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-
-TLS Working Group D. Taylor
-Internet-Draft Independent
-Expires: December 15, 2007 T. Wu
- Stanford University
- N. Mavrogiannopoulos
- T. Perrin
- Independent
- June 13, 2007
-
-
- Using SRP for TLS Authentication
- draft-ietf-tls-srp-14
-
-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 15, 2007.
-
-Copyright Notice
-
- Copyright (C) The IETF Trust (2007).
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-Abstract
-
- This memo presents a technique for using the Secure Remote Password
- protocol as an authentication method for the Transport Layer Security
- protocol.
-
-
-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 . . . . . . . . . . . . . . . . . 10
- 2.8.3. Client Key Exchange . . . . . . . . . . . . . . . . . 10
- 2.9. Error Alerts . . . . . . . . . . . . . . . . . . . . . . . 11
- 3. Security Considerations . . . . . . . . . . . . . . . . . . . 12
- 3.1. General Considerations for Implementors . . . . . . . . . 12
- 3.2. Accepting Group Parameters . . . . . . . . . . . . . . . . 12
- 3.3. Protocol Characteristics . . . . . . . . . . . . . . . . . 12
- 3.4. Hash Function Considerations . . . . . . . . . . . . . . . 13
- 4. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 14
- 5. References . . . . . . . . . . . . . . . . . . . . . . . . . . 15
- 5.1. Normative References . . . . . . . . . . . . . . . . . . . 15
- 5.2. Informative References . . . . . . . . . . . . . . . . . . 15
- Appendix A. SRP Group Parameters . . . . . . . . . . . . . . . . 17
- Appendix B. SRP Test Vectors . . . . . . . . . . . . . . . . . . 22
- Appendix C. Acknowledgements . . . . . . . . . . . . . . . . . . 24
- Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . . 25
- Intellectual Property and Copyright Statements . . . . . . . . . . 26
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-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 [REQ].
-
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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 [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.
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- 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 extension mechanism defined in [TLSEXT] (see Section 2.8.1).
- This user name extension is henceforth called the "SRP extension".
-
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- The following subsections give details of its use.
-
-2.5.1.1. Session Resumption
-
- When a client attempts to resume a session that uses SRP
- authentication, the client MUST include the SRP 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 Extension
-
- 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 SHOULD return a fatal
- "unknown_psk_identity" alert (see Section 2.9) immediately after
- processing the client hello message.
-
- A client receiving this alert MAY choose to reconnect and 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.
-
-2.5.1.3. Unknown SRP Username
-
- If the server doesn't have a verifier for the user name in the SRP
- extension, the server MAY abort the handshake with an
- "unknown_psk_identity" 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 | 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
- 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 "insufficient_security" 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(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.
-
- 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].
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- CipherSuite TLS_SRP_SHA_WITH_3DES_EDE_CBC_SHA = { 0xC0,0xTBD2 };
-
- CipherSuite TLS_SRP_SHA_RSA_WITH_3DES_EDE_CBC_SHA = { 0xC0,0xTBD3
- };
-
- CipherSuite TLS_SRP_SHA_DSS_WITH_3DES_EDE_CBC_SHA = { 0xC0,0xTBD4
- };
-
- CipherSuite TLS_SRP_SHA_WITH_AES_128_CBC_SHA = { 0xC0,0xTBD5 };
-
- CipherSuite TLS_SRP_SHA_RSA_WITH_AES_128_CBC_SHA = { 0xC0,0xTBD6
- };
-
- CipherSuite TLS_SRP_SHA_DSS_WITH_AES_128_CBC_SHA = { 0xC0,0xTBD7
- };
-
- CipherSuite TLS_SRP_SHA_WITH_AES_256_CBC_SHA = { 0xC0,0xTBD8 };
-
- CipherSuite TLS_SRP_SHA_RSA_WITH_AES_256_CBC_SHA = { 0xC0,0xTBD9
- };
-
- CipherSuite TLS_SRP_SHA_DSS_WITH_AES_256_CBC_SHA = { 0xC0,0xTBD10
- };
-
- 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 extension "srp" with value TBD1, has been added to the
- enumerated ExtensionType defined in [TLSEXT]. This value MUST be
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- 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 2.3.
-
-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.
-
- 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.
-
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- 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
-
- This document introduces four new uses of alerts:
-
- o "unknown_psk_identity" (115) - 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 fatal. See Section 2.5.1.2 for details.
-
- o "unknown_psk_identity" (115) - 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 "insufficient_security" (71) - 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.
-
- o "illegal_parameter" (47) - this alert MUST be sent by a client or
- server that receives a key exchange message with A % N = 0 or B %
- N = 0. This alert is always fatal. See Section 2.5.3 and
- Section 2.5.4 and for details.
-
- The "insufficient_security" and "illegal_parameter" alerts are
- defined in [TLS]. The "unknown_psk_identity" alert is defined in
- [PSK].
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-3. Security Considerations
-
-3.1. General Considerations for Implementors
-
- 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. See [TLS] section D.1 for advice on
- choosing cryptographically secure random numbers.
-
-3.2. Accepting Group Parameters
-
- An attacker who could calculate discrete logarithms % 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 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.
-
-3.3. Protocol Characteristics
-
- If an attacker learns a user's SRP verifier (e.g., by gaining access
- to a server's password file), the attacker can masquerade as the real
- server to that user, and can also attempt a dictionary attack to
- recover that user's password.
-
- 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 name.
-
- 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.
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- If the client receives an "unknown_psk_identity" alert in response to
- a client hello, this alert may have been inserted by an attacker.
- The client should be careful about making any decisions, or forming
- any conclusions, 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.
-
-3.4. Hash Function Considerations
-
- This protocol uses SHA-1 to derive several values:
-
- o u prevents an attacker who learns a user's verifier from being
- able to authenticate as that user (see [SRP-6]).
-
- o k prevents an attacker who can select group parameters from being
- able to launch a 2-for-1 guessing attack (see [SRP-6]).
-
- o x contains the user's password mixed with a salt.
-
- Cryptanalytic attacks against SHA-1 which only affect its collision-
- resistance do not compromise these uses. If attacks against SHA-1
- are discovered which do compromise these uses, new ciphersuites
- should be specified to use a different hash algorithm.
-
- In this situation, clients could send a Client Hello message
- containing new and/or old SRP ciphersuites along with a single SRP
- extension. The server could then select the appropriate ciphersuite
- based on the type of verifier it has stored for this user.
-
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-4. IANA Considerations
-
- This document defines a new TLS extension "srp" (value TBD1), whose
- value is to be assigned from the TLS ExtensionType Registry defined
- in [TLSEXT].
-
- This document defines nine new ciphersuites, whose values are to be
- assigned from the TLS Cipher Suite registry defined in [TLS].
-
- CipherSuite TLS_SRP_SHA_WITH_3DES_EDE_CBC_SHA = { 0xC0,0xTBD2 };
-
- CipherSuite TLS_SRP_SHA_RSA_WITH_3DES_EDE_CBC_SHA = { 0xC0,0xTBD3
- };
-
- CipherSuite TLS_SRP_SHA_DSS_WITH_3DES_EDE_CBC_SHA = { 0xC0,0xTBD4
- };
-
- CipherSuite TLS_SRP_SHA_WITH_AES_128_CBC_SHA = { 0xC0,0xTBD5 };
-
- CipherSuite TLS_SRP_SHA_RSA_WITH_AES_128_CBC_SHA = { 0xC0,0xTBD6
- };
-
- CipherSuite TLS_SRP_SHA_DSS_WITH_AES_128_CBC_SHA = { 0xC0,0xTBD7
- };
-
- CipherSuite TLS_SRP_SHA_WITH_AES_256_CBC_SHA = { 0xC0,0xTBD8 };
-
- CipherSuite TLS_SRP_SHA_RSA_WITH_AES_256_CBC_SHA = { 0xC0,0xTBD9
- };
-
- CipherSuite TLS_SRP_SHA_DSS_WITH_AES_256_CBC_SHA = { 0xC0,0xTBD10
- };
-
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-5. References
-
-5.1. Normative References
-
- [REQ] Bradner, S., "Key words for use in RFCs to Indicate
- Requirement Levels", BCP 14, RFC 2119, March 1997.
-
- [TLS] Dierks, T. and E. Rescorla, "The TLS Protocol version
- 1.1", RFC 4346, April 2006.
-
- [TLSEXT] Blake-Wilson, S., Nystrom, M., Hopwood, D., Mikkelsen, J.,
- and T. Wright, "Transport Layer Security (TLS)
- Extensions", RFC 4366, April 2006.
-
- [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] "Secure Hash Standard (SHS)", FIPS 180-2, August 2002.
-
- [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.
-
- [PSK] Eronen, P. and H. Tschofenig, "Pre-Shared Key Ciphersuites
- for Transport Layer Security (TLS)", RFC 4279,
- December 2005.
-
- [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.
-
-
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- [SRP-6] Wu, T., "SRP-6: Improvements and Refinements to the Secure
- Remote Password Protocol", Submission to IEEE P1363.2
- working group, October 2002,
- <http://grouper.ieee.org/groups/1363/>.
-
- [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.
-
- [TRAPDOOR]
- Gordon, D., "Designing and Detecting Trapdoors for
- Discrete Log Cryptosystems", Springer-Verlag Advances in
- Cryptology - Crypto '92, pp. 66-75, 1993.
-
-
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-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
-
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- 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
-
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- 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
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- 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
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- 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).
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
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-
-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
-
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- 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
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-Taylor, et al. Expires December 15, 2007 [Page 23]
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-Internet-Draft Using SRP for TLS Authentication June 2007
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-Appendix C. Acknowledgements
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- Thanks to all on the IETF TLS mailing list for ideas and analysis.
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-Taylor, et al. Expires December 15, 2007 [Page 24]
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-Internet-Draft Using SRP for TLS Authentication June 2007
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-Authors' Addresses
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- David Taylor
- Independent
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- Email: dtaylor@gnutls.org
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- Tom Wu
- Stanford University
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- Email: tjw@cs.stanford.edu
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- Nikos Mavrogiannopoulos
- Independent
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- Email: nmav@gnutls.org
- URI: http://www.gnutls.org/
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- Trevor Perrin
- Independent
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- Email: trevp@trevp.net
- URI: http://trevp.net/
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-Taylor, et al. Expires December 15, 2007 [Page 25]
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-Internet-Draft Using SRP for TLS Authentication June 2007
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-Full Copyright Statement
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- Copyright (C) The IETF Trust (2007).
-
- 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.
-
- This document and the information contained herein are provided on an
- "AS IS" basis and THE CONTRIBUTOR, THE ORGANIZATION HE/SHE REPRESENTS
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-Intellectual Property
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- The IETF takes no position regarding the validity or scope of any
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-Taylor, et al. Expires December 15, 2007 [Page 26]
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