Network Working Group T. Wu
Request for Comments: 2945 Stanford University
Category: Standards Track September 2000
The SRP Authentication and Key Exchange System
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 (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 defeat
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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]
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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
{ , , }
Password entries are generated as follows:
= random()
x = SHA( | SHA( | ":" | ))
= 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 = -->
<-- s =
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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 =
b = random()
<-- B = (v + g^b) % N
p =
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.
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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)
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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.
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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", RFC
1760, Feburary 1995.
[RFC 2095] Klensin, J., Catoe, R. and P. Krumviede, "IMAP/POP
AUTHorize Extension for Simple Challenge/Response", RFC
2095, 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.EDU
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7. Full Copyright Statement
Copyright (C) The Internet Society (2000). All Rights Reserved.
This document and translations of it may be copied and furnished to
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Acknowledgement
Funding for the RFC Editor function is currently provided by the
Internet Society.
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