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+
+TLS Working Group D. Taylor
+Internet-Draft Forge Research Pty Ltd
+Expires: December 6, 2004 T. Wu
+ Arcot Systems
+ N. Mavroyanopoulos
+ T. Perrin
+ June 7, 2004
+
+
+ Using SRP for TLS Authentication
+ draft-ietf-tls-srp-07
+
+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
+ 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 6, 2004.
+
+Copyright Notice
+
+ Copyright (C) The Internet Society (2004). All Rights Reserved.
+
+Abstract
+
+ This memo presents a technique for using the Secure Remote Password
+ protocol ([SRP], [SRP-6]) as an authentication method for the
+ Transport Layer Security protocol [TLS].
+
+
+
+
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+Taylor, et al. Expires December 6, 2004 [Page 1]
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+Internet-Draft Using SRP for TLS Authentication June 2004
+
+
+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 . . . . . . . . . . . . . . . . . 8
+ 2.8 New Message Structures . . . . . . . . . . . . . . . . . . 9
+ 2.8.1 Client Hello . . . . . . . . . . . . . . . . . . . . . 9
+ 2.8.2 Server Key Exchange . . . . . . . . . . . . . . . . . 9
+ 2.8.3 Client Key Exchange . . . . . . . . . . . . . . . . . 10
+ 2.9 Error Alerts . . . . . . . . . . . . . . . . . . . . . . . 11
+ 3. Security Considerations . . . . . . . . . . . . . . . . . . . 12
+ 4. References . . . . . . . . . . . . . . . . . . . . . . . . . . 13
+ 4.1 Normative References . . . . . . . . . . . . . . . . . . . . 13
+ 4.2 Informative References . . . . . . . . . . . . . . . . . . . 13
+ Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . 14
+ A. SRP Group Parameters . . . . . . . . . . . . . . . . . . . . . 15
+ B. Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . 19
+ Intellectual Property and Copyright Statements . . . . . . . . 20
+
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+Internet-Draft Using SRP for TLS Authentication June 2004
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+
+1. Introduction
+
+ At the time of writing TLS [TLS] uses public key certificates, or
+ Kerberos, for authentication.
+
+ These authentication methods do not seem well suited to the
+ applications now being adapted to use TLS ([IMAP] or [FTP], for
+ example). Given that these 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.
+
+
+
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+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 [RFC2945].
+
+ 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
+
+ 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 [RFC2945].
+
+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.
+
+ 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.
+
+
+
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+ 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 [RFC2945].
+ 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).
+
+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.
+
+
+
+
+
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+
+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.
+
+ 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.
+
+
+
+
+
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+
+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 | 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. The SRP group parameters in
+ Appendix A are proven to have these properties, so the client SHOULD
+ accept any parameters from this Appendix which have large enough N
+ values to meet his security requirements. The client MAY accept
+ other group parameters from the server, either by prior arrangement,
+ or by checking the parameters himself.
+
+ To check that N is a safe prime, the client should use some method
+ such as performing 64 iterations of the Miller-Rabin test with random
+ bases (selected from 2 to N-2) on both N and q (by performing 64
+ iterations, the probability of a false positive is no more than
+ 2^-128). To check that g is a generator of the group, the client can
+ check that 1 < g < N-1, and g^q % N equals N-1. Performing these
+ checks may be time-consuming; after checking new parameters, the
+ client may want to add them to a known-good list.
+
+ 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.
+
+
+
+
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+
+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(A | B)
+ k = SHA1(N | 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 | g)
+ B = k*v + g^b % N
+ A = <read from client>
+ u = SHA1(A | 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 [RFC2945]. 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.
+
+ 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 [RFC3268].
+
+
+
+
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+
+ CipherSuite TLS_SRP_SHA_WITH_3DES_EDE_CBC_SHA = { 0x00,0x50 };
+ CipherSuite TLS_SRP_SHA_RSA_WITH_3DES_EDE_CBC_SHA = { 0x00,0x51 };
+ CipherSuite TLS_SRP_SHA_DSS_WITH_3DES_EDE_CBC_SHA = { 0x00,0x52 };
+ CipherSuite TLS_SRP_SHA_WITH_AES_128_CBC_SHA = { 0x00,0x53 };
+ CipherSuite TLS_SRP_SHA_RSA_WITH_AES_128_CBC_SHA = { 0x00,0x54 };
+ CipherSuite TLS_SRP_SHA_DSS_WITH_AES_128_CBC_SHA = { 0x00,0x55 };
+ CipherSuite TLS_SRP_SHA_WITH_AES_256_CBC_SHA = { 0x00,0x56 };
+ CipherSuite TLS_SRP_SHA_RSA_WITH_AES_256_CBC_SHA = { 0x00,0x57 };
+ CipherSuite TLS_SRP_SHA_DSS_WITH_AES_256_CBC_SHA = { 0x00,0x58 };
+
+ 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.
+
+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 value, "srp(6)", 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
+
+
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+
+ 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.
+
+ 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;
+
+
+
+
+
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+
+2.9 Error Alerts
+
+ Three new error alerts are defined:
+
+ o "unknown_srp_username" (120) - 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.
+ o "missing_srp_username" (121) - 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" (122) - 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.
+
+
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+
+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.
+
+ 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
+ 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.
+
+
+
+
+
+
+
+
+
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+4. References
+
+4.1 Normative References
+
+ [TLS] Dierks, T. and C. Allen, "The TLS Protocol", RFC 2246,
+ January 1999.
+
+ [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", draft-ietf-sasl-saslprep-09 (work in
+ progress), April 2004.
+
+ [RFC2945] 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.
+
+ [RFC3268] 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.
+
+4.2 Informative References
+
+ [IMAP] Newman, C., "Using TLS with IMAP, POP3 and ACAP", RFC 2595,
+ June 1999.
+
+ [FTP] Ford-Hutchinson, P., Carpenter, M., Hudson, T., Murray, E.
+
+
+
+Taylor, et al. Expires December 6, 2004 [Page 13]
+
+Internet-Draft Using SRP for TLS Authentication June 2004
+
+
+ and V. Wiegand, "Securing FTP with TLS",
+ draft-murray-auth-ftp-ssl-13 (work in progress), March 2004.
+
+ [SRP] Wu, T., "The Secure Remote Password Protocol", Proceedings of
+ the 1998 Internet Society Network and Distributed System
+ Security Symposium pp. 97-111, March 1998.
+
+
+Authors' Addresses
+
+ David Taylor
+ Forge Research Pty Ltd
+
+ EMail: DavidTaylor@forge.com.au
+ URI: http://www.forge.com.au/
+
+
+ Tom Wu
+ Arcot Systems
+
+ EMail: tom@arcot.com
+ URI: http://www.arcot.com/
+
+
+ Nikos Mavroyanopoulos
+
+ EMail: nmav@gnutls.org
+ URI: http://www.gnutls.org/
+
+
+ Trevor Perrin
+
+ EMail: trevp@trevp.net
+ URI: http://trevp.net/
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+Taylor, et al. Expires December 6, 2004 [Page 14]
+
+Internet-Draft Using SRP for TLS Authentication June 2004
+
+
+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 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 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 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
+ 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 }
+
+
+
+Taylor, et al. Expires December 6, 2004 [Page 15]
+
+
+ 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
+ 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
+
+
+
+Taylor, et al. Expires December 6, 2004 [Page 16]
+
+Internet-Draft Using SRP for TLS Authentication June 2004
+
+
+ 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
+ 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
+
+
+
+Taylor, et al. Expires December 6, 2004 [Page 17]
+
+Internet-Draft Using SRP for TLS Authentication June 2004
+
+
+ 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
+ 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 6, 2004 [Page 18]
+
+Internet-Draft Using SRP for TLS Authentication June 2004
+
+
+Appendix B. Acknowledgements
+
+ Thanks to all on the IETF tls mailing list for ideas and analysis.
+
+
+
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+
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+Taylor, et al. Expires December 6, 2004 [Page 19]
+
+Internet-Draft Using SRP for TLS Authentication June 2004
+
+
+Intellectual Property Statement
+
+ The IETF takes no position regarding the validity or scope of any
+ intellectual property 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; neither does it represent that it
+ has made any effort to identify any such rights. Information on the
+ IETF's procedures with respect to rights in standards-track and
+ standards-related documentation can be found in BCP-11. Copies of
+ claims of rights made available for publication 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 implementors or users of this specification can
+ be obtained from the IETF Secretariat.
+
+ The IETF invites any interested party to bring to its attention any
+ copyrights, patents or patent applications, or other proprietary
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+ this standard. Please address the information to the IETF Executive
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+
+
+Full Copyright Statement
+
+ Copyright (C) The Internet Society (2004). All Rights Reserved.
+
+ This document and translations of it may be copied and furnished to
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+ BUT NOT LIMITED TO ANY WARRANTY THAT THE USE OF THE INFORMATION
+
+
+
+Taylor, et al. Expires December 6, 2004 [Page 20]
+
+Internet-Draft Using SRP for TLS Authentication June 2004
+
+
+ HEREIN WILL NOT INFRINGE ANY RIGHTS OR ANY IMPLIED WARRANTIES OF
+ MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE.
+
+
+Acknowledgment
+
+ Funding for the RFC Editor function is currently provided by the
+ Internet Society.
+
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+Taylor, et al. Expires December 6, 2004 [Page 21]
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+
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