RFC 8731

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


   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

Copyright Notice

   Copyright (c) 2020 IETF Trust and the persons identified as the
   document authors.  All rights reserved.

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   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

   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",
   "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

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

   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

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,

   [RFC4250]  Lehtinen, S. and C. Lonvick, Ed., "The Secure Shell (SSH)
              Protocol Assigned Numbers", RFC 4250,
              DOI 10.17487/RFC4250, January 2006,

   [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,

   [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,

6.2.  Informative References

   [IANA-KEX] IANA, "Secure Shell (SSH) Protocol Parameters: Key
              Exchange Method Names",

              IANA, "Secure Shell (SSH) Protocol Parameters:
              Disconnection Messages Reason Codes and Descriptions",

   [libssh]   libssh, "The SSH Library", <https://www.libssh.org/>.

   [OpenSSH]  OpenSSH group of OpenBSD, "The OpenSSH Project",

   [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,

   [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>.


   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

   Email: aris@badcode.be

   Simon Josefsson

   Email: simon@josefsson.org

   Mark D. Baushke
   Juniper Networks, Inc.

   Email: mdb@juniper.net