Network Working Group A. Adamantiadis
Internet-Draft libssh
Intended status: Informational S. Josefsson
Expires: May 21, 2016 SJD AB
November 18, 2015

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


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

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Table of Contents

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 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, 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.

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-sha256".

The methods are based on Curve25519 and Curve448 scalar multiplication, as described in [I-D.irtf-cfrg-curves]. 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 verify the length of the received public keys, but no further validation is required beyond what is discussed in [I-D.irtf-cfrg-curves]. 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].

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 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.

When K is encoded as mpint in order to calculate the exchange hash, its encoding will often be identical to X, but will vary as follows:

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.

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 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.

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, 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.
[I-D.irtf-cfrg-curves] Langley, A. and M. Hamburg, "Elliptic Curves for Security", Internet-Draft draft-irtf-cfrg-curves-11, October 2015.

6.2. Informative References

[Curve25519] Bernstein, J., "Curve25519: New Diffie-Hellman Speed Records", LNCS 3958, pp. 207-228, February 2006.
[Ed448-Goldilocks] Hamburg, , "Ed448-Goldilocks, a new elliptic curve", June 2015.

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: