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Versions: 00 01                                                         
INTERNET-DRAFT                                              Niels M÷ller
draft-nisse-secsh-srp-01.txt                               27 March 2001
Expires in September 2001

    Using the SRP protocol as a key exchange method in Secure Shell

Status of this Memo

   This document is an Internet-Draft and is in full conformance with
   all provisions of Section 10 of RFC2026.

   Internet-Drafts are working documents of the Internet Engineering
   Task Force (IETF), its areas, and its working groups. Note that other
   groups may also distribute working documents as Internet-Drafts.

   Internet-Drafts are draft documents valid for a maximum of six months
   and may be updated, replaced, or obsoleted by other documents at any
   time. It is inappropriate to use Internet-Drafts as reference
   material or to cite them other than as "work in progress."

   The list of current Internet-Drafts can be accessed at

   The list of Internet-Draft Shadow Directories can be accessed at

Copyright Notice

   Copyright (C) The Internet Society (2001). See the Full Copyright
   Notice below for details.


   This memo describes an experimental method for authentication and
   keyexchange in the Secure Shell protocol.

   The main virtue of the SRP protocol [SRP] is that it provides
   authentication based on a small secret (typically a password). It is
   useful in situations where no authentic host key is known. For Secure
   Shell, it can be used as a bootstrapping procedure to get the host
   key of a server in a safe way. SRP also provides authentication of
   the user, which means that it might make sense to either skip the
   secsh "ssh-userauth"-service [SSH-USERAUTH] when using SRP, or allow
   login with the "none" or "external-keyx" method.

Conventions and notations

Niels M÷ller                                                    [Page 1]

INTERNET-DRAFT     SRP key exchange with Secure Shell.     27 March 2001

   Some of the conventions used in this document are taken from [SSH-
   TRANS], others are from [SRP].

   C is the client, S is the server; q is a large safe prime, g is a
   primitive root. V_S is S's version string; V_C is C's version string;
   I_C is C's KEXINIT message and I_S S's KEXINIT message which have
   been exchanged before this part begins. (See [SSH-TRANS] for more

   The ^ operator is the exponentiation operation, and the mod operator
   is the integer remainder operation. Most implementations perform the
   exponentiation and remainder in a single stage to avoid generating
   unwieldy intermediate results.

   The | symbol indicates ssh-style string concatenation: For any
   strings A and B, A | B is the encoding of

     string A
     string B

   Computation takes place in the ring Z/q. Actually, most of the action
   takes place in its multiplicative group, which is generated by g. The
   ring structure is not absolutely essential, what we really need is a
   group G and and two mixing operations + and -, unrelated to the group
   operation, each mapping G x G onto a set that is "almost" equal to G
   (in the ring case, the image includes zero, which is outside the
   multiplicative group. This is not really a problem). We must have a =
   (a + b) - b, for all a, b in G such that also a + b is in G, and this
   is why it is convenient to use the ring structure.

   Furthermore, HASH is a hash function (currently SHA1), n is the
   user's name (used for looking up salt and verifier in the server's
   database), p is a password, and s is a random salt string.

   x is constructed from the strings n, p and s as HASH(s | HASH(n |
   p)), and the verifier is computed as g^x mod q. S keeps a database
   containing triples <n, s, v>, indexed by n.

Protocol description

   1. C renerates a random number a (lg(q) < a < q-1) and computes
      e = g^a mod q. C sends e and n to S.

   2. S uses n to find v and s in its database. S generates a random
      number b, (lg(q) < b < q-1) and computes f = v + g^b mod q. S
      selects u as the integer corresponding to the first 32 bits of
      HASH(f). If f or u happens to be zero, S must try another b. S
      computes K = (e * v^u)^b mod q. S sends s and f to C.

Niels M÷ller                                                    [Page 2]

INTERNET-DRAFT     SRP key exchange with Secure Shell.     27 March 2001

   3. C gets the password p and computes x = HASH(s | H(n | p)) and
      v = g^x mod q. C also computes u in the same way as S. Finally, C
      computes K = (f - v) ^ (a + u * x) mod q.

   Each party must check that e and f are in the range [1, q-1]. If not,
   the key exchange fails.

   Note the addition in step 2, v + g^b mod q, and the corresponding
   subtraction f - v in step 3, are the only operations that uses the
   ring structure. C should also check that f - v is non-zero, i.e.
   belongs to the multiplicative group generated by g.

   At this point C and S have a shared secret K. They must now prove
   that they know the same value. Even if we're primarily interested in
   authenticating the server, the user must prove knowledge of the key
   *first*. (Otherwise, the server leaks information about the

   To do this, the client sends m1 = HMAC(K, H) to the server, where H
   is the "exchange hash" defined below. After verifying the MAC, the
   server responds by sending m2 = HMAC(K, e | m1 | H) to the client.
   Actually, the purpose of this final message exchange is twofold: (i)
   to prove knowledge of the shared secret key K, completing the SRP
   protocol, and (ii) to use the shared key K to authenticate the
   exchange hash. The latter is needed in order to protect against
   attacks on the algorithm negotiation that happens before the SRP
   exchange, as well as version rollback attacks.

Protocol messages

   The name of the method, when listed in the SSH_MSG_KEXINIT message,
   is "srp-ring1-sha1". The SSH_MSG_KEXINIT negotiation determines which
   hash function is used, as well as the values of q and g.

   For the "srp-ring1-sha1", q is equal to 2^1024 - 2^960 - 1 + 2^64 *
   floor( 2^894 Pi + 129093 ). This is the same prime used for "diffie-
   hellman-group1-sha1" in [SSH-TRANS]. Its hexadecimal value is

     FFFFFFFF FFFFFFFF C90FDAA2 2168C234 C4C6628B 80DC1CD1
     29024E08 8A67CC74 020BBEA6 3B139B22 514A0879 8E3404DD
     EF9519B3 CD3A431B 302B0A6D F25F1437 4FE1356D 6D51C245
     E485B576 625E7EC6 F44C42E9 A637ED6B 0BFF5CB6 F406B7ED
     EE386BFB 5A899FA5 AE9F2411 7C4B1FE6 49286651 ECE65381

   In decimal, this value is


Niels M÷ller                                                    [Page 3]

INTERNET-DRAFT     SRP key exchange with Secure Shell.     27 March 2001


   The generator used for "srp-ring1-ring1" is g = 5. This is different
   from the generator used in [SSH-TRANS], because we need to generate
   the entire multiplicative group.

   First, the client sends:

     byte      SSH_MSG_KEXSRP_INIT
     string    n
     mpint     e

   The server responds with

     byte      SSH_MSG_KEXSRP_REPLY
     string    s
     mpint     f

   The server MUST NOT send this message until it has received the

   At this point, both sides can compute the exchange hash H, as the
   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    n, the user name
     string    s, the salt
     mpint     e, exchange value sent by the client
     mpint     f, exchange value sent by the server
     mpint     K, the shared secret

   The client computes m1 = HMAC(K, H), and sends it to the server, to
   prove that it knows the shared key. It sends

     string m1

   [ Would it be possible to instead send the exchange hash in the
     clear, e.g. use m1 = H? ]

   The server verifies that m1 is correct using its own K. If they don't

Niels M÷ller                                                    [Page 4]

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   match, the keyexchange fails, and the server MUST NOT send any proof
   back to the client.

   Finally, the server computes m2 as the HMAC(K, e | m1 | H) and sends

     string m2

   to the client. The client verifies that m2 is correct, and if so, the
   key exchange is successful and its output is H and K.

Message numbers

   The following message numbers have been defined in this protocol

     /* Numbers 30-49 used for kex packets.
        Different kex methods may reuse message numbers in
        this range. */
     #define SSH_MSG_KEXSRP_INIT            30
     #define SSH_MSG_KEXSRP_REPLY           31
     #define SSH_MSG_KEXSRP_PROOF           32

Ring negotiation

   This section sketches the changes needed in order to get away from
   using a fixed ring. The client MUST not use a ring unless its quality
   is checked in some way (see next section). I will assume that the
   client either keeps a list of trusted rings, or makes extensive
   quality checks at runtime. The name of this keyexchange method is

   Each verifier must be associated with a particular ring, which was
   used when computing the verifier in the first place. Therefore, the
   server's userdatabase will contain entries <n, s, v, q, g> where the
   first three elements are the name, salt and verifier as before, and q
   and g determines the ring and the generator.

   C initiates the protocol by sending its user name to the server:

     byte      SSH_MSG_KEXSRP_INIT
     string    n, username

   Note that e can not be computed yet, as the ring is not known. S
   replies with

     byte      SSH_MSG_KEXSRP_REPLY
     mpint     q
     mpint     g

Niels M÷ller                                                    [Page 5]

INTERNET-DRAFT     SRP key exchange with Secure Shell.     27 March 2001

     string    s, salt

   C computes e, and sends it to S:

     byte      SSH_MSG_KEXSRP_VALUE
     mpint     e

   S computes f and K, and responds with

     byte      SSH_MSG_KEXSRP_VALUE
     mpint     f

   The server MUST NOT send this message until after it has received e
   from the client.

   Now the client kan compute K. Both sides compute the exchange hash as
   the 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    n, the user name
     string    s, the salt
     mpint     q
     mpint     g
     mpint     e, exchange value sent by the client
     mpint     f, exchange value sent by the server
     mpint     K, the shared secret

   The final exchange of SSH_MSG_KEXSRP_PROOF is unchanged. Note that
   the ability use different rings costs one more roundtrip.

Security Considerations

   This entire draft discusses an authentication and key-exchange system
   that protects passwords and exchanges keys across an untrusted
   network. Most of this section is taken from [SRP], which also
   provides more details.

   Knowledge of the verifier enables an attacker to mount an offline
   search (also known as a "dictionary attack") on the user's password,
   as well as to impersonate the server. So the verifier should be kept
   secret. The <name, salt, verifier> entry can be created on the user's
   machine and transferred to the server, just like a user's public key,
   or it could be created on the server. The former approach has the
   advantage that the cleartext password is not even temporarily known
   by the server.

Niels M÷ller                                                    [Page 6]

INTERNET-DRAFT     SRP key exchange with Secure Shell.     27 March 2001

   SRP has been designed not only to counter the threat of casual
   password-sniffing, but also to prevent a determined attacker equipped
   with a dictionary of passwords from guessing at passwords using
   captured network traffic. The SRP protocol itself also resists active
   network attacks, and implementations can use the securely exchanged
   keys to protect the session against hijacking and provide

   The SRP keyexchange was originally designed primarily a user
   authentication method, but it also provides a peculiar form of host
   authentication. If SRP succeeds, using a particular user name and
   password, the client can be confident that the remote server knows
   some verifier corresponding to that password. But if the same
   password is used with several servers, the client can't distinguish
   them from eachother, even if the actual verifiers are not shared
   between servers.

   As some of the best know algorithms for computing discrete logarithms
   use extensive precomputations, it is desirable not to depend on a
   single fixed group like the multiplicative group used with "srp-
   ring1-sha1". However, care must be taken whenever the a client starts
   to use a new ring. Consider an attacker that knows how to compute
   discrete logarithms in the multiplicative group of a particular ring,
   and can convince the client to use that group.  According to Tom Wu,
   the worst the attacker can do is getting information that enables him
   to verify guessed passwords.

   In "diffie-hellman-group-exchange-sha1" [PROVOS] the client knows the
   server's hostkey a priori, and uses that to authenticate the groups
   the server proposes.

   With SRP, authenticating a proposed ring seems more difficult; if the
   ring is weak, authenticating it using the negotiated session key
   proves nothing.

   SRP also has the added advantage of permitting the host to store
   passwords in a form that is not directly useful to an attacker. Even
   if the host's password database were publicly revealed, the attacker
   would still need an expensive dictionary search to obtain any
   passwords. The exponential computation required to validate a guess
   in this case is much more time-consuming than the hash currently used
   by most UNIX systems. Hosts are still advised, though, to try their
   best to keep their password files secure.

   At the time of this writing, SRP is still quite a new protocol, and
   it is too early to say definitely that it is secure. It is therefore
   recommended not to use SRP for general remote access that lets the
   client to execute arbitrary programs on the server.

Niels M÷ller                                                    [Page 7]

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   SRP can be used for read-only access to public files (such as the
   server's host key, or a users known_hosts file). Used in this way,
   SRP can be used to obtain an authentic public key for the server,
   while a more conservative authentication mechanism is used for
   further access.

Further questions

   This document should give a list of rings that can be used, which
   should include the rings used by libsrp (is there any specification,
   besides the source code, that lists these rings)? In general, to what
   extent should the protocol be compatible with libsrp?

   Rings can be transmitted either by sending modulo and generator
   explicitly, like above, or by identifyng rings with names or numbers.

   It may be a good idea to optionally include the server's host key in
   the SSH_MSG_KEXSRP_REPLY above, and in the exchange hash. It is not
   needed for the SRP exchange, but it is a convenient way to transmit
   an authentic host key, and it is useful for key re-exchanges later

   To strengthen host authentication, in the case that a user has the
   same password on several servers, it may be a good idea to include
   the hostname somewhere in the computation of x, either in the user
   name or in the salt.

   One can also consider adding the description of the group as another
   element in the computation of x, to add robustness in the "middle-
   man-sends-booby-trapped-group" scenario. More analysis is needed to
   say if adding the group description would really help, though.

Author's Address

   Niels M÷ller
   LSH author
   Sl„tbaksv„gen 48
   120 51 Êrsta

   EMail: nisse@lysator.liu.se


   [PROVOS] Niels Provos, et al, "Diffie-Hellman Group Exchange for the
   SSH Transport Layer Protocol", Internet Draft,

Niels M÷ller                                                    [Page 8]

INTERNET-DRAFT     SRP key exchange with Secure Shell.     27 March 2001

   [SRP] T. Wu, "The SRP Authentication and Key Exchange System",
   RFC 2945

   [SSH-ARCH] Ylonen, T., et al, "SSH Protocol Architecture", Internet
   Draft, draft-ietf-secsh-architecture-07.txt

   [SSH-TRANS] Ylonen, T., et al, "SSH Transport Layer Protocol", Internet
   Draft, draft-ietf-secsh-transport-09.txt

   [SSH-USERAUTH] Ylonen, T., et al, "SSH Authentication Protocol",
   Internet Draft, draft-ietf-secsh-userauth-09.txt

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Niels M÷ller                                                    [Page 9]