Internet Engineering Task Force A. Adamantiadis
Internet-Draft libssh
Intended status: Standards Track S. Josefsson
Expires: November 12, 2017 SJD AB
M. Baushke
Juniper Networks, Inc.
May 11, 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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Table of Contents

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", "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 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:

Or, as pseudo code:

              k := x;
              while (k.length() > 0 && k[0] == 0) k = k[1:];
              assert(k.length() > 0);
              if 0 != (k[0] & 0x80) k = '\0' .. k;

Figure 1

When performing the X25519 or X448 operations, the integer values there will be encoded into byte strings by doing a fix-length unsigned litle-endian conversion, per [RFC7748]. It is only later when these byte strings are then passed to the ECDH code in SSH that the bytes are re-interpreted 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.

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 Möller, Matt Johnston, Eric Rescorla, Ron Frederick, Stefan Bühler.

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 has 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.
[RFC4250] Lehtinen, S. and C. Lonvick, "The Secure Shell (SSH) Protocol Assigned Numbers", RFC 4250, DOI 10.17487/RFC4250, January 2006.
[RFC4251] Ylonen, T. and C. Lonvick, "The Secure Shell (SSH) Protocol Architecture", RFC 4251, DOI 10.17487/RFC4251, January 2006.
[RFC4253] Ylonen, T. and C. Lonvick, "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.

6.2. Informative References

[IANA-KEX] Internet Assigned Numbers Authority (IANA), "Secure Shell (SSH) Protocol Parameters: Key Exchange Method Names", March 2017.
[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.

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.

Authors' Addresses

Aris Adamantiadis libssh EMail:
Simon Josefsson SJD AB EMail:
Mark D. Baushke Juniper Networks, Inc. EMail: