Network Working Group B. Harris
Request for Comments: 4432 March 2006
Category: Standards Track
RSA Key Exchange for the Secure Shell (SSH)
Transport Layer Protocol
Status of This Memo
This document specifies an Internet standards track protocol for the
Internet community, and requests discussion and suggestions for
improvements. Please refer to the current edition of the "Internet
Official Protocol Standards" (STD 1) for the standardization state
and status of this protocol. Distribution of this memo is unlimited.
Copyright Notice
Copyright (C) The Internet Society (2006).
Abstract
This memo describes a key-exchange method for the Secure Shell (SSH)
protocol based on Rivest-Shamir-Adleman (RSA) public-key encryption.
It uses much less client CPU time than the Diffie-Hellman algorithm
specified as part of the core protocol, and hence is particularly
suitable for slow client systems.
1. Introduction
Secure Shell (SSH) [RFC4251] is a secure remote-login protocol. The
core protocol uses Diffie-Hellman key exchange. On slow CPUs, this
key exchange can take tens of seconds to complete, which can be
irritating for the user. A previous version of the SSH protocol,
described in [SSH1], uses a key-exchange method based on
Rivest-Shamir-Adleman (RSA) public-key encryption, which consumes an
order of magnitude less CPU time on the client, and hence is
particularly suitable for slow client systems such as mobile devices.
This memo describes a key-exchange mechanism for the version of SSH
described in [RFC4251] that is similar to that used by the older
version, and about as fast, while retaining the security advantages
of the newer protocol.
Harris Standards Track [Page 1]RFC 4432 SSH RSA Key Exchange March 2006
2. Conventions Used in This Document
The key words "MUST" and "SHOULD" in this document are to be
interpreted as described in [RFC2119].
The data types "byte", "string", and "mpint" are defined in Section 5
of [RFC4251].
Other terminology and symbols have the same meaning as in [RFC4253].
3. Overview
The RSA key-exchange method consists of three messages. The server
sends to the client an RSA public key, K_T, to which the server holds
the private key. This may be a transient key generated solely for
this SSH connection, or it may be re-used for several connections.
The client generates a string of random bytes, K, encrypts it using
K_T, and sends the result back to the server, which decrypts it. The
client and server each hash K, K_T, and the various key-exchange
parameters to generate the exchange hash, H, which is used to
generate the encryption keys for the session, and the server signs H
with its host key and sends the signature to the client. The client
then verifies the host key as described in Section 8 of [RFC4253].
This method provides explicit server identification as defined in
Section 7 of [RFC4253]. It requires a signature-capable host key.
4. Details
The RSA key-exchange method has the following parameters:
HASH hash algorithm for calculating exchange hash, etc.
HLEN output length of HASH in bits
MINKLEN minimum transient RSA modulus length in bits
Their values are defined in Section 5 and Section 6 for the two
methods defined by this document.
The method uses the following messages.
First, the server sends:
byte SSH_MSG_KEXRSA_PUBKEY
string server public host key and certificates (K_S)
string K_T, transient RSA public key
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The key K_T is encoded according to the "ssh-rsa" scheme described in
Section 6.6 of [RFC4253]. Note that unlike an "ssh-rsa" host key,
K_T is used only for encryption, and not for signature. The modulus
of K_T MUST be at least MINKLEN bits long.
The client generates a random integer, K, in the range
0 <= K < 2^(KLEN-2*HLEN-49), where KLEN is the length of the modulus
of K_T, in bits. The client then uses K_T to encrypt:
mpint K, the shared secret
The encryption is performed according to the RSAES-OAEP scheme of
[RFC3447], with a mask generation function of MGF1-with-HASH, a hash
of HASH, and an empty label. See Appendix A for a proof that the
encoding of K is always short enough to be thus encrypted. Having
performed the encryption, the client sends:
byte SSH_MSG_KEXRSA_SECRET
string RSAES-OAEP-ENCRYPT(K_T, K)
Note that the last stage of RSAES-OAEP-ENCRYPT is to encode an
integer as an octet string using the I2OSP primitive of [RFC3447].
This, combined with encoding the result as an SSH "string", gives a
result that is similar, but not identical, to the SSH "mpint"
encoding applied to that integer. This is the same encoding as is
used by "ssh-rsa" signatures in [RFC4253].
The server decrypts K. If a decryption error occurs, the server
SHOULD send SSH_MESSAGE_DISCONNECT with a reason code of
SSH_DISCONNECT_KEY_EXCHANGE_FAILED and MUST disconnect. Otherwise,
the server responds with:
byte SSH_MSG_KEXRSA_DONE
string signature of H with host key
The hash H is computed as the HASH hash of the concatenation of the
following:
string V_C, the client's identification string
(CR and LF excluded)
string V_S, the server's identification string
(CR and LF excluded)
string I_C, the payload of the client's SSH_MSG_KEXINIT
string I_S, the payload of the server's SSH_MSG_KEXINIT
string K_S, the host key
string K_T, the transient RSA key
string RSAES_OAEP_ENCRYPT(K_T, K), the encrypted secret
mpint K, the shared secret
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This value is called the exchange hash, and it is used to
authenticate the key exchange. The exchange hash SHOULD be kept
secret.
The signature algorithm MUST be applied over H, not the original
data. Most signature algorithms include hashing and additional
padding. For example, "ssh-dss" specifies SHA-1 hashing. In such
cases, the data is first hashed with HASH to compute H, and H is then
hashed again as part of the signing operation.
5. rsa1024-sha1
The "rsa1024-sha1" method specifies RSA key exchange as described
above with the following parameters:
HASH SHA-1, as defined in [RFC3174]
HLEN 160
MINKLEN 1024
6. rsa2048-sha256
The "rsa2048-sha256" method specifies RSA key exchange as described
above with the following parameters:
HASH SHA-256, as defined in [FIPS-180-2]
HLEN 256
MINKLEN 2048
7. Message Numbers
The following message numbers are defined:
SSH_MSG_KEXRSA_PUBKEY 30
SSH_MSG_KEXRSA_SECRET 31
SSH_MSG_KEXRSA_DONE 32
8. Security Considerations
The security considerations in [RFC4251] apply.
If the RSA private key generated by the server is revealed, then the
session key is revealed. The server should thus arrange to erase
this from memory as soon as it is no longer required. If the same
RSA key is used for multiple SSH connections, an attacker who can
find the private key (either by factorising the public key or by
other means) will gain access to all of the sessions that used that
key. As a result, servers SHOULD use each RSA key for as few key
exchanges as possible.
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[RFC3447] recommends that RSA keys used with RSAES-OAEP not be used
with other schemes, or with RSAES-OAEP using a different hash
function. In particular, this means that K_T should not be used as a
host key, or as a server key in earlier versions of the SSH protocol.
Like all key-exchange mechanisms, this one depends for its security
on the randomness of the secrets generated by the client (the random
number K) and the server (the transient RSA private key). In
particular, it is essential that the client use a high-quality
cryptographic pseudo-random number generator to generate K. Using a
bad random number generator will allow an attacker to break all the
encryption and integrity protection of the Secure Shell transport
layer. See [RFC4086] for recommendations on random number
generation.
The size of transient key used should be sufficient to protect the
encryption and integrity keys generated by the key-exchange method.
For recommendations on this, see [RFC3766]. The strength of
RSAES-OAEP is in part dependent on the hash function it uses.
[RFC3447] suggests using a hash with an output length of twice the
security level required, so SHA-1 is appropriate for applications
requiring up to 80 bits of security, and SHA-256 for those requiring
up to 128 bits.
Unlike the Diffie-Hellman key-exchange method defined by [RFC4253],
this method allows the client to fully determine the shared secret,
K. This is believed not to be significant, since K is only ever used
when hashed with data provided in part by the server (usually in the
form of the exchange hash, H). If an extension to SSH were to use K
directly and to assume that it had been generated by Diffie-Hellman
key exchange, this could produce a security weakness. Protocol
extensions using K directly should be viewed with extreme suspicion.
This key-exchange method is designed to be resistant to collision
attacks on the exchange hash, by ensuring that neither side is able
to freely choose its input to the hash after seeing all of the other
side's input. The server's last input is in SSH_MSG_KEXRSA_PUBKEY,
before it has seen the client's choice of K. The client's last input
is K and its RSA encryption, and the one-way nature of RSA encryption
should ensure that the client cannot choose K so as to cause a
collision.
9. IANA Considerations
IANA has assigned the names "rsa1024-sha1" and "rsa2048-sha256" as
Key Exchange Method Names in accordance with [RFC4250].
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RFC 4432 SSH RSA Key Exchange March 2006
10. Acknowledgements
The author acknowledges the assistance of Simon Tatham with the
design of this key exchange method.
The text of this document is derived in part from [RFC4253].
11. References
11.1. Normative References
[RFC2119] Bradner, S., "Key words for use in RFCs to Indicate
Requirement Levels", BCP 14, RFC 2119, March 1997.
[RFC3174] Eastlake, D. and P. Jones, "US Secure Hash Algorithm 1
(SHA1)", RFC 3174, September 2001.
[RFC3447] Jonsson, J. and B. Kaliski, "Public-Key Cryptography
Standards (PKCS) #1: RSA Cryptography Specifications
Version 2.1", RFC 3447, February 2003.
[RFC4251] Ylonen, T. and C. Lonvick, "The Secure Shell (SSH)
Protocol Architecture", RFC 4251, January 2006.
[RFC4253] Ylonen, T. and C. Lonvick, "The Secure Shell (SSH)
Transport Layer Protocol", RFC 4253, January 2006.
[RFC4250] Lehtinen, S. and C. Lonvick, "The Secure Shell (SSH)
Protocol Assigned Numbers", RFC 4250, January 2006.
[FIPS-180-2] National Institute of Standards and Technology (NIST),
"Secure Hash Standard (SHS)", FIPS PUB 180-2,
August 2002.
11.2. Informative References
[SSH1] Ylonen, T., "SSH -- Secure Login Connections over the
Internet", 6th USENIX Security Symposium, pp. 37-42,
July 1996.
[RFC3766] Orman, H. and P. Hoffman, "Determining Strengths For
Public Keys Used For Exchanging Symmetric Keys",
BCP 86, RFC 3766, April 2004.
[RFC4086] Eastlake, D., Schiller, J., and S. Crocker, "Randomness
Requirements for Security", BCP 106, RFC 4086,
June 2005.
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Appendix A. On the Size of K
The requirements on the size of K are intended to ensure that it is
always possible to encrypt it under K_T. The mpint encoding of K
requires a leading zero bit, padding to a whole number of bytes, and
a four-byte length field, giving a maximum length in bytes,
B = (KLEN-2*HLEN-49+1+7)/8 + 4 = (KLEN-2*HLEN-9)/8 (where "/" denotes
integer division rounding down).
The maximum length of message that can be encrypted using RSAEP-OAEP
is defined by [RFC3447] in terms of the key length in bytes, which is
(KLEN+7)/8. The maximum length is thus L = (KLEN+7-2*HLEN-16)/8 =
(KLEN-2*HLEN-9)/8. Thus, the encoded version of K is always small
enough to be encrypted under K_T.
Author's Address
Ben Harris
2a Eachard Road
CAMBRIDGE
CB4 1XA
UNITED KINGDOM
EMail: bjh21@bjh21.me.uk
Harris Standards Track [Page 7]
RFC 4432 SSH RSA Key Exchange March 2006
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Harris Standards Track [Page 8]
