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Network Working Group Request for Comments: 4419 Category: Standards Track |
M. Friedl N. Provos W. Simpson March 2006 |
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 © The Internet Society (2006).
This memo describes a new key exchange method for the Secure Shell (SSH) protocol. It allows the SSH server to propose new groups on which to perform the Diffie-Hellman key exchange to the client. The proposed groups need not be fixed and can change with time.
SSH [RFC4251] is a very common protocol for secure remote login on the Internet. Currently, SSH performs the initial key exchange using the "diffie-hellman-group1-sha1" method [RFC4253]. This method prescribes a fixed group on which all operations are performed.
The Diffie-Hellman key exchange provides a shared secret that cannot be determined by either party alone. Furthermore, the shared secret is known only to the participant parties. In SSH, the key exchange is signed with the host key to provide host authentication.
The security of the Diffie-Hellman key exchange is based on the difficulty of solving the Discrete Logarithm Problem (DLP). Since we expect that the SSH protocol will be in use for many years in the future, we fear that extensive precomputation and more efficient algorithms to compute the discrete logarithm over a fixed group might pose a security threat to the SSH protocol.
The ability to propose new groups will reduce the incentive to use precomputation for more efficient calculation of the discrete logarithm. The server can constantly compute new groups in the background.
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 [RFC2119].
The server keeps a list of safe primes and corresponding generators
that it can select from. A prime p is safe if p = 2q + 1 and q is prime. New primes can be generated in the background.
The generator g should be chosen such that the order of the generated
subgroup does not factor into small primes; that is, with p = 2q + 1, the order has to be either q or p - 1. If the order is p - 1, then the exponents generate all possible public values, evenly distributed throughout the range of the modulus p, without cycling through a smaller subset. Such a generator is called a "primitive root" (which is trivial to find when p is "safe").
The client requests a modulus from the server indicating the preferred size. In the following description (C is the client, S is the server, the modulus p is a large safe prime, and g is a generator for a subgroup of GF(p), min is the minimal size of p in bits that is acceptable to the client, n is the size of the modulus p in bits that the client would like to receive from the server, max is the maximal size of p in bits that the client can accept, V_S is S's version string, V_C is C's version string, K_S is S's public host key, I_C is C's KEXINIT message, and I_S is S's KEXINIT message that has been exchanged before this part begins):
computes e = g^x mod p, and sends "e" to S.
computes f = g^y mod p. S receives "e". It computes K = e^y mod
p, H = hash(V_C || V_S || I_C || I_S || K_S || min || n || max ||
p || g || e || f || K) (these elements are encoded according to
their types; see below), and signature s on H with its private
host key. S sends "K_S || f || s" to C. The signing operation
may involve a second hashing operation.
many environments). C then computes K = f^x mod p, H = hash(V_C
|| V_S || I_C || I_S || K_S || min || n || max || p || g || e ||
f || K), and verifies the signature s on H.
Servers and clients SHOULD support groups with a modulus length of k bits, where 1024 <= k <= 8192. The recommended values for min and max are 1024 and 8192, respectively.
Either side MUST NOT send or accept e or f values that are not in the range [1, p-1]. If this condition is violated, the key exchange fails. To prevent confinement attacks, they MUST accept the shared secret K only if 1 < K < p - 1.
The server should return the smallest group it knows that is larger than the size the client requested. If the server does not know a group that is larger than the client request, then it SHOULD return the largest group it knows. In all cases, the size of the returned group SHOULD be at least 1024 bits.
This is implemented with the following messages. The hash algorithm for computing the exchange hash is defined by the method name, and is called HASH. The public key algorithm for signing is negotiated with the KEXINIT messages.
First, the client sends:
byte SSH_MSG_KEY_DH_GEX_REQUEST
uint32 min, minimal size in bits of an acceptable group
uint32 n, preferred size in bits of the group the server will send
uint32 max, maximal size in bits of an acceptable group
The server responds with
byte SSH_MSG_KEX_DH_GEX_GROUP
mpint p, safe prime
mpint g, generator for subgroup in GF(p)
The client responds with:
byte SSH_MSG_KEX_DH_GEX_INIT
mpint e
The server responds with:
byte SSH_MSG_KEX_DH_GEX_REPLY
string server public host key and certificates (K_S)
mpint f
string signature of H
The hash H is computed as the HASH hash of the concatenation of the following:
string V_C, the client's version string (CR and NL excluded)
string V_S, the server's version string (CR and NL 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
uint32 min, minimal size in bits of an acceptable group
uint32 n, preferred size in bits of the group the server will send
uint32 max, maximal size in bits of an acceptable group
mpint p, safe prime
mpint g, generator for subgroup
mpint e, exchange value sent by the client
mpint f, exchange value sent by the server
mpint K, the shared secret
This value is called the exchange hash, and it is used to authenticate the key exchange as per [RFC4253].
This document defines two new key exchange methods:
"diffie-hellman-group-exchange-sha1" and
"diffie-hellman-group-exchange-sha256".
The "diffie-hellman-group-exchange-sha1" method specifies Diffie-Hellman Group and Key Exchange with SHA-1 [FIPS-180-2] as HASH.
The "diffie-hellman-group-exchange-sha256" method specifies Diffie-Hellman Group and Key Exchange with SHA-256 [FIPS-180-2] as HASH.
Note that the hash used in key exchange (in this case, SHA-256) must also be used in the key derivation pseudo-random function (PRF), as per the requirement in the "Output from Key Exchange" section in [RFC4253].
The following message numbers have been defined in this document. They are in a name space private to this document and not assigned by IANA.
#define SSH_MSG_KEX_DH_GEX_REQUEST_OLD 30
#define SSH_MSG_KEX_DH_GEX_REQUEST 34
#define SSH_MSG_KEX_DH_GEX_GROUP 31
#define SSH_MSG_KEX_DH_GEX_INIT 32
#define SSH_MSG_KEX_DH_GEX_REPLY 33
SSH_MSG_KEX_DH_GEX_REQUEST_OLD is used for backward compatibility. Instead of sending "min || n || max", the client only sends "n". In addition, the hash is calculated using only "n" instead of "min || n
|| max".
The numbers 30-49 are key exchange specific and may be redefined by other kex methods.
One useful technique is to select the generator, and then limit the modulus selection sieve to primes with that generator:
2 when p (mod 24) = 11.
5 when p (mod 10) = 3 or 7.
It is recommended to use 2 as generator, because it improves efficiency in multiplication performance. It is usable even when it is not a primitive root, as it still covers half of the space of possible residues.
To increase the speed of the key exchange, both client and server may reduce the size of their private exponents. It should be at least twice as long as the key material that is generated from the shared secret. For more details, see the paper by van Oorschot and Wiener [VAN-OORSCHOT].
This protocol aims to be simple and uses only well-understood primitives. This encourages acceptance by the community and allows for ease of implementation, which hopefully leads to a more secure system.
The use of multiple moduli inhibits a determined attacker from precalculating moduli exchange values, and discourages dedication of resources for analysis of any particular modulus.
It is important to employ only safe primes as moduli, as they allow us to find a generator g so that the order of the generated subgroup
does not factor into small primes, that is, with p = 2q + 1, the order has to be either q or p - 1. If the order is p - 1, then the exponents generate all possible public values, evenly distributed throughout the range of the modulus p, without cycling through a smaller subset. Van Oorshot and Wiener note that using short private exponents with a random prime modulus p makes the computation of the discrete logarithm easy [VAN-OORSCHOT]. However, they also state that this problem does not apply to safe primes.
The least significant bit of the private exponent can be recovered when the modulus is a safe prime [MENEZES]. However, this is not a problem if the size of the private exponent is big enough. Related to this, Waldvogel and Massey note: When private exponents are chosen independently and uniformly at random from {0,...,p-2}, the key entropy is less than 2 bits away from the maximum, lg(p-1) [WALDVOGEL].
The security considerations in [RFC4251] also apply to this key exchange method.
The document is derived in part from "SSH Transport Layer Protocol" [RFC4253] by T. Ylonen, T. Kivinen, M. Saarinen, T. Rinne, and S. Lehtinen.
Markku-Juhani Saarinen pointed out that the least significant bit of the private exponent can be recovered efficiently when using safe primes and a subgroup with an order divisible by two.
Bodo Moeller suggested that the server send only one group, reducing the complexity of the implementation and the amount of data that needs to be exchanged between client and server.
The "Handbook of Applied Cryptography" [MENEZES] lists the following algorithm to generate a k-bit safe prime p. It has been modified so that 2 is a generator for the multiplicative group mod p.
1. Select a random (k-1)-bit prime q, so that q mod 12 = 5.
If an implementation uses the OpenSSL libraries, a group consisting of a 1024-bit safe prime and 2 as generator can be created as follows:
DH *d = NULL;
d = DH_generate_parameters(1024, DH_GENERATOR_2, NULL, NULL);
BN_print_fp(stdout, d->p);
The order of the subgroup generated by 2 is q = p - 1.
[FIPS-180-2] National Institute of Standards and Technology (NIST),
"Secure Hash Standard (SHS)", FIPS PUB 180-2,
August 2002.
[RFC4251] Ylonen, T. and C. Lonvick, "The Secure Shell (SSH)
Protocol Architecture", RFC 4251, January 2006.
[RFC4253] Lonvick, C., "The Secure Shell (SSH) Transport Layer
Protocol", RFC 4253, January 2006.
[RFC2119] Bradner, S., "Key words for use in RFCs to Indicate
Requirement Levels", BCP 14, RFC 2119, March 1997.
[MENEZES] Menezes, A., van Oorschot, P., and S. Vanstone,
"Handbook of Applied Cryptography", CRC Press, p. 537,
1996.
[VAN-OORSCHOT] van Oorschot, P. and M. Wiener, "On Diffie-Hellman key
agreement with short exponents", Advances in
Cryptology -EUROCRYPT'96, LNCS 1070,
Springer-Verlag, pp. 332-343, 1996.
[WALDVOGEL] Waldvogel, C. and J. Massey, "The probability
distribution of the Diffie-Hellman key", Proceedings
of AUSCRYPT 92, LNCS 718, Springer-Verlag, pp.
492-504, 1993.
Markus Friedl
EMail: markus@openbsd.org
Niels Provos
EMail: provos@citi.umich.edu
William A. Simpson
EMail: wsimpson@greendragon.com
Copyright © The Internet Society (2006).
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