Internet DRAFT - draft-josefsson-ssh-curves
draft-josefsson-ssh-curves
Network Working Group A. Adamantiadis
Internet-Draft libssh
Intended status: Informational S. Josefsson
Expires: September 2, 2016 SJD AB
March 1, 2016
Secure Shell (SSH) Key Exchange Method using Curve25519 and Curve448
draft-josefsson-ssh-curves-04
Abstract
How to implement the Curve25519 and Curve448 key exchange methods in
the Secure Shell (SSH) protocol is described.
Status of This Memo
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This Internet-Draft will expire on September 2, 2016.
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Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 2
2. Key Exchange Methods . . . . . . . . . . . . . . . . . . . . 3
2.1. Shared Secret Encoding . . . . . . . . . . . . . . . . . 3
3. Acknowledgements . . . . . . . . . . . . . . . . . . . . . . 4
4. Security Considerations . . . . . . . . . . . . . . . . . . . 4
5. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 4
6. References . . . . . . . . . . . . . . . . . . . . . . . . . 5
6.1. Normative References . . . . . . . . . . . . . . . . . . 5
6.2. Informative References . . . . . . . . . . . . . . . . . 5
Appendix A. Copying conditions . . . . . . . . . . . . . . . . . 5
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 6
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
[RFC7748], the Diffie-Hellman functions using Curve25519 and Curve448
are specified.
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 Curve448 in SSH. For Curve25519 with SHA-256
[RFC4634], the algorithm we describe is equivalent to the privately
defined algorithm "curve25519-sha256@libssh.org", 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 [RFC4634] 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",
"SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this
document are to be interpreted as described in RFC 2119 [RFC2119].
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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.
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
document.
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
follows:
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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
smaller.
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, Niels Moeller, Matt Johnston, Mark D. Baushke.
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 that was created in
RFC 4250 section 4.10 [RFC4250].
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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>.
[RFC4634] Eastlake, D. and T. Hansen, "US Secure Hash Algorithms
(SHA and HMAC-SHA)", RFC 4634, July 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,
<http://www.rfc-editor.org/info/rfc5656>.
[RFC7748] Langley, A., Hamburg, M., and S. Turner, "Elliptic Curves
for Security", RFC 7748, DOI 10.17487/RFC7748, January
2016, <http://www.rfc-editor.org/info/rfc7748>.
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>.
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
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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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