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Network Working Group                                              T. WuRequest for Comments: 2945                           Stanford UniversityCategory: Standards Track                                 September 2000The SRP Authentication and Key Exchange SystemStatus 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 (2000).  All Rights Reserved.Abstract   This document describes a cryptographically strong network   authentication mechanism known as the Secure Remote Password (SRP)   protocol.  This mechanism is suitable for negotiating secure   connections using a user-supplied password, while eliminating the   security problems traditionally associated with reusable passwords.   This system also performs a secure key exchange in the process of   authentication, allowing security layers (privacy and/or integrity   protection) to be enabled during the session.  Trusted key servers   and certificate infrastructures are not required, and clients are not   required to store or manage any long-term keys.  SRP offers both   security and deployment advantages over existing challenge-response   techniques, making it an ideal drop-in replacement where secure   password authentication is needed.1. Introduction   The lack of a secure authentication mechanism that is also easy to   use has been a long-standing problem with the vast majority of   Internet protocols currently in use.  The problem is two-fold: Users   like to use passwords that they can remember, but most password-based   authentication systems offer little protection against even passive   attackers, especially if weak and easily-guessed passwords are used.   Eavesdropping on a TCP/IP network can be carried out very easily and   very effectively against protocols that transmit passwords in the   clear.  Even so-called "challenge-response" techniques like the one   described in [RFC 2095] and [RFC 1760], which are designed to defeatWu                          Standards Track                     [Page 1]

RFC 2945        SRP Authentication & Key Exchange System  September 2000   simple sniffing attacks, can be compromised by what is known as a   "dictionary attack".  This occurs when an attacker captures the   messages exchanged during a legitimate run of the protocol and uses   that information to verify a series of guessed passwords taken from a   precompiled "dictionary" of common passwords.  This works because   users often choose simple, easy-to-remember passwords, which   invariably are also easy to guess.   Many existing mechanisms also require the password database on the   host to be kept secret because the password P or some private hash   h(P) is stored there and would compromise security if revealed.  That   approach often degenerates into "security through obscurity" and goes   against the UNIX convention of keeping a "public" password file whose   contents can be revealed without destroying system security.   SRP meets the strictest requirements laid down in [RFC 1704] for a   non-disclosing authentication protocol.  It offers complete   protection against both passive and active attacks, and accomplishes   this efficiently using a single Diffie-Hellman-style round of   computation, making it feasible to use in both interactive and non-   interactive authentication for a wide range of Internet protocols.   Since it retains its security when used with low-entropy passwords,   it can be seamlessly integrated into existing user applications.2. Conventions and Terminology   The protocol described by this document is sometimes referred to as   "SRP-3" for historical purposes.  This particular protocol is   described in [SRP] and is believed to have very good logical and   cryptographic resistance to both eavesdropping and active attacks.   This document does not attempt to describe SRP in the context of any   particular Internet protocol; instead it describes an abstract   protocol that can be easily fitted to a particular application.  For   example, the specific format of messages (including padding) is not   specified.  Those issues have been left to the protocol implementor   to decide.   The one implementation issue worth specifying here is the mapping   between strings and integers.  Internet protocols are byte-oriented,   while SRP performs algebraic operations on its messages, so it is   logical to define at least one method by which integers can be   converted into a string of bytes and vice versa.   An n-byte string S can be converted to an integer as follows:   i = S[n-1] + 256 * S[n-2] + 256^2 * S[n-3] + ... + 256^(n-1) * S[0]Wu                          Standards Track                     [Page 2]

RFC 2945        SRP Authentication & Key Exchange System  September 2000   where i is the integer and S[x] is the value of the x'th byte of S.   In human terms, the string of bytes is the integer expressed in base   256, with the most significant digit first.  When converting back to   a string, S[0] must be non-zero (padding is considered to be a   separate, independent process).  This conversion method is suitable   for file storage, in-memory representation, and network transmission   of large integer values.  Unless otherwise specified, this mapping   will be assumed.   If implementations require padding a string that represents an   integer value, it is recommended that they use zero bytes and add   them to the beginning of the string.  The conversion back to integer   automatically discards leading zero bytes, making this padding scheme   less prone to error.   The SHA hash function, when used in this document, refers to the   SHA-1 message digest algorithm described in [SHA1].3. The SRP-SHA1 mechanism   This section describes an implementation of the SRP authentication   and key-exchange protocol that employs the SHA hash function to   generate session keys and authentication proofs.   The host stores user passwords as triplets of the form        { <username>, <password verifier>, <salt> }   Password entries are generated as follows:        <salt> = random()        x = SHA(<salt> | SHA(<username> | ":" | <raw password>))        <password verifier> = v = g^x % N   The | symbol indicates string concatenation, the ^ operator is the   exponentiation operation, and the % operator is the integer remainder   operation.  Most implementations perform the exponentiation and   remainder in a single stage to avoid generating unwieldy intermediate   results.  Note that the 160-bit output of SHA is implicitly converted   to an integer before it is operated upon.   Authentication is generally initiated by the client.      Client                             Host     --------                           ------      U = <username>              -->                                     <--    s = <salt from passwd file>Wu                          Standards Track                     [Page 3]

RFC 2945        SRP Authentication & Key Exchange System  September 2000   Upon identifying himself to the host, the client will receive the   salt stored on the host under his username.      a = random()      A = g^a % N                 -->                                         v = <stored password verifier>                                         b = random()                                  <--    B = (v + g^b) % N      p = <raw password>      x = SHA(s | SHA(U | ":" | p))      S = (B - g^x) ^ (a + u * x) % N    S = (A * v^u) ^ b % N      K = SHA_Interleave(S)              K = SHA_Interleave(S)      (this function is described       in the next section)   The client generates a random number, raises g to that power modulo   the field prime, and sends the result to the host.  The host does the   same thing and also adds the public verifier before sending it to the   client.  Both sides then construct the shared session key based on   the respective formulae.   The parameter u is a 32-bit unsigned integer which takes its value   from the first 32 bits of the SHA1 hash of B, MSB first.   The client MUST abort authentication if B % N is zero.   The host MUST abort the authentication attempt if A % N is zero.  The   host MUST send B after receiving A from the client, never before.   At this point, the client and server should have a common session key   that is secure (i.e. not known to an outside party).  To finish   authentication, they must prove to each other that their keys are   identical.        M = H(H(N) XOR H(g) | H(U) | s | A | B | K)                                    -->                                    <--    H(A | M | K)   The server will calculate M using its own K and compare it against   the client's response.  If they do not match, the server MUST abort   and signal an error before it attempts to answer the client's   challenge.  Not doing so could compromise the security of the user's   password.Wu                          Standards Track                     [Page 4]

RFC 2945        SRP Authentication & Key Exchange System  September 2000   If the server receives a correct response, it issues its own proof to   the client.  The client will compute the expected response using its   own K to verify the authenticity of the server.  If the client   responded correctly, the server MUST respond with its hash value.   The transactions in this protocol description do not necessarily have   a one-to-one correspondence with actual protocol messages.  This   description is only intended to illustrate the relationships between   the different parameters and how they are computed.  It is possible,   for example, for an implementation of the SRP-SHA1 mechanism to   consolidate some of the flows as follows:        Client                             Host       --------                           ------        U, A                        -->                                    <--    s, B        H(H(N) XOR H(g) | H(U) | s | A | B | K)                                    -->                                    <--    H(A | M | K)   The values of N and g used in this protocol must be agreed upon by   the two parties in question.  They can be set in advance, or the host   can supply them to the client.  In the latter case, the host should   send the parameters in the first message along with the salt.  For   maximum security, N should be a safe prime (i.e. a number of the form   N = 2q + 1, where q is also prime).  Also, g should be a generator   modulo N (see [SRP] for details), which means that for any X where 0   < X < N, there exists a value x for which g^x % N == X.3.1.  Interleaved SHA   The SHA_Interleave function used in SRP-SHA1 is used to generate a   session key that is twice as long as the 160-bit output of SHA1.  To   compute this function, remove all leading zero bytes from the input.   If the length of the resulting string is odd, also remove the first   byte.  Call the resulting string T.  Extract the even-numbered bytes   into a string E and the odd-numbered bytes into a string F, i.e.     E = T[0] | T[2] | T[4] | ...     F = T[1] | T[3] | T[5] | ...   Both E and F should be exactly half the length of T.  Hash each one   with regular SHA1, i.e.     G = SHA(E)     H = SHA(F)Wu                          Standards Track                     [Page 5]

RFC 2945        SRP Authentication & Key Exchange System  September 2000   Interleave the two hashes back together to form the output, i.e.     result = G[0] | H[0] | G[1] | H[1] | ... | G[19] | H[19]   The result will be 40 bytes (320 bits) long.3.2.  Other Hash Algorithms   SRP can be used with hash functions other than SHA.  If the hash   function produces an output of a different length than SHA (20   bytes), it may change the length of some of the messages in the   protocol, but the fundamental operation will be unaffected.   Earlier versions of the SRP mechanism used the MD5 hash function,   described in [RFC 1321].  Keyed hash transforms are also recommended   for use with SRP; one possible construction uses HMAC [RFC 2104],   using K to key the hash in each direction instead of concatenating it   with the other parameters.   Any hash function used with SRP should produce an output of at least   16 bytes and have the property that small changes in the input cause   significant nonlinear changes in the output.  [SRP] covers these   issues in more depth.4. Security Considerations   This entire memo discusses an authentication and key-exchange system   that protects passwords and exchanges keys across an untrusted   network.  This system improves security by eliminating the need to   send cleartext passwords over the network and by enabling encryption   through its secure key-exchange mechanism.   The private values for a and b correspond roughly to the private   values in a Diffie-Hellman exchange and have similar constraints of   length and entropy.  Implementations may choose to increase the   length of the parameter u, as long as both client and server agree,   but it is not recommended that it be shorter than 32 bits.   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   confidentiality.Wu                          Standards Track                     [Page 6]

RFC 2945        SRP Authentication & Key Exchange System  September 2000   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.5. References   [RFC 1321]  Rivest, R., "The MD5 Message-Digest Algorithm",RFC 1321,               April 1992.   [RFC 1704]  Haller, N. and R. Atkinson, "On Internet Authentication",RFC 1704, October 1994.   [RFC 1760]  Haller, N., "The S/Key One-Time Password System",RFC1760, Feburary 1995.   [RFC 2095]  Klensin, J., Catoe, R. and P. Krumviede, "IMAP/POP               AUTHorize Extension for Simple Challenge/Response",RFC2095, January 1997.   [RFC 2104]  Krawczyk, H., Bellare, M. and  R. Canetti, "HMAC: Keyed-               Hashing for Message Authentication",RFC 2104, February               1997.   [SHA1]      National Institute of Standards and Technology (NIST),               "Announcing the Secure Hash Standard", FIPS 180-1, U.S.               Department of Commerce, April 1995.   [SRP]       T. Wu, "The Secure Remote Password Protocol", In               Proceedings of the 1998 Internet Society Symposium on               Network and Distributed Systems Security, San Diego, CA,               pp. 97-111.6. Author's Address   Thomas Wu   Stanford University   Stanford, CA 94305   EMail: tjw@cs.Stanford.EDUWu                          Standards Track                     [Page 7]

RFC 2945        SRP Authentication & Key Exchange System  September 20007.  Full Copyright Statement   Copyright (C) The Internet Society (2000).  All Rights Reserved.   This document and translations of it may be copied and furnished to   others, and derivative works that comment on or otherwise explain it   or assist in its implementation may be prepared, copied, published   and distributed, in whole or in part, without restriction of any   kind, provided that the above copyright notice and this paragraph are   included on all such copies and derivative works.  However, this   document itself may not be modified in any way, such as by removing   the copyright notice or references to the Internet Society or other   Internet organizations, except as needed for the purpose of   developing Internet standards in which case the procedures for   copyrights defined in the Internet Standards process must be   followed, or as required to translate it into languages other than   English.   The limited permissions granted above are perpetual and will not be   revoked by the Internet Society or its successors or assigns.   This document and the information contained herein is provided on an   "AS IS" basis and THE INTERNET SOCIETY AND THE INTERNET ENGINEERING   TASK FORCE DISCLAIMS ALL WARRANTIES, EXPRESS OR IMPLIED, INCLUDING   BUT NOT LIMITED TO ANY WARRANTY THAT THE USE OF THE INFORMATION   HEREIN WILL NOT INFRINGE ANY RIGHTS OR ANY IMPLIED WARRANTIES OF   MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE.Acknowledgement   Funding for the RFC Editor function is currently provided by the   Internet Society.Wu                          Standards Track                     [Page 8]