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Network Working Group                                    A. Adamantiadis
Internet-Draft                                                    libssh
Intended status: Informational                              S. Josefsson
Expires: May 15, 2016                                             SJD AB
                                                       November 12, 2015


  Secure Shell (SSH) Key Exchange Method using Curve25519 and Curve448
                     draft-josefsson-ssh-curves-01

Abstract

   How to implement the Curve25519 and Curve448 key exchange methods in
   the Secure Shell (SSH) protocol is described.

Status of This Memo

   This Internet-Draft is submitted in full conformance with the
   provisions of BCP 78 and BCP 79.

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   This Internet-Draft will expire on May 15, 2016.

Copyright Notice

   Copyright (c) 2015 IETF Trust and the persons identified as the
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   described in the Simplified BSD License.





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Table of Contents

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

1.  Introduction

   In [Curve25519], a new elliptic curve function for use in
   cryptographic applications was introduced.  In [Ed448-Goldilocks] the
   Ed448-Goldilocks curve (also known as Curve448) is described.  In
   [I-D.irtf-cfrg-curves], the Diffie-Hellman functions using Curve25519
   and Curve448 are specified.

   Secure Shell (SSH) [RFC4251] is a secure remote login protocol.  The
   key exchange key exchange protocol described in [RFC4253] supports an
   extensible set of methods.  In [RFC5656] it is described how elliptic
   curves are integrated in SSH, and this document reuses those protocol
   messages.

   This document describe how key exchange based on Curve25519 and
   Curve448 is achieved in SSH.  For Curve25519 what we described is
   identical to an already implemented (in libssh and OpenSSH) and
   widely deployed proposal registered in the private namespace
   ("curve25519-sha256@libssh.org").  The Curve448 key exchange method
   is novel but similar in spirit.

   The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
   "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this
   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 transmitted over SSH encapsulated into 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 with chapter 4 of [RFC5656].



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   The method names registered by this document are "curve25519-sha256"
   and "curve448-sha256".

   The whole method is based on the Curve25519 and Curve448 scalar
   multiplication, as described in [I-D.irtf-cfrg-curves].  Private and
   public keys are generated as described therein, and no special
   validation is required beyond what is discussed there.  Public keys
   are defined as strings of 32 bytes for Curve25519 and 56 bytes for
   Curve448.  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 [I-D.irtf-cfrg-curves].

   The shared secret, k, is defined in SSH specifications to be a
   multiple precision integer (mpint).  Curve25519/448 outputs a binary
   string.  The binary string is converted into a number as follows.
   This step differs from [RFC5656] which do not need this conversion.
   X is the 32 or 56 bytes point obtained by the scalar multiplication
   of the other side's public key and the local private key scalar.  The
   whole 32 or 56 bytes of the number X is then converted into a
   multiple precision integer (mpint) k.  This conversion follows the
   network byte order.  Since the SSH mpint encoding use the most
   significant bit to signal negative integers, this means that if the
   most significant bit of the derived secret is set, a zero byte is
   prepended to encode the correct value.

3.  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.

4.  Security Considerations

   The security considerations of [RFC4251], [RFC5656], and
   [I-D.irtf-cfrg-curves] are inherited.

   The way the derived binary secret string is encoded into a mpint
   before it is hashed (i.e., adding a zero byte when the most
   significant bit of the secret is set) raise the potential for a side-
   channel attack determining the length of what is hashed which would
   leak the most significant bit of the derived secret.







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5.  IANA Considerations

   IANA is requested to add "curve25519-sha256" and "curve448-sha256" to
   the "Key Exchange Method Names" registry for SSH 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, March 1997.

   [RFC4250]  Lehtinen, S. and C. Lonvick, Ed., "The Secure Shell (SSH)
              Protocol Assigned Numbers", RFC 4250, DOI 10.17487/
              RFC4250, January 2006,
              <http://www.rfc-editor.org/info/rfc4250>.

   [RFC4251]  Ylonen, T. and C. Lonvick, "The Secure Shell (SSH)
              Protocol Architecture", RFC 4251, January 2006.

   [RFC4253]  Ylonen, T. and C. Lonvick, Ed., "The Secure Shell (SSH)
              Transport Layer Protocol", RFC 4253, DOI 10.17487/RFC4253,
              January 2006, <http://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,
              <http://www.rfc-editor.org/info/rfc5656>.

   [I-D.irtf-cfrg-curves]
              Langley, A. and M. Hamburg, "Elliptic Curves for
              Security", draft-irtf-cfrg-curves-10 (work in progress),
              October 2015.

6.2.  Informative References

   [Curve25519]
              Bernstein, J., "Curve25519: New Diffie-Hellman Speed
              Records", LNCS 3958, pp. 207-228, February 2006,
              <http://dx.doi.org/10.1007/11745853_14>.

   [Ed448-Goldilocks]
              Hamburg, , "Ed448-Goldilocks, a new elliptic curve", June
              2015, <https://eprint.iacr.org/2015/625>.






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Appendix A.  Copying conditions

   Regarding this entire document or any portion of it, the authors
   makes no guarantees and is not responsible for any damage resulting
   from its use.  The authors grants 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.

Authors' Addresses

   Aris Adamantiadis
   libssh

   Email: aris@badcode.be


   Simon Josefsson
   SJD AB

   Email: simon@josefsson.org




























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