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<front> <front>
<title abbrev="Curve25519/448 for SSH"> <title abbrev="Curve25519/448 for SSH">
Secure Shell (SSH) Key Exchange Method using Curve25519 and Secure Shell (SSH) Key Exchange Method Using Curve25519 and
Curve448 Curve448
</title> </title>
<seriesInfo name="RFC" value="8731" />
<author initials="A." surname="Adamantiadis" fullname="Aris Adamantiadis"> <author initials="A." surname="Adamantiadis" fullname="Aris Adamantiadis">
<organization>libssh</organization> <organization>libssh</organization>
<address> <address>
<email>aris@badcode.be</email> <email>aris@badcode.be</email>
</address> </address>
</author> </author>
<author initials="S." surname="Josefsson" fullname="Simon Josefsson"> <author initials="S." surname="Josefsson" fullname="Simon Josefsson">
<organization>SJD AB</organization> <organization>SJD AB</organization>
<address> <address>
<email>simon@josefsson.org</email> <email>simon@josefsson.org</email>
</address> </address>
</author> </author>
<author initials="M." surname="Baushke" fullname="Mark D. Baushke">
<author initials="M. D." surname="Baushke" fullname="Mark D. Baushke">
<organization>Juniper Networks, Inc.</organization> <organization>Juniper Networks, Inc.</organization>
<address> <address>
<email>mdb@juniper.net</email> <email>mdb@juniper.net</email>
</address> </address>
</author> </author>
<date month="February" year="2020"/>
<date year="2019"/>
<workgroup>Internet Engineering Task Force</workgroup> <workgroup>Internet Engineering Task Force</workgroup>
<abstract> <keyword>Elliptic</keyword>
<keyword>Curve</keyword>
<keyword>Diffie</keyword>
<keyword>Hellman</keyword>
<keyword>ECDH</keyword>
<abstract>
<t> <t>
This document describes the specification for using Curve25519 This document describes the specification for using Curve25519
and Curve448 key exchange methods in the Secure Shell (SSH) and Curve448 key exchange methods in the Secure Shell (SSH)
protocol. protocol.
</t> </t>
</abstract> </abstract>
</front> </front>
<middle> <middle>
<section numbered="true" toc="default">
<section title="Introduction"> <name>Introduction</name>
<t> <t>
Secure Shell (SSH) <xref target="RFC4251"/> is a secure remote Secure Shell (SSH) <xref target="RFC4251" format="default"/> is a secure remote
login protocol. The key exchange protocol described in <xref login protocol. The key exchange protocol described in <xref
target="RFC4253"/> supports an extensible set of methods. target="RFC4253" format="default"/> supports an extensible set of
<xref target="RFC5656"/> defines how elliptic curves are methods.
<xref target="RFC5656" format="default"/> defines how elliptic curves ar
e
integrated into this extensible SSH framework, and this integrated into this extensible SSH framework, and this
document reuses the Elliptic Curve Diffie-Hellman (ECDH) key document reuses the Elliptic Curve Diffie-Hellman (ECDH) key
exchange protocol messages defined in section 7.1 "ECDH exchange protocol messages defined in Section
Message Numbers" <xref target="RFC5656"/>. Other parts of <xref target="RFC5656" sectionFormat="bare" section="7.1">ECDH Message
<xref target="RFC5656"/>, such as Elliptic Curve Numbers</xref> of <xref target="RFC5656"/>. Other parts of
Menezes-Qu-Vanstone (ECMQV) key agreement, and Elliptic Curve <xref target="RFC5656" format="default"/>, such as Elliptic Curve
Digital Signature Algorithm (ECDSA) are not considered in this Menezes-Qu-Vanstone (ECMQV) key agreement and Elliptic Curve
Digital Signature Algorithm (ECDSA), are not considered in this
document. document.
</t> </t>
<t> <t>
This document describes how to implement key exchange based on This document describes how to implement key exchange based on
Curve25519 and Curve448 <xref target="RFC7748"/> in SSH. For Curve25519 and Curve448 <xref target="RFC7748" format="default"/> in SSH
Curve25519 with SHA-256 <xref target="RFC6234"/> and <xref . For
target="SHS"/>, the algorithm described is equivalent to the Curve25519 with SHA-256 <xref target="RFC6234" format="default"/><xref
target="SHS" format="default"/>, the algorithm described is equivalent
to the
privately defined algorithm "curve25519-sha256@libssh.org", privately defined algorithm "curve25519-sha256@libssh.org",
which at the time of publication was implemented and widely which at the time of publication was implemented and widely
deployed in libssh <xref target="libssh"/> and OpenSSH <xref deployed in libssh <xref target="libssh" format="default"/> and
target="OpenSSH"/>. The Curve448 key exchange method is OpenSSH <xref target="OpenSSH" format="default"/>. The Curve448 key
similar but uses SHA-512 <xref target="RFC6234"/> and <xref exchange method is
target="SHS"/>. similar but uses SHA-512 <xref target="RFC6234"
format="default"/><xref target="SHS" format="default"/>.
</t> </t>
</section> </section>
<section numbered="true" toc="default">
<section title="Requirements Language"> <name>Requirements Language</name>
<t>
<t> The key words "<bcp14>MUST</bcp14>", "<bcp14>MUST NOT</bcp14>",
The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL "<bcp14>REQUIRED</bcp14>", "<bcp14>SHALL</bcp14>", "<bcp14>SHALL
NOT", "SHOULD", "SHOULD NOT", "RECOMMENDED", "NOT NOT</bcp14>", "<bcp14>SHOULD</bcp14>", "<bcp14>SHOULD NOT</bcp14>",
RECOMMENDED", "MAY", and "OPTIONAL" in this document are to be "<bcp14>RECOMMENDED</bcp14>", "<bcp14>NOT RECOMMENDED</bcp14>",
interpreted as described in BCP&nbsp;14 <xref "<bcp14>MAY</bcp14>", and "<bcp14>OPTIONAL</bcp14>" in this document are to
target="RFC2119"/> <xref target="RFC8174"/> when, and only be interpreted as
when, they appear in all capitals, as shown here. described in BCP&nbsp;14 <xref target="RFC2119"/> <xref target="RFC8174"/>
</t> when, and only when, they appear in all capitals, as shown here.
</t>
</section> </section>
<section numbered="true" toc="default">
<section title="Key Exchange Methods"> <name>Key Exchange Methods</name>
<t> <t>
The key exchange procedure is similar to the ECDH method The key exchange procedure is similar to the ECDH method
described in chapter 4 of <xref target="RFC5656" />, though described in <xref target="RFC5656" sectionFormat="of" section="4"/>, th ough
with a different wire encoding used for public values and the with a different wire encoding used for public values and the
final shared secret. Public ephemeral keys are encoded for final shared secret. Public ephemeral keys are encoded for
transmission as standard SSH strings. transmission as standard SSH strings.
</t> </t>
<t> <t>
The protocol flow, the SSH_MSG_KEX_ECDH_INIT and The protocol flow, the SSH_MSG_KEX_ECDH_INIT and
SSH_MSG_KEX_ECDH_REPLY messages, and the structure of the SSH_MSG_KEX_ECDH_REPLY messages, and the structure of the
exchange hash are identical to chapter 4 of <xref exchange hash are identical to <xref target="RFC5656"
target="RFC5656" />. sectionFormat="of" section="4"/>.
</t> </t>
<t> <t>
The method names registered by this document are The method names registered by this document are
"curve25519-sha256" and "curve448-sha512". "curve25519-sha256" and "curve448-sha512".
</t> </t>
<t> <t>
The methods are based on Curve25519 and Curve448 scalar The methods are based on Curve25519 and Curve448 scalar
multiplication, as described in <xref target="RFC7748"/>. multiplication, as described in <xref target="RFC7748" format="default"/ >.
Private and public keys are generated as described therein. Private and public keys are generated as described therein.
Public keys are defined as strings of 32 bytes for Curve25519 Public keys are defined as strings of 32 bytes for Curve25519
and 56 bytes for Curve448. and 56 bytes for Curve448.
</t> </t>
<t> <t>
Key-agreement schemes "curve25519-sha256" and The key-agreement schemes "curve25519-sha256" and
"curve448-sha512" perform the Diffie-Hellman protocol using "curve448-sha512" perform the Diffie-Hellman protocol using
the functions X25519 and X448, respectively. Implementations the functions X25519 and X448, respectively. Implementations
SHOULD compute these functions using the algorithms described <bcp14>SHOULD</bcp14> compute these functions using the algorithms descr
in [RFC7748]. When they do so, implementations MUST check ibed
in <xref target="RFC7748" format="default"/>. When they do so,
implementations <bcp14>MUST</bcp14> check
whether the computed Diffie-Hellman shared secret is the whether the computed Diffie-Hellman shared secret is the
all-zero value and abort if so, as described in Section 6 of all-zero value and abort if so, as described in <xref target="RFC7748"
[RFC7748]. Alternative implementations of these functions sectionFormat="of" section="6"/>.
SHOULD abort when either input forces the shared secret to one Alternative implementations of these functions
of a small set of values, as described in Section 7 of <bcp14>SHOULD</bcp14> abort when either the client or the server input
[RFC7748]. Clients and servers MUST also abort if forces the shared secret to one of a small set of values, as
described in Sections <xref target="RFC7748" section="6"
sectionFormat="bare"/> and <xref target="RFC7748" section="7"
sectionFormat="bare"/> of <xref target="RFC7748"/>. Clients and servers <
bcp14>MUST</bcp14> also abort if
the length of the received public keys are not the expected the length of the received public keys are not the expected
lengths. An abort for these purposes is defined as a lengths. An abort for these purposes is defined as a
disconnect (SSH_MSG_DISCONNECT) of the session and SHOULD use disconnect (SSH_MSG_DISCONNECT) of the session and <bcp14>SHOULD</bcp14> use
the SSH_DISCONNECT_KEY_EXCHANGE_FAILED reason for the message the SSH_DISCONNECT_KEY_EXCHANGE_FAILED reason for the message
<xref target="IANA-REASON"/>. <xref target="IANA-REASON" format="default"/>.
No further validation is required beyond what is described in No further validation is required beyond what is described in
<xref target="RFC7748"/>. The derived shared secret is 32 <xref target="RFC7748" format="default"/>. The derived shared secret is 32
bytes when "curve25519-sha256" is used and 56 bytes when bytes when "curve25519-sha256" is used and 56 bytes when
"curve448-sha512" is used. The encodings of all values are "curve448-sha512" is used. The encodings of all values are
defined in <xref target="RFC7748"/>. The hash used is SHA-256 defined in <xref target="RFC7748" format="default"/>. The hash used is S HA-256
for "curve25519-sha256" and SHA-512 for "curve448-sha512". for "curve25519-sha256" and SHA-512 for "curve448-sha512".
</t> </t>
<section numbered="true" toc="default">
<section title="Shared Secret Encoding"> <name>Shared Secret Encoding</name>
<t> <t>
The following step differs from <xref target="RFC5656"/>, The following step differs from <xref target="RFC5656" format="default
which uses a different conversion. This is not intended to "/>,
which uses a different conversion. This is not intended to
modify that text generally, but only to be applicable to the modify that text generally, but only to be applicable to the
scope of the mechanism described in this document. scope of the mechanism described in this document.
</t> </t>
<t> <t>
The shared secret, K, is defined in <xref target="RFC4253"/> The shared secret, K, is defined in <xref target="RFC4253" format="def
and <xref target="RFC5656"/> as an integer encoded ault"/>
as a multiple precision integer (mpint). Curve25519/448 and <xref target="RFC5656" format="default"/> as an integer encoded
outputs a binary string X, which is the 32 or 56 byte point 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 obtained by scalar multiplication of the other side's public
key and the local private key scalar. The 32 or 56 bytes of key and the local private key scalar. The 32 or 56 bytes of
X are converted into K by interpreting the octets as an X are converted into K by interpreting the octets as an
unsigned fixed-length integer encoded in network byte order. unsigned fixed-length integer encoded in network byte order.
</t> </t>
<t> <t>
The integer K is then encoded as an mpint using the process The mpint K is then encoded using the process
described in section 5 of <xref target="RFC4251"/> and the described in <xref target="RFC4251" sectionFormat="of" section="5"/>,
resulting bytes are fed as described in <xref and the
target="RFC4253"/> to the key exchange method's hash resulting bytes are fed as described in <xref target="RFC4253" format=
"default"/> to the key exchange method's hash
function to generate encryption keys. function to generate encryption keys.
</t> </t>
<t> <t>
When performing the X25519 or X448 operations, the integer When performing the X25519 or X448 operations, the integer
values there will be encoded into byte strings by doing a values there will be encoded into byte strings by doing a
fixed-length unsigned little-endian conversion, per <xref fixed-length unsigned little-endian conversion, per <xref
target="RFC7748"/>. It is only later when these byte strings target="RFC7748" format="default"/>. It is only later when these
byte strings
are then passed to the ECDH function in SSH that the bytes are then passed to the ECDH function in SSH that the bytes
are re-interpreted as a fixed-length unsigned big-endian are reinterpreted as a fixed-length unsigned big-endian
integer value K, and then later that K value is encoded as a integer value K, and then later that K value is encoded as a
variable-length signed "mpint" before being fed to the hash variable-length signed "mpint" before being fed to the hash
algorithm used for key generation. The mpint K is then fed algorithm used for key generation. The mpint K is then fed
along with other data to the key exchange method's hash along with other data to the key exchange method's hash
function to generate encryption keys. function to generate encryption keys.
</t> </t>
</section> </section>
</section> </section>
<section title="Acknowledgements"> <section numbered="true" toc="default">
<name>Security Considerations</name>
<t>
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.
</t>
<t>
Thanks to the following people for review and comments: Denis
Bider, Damien Miller, Niels Mller, Matt Johnston, Eric
Rescorla, Ron Frederick, Stefan Bhler.
</t>
</section>
<section title="Security Considerations">
<t> <t>
The security considerations of <xref target="RFC4251"/>, <xref The security considerations of <xref target="RFC4251" format="default"/>
target="RFC5656"/>, and <xref target="RFC7748"/> are , <xref target="RFC5656" format="default"/>, and <xref target="RFC7748" format="
default"/> are
inherited. inherited.
</t> </t>
<t> <t>
Curve25519 with SHA-256 provides strong (~128 bits) security Curve25519 with SHA-256 provides strong (~128 bits) security,
and is efficient on a wide range of architectures, and has is efficient on a wide range of architectures, and has
properties that allows better implementation properties characteristics that allow for better implementation properties
compared to traditional elliptic curves. Curve448 with SHA-512 compared to traditional elliptic curves. Curve448 with SHA-512
provides stronger (~224 bits) security with similar provides stronger (~224 bits) security with similar
implementation properties, but has not received the same implementation properties; however, it has not received the same
cryptographic review as Curve25519, and is slower (larger key cryptographic review as Curve25519. It is also slower (larger key
material and larger secure hash algorithm), but it is provided material and larger secure hash algorithm), but it is provided
as a hedge to combat unforeseen analytical advances against as a hedge to combat unforeseen analytical advances against
Curve25519 and SHA-256 due to the larger number of security Curve25519 and SHA-256 due to the larger number of security
bits. bits.
</t> </t>
<t> <t>
The way the derived binary secret string is encoded into a The way the derived mpint binary secret string is encoded
mpint before it is hashed (i.e., adding or removing zero-bytes before it is hashed (i.e., adding or removing zero bytes
for encoding) raises the potential for a side-channel attack for encoding) raises the potential for a side-channel attack,
which could determine the length of what is hashed. This which could determine the length of what is hashed. This
would leak the most significant bit of the derived secret, would leak the most significant bit of the derived secret
and/or allow detection of when the most significant bytes are and/or allow detection of when the most significant bytes are
zero. For backwards compatibility reasons it was decided not zero. For backwards-compatibility reasons, it was decided not
to address this potential problem. to address this potential problem.
</t> </t>
<t> <t>
This document provides "curve25519-sha256" as the preferred This document provides "curve25519-sha256" as the preferred
choice, but suggests that the "curve448-sha512" is implemented choice but suggests that the "curve448-sha512" be implemented
to provide more than 128 bits of security strength should that to provide more than 128 bits of security strength should that
become a requirement. become a requirement.
</t> </t>
</section> </section>
<section anchor="iana-considerations" numbered="true" toc="default">
<section anchor="iana-considerations" title="IANA Considerations"> <name>IANA Considerations</name>
<t> <t>
IANA is requested to add "curve25519-sha256" and IANA has added "curve25519-sha256" and
"curve448-sha512" to the "Key Exchange Method Names" registry "curve448-sha512" to the "Key Exchange Method Names" registry
for SSH <xref target="IANA-KEX"/> that was created in <xref for SSH <xref target="IANA-KEX" format="default"/> that was created in
target="RFC4250">RFC 4250 section 4.10</xref>. <xref target="RFC4250" sectionFormat="of" section="4.10"/>.
</t> </t>
</section> </section>
</middle> </middle>
<back> <back>
<references>
<name>References</name>
<references>
<name>Normative References</name>
<xi:include href="https://xml2rfc.tools.ietf.org/public/rfc/bibxml/refer
ence.RFC.2119.xml"/>
<xi:include href="https://xml2rfc.tools.ietf.org/public/rfc/bibxml/refer
ence.RFC.4250.xml"/>
<xi:include href="https://xml2rfc.tools.ietf.org/public/rfc/bibxml/refer
ence.RFC.4251.xml"/>
<xi:include href="https://xml2rfc.tools.ietf.org/public/rfc/bibxml/refer
ence.RFC.4253.xml"/>
<xi:include href="https://xml2rfc.tools.ietf.org/public/rfc/bibxml/refer
ence.RFC.5656.xml"/>
<xi:include href="https://xml2rfc.tools.ietf.org/public/rfc/bibxml/refer
ence.RFC.8174.xml"/>
<references title="Normative References"> <reference anchor="SHS" target="https://nvlpubs.nist.gov/nistpubs/FIPS/N
IST.FIPS.180-4.pdf">
&rfc2119; <front>
&rfc4250; <title>Secure Hash Standard (SHS)</title>
&rfc4251; <author>
&rfc4253; <organization>
&rfc5656;
&rfc8174;
<reference
anchor="SHS"
target="http://dx.doi.org/10.6028/NIST.FIPS.180-4">
<front>
<title>Secure Hash Standard (SHS)</title>
<author>
<organization>Information Technology Laboratory
National Institute of Standards and Technology</organization> National Institute of Standards and Technology</organization>
</author> </author>
<date month="August" year="2015"/> <date month="August" year="2015"/>
</front> </front>
</reference> <seriesInfo name="FIPS PUB" value="180-4"/>
<seriesInfo name="DOI" value="10.6028/NIST.FIPS.180-4"/>
</references> </reference>
</references>
<references title="Informative References"> <references>
<reference <name>Informative References</name>
anchor="IANA-KEX" <reference anchor="IANA-KEX" target="https://www.iana.org/assignments/ss
target="http://www.iana.org/assignments/ssh-parameters/ssh-parameters.x h-parameters/">
html#ssh-parameters-16"> <front>
<front> <title>Secure Shell (SSH) Protocol Parameters:
<title>Secure Shell (SSH) Protocol Parameters:
Key Exchange Method Names</title> Key Exchange Method Names</title>
<author> <author>
<organization>Internet Assigned Numbers Authority (IANA) <organization>IANA
</organization> </organization>
</author> </author>
<date month="August" year="2019"/> <date/>
</front> </front>
</reference> </reference>
<reference <reference anchor="IANA-REASON" target="https://www.iana.org/assignments
anchor="IANA-REASON" /ssh-parameters/">
target="http://www.iana.org/assignments/ssh-parameters/ssh-parameters.x <front>
html#ssh-parameters-3"> <title>Secure Shell (SSH) Protocol Parameters:
<front>
<title>Secure Shell (SSH) Protocol Parameters:
Disconnection Messages Reason Codes and Descriptions</title> Disconnection Messages Reason Codes and Descriptions</title>
<author> <author>
<organization>Internet Assigned Numbers Authority (IANA) <organization>IANA
</organization> </organization>
</author> </author>
<date month="August" year="2019"/> <date/>
</front> </front>
</reference> </reference>
&rfc6234;
&rfc7748;
<reference <xi:include href="https://xml2rfc.tools.ietf.org/public/rfc/bibxml/refer
anchor="libssh" ence.RFC.6234.xml"/>
target="https://www.libssh.org/"> <xi:include href="https://xml2rfc.tools.ietf.org/public/rfc/bibxml/refer
<front> ence.RFC.7748.xml"/>
<title>The SSH Library</title>
<author>
<organization>libssh</organization>
</author>
<date month="September" year="2019"/>
</front>
</reference>
<reference <reference anchor="libssh" target="https://www.libssh.org/">
anchor="OpenSSH" <front>
target="https://www.openssh.com/"> <title>The SSH Library</title>
<front> <author>
<title>The OpenSSH Project</title> <organization>libssh</organization>
<author> </author>
<organization>OpenSSH group of OpenBSD</organization> <date month="" year=""/>
</author> </front>
<date month="September" year="2019"/> </reference>
</front>
</reference>
<reference anchor="OpenSSH" target="https://www.openssh.com/">
<front>
<title>The OpenSSH Project</title>
<author>
<organization>OpenSSH group of OpenBSD</organization>
</author>
<date month="" year=""/>
</front>
</reference>
</references>
</references> </references>
<!-- Change Log <section numbered="false" toc="default">
<name>Acknowledgements</name>
v01 2017-03-17 MDB Updated draft-josefsson-ssh-curves-04 as <t>
draft-ietf-curdle-ssh-curves-01. Fixed The "curve25519-sha256" key exchange method is identical to
initials="" for Curve25519. Expanded LNCS. the "curve25519-sha256@libssh.org" key exchange method created
Trimmed trailing whitespace. by <contact fullname="Aris Adamantiadis"/> and implemented in libssh and
OpenSSH.
v02 2017-04-11 MDB Moved to Standards Track, updated Abstract, and </t>
updated Introduction per Daniel Migault. <t>
Add initils for Mike Hamburg citation. Thanks to the following people for review and comments: <contact fullnam
Add an IANA-KEX reference. e="Denis
Bider"/>, <contact fullname="Damien Miller"/>, <contact fullname="Niels
v03 2017-04-12 MDB Fix NIT RFC4634 -> RFC6234 Moeller"/>, <contact fullname="Matt Johnston"/>, <contact fullname="Eric
Rescorla"/>, <contact fullname="Ron Frederick"/>, and <contact fullname=
v04 2017-04-12 MDB Use Curve25519 and Curve448 from RFC7748 rather "Stefan Buehler"/>.
than reference informative papers on the curves </t>
per Sean Turner <sean@sn3rd.com> comments. </section>
</back>
v05 2017-05-11 MDB Fix grammar per Eric Rescorla <ekr@rtfm.com>.
Add clarifications to shared secret encoding per
Ron Frederick. Add Ron to Acknowledgements.
Add pseudo-code from Stefan Bhler and
acknowlegement.
v06 2017-05-16 MDB Additional updates suggested by Ron Frederick.
v07 2018-01-02 MDB Add requirements language section.
v08 2018-06-27 MDB Minor cleanup for expired draft.
v09 2019-08-01 MDB Clean up for expired draft. Address ekr comments.
v10 2019-08-12 MDB Fix comment from Ron Frederick and Benjamin Kaduk.
2019-08-25 MDB Fix nit from Tobias Gondrom.
2019-08-26 MDB Fix GenArt comments from Christer Holmberg.
2019-09-03 MDB Fix ric Vyncke comments.
Remove "Copying conditions" section.
v11 2019-09-03 MDB Adopt revised sentence from Ron Fredericks in section 3.
2019-09-04 MDB Fix per Roman Danyliw comments.
-->
</back>
</rfc> </rfc>
 End of changes. 79 change blocks. 
282 lines changed or deleted 213 lines changed or added

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