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+Network Working Group D. Taylor
+Request for Comments: 5054 Independent
+Category: Informational T. Wu
+ Cisco
+ N. Mavrogiannopoulos
+ T. Perrin
+ Independent
+ November 2007
+
+
+ Using the Secure Remote Password (SRP) Protocol for TLS Authentication
+
+Status of This Memo
+
+ This memo provides information for the Internet community. It does
+ not specify an Internet standard of any kind. Distribution of this
+ memo is unlimited.
+
+Abstract
+
+ This memo presents a technique for using the Secure Remote Password
+ protocol as an authentication method for the Transport Layer Security
+ protocol.
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+Taylor, et al. Informational [Page 1]
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+RFC 5054 Using SRP for TLS Authentication November 2007
+
+
+Table of Contents
+
+ 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 3
+ 2. SRP Authentication in TLS . . . . . . . . . . . . . . . . . . 3
+ 2.1. Notation and Terminology . . . . . . . . . . . . . . . . . 3
+ 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 . . . . . . . . . . . . . . . . . . . . . 6
+ 2.5.2. Server Certificate . . . . . . . . . . . . . . . . . . 7
+ 2.5.3. Server Key Exchange . . . . . . . . . . . . . . . . . 7
+ 2.5.4. Client Key Exchange . . . . . . . . . . . . . . . . . 8
+ 2.6. Calculating the Premaster Secret . . . . . . . . . . . . . 8
+ 2.7. Ciphersuite Definitions . . . . . . . . . . . . . . . . . 9
+ 2.8. New Message Structures . . . . . . . . . . . . . . . . . . 9
+ 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 . . . . . . . . . . . . . . . . . . . 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 . . . . . . . . . . . . . . . . . . . . . 13
+ 5. References . . . . . . . . . . . . . . . . . . . . . . . . . . 14
+ 5.1. Normative References . . . . . . . . . . . . . . . . . . . 14
+ 5.2. Informative References . . . . . . . . . . . . . . . . . . 15
+ Appendix A. SRP Group Parameters . . . . . . . . . . . . . . . . 16
+ Appendix B. SRP Test Vectors . . . . . . . . . . . . . . . . . . 21
+ Appendix C. Acknowledgements . . . . . . . . . . . . . . . . . . 22
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+Taylor, et al. Informational [Page 2]
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+RFC 5054 Using SRP for TLS Authentication November 2007
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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].
+
+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]. For convenience, this document
+ and [SRP-RFC] include the details necessary to implement SRP-6;
+ [SRP-6] is cited for informative purposes only.
+
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+ 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 that 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.
+
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+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".
+ 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 that attackers cannot replace the authenticated
+ identity without supplying the proper authentication information.
+
+2.5.1.2. Missing SRP Extension
+
+ The client may offer SRP cipher suites in the hello message but omit
+ the SRP extension. If the server would like to select an SRP cipher
+ suite 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 User Name
+
+ 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
+
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+Taylor, et al. Informational [Page 6]
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+ 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 cipher suites 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 that 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 that 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 that 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.
+
+
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+ 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.
+
+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 that 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 Premaster Secret
+
+ The premaster 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 premaster 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 calculates 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.
+
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+2.7. Ciphersuite Definitions
+
+ The following cipher suites are added by this document. The usage of
+ Advanced Encryption Standard (AES) cipher suites is as defined in
+ [AESCIPH].
+
+ CipherSuite TLS_SRP_SHA_WITH_3DES_EDE_CBC_SHA = { 0xC0,0x1A };
+
+ CipherSuite TLS_SRP_SHA_RSA_WITH_3DES_EDE_CBC_SHA = { 0xC0,0x1B };
+
+ CipherSuite TLS_SRP_SHA_DSS_WITH_3DES_EDE_CBC_SHA = { 0xC0,0x1C };
+
+ CipherSuite TLS_SRP_SHA_WITH_AES_128_CBC_SHA = { 0xC0,0x1D };
+
+ CipherSuite TLS_SRP_SHA_RSA_WITH_AES_128_CBC_SHA = { 0xC0,0x1E };
+
+ CipherSuite TLS_SRP_SHA_DSS_WITH_AES_128_CBC_SHA = { 0xC0,0x1F };
+
+ CipherSuite TLS_SRP_SHA_WITH_AES_256_CBC_SHA = { 0xC0,0x20 };
+
+ CipherSuite TLS_SRP_SHA_RSA_WITH_AES_256_CBC_SHA = { 0xC0,0x21 };
+
+ CipherSuite TLS_SRP_SHA_DSS_WITH_AES_256_CBC_SHA = { 0xC0,0x22 };
+
+ 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 that the server is authenticated by its possession
+ of the SRP verifier.
+
+ Implementations conforming to this specification MUST implement the
+ TLS_SRP_SHA_WITH_3DES_EDE_CBC_SHA cipher suite, SHOULD implement the
+ TLS_SRP_SHA_WITH_AES_128_CBC_SHA and TLS_SRP_SHA_WITH_AES_256_CBC_SHA
+ cipher suites, and MAY implement the remaining cipher suites.
+
+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].
+
+
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+2.8.1. Client Hello
+
+ A new extension "srp", with value 12, 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 2.3.
+
+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 */
+
+
+
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+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
+
+ 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 cipher suite, 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
+ 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 that is large enough to
+ be secure, but that 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 that only affect its collision-
+ resistance do not compromise these uses. If attacks against SHA-1
+ are discovered that do compromise these uses, new cipher suites
+ 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 cipher suites along with a single SRP
+ extension. The server could then select the appropriate cipher suite
+ based on the type of verifier it has stored for this user.
+
+4. IANA Considerations
+
+ This document defines a new TLS extension "srp" (value 12), whose
+ value has been assigned from the TLS ExtensionType Registry defined
+ in [TLSEXT].
+
+ This document defines nine new cipher suites, whose values have been
+ assigned from the TLS Ciphersuite registry defined in [TLS].
+
+ CipherSuite TLS_SRP_SHA_WITH_3DES_EDE_CBC_SHA = { 0xC0,0x1A };
+
+ CipherSuite TLS_SRP_SHA_RSA_WITH_3DES_EDE_CBC_SHA = { 0xC0,0x1B };
+
+ CipherSuite TLS_SRP_SHA_DSS_WITH_3DES_EDE_CBC_SHA = { 0xC0,0x1C };
+
+
+
+
+Taylor, et al. Informational [Page 13]
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+
+
+ CipherSuite TLS_SRP_SHA_WITH_AES_128_CBC_SHA = { 0xC0,0x1D };
+
+ CipherSuite TLS_SRP_SHA_RSA_WITH_AES_128_CBC_SHA = { 0xC0,0x1E };
+
+ CipherSuite TLS_SRP_SHA_DSS_WITH_AES_128_CBC_SHA = { 0xC0,0x1F };
+
+ CipherSuite TLS_SRP_SHA_WITH_AES_256_CBC_SHA = { 0xC0,0x20 };
+
+ CipherSuite TLS_SRP_SHA_RSA_WITH_AES_256_CBC_SHA = { 0xC0,0x21 };
+
+ CipherSuite TLS_SRP_SHA_DSS_WITH_AES_256_CBC_SHA = { 0xC0,0x22 };
+
+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.
+
+
+
+
+
+
+Taylor, et al. Informational [Page 14]
+
+RFC 5054 Using SRP for TLS Authentication November 2007
+
+
+ [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.
+
+ [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.
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+Taylor, et al. Informational [Page 15]
+
+RFC 5054 Using SRP for TLS Authentication November 2007
+
+
+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.
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+Taylor, et al. Informational [Page 16]
+
+RFC 5054 Using SRP for TLS Authentication November 2007
+
+
+ 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
+ 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.
+
+
+
+
+
+
+
+
+
+
+
+Taylor, et al. Informational [Page 17]
+
+RFC 5054 Using SRP for TLS Authentication November 2007
+
+
+ 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.
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+Taylor, et al. Informational [Page 18]
+
+RFC 5054 Using SRP for TLS Authentication November 2007
+
+
+ 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
+ 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.
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+Taylor, et al. Informational [Page 19]
+
+RFC 5054 Using SRP for TLS Authentication November 2007
+
+
+ 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
+ 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. Informational [Page 20]
+
+RFC 5054 Using SRP for TLS Authentication November 2007
+
+
+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
+
+
+
+
+
+
+
+
+
+Taylor, et al. Informational [Page 21]
+
+RFC 5054 Using SRP for TLS Authentication November 2007
+
+
+ B =
+
+ BD0C6151 2C692C0C B6D041FA 01BB152D 4916A1E7 7AF46AE1 05393011
+ BAF38964 DC46A067 0DD125B9 5A981652 236F99D9 B681CBF8 7837EC99
+ 6C6DA044 53728610 D0C6DDB5 8B318885 D7D82C7F 8DEB75CE 7BD4FBAA
+ 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
+
+Appendix C. Acknowledgements
+
+ Thanks to all on the IETF TLS mailing list for ideas and analysis.
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+Taylor, et al. Informational [Page 22]
+
+RFC 5054 Using SRP for TLS Authentication November 2007
+
+
+Authors' Addresses
+
+ David Taylor
+ Independent
+
+ EMail: dtaylor@gnutls.org
+
+
+ Tom Wu
+ Cisco
+
+ EMail: thomwu@cisco.com
+
+
+ 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. Informational [Page 23]
+
+RFC 5054 Using SRP for TLS Authentication November 2007
+
+
+Full Copyright Statement
+
+ Copyright (C) The IETF Trust (2007).
+
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+Taylor, et al. Informational [Page 24]
+