One document matched: draft-ietf-tls-srp-12.txt
Differences from draft-ietf-tls-srp-11.txt
TLS Working Group D. Taylor
Internet-Draft Independent
Expires: December 28, 2006 T. Wu
Stanford University
N. Mavrogiannopoulos
T. Perrin
Independent
June 26, 2006
Using SRP for TLS Authentication
draft-ietf-tls-srp-12
Status of this Memo
By submitting this Internet-Draft, each author represents that any
applicable patent or other IPR claims of which he or she is aware
have been or will be disclosed, and any of which he or she becomes
aware will be disclosed, in accordance with Section 6 of BCP 79.
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
http://www.ietf.org/ietf/1id-abstracts.txt.
The list of Internet-Draft Shadow Directories can be accessed at
http://www.ietf.org/shadow.html.
This Internet-Draft will expire on December 28, 2006.
Copyright Notice
Copyright (C) The Internet Society (2006).
Abstract
This memo presents a technique for using the Secure Remote Password
protocol as an authentication method for the Transport Layer Security
protocol.
Taylor, et al. Expires December 28, 2006 [Page 1]
Internet-Draft Using SRP for TLS Authentication June 2006
Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 3
2. SRP Authentication in TLS . . . . . . . . . . . . . . . . . . 4
2.1. Notation and Terminology . . . . . . . . . . . . . . . . . 4
2.2. Handshake Protocol Overview . . . . . . . . . . . . . . . 4
2.3. Text Preparation . . . . . . . . . . . . . . . . . . . . . 5
2.4. SRP Verifier Creation . . . . . . . . . . . . . . . . . . 5
2.5. Changes to the Handshake Message Contents . . . . . . . . 5
2.5.1. Client Hello . . . . . . . . . . . . . . . . . . . . . 5
2.5.2. Server Certificate . . . . . . . . . . . . . . . . . . 7
2.5.3. Server Key Exchange . . . . . . . . . . . . . . . . . 7
2.5.4. Client Key Exchange . . . . . . . . . . . . . . . . . 8
2.6. Calculating the Pre-master Secret . . . . . . . . . . . . 8
2.7. Cipher Suite Definitions . . . . . . . . . . . . . . . . . 9
2.8. New Message Structures . . . . . . . . . . . . . . . . . . 10
2.8.1. Client Hello . . . . . . . . . . . . . . . . . . . . . 10
2.8.2. Server Key Exchange . . . . . . . . . . . . . . . . . 10
2.8.3. Client Key Exchange . . . . . . . . . . . . . . . . . 11
2.9. Error Alerts . . . . . . . . . . . . . . . . . . . . . . . 11
3. Security Considerations . . . . . . . . . . . . . . . . . . . 13
4. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 15
5. References . . . . . . . . . . . . . . . . . . . . . . . . . . 16
5.1. Normative References . . . . . . . . . . . . . . . . . . . 16
5.2. Informative References . . . . . . . . . . . . . . . . . . 16
Appendix A. SRP Group Parameters . . . . . . . . . . . . . . . . 18
Appendix B. SRP Test Vectors . . . . . . . . . . . . . . . . . . 23
Appendix C. Acknowledgements . . . . . . . . . . . . . . . . . . 25
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . . 26
Intellectual Property and Copyright Statements . . . . . . . . . . 27
Taylor, et al. Expires December 28, 2006 [Page 2]
Internet-Draft Using SRP for TLS Authentication June 2006
1. Introduction
At the time of writing TLS [TLS] uses public key certificates, pre-
shared keys, or Kerberos for authentication.
These authentication methods do not seem well suited to certain
applications now being adapted to use TLS ([IMAP] for example).
Given that many protocols are designed to use the user name and
password method of authentication, being able to safely use user
names and passwords provides an easier route to additional security.
SRP ([SRP], [SRP-6]) is an authentication method that allows the use
of user names and passwords over unencrypted channels without
revealing the password to an eavesdropper. SRP also supplies a
shared secret at the end of the authentication sequence that can be
used to generate encryption keys.
This document describes the use of the SRP authentication method for
TLS.
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 RFC 2119.
Taylor, et al. Expires December 28, 2006 [Page 3]
Internet-Draft Using SRP for TLS Authentication June 2006
2. SRP Authentication in TLS
2.1. Notation and Terminology
The version of SRP used here is sometimes referred to as "SRP-6"
[SRP-6]. This version is a slight improvement over "SRP-3", which
was described in [SRP] and [SRP-RFC].
This document uses the variable names defined in [SRP-6]:
N, g: group parameters (prime and generator)
s: salt
B, b: server's public and private values
A, a: client's public and private values
I: user name (aka "identity")
P: password
v: verifier
k: SRP-6 multiplier
The | symbol indicates string concatenation, the ^ operator is the
exponentiation operation, and the % operator is the integer remainder
operation.
Conversion between integers and byte-strings assumes the most-
significant bytes are stored first, as per [TLS] and [SRP-RFC]. In
the following text, if a conversion from integer to byte-string is
implicit, the most-significant byte in the resultant byte-string MUST
be non-zero. If a conversion is explicitly specified with the
operator PAD(), the integer will first be implicitly converted, then
the resultant byte-string will be left-padded with zeros (if
necessary) until its length equals the implicitly-converted length of
N.
2.2. Handshake Protocol Overview
The advent of [SRP-6] allows the SRP protocol to be implemented using
the standard sequence of handshake messages defined in [TLS].
The parameters to various messages are given in the following
diagram.
Taylor, et al. Expires December 28, 2006 [Page 4]
Internet-Draft Using SRP for TLS Authentication June 2006
Client Server
Client Hello (I) -------->
Server Hello
Certificate*
Server Key Exchange (N, g, s, B)
<-------- Server Hello Done
Client Key Exchange (A) -------->
[Change cipher spec]
Finished -------->
[Change cipher spec]
<-------- Finished
Application Data <-------> Application Data
* Indicates an optional message which is not always sent.
Figure 1
2.3. Text Preparation
The user name and password strings shall be UTF-8 encoded Unicode,
prepared using the [SASLPREP] profile of [STRINGPREP].
2.4. SRP Verifier Creation
The verifier is calculated as described in section 3 of [SRP-RFC].
We give the algorithm here for convenience.
The verifier (v) is computed based on the salt (s), user name (I),
password (P), and group parameters (N, g). The computation uses the
[SHA1] hash algorithm:
x = SHA1(s | SHA1(I | ":" | P))
v = g^x % N
2.5. Changes to the Handshake Message Contents
This section describes the changes to the TLS handshake message
contents when SRP is being used for authentication. The definitions
of the new message contents and the on-the-wire changes are given in
Section 2.8.
2.5.1. Client Hello
The user name is appended to the standard client hello message using
the hello message extension mechanism defined in [TLSEXT] (see
Section 2.8.1).
Taylor, et al. Expires December 28, 2006 [Page 5]
Internet-Draft Using SRP for TLS Authentication June 2006
2.5.1.1. Session Resumption
When a client attempts to resume a session that uses SRP
authentication, the client MUST include the user name extension in
the client hello message, in case the server cannot or will not allow
session resumption, meaning a full handshake is required.
If the server does agree to resume an existing session the server
MUST ignore the information in the SRP extension of the client hello
message, except for its inclusion in the finished message hashes.
This is to ensure attackers cannot replace the authenticated identity
without supplying the proper authentication information.
2.5.1.2. Missing SRP Username
The client may offer SRP ciphersuites in the hello message but omit
the SRP extension. If the server would like to select an SRP
ciphersuite in this case, the server MAY return a
"missing_srp_username" alert (see Section 2.9) immediately after
processing the client hello message. This alert signals the client
to resend the hello message, this time with the SRP extension. This
allows the client to advertise that it supports SRP, but not have to
prompt the user for his user name and password, nor expose the user
name in the clear, unless necessary.
After sending the "missing_srp_username" alert, the server MUST leave
the TLS connection open, yet reset its handshake protocol state so it
is prepared to receive a second client hello message. Upon receiving
the "missing_srp_username" alert, the client MUST either send a
second client hello message, or send a fatal user_cancelled alert.
If the client sends a second hello message, the second hello message
MUST offer SRP ciphersuites, and MUST contain the SRP extension, and
the server MUST choose one of the SRP ciphersuites. Both client
hello messages MUST be treated as handshake messages and included in
the hash calculations for the TLS Finished message. The premaster
and master secret calculations will use the random value from the
second client hello message, not the first.
2.5.1.3. Unknown SRP Username
If the server doesn't have a verifier for the given user name, the
server MAY abort the handshake with an "unknown_srp_username" alert
(see Section 2.9). Alternatively, if the server wishes to hide the
fact that this user name doesn't have a verifier, the server MAY
simulate the protocol as if a verifier existed, but then reject the
client's finished message with a "bad_record_mac" alert, as if the
password was incorrect.
Taylor, et al. Expires December 28, 2006 [Page 6]
Internet-Draft Using SRP for TLS Authentication June 2006
To simulate the existence of an entry for each user name, the server
must consistently return the same salt (s) and group (N, g) values
for the same user name. For example, the server could store a secret
"seed key" and then use HMAC-SHA1(seed_key, "salt" | user_name) to
generate the salts [HMAC]. For B, the server can return a random
value between 1 and N-1 inclusive. However, the server should take
care to simulate computation delays. One way to do this is to
generate a fake verifier using the "seed key" approach, and then
proceed with the protocol as usual.
2.5.2. Server Certificate
The server MUST send a certificate if it agrees to an SRP cipher
suite that requires the server to provide additional authentication
in the form of a digital signature. See Section 2.7 for details of
which ciphersuites defined in this document require a server
certificate to be sent.
2.5.3. Server Key Exchange
The server key exchange message contains the prime (N), the generator
(g), and the salt value (s) read from the SRP password file based on
the user name (I) received in the client hello extension.
The server key exchange message also contains the server's public
value (B). The server calculates this value as B = k*v + g^b % N,
where b is a random number which SHOULD be at least 256 bits in
length, and k = SHA1(N | PAD(g)).
If the server has sent a certificate message, the server key exchange
message MUST be signed.
The group parameters (N, g) sent in this message MUST have N as a
safe prime (a prime of the form N=2q+1, where q is also prime). The
integers from 1 to N-1 will form a group under multiplication % N,
and g MUST be a generator of this group. In addition, the group
parameters MUST NOT be specially chosen to allow efficient
computation of discrete logarithms.
The SRP group parameters in Appendix A satisfy the above
requirements, so the client SHOULD accept any parameters from this
Appendix which have large enough N values to meet her security
requirements.
The client MAY accept other group parameters from the server, if the
client has reason to believe these parameters satisfy the above
requirements, and the parameters have large enough N values. For
example, if the parameters transmitted by the server match parameters
Taylor, et al. Expires December 28, 2006 [Page 7]
Internet-Draft Using SRP for TLS Authentication June 2006
on a "known-good" list, the client may choose to accept them. See
Section 3 for additional security considerations relevant to the
acceptance of the group parameters.
Group parameters that are not accepted via one of the above methods
MUST be rejected with an "untrusted_srp_parameters" alert (see
Section 2.9).
The client MUST abort the handshake with an "illegal_parameter" alert
if B % N = 0.
2.5.4. Client Key Exchange
The client key exchange message carries the client's public value
(A). The client calculates this value as A = g^a % N, where a is a
random number which SHOULD be at least 256 bits in length.
The server MUST abort the handshake with an "illegal_parameter" alert
if A % N = 0.
2.6. Calculating the Pre-master Secret
The pre-master secret is calculated by the client as follows:
I, P = <read from user>
N, g, s, B = <read from server>
a = random()
A = g^a % N
u = SHA1(PAD(A) | PAD(B))
k = SHA1(N | PAD(g))
x = SHA1(s | SHA1(I | ":" | P))
<premaster secret> = (B - (k * g^x)) ^ (a + (u * x)) % N
The pre-master secret is calculated by the server as follows:
N, g, s, v = <read from password file>
b = random()
k = SHA1(N | PAD(g))
B = k*v + g^b % N
A = <read from client>
u = SHA1(PAD(A) | PAD(B))
<premaster secret> = (A * v^u) ^ b % N
The finished messages perform the same function as the client and
server evidence messages (M1 and M2) specified in [SRP-RFC]. If
either the client or the server calculate an incorrect premaster
secret, the finished messages will fail to decrypt properly, and the
other party will return a "bad_record_mac" alert.
Taylor, et al. Expires December 28, 2006 [Page 8]
Internet-Draft Using SRP for TLS Authentication June 2006
If a client application receives a "bad_record_mac" alert when
performing an SRP handshake, it should inform the user that the
entered user name and password are incorrect.
2.7. Cipher Suite Definitions
The following cipher suites are added by this draft. The usage of
AES ciphersuites is as defined in [AESCIPH].
CipherSuite TLS_SRP_SHA_WITH_3DES_EDE_CBC_SHA = { 0x00,0xTBD5 };
CipherSuite TLS_SRP_SHA_RSA_WITH_3DES_EDE_CBC_SHA = { 0x00,0xTBD6
};
CipherSuite TLS_SRP_SHA_DSS_WITH_3DES_EDE_CBC_SHA = { 0x00,0xTBD7
};
CipherSuite TLS_SRP_SHA_WITH_AES_128_CBC_SHA = { 0x00,0xTBD8 };
CipherSuite TLS_SRP_SHA_RSA_WITH_AES_128_CBC_SHA = { 0x00,0xTBD9
};
CipherSuite TLS_SRP_SHA_DSS_WITH_AES_128_CBC_SHA = { 0x00,0xTBD10
};
CipherSuite TLS_SRP_SHA_WITH_AES_256_CBC_SHA = { 0x00,0xTBD11 };
CipherSuite TLS_SRP_SHA_RSA_WITH_AES_256_CBC_SHA = { 0x00,0xTBD12
};
CipherSuite TLS_SRP_SHA_DSS_WITH_AES_256_CBC_SHA = { 0x00,0xTBD13
};
Cipher suites that begin with TLS_SRP_SHA_RSA or TLS_SRP_SHA_DSS
require the server to send a certificate message containing a
certificate with the specified type of public key, and to sign the
server key exchange message using a matching private key.
Cipher suites that do not include a digital signature algorithm
identifier assume the server is authenticated by its possesion of the
SRP verifier.
Implementations conforming to this specification MUST implement the
TLS_SRP_SHA_WITH_3DES_EDE_CBC_SHA ciphersuite, SHOULD implement the
TLS_SRP_SHA_WITH_AES_128_CBC_SHA and TLS_SRP_SHA_WITH_AES_256_CBC_SHA
ciphersuites, and MAY implement the remaining ciphersuites.
Taylor, et al. Expires December 28, 2006 [Page 9]
Internet-Draft Using SRP for TLS Authentication June 2006
2.8. New Message Structures
This section shows the structure of the messages passed during a
handshake that uses SRP for authentication. The representation
language used is the same as that used in [TLS].
2.8.1. Client Hello
A new extension "srp" with value TBD1, has been added to the
enumerated ExtensionType defined in [TLSEXT]. This value MUST be
used as the extension number for the SRP extension.
The "extension_data" field of the SRP extension SHALL contain:
opaque srp_I<1..2^8-1>
where srp_I is the user name, encoded per Section 2.4.
2.8.2. Server Key Exchange
A new value, "srp", has been added to the enumerated
KeyExchangeAlgorithm originally defined in [TLS].
When the value of KeyExchangeAlgorithm is set to "srp", the server's
SRP parameters are sent in the server key exchange message, encoded
in a ServerSRPParams structure.
If a certificate is sent to the client the server key exchange
message must be signed.
Taylor, et al. Expires December 28, 2006 [Page 10]
Internet-Draft Using SRP for TLS Authentication June 2006
enum { rsa, diffie_hellman, srp } KeyExchangeAlgorithm;
struct {
select (KeyExchangeAlgorithm) {
case diffie_hellman:
ServerDHParams params;
Signature signed_params;
case rsa:
ServerRSAParams params;
Signature signed_params;
case srp: /* new entry */
ServerSRPParams params;
Signature signed_params;
};
} ServerKeyExchange;
struct {
opaque srp_N<1..2^16-1>;
opaque srp_g<1..2^16-1>;
opaque srp_s<1..2^8-1>
opaque srp_B<1..2^16-1>;
} ServerSRPParams; /* SRP parameters */
2.8.3. Client Key Exchange
When the value of KeyExchangeAlgorithm is set to "srp", the client's
public value (A) is sent in the client key exchange message, encoded
in a ClientSRPPublic structure.
struct {
select (KeyExchangeAlgorithm) {
case rsa: EncryptedPreMasterSecret;
case diffie_hellman: ClientDiffieHellmanPublic;
case srp: ClientSRPPublic; /* new entry */
} exchange_keys;
} ClientKeyExchange;
struct {
opaque srp_A<1..2^16-1>;
} ClientSRPPublic;
2.9. Error Alerts
Three new error alerts are defined:
o "unknown_srp_username" (TBD2) - this alert MAY be sent by a server
that receives an unknown user name. This alert is always fatal.
See Section 2.5.1.3 for details.
Taylor, et al. Expires December 28, 2006 [Page 11]
Internet-Draft Using SRP for TLS Authentication June 2006
o "missing_srp_username" (TBD3) - this alert MAY be sent by a server
that would like to select an offered SRP ciphersuite, if the SRP
extension is absent from the client's hello message. This alert
is always a warning. Upon receiving this alert, the client MAY
send a new hello message on the same connection, this time
including the SRP extension. See Section 2.5.1.2 for details.
o "untrusted_srp_parameters" (TBD4) - this alert MUST be sent by a
client that receives unknown or untrusted (N, g) values. This
alert is always fatal. See Section 2.5.3 for details.
Taylor, et al. Expires December 28, 2006 [Page 12]
Internet-Draft Using SRP for TLS Authentication June 2006
3. Security Considerations
If an attacker is able to steal the SRP verifier file, the attacker
can masquerade as the real server, and can also use dictionary
attacks to recover client passwords.
An attacker could repeatedly contact an SRP server and try to guess a
legitimate user's password. Servers SHOULD take steps to prevent
this, such as limiting the rate of authentication attempts from a
particular IP address, or against a particular user account, or
locking the user account once a threshold of failed attempts is
reached.
The client's user name is sent in the clear in the Client Hello
message. To avoid sending the user name in the clear, the client
could first open a conventional anonymous, or server-authenticated
connection, then renegotiate an SRP-authenticated connection with the
handshake protected by the first connection.
An attacker who could calculate discrete logarithms in the
multiplicative group % N could compromise user passwords, and could
also compromise the the confidentiality and integrity of TLS
sessions. Clients MUST ensure that the received parameter N is large
enough to make calculating discrete logarithms computationally
infeasible.
An attacker may try to send a prime value N which is large enough to
be secure, but which has a special form for which the attacker can
more easily compute discrete logarithms (e.g., using the algorithm
discussed in [TRAPDOOR]). If the client executes the protocol using
such a prime, the client's password could be compromised. Because of
the difficulty of checking for such special primes in real-time,
clients SHOULD only accept group parameters that come from a trusted
source, such as those listed in Appendix A, or parameters configured
locally by a trusted administrator.
The checks described in Section 2.5.3 and Section 2.5.4 on the
received values for A and B are crucial for security and MUST be
performed.
The private values a and b SHOULD be at least 256 bit random numbers,
to give approximately 128 bits of security against certain methods of
calculating discrete logarithms.
If the client receives a missing_srp_username alert, the client
should be aware that unless the handshake protocol is run to
completion, this alert may have been inserted by an attacker. If the
handshake protocol is not run to completion, the client should not
Taylor, et al. Expires December 28, 2006 [Page 13]
Internet-Draft Using SRP for TLS Authentication June 2006
make any decisions, nor form any assumptions, based on receiving this
alert.
It is possible to choose a (user name, password) pair such that the
resulting verifier will also match other, related, (user name,
password) pairs. Thus, anyone using verifiers should be careful not
to assume that only a single (user name, password) pair matches the
verifier.
Taylor, et al. Expires December 28, 2006 [Page 14]
Internet-Draft Using SRP for TLS Authentication June 2006
4. IANA Considerations
This document defines a new TLS extension "srp", assigned the value
TBD1 (the value 6 is suggested) from the TLS ExtensionType registry
defined in [TLSEXT].
The error alerts that are defined in this document are assigned to
the TLS Alert registry defined in [TLS]. The alerts together with
their assigned number (the values 120-122 are suggested) are shown
below.
o "unknown_srp_username" (TBD2)
o "missing_srp_username" (TBD3)
o "untrusted_srp_parameters" (TBD4)
IANA assigned the cipher suites' numbers to the Cipher Suite
Registry, defined in [TLS]. The assigned values are listed below
(the numbers between 0x50 to 0x58 are suggested).
CipherSuite TLS_SRP_SHA_WITH_3DES_EDE_CBC_SHA = { 0x00,0xTBD5 };
CipherSuite TLS_SRP_SHA_RSA_WITH_3DES_EDE_CBC_SHA = { 0x00,0xTBD6
};
CipherSuite TLS_SRP_SHA_DSS_WITH_3DES_EDE_CBC_SHA = { 0x00,0xTBD7
};
CipherSuite TLS_SRP_SHA_WITH_AES_128_CBC_SHA = { 0x00,0xTBD8 };
CipherSuite TLS_SRP_SHA_RSA_WITH_AES_128_CBC_SHA = { 0x00,0xTBD9
};
CipherSuite TLS_SRP_SHA_DSS_WITH_AES_128_CBC_SHA = { 0x00,0xTBD10
};
CipherSuite TLS_SRP_SHA_WITH_AES_256_CBC_SHA = { 0x00,0xTBD11 };
CipherSuite TLS_SRP_SHA_RSA_WITH_AES_256_CBC_SHA = { 0x00,0xTBD12
};
CipherSuite TLS_SRP_SHA_DSS_WITH_AES_256_CBC_SHA = { 0x00,0xTBD13
};
Taylor, et al. Expires December 28, 2006 [Page 15]
Internet-Draft Using SRP for TLS Authentication June 2006
5. References
5.1. Normative References
[TLS] Dierks, T. and E. Rescorla, "The TLS Protocol version
1.1", RFC 4346, April 2006.
[SRP-6] Wu, T., "SRP-6: Improvements and Refinements to the Secure
Remote Password Protocol", October 2002,
<http://srp.stanford.edu/srp6.ps>.
[TLSEXT] Blake-Wilson, S., Nystrom, M., Hopwood, D., Mikkelsen, J.,
and T. Wright, "TLS Extensions", RFC 3546, June 2003.
[STRINGPREP]
Hoffman, P. and M. Blanchet, "Preparation of
Internationalized Strings ("stringprep")", RFC 3454,
December 2002.
[SASLPREP]
Zeilenga, K., "SASLprep: Stringprep profile for user names
and passwords", RFC 4013, February 2005.
[SRP-RFC] Wu, T., "The SRP Authentication and Key Exchange System",
RFC 2945, September 2000.
[SHA1] "Announcing the Secure Hash Standard", FIPS 180-1,
September 2000.
[HMAC] Krawczyk, H., Bellare, M., and R. Canetti, "HMAC: Keyed-
Hashing for Message Authentication", RFC 2104,
February 1997.
[AESCIPH] Chown, P., "Advanced Encryption Standard (AES)
Ciphersuites for Transport Layer Security (TLS)",
RFC 3268, June 2002.
[MODP] Kivinen, T. and M. Kojo, "More Modular Exponentiation
(MODP) Diffie-Hellman groups for Internet Key Exchange
(IKE)", RFC 3526, May 2003.
5.2. Informative References
[IMAP] Newman, C., "Using TLS with IMAP, POP3 and ACAP",
RFC 2595, June 1999.
[SRP] Wu, T., "The Secure Remote Password Protocol", Proceedings
of the 1998 Internet Society Network and Distributed
Taylor, et al. Expires December 28, 2006 [Page 16]
Internet-Draft Using SRP for TLS Authentication June 2006
System Security Symposium pp. 97-111, March 1998.
[TRAPDOOR]
Gordon, D., "Designing and Detecting Trapdoors for
Discrete Log Cryptosystems", Springer-Verlag Advances in
Cryptology - Crypto '92, pp. 66-75, 1993.
Taylor, et al. Expires December 28, 2006 [Page 17]
Internet-Draft Using SRP for TLS Authentication June 2006
Appendix A. SRP Group Parameters
The 1024, 1536, and 2048-bit groups are taken from software developed
by Tom Wu and Eugene Jhong for the Stanford SRP distribution, and
subsequently proven to be prime. The larger primes are taken from
[MODP], but generators have been calculated that are primitive roots
of N, unlike the generators in [MODP].
The 1024-bit and 1536-bit groups MUST be supported.
1. 1024-bit Group
The hexadecimal value for the prime is:
EEAF0AB9 ADB38DD6 9C33F80A FA8FC5E8 60726187 75FF3C0B 9EA2314C
9C256576 D674DF74 96EA81D3 383B4813 D692C6E0 E0D5D8E2 50B98BE4
8E495C1D 6089DAD1 5DC7D7B4 6154D6B6 CE8EF4AD 69B15D49 82559B29
7BCF1885 C529F566 660E57EC 68EDBC3C 05726CC0 2FD4CBF4 976EAA9A
FD5138FE 8376435B 9FC61D2F C0EB06E3
The generator is: 2.
2. 1536-bit Group
The hexadecimal value for the prime is:
9DEF3CAF B939277A B1F12A86 17A47BBB DBA51DF4 99AC4C80 BEEEA961
4B19CC4D 5F4F5F55 6E27CBDE 51C6A94B E4607A29 1558903B A0D0F843
80B655BB 9A22E8DC DF028A7C EC67F0D0 8134B1C8 B9798914 9B609E0B
E3BAB63D 47548381 DBC5B1FC 764E3F4B 53DD9DA1 158BFD3E 2B9C8CF5
6EDF0195 39349627 DB2FD53D 24B7C486 65772E43 7D6C7F8C E442734A
F7CCB7AE 837C264A E3A9BEB8 7F8A2FE9 B8B5292E 5A021FFF 5E91479E
8CE7A28C 2442C6F3 15180F93 499A234D CF76E3FE D135F9BB
The generator is: 2.
3. 2048-bit Group
The hexadecimal value for the prime is:
AC6BDB41 324A9A9B F166DE5E 1389582F AF72B665 1987EE07 FC319294
3DB56050 A37329CB B4A099ED 8193E075 7767A13D D52312AB 4B03310D
CD7F48A9 DA04FD50 E8083969 EDB767B0 CF609517 9A163AB3 661A05FB
D5FAAAE8 2918A996 2F0B93B8 55F97993 EC975EEA A80D740A DBF4FF74
Taylor, et al. Expires December 28, 2006 [Page 18]
Internet-Draft Using SRP for TLS Authentication June 2006
7359D041 D5C33EA7 1D281E44 6B14773B CA97B43A 23FB8016 76BD207A
436C6481 F1D2B907 8717461A 5B9D32E6 88F87748 544523B5 24B0D57D
5EA77A27 75D2ECFA 032CFBDB F52FB378 61602790 04E57AE6 AF874E73
03CE5329 9CCC041C 7BC308D8 2A5698F3 A8D0C382 71AE35F8 E9DBFBB6
94B5C803 D89F7AE4 35DE236D 525F5475 9B65E372 FCD68EF2 0FA7111F
9E4AFF73
The generator is: 2.
4. 3072-bit Group
This prime is: 2^3072 - 2^3008 - 1 + 2^64 * { [2^2942 pi] +
1690314 }
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 ECE45B3D C2007CB8 A163BF05 98DA4836 1C55D39A 69163FA8
FD24CF5F 83655D23 DCA3AD96 1C62F356 208552BB 9ED52907 7096966D
670C354E 4ABC9804 F1746C08 CA18217C 32905E46 2E36CE3B E39E772C
180E8603 9B2783A2 EC07A28F B5C55DF0 6F4C52C9 DE2BCBF6 95581718
3995497C EA956AE5 15D22618 98FA0510 15728E5A 8AAAC42D AD33170D
04507A33 A85521AB DF1CBA64 ECFB8504 58DBEF0A 8AEA7157 5D060C7D
B3970F85 A6E1E4C7 ABF5AE8C DB0933D7 1E8C94E0 4A25619D CEE3D226
1AD2EE6B F12FFA06 D98A0864 D8760273 3EC86A64 521F2B18 177B200C
BBE11757 7A615D6C 770988C0 BAD946E2 08E24FA0 74E5AB31 43DB5BFC
E0FD108E 4B82D120 A93AD2CA FFFFFFFF FFFFFFFF
The generator is: 5.
5. 4096-bit Group
This prime is: 2^4096 - 2^4032 - 1 + 2^64 * { [2^3966 pi] +
240904 }
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
Taylor, et al. Expires December 28, 2006 [Page 19]
Internet-Draft Using SRP for TLS Authentication June 2006
49286651 ECE45B3D C2007CB8 A163BF05 98DA4836 1C55D39A 69163FA8
FD24CF5F 83655D23 DCA3AD96 1C62F356 208552BB 9ED52907 7096966D
670C354E 4ABC9804 F1746C08 CA18217C 32905E46 2E36CE3B E39E772C
180E8603 9B2783A2 EC07A28F B5C55DF0 6F4C52C9 DE2BCBF6 95581718
3995497C EA956AE5 15D22618 98FA0510 15728E5A 8AAAC42D AD33170D
04507A33 A85521AB DF1CBA64 ECFB8504 58DBEF0A 8AEA7157 5D060C7D
B3970F85 A6E1E4C7 ABF5AE8C DB0933D7 1E8C94E0 4A25619D CEE3D226
1AD2EE6B F12FFA06 D98A0864 D8760273 3EC86A64 521F2B18 177B200C
BBE11757 7A615D6C 770988C0 BAD946E2 08E24FA0 74E5AB31 43DB5BFC
E0FD108E 4B82D120 A9210801 1A723C12 A787E6D7 88719A10 BDBA5B26
99C32718 6AF4E23C 1A946834 B6150BDA 2583E9CA 2AD44CE8 DBBBC2DB
04DE8EF9 2E8EFC14 1FBECAA6 287C5947 4E6BC05D 99B2964F A090C3A2
233BA186 515BE7ED 1F612970 CEE2D7AF B81BDD76 2170481C D0069127
D5B05AA9 93B4EA98 8D8FDDC1 86FFB7DC 90A6C08F 4DF435C9 34063199
FFFFFFFF FFFFFFFF
The generator is: 5.
6. 6144-bit Group
This prime is: 2^6144 - 2^6080 - 1 + 2^64 * { [2^6014 pi] +
929484 }
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 ECE45B3D C2007CB8 A163BF05 98DA4836 1C55D39A 69163FA8
FD24CF5F 83655D23 DCA3AD96 1C62F356 208552BB 9ED52907 7096966D
670C354E 4ABC9804 F1746C08 CA18217C 32905E46 2E36CE3B E39E772C
180E8603 9B2783A2 EC07A28F B5C55DF0 6F4C52C9 DE2BCBF6 95581718
3995497C EA956AE5 15D22618 98FA0510 15728E5A 8AAAC42D AD33170D
04507A33 A85521AB DF1CBA64 ECFB8504 58DBEF0A 8AEA7157 5D060C7D
B3970F85 A6E1E4C7 ABF5AE8C DB0933D7 1E8C94E0 4A25619D CEE3D226
1AD2EE6B F12FFA06 D98A0864 D8760273 3EC86A64 521F2B18 177B200C
BBE11757 7A615D6C 770988C0 BAD946E2 08E24FA0 74E5AB31 43DB5BFC
E0FD108E 4B82D120 A9210801 1A723C12 A787E6D7 88719A10 BDBA5B26
99C32718 6AF4E23C 1A946834 B6150BDA 2583E9CA 2AD44CE8 DBBBC2DB
04DE8EF9 2E8EFC14 1FBECAA6 287C5947 4E6BC05D 99B2964F A090C3A2
233BA186 515BE7ED 1F612970 CEE2D7AF B81BDD76 2170481C D0069127
D5B05AA9 93B4EA98 8D8FDDC1 86FFB7DC 90A6C08F 4DF435C9 34028492
36C3FAB4 D27C7026 C1D4DCB2 602646DE C9751E76 3DBA37BD F8FF9406
AD9E530E E5DB382F 413001AE B06A53ED 9027D831 179727B0 865A8918
DA3EDBEB CF9B14ED 44CE6CBA CED4BB1B DB7F1447 E6CC254B 33205151
Taylor, et al. Expires December 28, 2006 [Page 20]
Internet-Draft Using SRP for TLS Authentication June 2006
2BD7AF42 6FB8F401 378CD2BF 5983CA01 C64B92EC F032EA15 D1721D03
F482D7CE 6E74FEF6 D55E702F 46980C82 B5A84031 900B1C9E 59E7C97F
BEC7E8F3 23A97A7E 36CC88BE 0F1D45B7 FF585AC5 4BD407B2 2B4154AA
CC8F6D7E BF48E1D8 14CC5ED2 0F8037E0 A79715EE F29BE328 06A1D58B
B7C5DA76 F550AA3D 8A1FBFF0 EB19CCB1 A313D55C DA56C9EC 2EF29632
387FE8D7 6E3C0468 043E8F66 3F4860EE 12BF2D5B 0B7474D6 E694F91E
6DCC4024 FFFFFFFF FFFFFFFF
The generator is: 5.
7. 8192-bit Group
This prime is: 2^8192 - 2^8128 - 1 + 2^64 * { [2^8062 pi] +
4743158 }
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 ECE45B3D C2007CB8 A163BF05 98DA4836 1C55D39A 69163FA8
FD24CF5F 83655D23 DCA3AD96 1C62F356 208552BB 9ED52907 7096966D
670C354E 4ABC9804 F1746C08 CA18217C 32905E46 2E36CE3B E39E772C
180E8603 9B2783A2 EC07A28F B5C55DF0 6F4C52C9 DE2BCBF6 95581718
3995497C EA956AE5 15D22618 98FA0510 15728E5A 8AAAC42D AD33170D
04507A33 A85521AB DF1CBA64 ECFB8504 58DBEF0A 8AEA7157 5D060C7D
B3970F85 A6E1E4C7 ABF5AE8C DB0933D7 1E8C94E0 4A25619D CEE3D226
1AD2EE6B F12FFA06 D98A0864 D8760273 3EC86A64 521F2B18 177B200C
BBE11757 7A615D6C 770988C0 BAD946E2 08E24FA0 74E5AB31 43DB5BFC
E0FD108E 4B82D120 A9210801 1A723C12 A787E6D7 88719A10 BDBA5B26
99C32718 6AF4E23C 1A946834 B6150BDA 2583E9CA 2AD44CE8 DBBBC2DB
04DE8EF9 2E8EFC14 1FBECAA6 287C5947 4E6BC05D 99B2964F A090C3A2
233BA186 515BE7ED 1F612970 CEE2D7AF B81BDD76 2170481C D0069127
D5B05AA9 93B4EA98 8D8FDDC1 86FFB7DC 90A6C08F 4DF435C9 34028492
36C3FAB4 D27C7026 C1D4DCB2 602646DE C9751E76 3DBA37BD F8FF9406
AD9E530E E5DB382F 413001AE B06A53ED 9027D831 179727B0 865A8918
DA3EDBEB CF9B14ED 44CE6CBA CED4BB1B DB7F1447 E6CC254B 33205151
2BD7AF42 6FB8F401 378CD2BF 5983CA01 C64B92EC F032EA15 D1721D03
F482D7CE 6E74FEF6 D55E702F 46980C82 B5A84031 900B1C9E 59E7C97F
BEC7E8F3 23A97A7E 36CC88BE 0F1D45B7 FF585AC5 4BD407B2 2B4154AA
CC8F6D7E BF48E1D8 14CC5ED2 0F8037E0 A79715EE F29BE328 06A1D58B
B7C5DA76 F550AA3D 8A1FBFF0 EB19CCB1 A313D55C DA56C9EC 2EF29632
387FE8D7 6E3C0468 043E8F66 3F4860EE 12BF2D5B 0B7474D6 E694F91E
6DBE1159 74A3926F 12FEE5E4 38777CB6 A932DF8C D8BEC4D0 73B931BA
3BC832B6 8D9DD300 741FA7BF 8AFC47ED 2576F693 6BA42466 3AAB639C
Taylor, et al. Expires December 28, 2006 [Page 21]
Internet-Draft Using SRP for TLS Authentication June 2006
5AE4F568 3423B474 2BF1C978 238F16CB E39D652D E3FDB8BE FC848AD9
22222E04 A4037C07 13EB57A8 1A23F0C7 3473FC64 6CEA306B 4BCBC886
2F8385DD FA9D4B7F A2C087E8 79683303 ED5BDD3A 062B3CF5 B3A278A6
6D2A13F8 3F44F82D DF310EE0 74AB6A36 4597E899 A0255DC1 64F31CC5
0846851D F9AB4819 5DED7EA1 B1D510BD 7EE74D73 FAF36BC3 1ECFA268
359046F4 EB879F92 4009438B 481C6CD7 889A002E D5EE382B C9190DA6
FC026E47 9558E447 5677E9AA 9E3050E2 765694DF C81F56E8 80B96E71
60C980DD 98EDD3DF FFFFFFFF FFFFFFFF
The generator is: 19 (decimal).
Taylor, et al. Expires December 28, 2006 [Page 22]
Internet-Draft Using SRP for TLS Authentication June 2006
Appendix B. SRP Test Vectors
The following test vectors demonstrate calculation of the verifier
and premaster secret.
I = "alice"
P = "password123"
s = BEB25379 D1A8581E B5A72767 3A2441EE
N, g = <1024-bit parameters from Appendix A>
k = 7556AA04 5AEF2CDD 07ABAF0F 665C3E81 8913186F
x = 94B7555A ABE9127C C58CCF49 93DB6CF8 4D16C124
v =
7E273DE8 696FFC4F 4E337D05 B4B375BE B0DDE156 9E8FA00A 9886D812
9BADA1F1 822223CA 1A605B53 0E379BA4 729FDC59 F105B478 7E5186F5
C671085A 1447B52A 48CF1970 B4FB6F84 00BBF4CE BFBB1681 52E08AB5
EA53D15C 1AFF87B2 B9DA6E04 E058AD51 CC72BFC9 033B564E 26480D78
E955A5E2 9E7AB245 DB2BE315 E2099AFB
a =
60975527 035CF2AD 1989806F 0407210B C81EDC04 E2762A56 AFD529DD
DA2D4393
b =
E487CB59 D31AC550 471E81F0 0F6928E0 1DDA08E9 74A004F4 9E61F5D1
05284D20
A =
61D5E490 F6F1B795 47B0704C 436F523D D0E560F0 C64115BB 72557EC4
4352E890 3211C046 92272D8B 2D1A5358 A2CF1B6E 0BFCF99F 921530EC
8E393561 79EAE45E 42BA92AE ACED8251 71E1E8B9 AF6D9C03 E1327F44
BE087EF0 6530E69F 66615261 EEF54073 CA11CF58 58F0EDFD FE15EFEA
B349EF5D 76988A36 72FAC47B 0769447B
B =
BD0C6151 2C692C0C B6D041FA 01BB152D 4916A1E7 7AF46AE1 05393011
BAF38964 DC46A067 0DD125B9 5A981652 236F99D9 B681CBF8 7837EC99
6C6DA044 53728610 D0C6DDB5 8B318885 D7D82C7F 8DEB75CE 7BD4FBAA
Taylor, et al. Expires December 28, 2006 [Page 23]
Internet-Draft Using SRP for TLS Authentication June 2006
37089E6F 9C6059F3 88838E7A 00030B33 1EB76840 910440B1 B27AAEAE
EB4012B7 D7665238 A8E3FB00 4B117B58
u =
CE38B959 3487DA98 554ED47D 70A7AE5F 462EF019
<premaster secret> =
B0DC82BA BCF30674 AE450C02 87745E79 90A3381F 63B387AA F271A10D
233861E3 59B48220 F7C4693C 9AE12B0A 6F67809F 0876E2D0 13800D6C
41BB59B6 D5979B5C 00A172B4 A2A5903A 0BDCAF8A 709585EB 2AFAFA8F
3499B200 210DCC1F 10EB3394 3CD67FC8 8A2F39A4 BE5BEC4E C0A3212D
C346D7E4 74B29EDE 8A469FFE CA686E5A
Taylor, et al. Expires December 28, 2006 [Page 24]
Internet-Draft Using SRP for TLS Authentication June 2006
Appendix C. Acknowledgements
Thanks to all on the IETF TLS mailing list for ideas and analysis.
Taylor, et al. Expires December 28, 2006 [Page 25]
Internet-Draft Using SRP for TLS Authentication June 2006
Authors' Addresses
David Taylor
Independent
Email: dtaylor@gnutls.org
Tom Wu
Stanford University
Email: tjw@cs.stanford.edu
Nikos Mavrogiannopoulos
Independent
Email: nmav@gnutls.org
URI: http://www.gnutls.org/
Trevor Perrin
Independent
Email: trevp@trevp.net
URI: http://trevp.net/
Taylor, et al. Expires December 28, 2006 [Page 26]
Internet-Draft Using SRP for TLS Authentication June 2006
Intellectual Property Statement
The IETF takes no position regarding the validity or scope of any
Intellectual Property Rights or other rights that might be claimed to
pertain to the implementation or use of the technology described in
this document or the extent to which any license under such rights
might or might not be available; nor does it represent that it has
made any independent effort to identify any such rights. Information
on the procedures with respect to rights in RFC documents can be
found in BCP 78 and BCP 79.
Copies of IPR disclosures made to the IETF Secretariat and any
assurances of licenses to be made available, or the result of an
attempt made to obtain a general license or permission for the use of
such proprietary rights by implementers or users of this
specification can be obtained from the IETF on-line IPR repository at
http://www.ietf.org/ipr.
The IETF invites any interested party to bring to its attention any
copyrights, patents or patent applications, or other proprietary
rights that may cover technology that may be required to implement
this standard. Please address the information to the IETF at
ietf-ipr@ietf.org.
Disclaimer of Validity
This document and the information contained herein are provided on an
"AS IS" basis and THE CONTRIBUTOR, THE ORGANIZATION HE/SHE REPRESENTS
OR IS SPONSORED BY (IF ANY), THE INTERNET SOCIETY AND THE INTERNET
ENGINEERING TASK FORCE DISCLAIM 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.
Copyright Statement
Copyright (C) The Internet Society (2006). This document is subject
to the rights, licenses and restrictions contained in BCP 78, and
except as set forth therein, the authors retain all their rights.
Acknowledgment
Funding for the RFC Editor function is currently provided by the
Internet Society.
Taylor, et al. Expires December 28, 2006 [Page 27]
| PAFTECH AB 2003-2026 | 2026-04-21 18:26:31 |