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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Copyright Notice

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Table of Contents

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

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].

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:

• 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.
• 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 Möller, 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].

6. References

6.1. Normative References

6.2. Informative References

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