adamantiadis and implemented in libssh and OpenSSH.
Thanks to the following people for review and comments: Denis Bider,
Damien Miller, Niels Moeller, Matt Johnston, Eric Rescorla, Ron
Frederick, and Stefan Buehler.
Authors' Addresses
Aris Adamantiadis
libssh
Email: aris@badcode.be
Simon Josefsson
SJD AB
Email: simon@josefsson.org
Mark D. Baushke
Juniper Networks, Inc.
Email: mdb@juniper.net
ISO Plain Language
On this page
§1Elliptic Curve Key Exchange for SSH
Secure Shell (SSH) (RFC 4251) is a protocol for secure remote login. Its key exchange protocol (RFC 4253) supports an extensible set of methods, and RFC 5656 defines how elliptic curves are integrated into that framework. This document reuses the Elliptic Curve Diffie-Hellman (ECDH) key exchange protocol messages defined in Section 7.1 of RFC 5656. The other parts of RFC 5656, such as Elliptic Curve Menezes-Qu-Vanstone key agreement and the Elliptic Curve Digital Signature Algorithm, are not considered here.
The RFC describes how to implement key exchange based on Curve25519 and Curve448 (RFC 7748) in SSH. For Curve25519 with SHA-256, the algorithm described is equivalent to the privately defined algorithm curve25519-sha256@libssh.org, which at the time of publication was implemented and widely deployed in libssh and OpenSSH. The Curve448 key exchange method is similar but uses SHA-512.
SSH (Secure Shell) has a pluggable set of key exchange methods. This RFC adds two built on modern elliptic curves, so that a client and a server can agree on a shared secret without either of them sending a secret over the connection.
§3How the Key Exchange Runs
The key exchange procedure is similar to the ECDH method described in Section 4 of RFC 5656, though with a different wire encoding used for public values and for the final shared secret. Public ephemeral keys are encoded for transmission as standard SSH strings. The protocol flow, the SSH_MSG_KEX_ECDH_INIT and SSH_MSG_KEX_ECDH_REPLY messages, and the structure of the exchange hash are identical to that section of RFC 5656.
Both methods are based on Curve25519 and Curve448 scalar multiplication as described in RFC 7748, with private and public keys generated as described there. Public keys are defined as strings of 32 bytes for Curve25519 and 56 bytes for Curve448. The schemes curve25519-sha256 and curve448-sha512 perform the Diffie-Hellman protocol using the functions X25519 and X448 respectively. Implementations SHOULD compute these functions with the algorithms described in RFC 7748.
When they do, implementations MUST check whether the computed Diffie-Hellman shared secret is the all-zero value and abort if it is. Alternative implementations SHOULD abort when either the client or the server input forces the shared secret to one of a small set of values. Clients and servers MUST also abort if the length of the received public keys is not the expected length. An abort for these purposes is defined as a disconnect, SSH_MSG_DISCONNECT, of the session, and it SHOULD use the SSH_DISCONNECT_KEY_EXCHANGE_FAILED reason. No further validation is required beyond what RFC 7748 describes. The derived shared secret is 32 bytes when curve25519-sha256 is used and 56 bytes when curve448-sha512 is used, and the hash used is SHA-256 for the first method and SHA-512 for the second.
The client sends an ephemeral public key and the server sends one back, and each side computes the same shared secret from the other's key and its own private key. Both sides must check two things before going on: that the received key is the right length, and that the shared secret is not all zeros, which would mean the other side sent a degenerate key.
- SSH_MSG_KEX_ECDH_INITCarries the client's ephemeral public key, encoded as a standard SSH string.
- SSH_MSG_KEX_ECDH_REPLYCarries the server's public key; the exchange hash covers both sides' values.
| Method name | Curve function | Hash | Public key | Shared secret |
|---|---|---|---|---|
| curve25519-sha256 THIS RFC | X25519 | SHA-256 | 32 bytes | 32 bytes |
| curve448-sha512 | X448 | SHA-512 | 56 bytes | 56 bytes |
§3.1How the Shared Secret Is Encoded
The shared secret K is defined in RFC 4253 and RFC 5656 as an integer encoded as a multiple precision integer, an mpint. Curve25519 and Curve448 output a binary string X, which is the 32- or 56-byte point obtained by scalar multiplication of the other side's public key and the local private key scalar. The 32 or 56 bytes of X are converted into K by interpreting the octets as an unsigned fixed-length integer encoded in network byte order.
The mpint K is then encoded using the process described in Section 5 of RFC 4251, and the resulting bytes are fed as described in RFC 4253 to the key exchange method's hash function to generate the encryption keys. This step is the one that differs from RFC 5656, which uses a different conversion. The change is not intended to modify RFC 5656 generally, but applies only to the mechanism described in this document.
The order of the conversions matters. When the X25519 or X448 operations run, the integer values there are encoded into byte strings by a fixed-length unsigned little-endian conversion, as in RFC 7748. Only later, when those byte strings are passed to the ECDH function in SSH, are the bytes reinterpreted as a fixed-length unsigned big-endian integer value K. K is then encoded as a variable-length signed mpint before it is fed, along with other data, to the hash algorithm used for key generation.
The curve functions hand back a fixed-length byte string, but SSH expects the shared secret as a multiple precision integer. The RFC spells out the order: little-endian inside the curve math, then big-endian when it becomes the SSH secret, then the usual SSH integer encoding before it is hashed.
§4Security Considerations
The security considerations of RFC 4251, RFC 5656 and RFC 7748 are inherited.
Curve25519 with SHA-256 provides strong security of about 128 bits, is efficient on a wide range of architectures, and has characteristics that allow for better implementation properties compared to traditional elliptic curves. Curve448 with SHA-512 provides stronger security of about 224 bits with similar implementation properties. However, it has not received the same cryptographic review as Curve25519, and it is slower, because of larger key material and a larger secure hash algorithm. It is provided as a hedge to combat unforeseen analytical advances against Curve25519 and SHA-256, due to the larger number of security bits.
The way the derived mpint binary secret string is encoded before it is hashed, which means adding or removing zero bytes for encoding, raises the potential for a side-channel attack that could determine the length of what is hashed. That would leak the most significant bit of the derived secret, or allow detection of when the most significant bytes are zero. For backwards-compatibility reasons, it was decided not to address this potential problem.
The document provides curve25519-sha256 as the preferred choice but suggests that curve448-sha512 be implemented, to provide more than 128 bits of security strength should that become a requirement.
Curve25519 with SHA-256 is the preferred choice, giving about 128 bits of security. Curve448 with SHA-512 gives about 224 bits and is slower, and it is offered as a backup in case the mathematics of the first is ever broken. The encoding step has a known side channel that leaks one bit of the secret; the RFC leaves it in place for compatibility.
- About 128 bitsSecurity strength of Curve25519 with SHA-256, the preferred choice.
- About 224 bitsSecurity strength of Curve448 with SHA-512, which is slower.
- Less reviewCurve448 has not received the same cryptographic review as Curve25519.
- A known leakThe mpint encoding can reveal the length of the hashed secret; it was kept for compatibility.
§5IANA Registration
IANA has added curve25519-sha256 and curve448-sha512 to the "Key Exchange Method Names" registry for SSH, the registry created in Section 4.10 of RFC 4250. Those are the names that an SSH client and server use to name the method they are running.
The two method names have been registered so that SSH implementations can refer to them by a standard name.