Internet Engineering Task Force                          A. Adamantiadis
Internet-Draft                                                    libssh
Intended status: Standards Track                            S. Josefsson
Expires: October 12, 2017                                         SJD AB
                                                              M. Baushke
                                                  Juniper Networks, Inc.
                                                          April 10, 2017

  Secure Shell (SSH) Key Exchange Method using Curve25519 and Curve448


   This document describes the conventions for using Curve25519 and
   Curve448 key exchange methods in the Secure Shell (SSH) protocol.

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   This Internet-Draft will expire on October 12, 2017.

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Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   2
   2.  Key Exchange Methods  . . . . . . . . . . . . . . . . . . . .   2
     2.1.  Shared Secret Encoding  . . . . . . . . . . . . . . . . .   3
   3.  Acknowledgements  . . . . . . . . . . . . . . . . . . . . . .   4
   4.  Security Considerations . . . . . . . . . . . . . . . . . . .   4
   5.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .   4
   6.  References  . . . . . . . . . . . . . . . . . . . . . . . . .   4
     6.1.  Normative References  . . . . . . . . . . . . . . . . . .   4
     6.2.  Informative References  . . . . . . . . . . . . . . . . .   5
   Appendix A.  Copying conditions . . . . . . . . . . . . . . . . .   5
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .   6

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] describes how elliptic curves are
   integrated in SSH, and this document reuses those protocol messages.

   This document describes how to implement key exchange based on
   Curve25519 and Ed448-Goldilocks [RFC7748] in SSH.  For Curve25519
   with SHA-256 [RFC6234], the algorithm we describe is equivalent to
   the privately defined algorithm "", which
   is currently implemented and widely deployed in libssh and OpenSSH.
   The Curve448 key exchange method is novel but similar in spirit, and
   we chose to couple it with SHA-512 [RFC6234] to further separate it
   from the Curve25519 alternative.

   This document provide Curve25519 as the prefered choice, but suggests
   that the fall back option Curve448 is implemented to provide an hedge
   against unforseen analytical advances against Curve25519 and SHA-256.
   Due to different implementation status of these two curves (high-
   quality free implementations of Curve25519 has been in deployed use
   for several years, while Curve448 implementations are slowly
   appearing), it is accepted that adoption of Curve448 will be slower.

   The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
   document are to be interpreted as described in RFC 2119 [RFC2119].

2.  Key Exchange Methods

   The key exchange procedure is similar to the ECDH method described in
   chapter 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.

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   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 chapter 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.
   Clients and servers MUST fail the key exchange if the length of the
   received public keys are not the expected lengths, or if the derived
   shared secret only consists of zero bits.  No further validation is
   required beyond what is discussed in [RFC7748].  The derived shared
   secret is 32 bytes when Curve25519 is used and 56 bytes when Curve448
   is used.  The encodings of all values are defined in [RFC7748].  The
   hash used is SHA-256 for Curve25519 and SHA-512 for Curve448.

2.1.  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] 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 bytes as an
   unsigned fixed-length integer encoded in network byte order.  This
   conversion follows the normal "mpint" process as described in section
   5 of [RFC4251].

   To clarify a corner-case in this conversion, when X is encoded as an
   mpint K, in order to calculate the exchange hash, it may vary as

   o  If the high bit of X is set, the mpint format requires a zero byte
      to be prepended.  In this case, the length of the encoded K will
      be larger.

   o  If X has leading zero bytes, the mpint format requires such bytes
      to be skipped.  In this case, the length of the encoded K will be

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3.  Acknowledgements

   The "curve25519-sha256" key exchange method is identical to the
   "" 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.

4.  Security Considerations

   The security considerations of [RFC4251], [RFC5656], and [RFC7748]
   are inherited.

   Curve25519 provide strong security and is efficient on a wide range
   of architectures, and has properties that allows better
   implementation properties compared to traditional elliptic curves.
   Curve448 with SHA-512 is similar, but have not received the same
   cryptographic review as Curve25519, and is slower, but it is provided
   as an hedge to combat unforseen analytical advances against
   Curve25519 and SHA-256.

   The way the derived binary secret string is encoded into a mpint
   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 adress this potential problem.

5.  IANA Considerations

   IANA is requested to add "curve25519-sha256" and "curve448-sha512" to
   the "Key Exchange Method Names" registry for SSH [IANA-KEX] that was
   created in RFC 4250 section 4.10 [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,

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   [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, <>.

   [RFC4253]  Ylonen, T. and C. Lonvick, Ed., "The Secure Shell (SSH)
              Transport Layer Protocol", RFC 4253, DOI 10.17487/RFC4253,
              January 2006, <>.

   [RFC5656]  Stebila, D. and J. Green, "Elliptic Curve Algorithm
              Integration in the Secure Shell Transport Layer",
              RFC 5656, DOI 10.17487/RFC5656, December 2009,

   [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, <>.

6.2.  Informative References

              Internet Assigned Numbers Authority (IANA), "Secure Shell
              (SSH) Protocol Parameters: Key Exchange Method Names",
              March 2017, <

Appendix A.  Copying conditions

   Regarding this entire document or any portion of it, the authors make
   no guarantees and are not responsible for any damage resulting from
   its use.  The authors grant irrevocable permission to anyone to use,
   modify, and distribute it in any way that does not diminish the
   rights of anyone else to use, modify, and distribute it, provided
   that redistributed derivative works do not contain misleading author
   or version information.  Derivative works need not be licensed under
   similar terms.

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Authors' Addresses

   Aris Adamantiadis


   Simon Josefsson


   Mark D. Baushke
   Juniper Networks, Inc.


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