4 TLS Working Group D. Taylor
5 Internet-Draft Independent
6 Expires: December 28, 2006 T. Wu
14 Using SRP for TLS Authentication
19 By submitting this Internet-Draft, each author represents that any
20 applicable patent or other IPR claims of which he or she is aware
21 have been or will be disclosed, and any of which he or she becomes
22 aware will be disclosed, in accordance with Section 6 of BCP 79.
24 Internet-Drafts are working documents of the Internet Engineering
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29 Internet-Drafts are draft documents valid for a maximum of six months
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32 material or to cite them other than as "work in progress."
34 The list of current Internet-Drafts can be accessed at
35 http://www.ietf.org/ietf/1id-abstracts.txt.
37 The list of Internet-Draft Shadow Directories can be accessed at
38 http://www.ietf.org/shadow.html.
40 This Internet-Draft will expire on December 28, 2006.
44 Copyright (C) The Internet Society (2006).
48 This memo presents a technique for using the Secure Remote Password
49 protocol as an authentication method for the Transport Layer Security
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62 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 3
63 2. SRP Authentication in TLS . . . . . . . . . . . . . . . . . . 4
64 2.1. Notation and Terminology . . . . . . . . . . . . . . . . . 4
65 2.2. Handshake Protocol Overview . . . . . . . . . . . . . . . 4
66 2.3. Text Preparation . . . . . . . . . . . . . . . . . . . . . 5
67 2.4. SRP Verifier Creation . . . . . . . . . . . . . . . . . . 5
68 2.5. Changes to the Handshake Message Contents . . . . . . . . 5
69 2.5.1. Client Hello . . . . . . . . . . . . . . . . . . . . . 5
70 2.5.2. Server Certificate . . . . . . . . . . . . . . . . . . 7
71 2.5.3. Server Key Exchange . . . . . . . . . . . . . . . . . 7
72 2.5.4. Client Key Exchange . . . . . . . . . . . . . . . . . 8
73 2.6. Calculating the Pre-master Secret . . . . . . . . . . . . 8
74 2.7. Cipher Suite Definitions . . . . . . . . . . . . . . . . . 9
75 2.8. New Message Structures . . . . . . . . . . . . . . . . . . 10
76 2.8.1. Client Hello . . . . . . . . . . . . . . . . . . . . . 10
77 2.8.2. Server Key Exchange . . . . . . . . . . . . . . . . . 10
78 2.8.3. Client Key Exchange . . . . . . . . . . . . . . . . . 11
79 2.9. Error Alerts . . . . . . . . . . . . . . . . . . . . . . . 11
80 3. Security Considerations . . . . . . . . . . . . . . . . . . . 13
81 4. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 15
82 5. References . . . . . . . . . . . . . . . . . . . . . . . . . . 16
83 5.1. Normative References . . . . . . . . . . . . . . . . . . . 16
84 5.2. Informative References . . . . . . . . . . . . . . . . . . 16
85 Appendix A. SRP Group Parameters . . . . . . . . . . . . . . . . 18
86 Appendix B. SRP Test Vectors . . . . . . . . . . . . . . . . . . 23
87 Appendix C. Acknowledgements . . . . . . . . . . . . . . . . . . 25
88 Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . . 26
89 Intellectual Property and Copyright Statements . . . . . . . . . . 27
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118 At the time of writing TLS [TLS] uses public key certificates, pre-
119 shared keys, or Kerberos for authentication.
121 These authentication methods do not seem well suited to certain
122 applications now being adapted to use TLS ([IMAP] for example).
123 Given that many protocols are designed to use the user name and
124 password method of authentication, being able to safely use user
125 names and passwords provides an easier route to additional security.
127 SRP ([SRP], [SRP-6]) is an authentication method that allows the use
128 of user names and passwords over unencrypted channels without
129 revealing the password to an eavesdropper. SRP also supplies a
130 shared secret at the end of the authentication sequence that can be
131 used to generate encryption keys.
133 This document describes the use of the SRP authentication method for
136 The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
137 "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this
138 document are to be interpreted as described in RFC 2119.
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172 2. SRP Authentication in TLS
174 2.1. Notation and Terminology
176 The version of SRP used here is sometimes referred to as "SRP-6"
177 [SRP-6]. This version is a slight improvement over "SRP-3", which
178 was described in [SRP] and [SRP-RFC].
180 This document uses the variable names defined in [SRP-6]:
182 N, g: group parameters (prime and generator)
186 B, b: server's public and private values
188 A, a: client's public and private values
190 I: user name (aka "identity")
198 The | symbol indicates string concatenation, the ^ operator is the
199 exponentiation operation, and the % operator is the integer remainder
202 Conversion between integers and byte-strings assumes the most-
203 significant bytes are stored first, as per [TLS] and [SRP-RFC]. In
204 the following text, if a conversion from integer to byte-string is
205 implicit, the most-significant byte in the resultant byte-string MUST
206 be non-zero. If a conversion is explicitly specified with the
207 operator PAD(), the integer will first be implicitly converted, then
208 the resultant byte-string will be left-padded with zeros (if
209 necessary) until its length equals the implicitly-converted length of
212 2.2. Handshake Protocol Overview
214 The advent of [SRP-6] allows the SRP protocol to be implemented using
215 the standard sequence of handshake messages defined in [TLS].
217 The parameters to various messages are given in the following
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230 Client Hello (I) -------->
233 Server Key Exchange (N, g, s, B)
234 <-------- Server Hello Done
235 Client Key Exchange (A) -------->
241 Application Data <-------> Application Data
243 * Indicates an optional message which is not always sent.
247 2.3. Text Preparation
249 The user name and password strings shall be UTF-8 encoded Unicode,
250 prepared using the [SASLPREP] profile of [STRINGPREP].
252 2.4. SRP Verifier Creation
254 The verifier is calculated as described in section 3 of [SRP-RFC].
255 We give the algorithm here for convenience.
257 The verifier (v) is computed based on the salt (s), user name (I),
258 password (P), and group parameters (N, g). The computation uses the
259 [SHA1] hash algorithm:
261 x = SHA1(s | SHA1(I | ":" | P))
264 2.5. Changes to the Handshake Message Contents
266 This section describes the changes to the TLS handshake message
267 contents when SRP is being used for authentication. The definitions
268 of the new message contents and the on-the-wire changes are given in
273 The user name is appended to the standard client hello message using
274 the hello message extension mechanism defined in [TLSEXT] (see
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284 2.5.1.1. Session Resumption
286 When a client attempts to resume a session that uses SRP
287 authentication, the client MUST include the user name extension in
288 the client hello message, in case the server cannot or will not allow
289 session resumption, meaning a full handshake is required.
291 If the server does agree to resume an existing session the server
292 MUST ignore the information in the SRP extension of the client hello
293 message, except for its inclusion in the finished message hashes.
294 This is to ensure attackers cannot replace the authenticated identity
295 without supplying the proper authentication information.
297 2.5.1.2. Missing SRP Username
299 The client may offer SRP ciphersuites in the hello message but omit
300 the SRP extension. If the server would like to select an SRP
301 ciphersuite in this case, the server MAY return a
302 "missing_srp_username" alert (see Section 2.9) immediately after
303 processing the client hello message. This alert signals the client
304 to resend the hello message, this time with the SRP extension. This
305 allows the client to advertise that it supports SRP, but not have to
306 prompt the user for his user name and password, nor expose the user
307 name in the clear, unless necessary.
309 After sending the "missing_srp_username" alert, the server MUST leave
310 the TLS connection open, yet reset its handshake protocol state so it
311 is prepared to receive a second client hello message. Upon receiving
312 the "missing_srp_username" alert, the client MUST either send a
313 second client hello message, or send a fatal user_cancelled alert.
315 If the client sends a second hello message, the second hello message
316 MUST offer SRP ciphersuites, and MUST contain the SRP extension, and
317 the server MUST choose one of the SRP ciphersuites. Both client
318 hello messages MUST be treated as handshake messages and included in
319 the hash calculations for the TLS Finished message. The premaster
320 and master secret calculations will use the random value from the
321 second client hello message, not the first.
323 2.5.1.3. Unknown SRP Username
325 If the server doesn't have a verifier for the given user name, the
326 server MAY abort the handshake with an "unknown_srp_username" alert
327 (see Section 2.9). Alternatively, if the server wishes to hide the
328 fact that this user name doesn't have a verifier, the server MAY
329 simulate the protocol as if a verifier existed, but then reject the
330 client's finished message with a "bad_record_mac" alert, as if the
331 password was incorrect.
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340 To simulate the existence of an entry for each user name, the server
341 must consistently return the same salt (s) and group (N, g) values
342 for the same user name. For example, the server could store a secret
343 "seed key" and then use HMAC-SHA1(seed_key, "salt" | user_name) to
344 generate the salts [HMAC]. For B, the server can return a random
345 value between 1 and N-1 inclusive. However, the server should take
346 care to simulate computation delays. One way to do this is to
347 generate a fake verifier using the "seed key" approach, and then
348 proceed with the protocol as usual.
350 2.5.2. Server Certificate
352 The server MUST send a certificate if it agrees to an SRP cipher
353 suite that requires the server to provide additional authentication
354 in the form of a digital signature. See Section 2.7 for details of
355 which ciphersuites defined in this document require a server
356 certificate to be sent.
358 2.5.3. Server Key Exchange
360 The server key exchange message contains the prime (N), the generator
361 (g), and the salt value (s) read from the SRP password file based on
362 the user name (I) received in the client hello extension.
364 The server key exchange message also contains the server's public
365 value (B). The server calculates this value as B = k*v + g^b % N,
366 where b is a random number which SHOULD be at least 256 bits in
367 length, and k = SHA1(N | PAD(g)).
369 If the server has sent a certificate message, the server key exchange
370 message MUST be signed.
372 The group parameters (N, g) sent in this message MUST have N as a
373 safe prime (a prime of the form N=2q+1, where q is also prime). The
374 integers from 1 to N-1 will form a group under multiplication % N,
375 and g MUST be a generator of this group. In addition, the group
376 parameters MUST NOT be specially chosen to allow efficient
377 computation of discrete logarithms.
379 The SRP group parameters in Appendix A satisfy the above
380 requirements, so the client SHOULD accept any parameters from this
381 Appendix which have large enough N values to meet her security
384 The client MAY accept other group parameters from the server, if the
385 client has reason to believe these parameters satisfy the above
386 requirements, and the parameters have large enough N values. For
387 example, if the parameters transmitted by the server match parameters
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396 on a "known-good" list, the client may choose to accept them. See
397 Section 3 for additional security considerations relevant to the
398 acceptance of the group parameters.
400 Group parameters that are not accepted via one of the above methods
401 MUST be rejected with an "untrusted_srp_parameters" alert (see
404 The client MUST abort the handshake with an "illegal_parameter" alert
407 2.5.4. Client Key Exchange
409 The client key exchange message carries the client's public value
410 (A). The client calculates this value as A = g^a % N, where a is a
411 random number which SHOULD be at least 256 bits in length.
413 The server MUST abort the handshake with an "illegal_parameter" alert
416 2.6. Calculating the Pre-master Secret
418 The pre-master secret is calculated by the client as follows:
420 I, P = <read from user>
421 N, g, s, B = <read from server>
424 u = SHA1(PAD(A) | PAD(B))
426 x = SHA1(s | SHA1(I | ":" | P))
427 <premaster secret> = (B - (k * g^x)) ^ (a + (u * x)) % N
429 The pre-master secret is calculated by the server as follows:
431 N, g, s, v = <read from password file>
435 A = <read from client>
436 u = SHA1(PAD(A) | PAD(B))
437 <premaster secret> = (A * v^u) ^ b % N
439 The finished messages perform the same function as the client and
440 server evidence messages (M1 and M2) specified in [SRP-RFC]. If
441 either the client or the server calculate an incorrect premaster
442 secret, the finished messages will fail to decrypt properly, and the
443 other party will return a "bad_record_mac" alert.
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452 If a client application receives a "bad_record_mac" alert when
453 performing an SRP handshake, it should inform the user that the
454 entered user name and password are incorrect.
456 2.7. Cipher Suite Definitions
458 The following cipher suites are added by this draft. The usage of
459 AES ciphersuites is as defined in [AESCIPH].
461 CipherSuite TLS_SRP_SHA_WITH_3DES_EDE_CBC_SHA = { 0x00,0xTBD5 };
463 CipherSuite TLS_SRP_SHA_RSA_WITH_3DES_EDE_CBC_SHA = { 0x00,0xTBD6
466 CipherSuite TLS_SRP_SHA_DSS_WITH_3DES_EDE_CBC_SHA = { 0x00,0xTBD7
469 CipherSuite TLS_SRP_SHA_WITH_AES_128_CBC_SHA = { 0x00,0xTBD8 };
471 CipherSuite TLS_SRP_SHA_RSA_WITH_AES_128_CBC_SHA = { 0x00,0xTBD9
474 CipherSuite TLS_SRP_SHA_DSS_WITH_AES_128_CBC_SHA = { 0x00,0xTBD10
477 CipherSuite TLS_SRP_SHA_WITH_AES_256_CBC_SHA = { 0x00,0xTBD11 };
479 CipherSuite TLS_SRP_SHA_RSA_WITH_AES_256_CBC_SHA = { 0x00,0xTBD12
482 CipherSuite TLS_SRP_SHA_DSS_WITH_AES_256_CBC_SHA = { 0x00,0xTBD13
485 Cipher suites that begin with TLS_SRP_SHA_RSA or TLS_SRP_SHA_DSS
486 require the server to send a certificate message containing a
487 certificate with the specified type of public key, and to sign the
488 server key exchange message using a matching private key.
490 Cipher suites that do not include a digital signature algorithm
491 identifier assume the server is authenticated by its possesion of the
494 Implementations conforming to this specification MUST implement the
495 TLS_SRP_SHA_WITH_3DES_EDE_CBC_SHA ciphersuite, SHOULD implement the
496 TLS_SRP_SHA_WITH_AES_128_CBC_SHA and TLS_SRP_SHA_WITH_AES_256_CBC_SHA
497 ciphersuites, and MAY implement the remaining ciphersuites.
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508 2.8. New Message Structures
510 This section shows the structure of the messages passed during a
511 handshake that uses SRP for authentication. The representation
512 language used is the same as that used in [TLS].
516 A new extension "srp" with value TBD1, has been added to the
517 enumerated ExtensionType defined in [TLSEXT]. This value MUST be
518 used as the extension number for the SRP extension.
520 The "extension_data" field of the SRP extension SHALL contain:
522 opaque srp_I<1..2^8-1>
524 where srp_I is the user name, encoded per Section 2.4.
526 2.8.2. Server Key Exchange
528 A new value, "srp", has been added to the enumerated
529 KeyExchangeAlgorithm originally defined in [TLS].
531 When the value of KeyExchangeAlgorithm is set to "srp", the server's
532 SRP parameters are sent in the server key exchange message, encoded
533 in a ServerSRPParams structure.
535 If a certificate is sent to the client the server key exchange
536 message must be signed.
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564 enum { rsa, diffie_hellman, srp } KeyExchangeAlgorithm;
567 select (KeyExchangeAlgorithm) {
569 ServerDHParams params;
570 Signature signed_params;
572 ServerRSAParams params;
573 Signature signed_params;
574 case srp: /* new entry */
575 ServerSRPParams params;
576 Signature signed_params;
581 opaque srp_N<1..2^16-1>;
582 opaque srp_g<1..2^16-1>;
583 opaque srp_s<1..2^8-1>
584 opaque srp_B<1..2^16-1>;
585 } ServerSRPParams; /* SRP parameters */
587 2.8.3. Client Key Exchange
589 When the value of KeyExchangeAlgorithm is set to "srp", the client's
590 public value (A) is sent in the client key exchange message, encoded
591 in a ClientSRPPublic structure.
594 select (KeyExchangeAlgorithm) {
595 case rsa: EncryptedPreMasterSecret;
596 case diffie_hellman: ClientDiffieHellmanPublic;
597 case srp: ClientSRPPublic; /* new entry */
602 opaque srp_A<1..2^16-1>;
607 Three new error alerts are defined:
609 o "unknown_srp_username" (TBD2) - this alert MAY be sent by a server
610 that receives an unknown user name. This alert is always fatal.
611 See Section 2.5.1.3 for details.
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620 o "missing_srp_username" (TBD3) - this alert MAY be sent by a server
621 that would like to select an offered SRP ciphersuite, if the SRP
622 extension is absent from the client's hello message. This alert
623 is always a warning. Upon receiving this alert, the client MAY
624 send a new hello message on the same connection, this time
625 including the SRP extension. See Section 2.5.1.2 for details.
627 o "untrusted_srp_parameters" (TBD4) - this alert MUST be sent by a
628 client that receives unknown or untrusted (N, g) values. This
629 alert is always fatal. See Section 2.5.3 for details.
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676 3. Security Considerations
678 If an attacker is able to steal the SRP verifier file, the attacker
679 can masquerade as the real server, and can also use dictionary
680 attacks to recover client passwords.
682 An attacker could repeatedly contact an SRP server and try to guess a
683 legitimate user's password. Servers SHOULD take steps to prevent
684 this, such as limiting the rate of authentication attempts from a
685 particular IP address, or against a particular user account, or
686 locking the user account once a threshold of failed attempts is
689 The client's user name is sent in the clear in the Client Hello
690 message. To avoid sending the user name in the clear, the client
691 could first open a conventional anonymous, or server-authenticated
692 connection, then renegotiate an SRP-authenticated connection with the
693 handshake protected by the first connection.
695 An attacker who could calculate discrete logarithms in the
696 multiplicative group % N could compromise user passwords, and could
697 also compromise the the confidentiality and integrity of TLS
698 sessions. Clients MUST ensure that the received parameter N is large
699 enough to make calculating discrete logarithms computationally
702 An attacker may try to send a prime value N which is large enough to
703 be secure, but which has a special form for which the attacker can
704 more easily compute discrete logarithms (e.g., using the algorithm
705 discussed in [TRAPDOOR]). If the client executes the protocol using
706 such a prime, the client's password could be compromised. Because of
707 the difficulty of checking for such special primes in real-time,
708 clients SHOULD only accept group parameters that come from a trusted
709 source, such as those listed in Appendix A, or parameters configured
710 locally by a trusted administrator.
712 The checks described in Section 2.5.3 and Section 2.5.4 on the
713 received values for A and B are crucial for security and MUST be
716 The private values a and b SHOULD be at least 256 bit random numbers,
717 to give approximately 128 bits of security against certain methods of
718 calculating discrete logarithms.
720 If the client receives a missing_srp_username alert, the client
721 should be aware that unless the handshake protocol is run to
722 completion, this alert may have been inserted by an attacker. If the
723 handshake protocol is not run to completion, the client should not
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732 make any decisions, nor form any assumptions, based on receiving this
735 It is possible to choose a (user name, password) pair such that the
736 resulting verifier will also match other, related, (user name,
737 password) pairs. Thus, anyone using verifiers should be careful not
738 to assume that only a single (user name, password) pair matches the
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788 4. IANA Considerations
790 This document defines a new TLS extension "srp", assigned the value
791 TBD1 (the value 6 is suggested) from the TLS ExtensionType registry
794 The error alerts that are defined in this document are assigned to
795 the TLS Alert registry defined in [TLS]. The alerts together with
796 their assigned number (the values 120-122 are suggested) are shown
799 o "unknown_srp_username" (TBD2)
801 o "missing_srp_username" (TBD3)
803 o "untrusted_srp_parameters" (TBD4)
805 IANA assigned the cipher suites' numbers to the Cipher Suite
806 Registry, defined in [TLS]. The assigned values are listed below
807 (the numbers between 0x50 to 0x58 are suggested).
809 CipherSuite TLS_SRP_SHA_WITH_3DES_EDE_CBC_SHA = { 0x00,0xTBD5 };
811 CipherSuite TLS_SRP_SHA_RSA_WITH_3DES_EDE_CBC_SHA = { 0x00,0xTBD6
814 CipherSuite TLS_SRP_SHA_DSS_WITH_3DES_EDE_CBC_SHA = { 0x00,0xTBD7
817 CipherSuite TLS_SRP_SHA_WITH_AES_128_CBC_SHA = { 0x00,0xTBD8 };
819 CipherSuite TLS_SRP_SHA_RSA_WITH_AES_128_CBC_SHA = { 0x00,0xTBD9
822 CipherSuite TLS_SRP_SHA_DSS_WITH_AES_128_CBC_SHA = { 0x00,0xTBD10
825 CipherSuite TLS_SRP_SHA_WITH_AES_256_CBC_SHA = { 0x00,0xTBD11 };
827 CipherSuite TLS_SRP_SHA_RSA_WITH_AES_256_CBC_SHA = { 0x00,0xTBD12
830 CipherSuite TLS_SRP_SHA_DSS_WITH_AES_256_CBC_SHA = { 0x00,0xTBD13
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846 5.1. Normative References
848 [TLS] Dierks, T. and E. Rescorla, "The TLS Protocol version
849 1.1", RFC 4346, April 2006.
851 [SRP-6] Wu, T., "SRP-6: Improvements and Refinements to the Secure
852 Remote Password Protocol", October 2002,
853 <http://srp.stanford.edu/srp6.ps>.
855 [TLSEXT] Blake-Wilson, S., Nystrom, M., Hopwood, D., Mikkelsen, J.,
856 and T. Wright, "TLS Extensions", RFC 3546, June 2003.
859 Hoffman, P. and M. Blanchet, "Preparation of
860 Internationalized Strings ("stringprep")", RFC 3454,
864 Zeilenga, K., "SASLprep: Stringprep profile for user names
865 and passwords", RFC 4013, February 2005.
867 [SRP-RFC] Wu, T., "The SRP Authentication and Key Exchange System",
868 RFC 2945, September 2000.
870 [SHA1] "Announcing the Secure Hash Standard", FIPS 180-1,
873 [HMAC] Krawczyk, H., Bellare, M., and R. Canetti, "HMAC: Keyed-
874 Hashing for Message Authentication", RFC 2104,
877 [AESCIPH] Chown, P., "Advanced Encryption Standard (AES)
878 Ciphersuites for Transport Layer Security (TLS)",
881 [MODP] Kivinen, T. and M. Kojo, "More Modular Exponentiation
882 (MODP) Diffie-Hellman groups for Internet Key Exchange
883 (IKE)", RFC 3526, May 2003.
885 5.2. Informative References
887 [IMAP] Newman, C., "Using TLS with IMAP, POP3 and ACAP",
890 [SRP] Wu, T., "The Secure Remote Password Protocol", Proceedings
891 of the 1998 Internet Society Network and Distributed
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900 System Security Symposium pp. 97-111, March 1998.
903 Gordon, D., "Designing and Detecting Trapdoors for
904 Discrete Log Cryptosystems", Springer-Verlag Advances in
905 Cryptology - Crypto '92, pp. 66-75, 1993.
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956 Appendix A. SRP Group Parameters
958 The 1024, 1536, and 2048-bit groups are taken from software developed
959 by Tom Wu and Eugene Jhong for the Stanford SRP distribution, and
960 subsequently proven to be prime. The larger primes are taken from
961 [MODP], but generators have been calculated that are primitive roots
962 of N, unlike the generators in [MODP].
964 The 1024-bit and 1536-bit groups MUST be supported.
968 The hexadecimal value for the prime is:
970 EEAF0AB9 ADB38DD6 9C33F80A FA8FC5E8 60726187 75FF3C0B 9EA2314C
971 9C256576 D674DF74 96EA81D3 383B4813 D692C6E0 E0D5D8E2 50B98BE4
972 8E495C1D 6089DAD1 5DC7D7B4 6154D6B6 CE8EF4AD 69B15D49 82559B29
973 7BCF1885 C529F566 660E57EC 68EDBC3C 05726CC0 2FD4CBF4 976EAA9A
974 FD5138FE 8376435B 9FC61D2F C0EB06E3
982 The hexadecimal value for the prime is:
984 9DEF3CAF B939277A B1F12A86 17A47BBB DBA51DF4 99AC4C80 BEEEA961
985 4B19CC4D 5F4F5F55 6E27CBDE 51C6A94B E4607A29 1558903B A0D0F843
986 80B655BB 9A22E8DC DF028A7C EC67F0D0 8134B1C8 B9798914 9B609E0B
987 E3BAB63D 47548381 DBC5B1FC 764E3F4B 53DD9DA1 158BFD3E 2B9C8CF5
988 6EDF0195 39349627 DB2FD53D 24B7C486 65772E43 7D6C7F8C E442734A
989 F7CCB7AE 837C264A E3A9BEB8 7F8A2FE9 B8B5292E 5A021FFF 5E91479E
990 8CE7A28C 2442C6F3 15180F93 499A234D CF76E3FE D135F9BB
998 The hexadecimal value for the prime is:
1000 AC6BDB41 324A9A9B F166DE5E 1389582F AF72B665 1987EE07 FC319294
1001 3DB56050 A37329CB B4A099ED 8193E075 7767A13D D52312AB 4B03310D
1002 CD7F48A9 DA04FD50 E8083969 EDB767B0 CF609517 9A163AB3 661A05FB
1003 D5FAAAE8 2918A996 2F0B93B8 55F97993 EC975EEA A80D740A DBF4FF74
1007 Taylor, et al. Expires December 28, 2006 [Page 18]
1009 Internet-Draft Using SRP for TLS Authentication June 2006
1012 7359D041 D5C33EA7 1D281E44 6B14773B CA97B43A 23FB8016 76BD207A
1013 436C6481 F1D2B907 8717461A 5B9D32E6 88F87748 544523B5 24B0D57D
1014 5EA77A27 75D2ECFA 032CFBDB F52FB378 61602790 04E57AE6 AF874E73
1015 03CE5329 9CCC041C 7BC308D8 2A5698F3 A8D0C382 71AE35F8 E9DBFBB6
1016 94B5C803 D89F7AE4 35DE236D 525F5475 9B65E372 FCD68EF2 0FA7111F
1020 The generator is: 2.
1025 This prime is: 2^3072 - 2^3008 - 1 + 2^64 * { [2^2942 pi] +
1028 Its hexadecimal value is:
1030 FFFFFFFF FFFFFFFF C90FDAA2 2168C234 C4C6628B 80DC1CD1 29024E08
1031 8A67CC74 020BBEA6 3B139B22 514A0879 8E3404DD EF9519B3 CD3A431B
1032 302B0A6D F25F1437 4FE1356D 6D51C245 E485B576 625E7EC6 F44C42E9
1033 A637ED6B 0BFF5CB6 F406B7ED EE386BFB 5A899FA5 AE9F2411 7C4B1FE6
1034 49286651 ECE45B3D C2007CB8 A163BF05 98DA4836 1C55D39A 69163FA8
1035 FD24CF5F 83655D23 DCA3AD96 1C62F356 208552BB 9ED52907 7096966D
1036 670C354E 4ABC9804 F1746C08 CA18217C 32905E46 2E36CE3B E39E772C
1037 180E8603 9B2783A2 EC07A28F B5C55DF0 6F4C52C9 DE2BCBF6 95581718
1038 3995497C EA956AE5 15D22618 98FA0510 15728E5A 8AAAC42D AD33170D
1039 04507A33 A85521AB DF1CBA64 ECFB8504 58DBEF0A 8AEA7157 5D060C7D
1040 B3970F85 A6E1E4C7 ABF5AE8C DB0933D7 1E8C94E0 4A25619D CEE3D226
1041 1AD2EE6B F12FFA06 D98A0864 D8760273 3EC86A64 521F2B18 177B200C
1042 BBE11757 7A615D6C 770988C0 BAD946E2 08E24FA0 74E5AB31 43DB5BFC
1043 E0FD108E 4B82D120 A93AD2CA FFFFFFFF FFFFFFFF
1046 The generator is: 5.
1051 This prime is: 2^4096 - 2^4032 - 1 + 2^64 * { [2^3966 pi] +
1054 Its hexadecimal value is:
1056 FFFFFFFF FFFFFFFF C90FDAA2 2168C234 C4C6628B 80DC1CD1 29024E08
1057 8A67CC74 020BBEA6 3B139B22 514A0879 8E3404DD EF9519B3 CD3A431B
1058 302B0A6D F25F1437 4FE1356D 6D51C245 E485B576 625E7EC6 F44C42E9
1059 A637ED6B 0BFF5CB6 F406B7ED EE386BFB 5A899FA5 AE9F2411 7C4B1FE6
1063 Taylor, et al. Expires December 28, 2006 [Page 19]
1065 Internet-Draft Using SRP for TLS Authentication June 2006
1068 49286651 ECE45B3D C2007CB8 A163BF05 98DA4836 1C55D39A 69163FA8
1069 FD24CF5F 83655D23 DCA3AD96 1C62F356 208552BB 9ED52907 7096966D
1070 670C354E 4ABC9804 F1746C08 CA18217C 32905E46 2E36CE3B E39E772C
1071 180E8603 9B2783A2 EC07A28F B5C55DF0 6F4C52C9 DE2BCBF6 95581718
1072 3995497C EA956AE5 15D22618 98FA0510 15728E5A 8AAAC42D AD33170D
1073 04507A33 A85521AB DF1CBA64 ECFB8504 58DBEF0A 8AEA7157 5D060C7D
1074 B3970F85 A6E1E4C7 ABF5AE8C DB0933D7 1E8C94E0 4A25619D CEE3D226
1075 1AD2EE6B F12FFA06 D98A0864 D8760273 3EC86A64 521F2B18 177B200C
1076 BBE11757 7A615D6C 770988C0 BAD946E2 08E24FA0 74E5AB31 43DB5BFC
1077 E0FD108E 4B82D120 A9210801 1A723C12 A787E6D7 88719A10 BDBA5B26
1078 99C32718 6AF4E23C 1A946834 B6150BDA 2583E9CA 2AD44CE8 DBBBC2DB
1079 04DE8EF9 2E8EFC14 1FBECAA6 287C5947 4E6BC05D 99B2964F A090C3A2
1080 233BA186 515BE7ED 1F612970 CEE2D7AF B81BDD76 2170481C D0069127
1081 D5B05AA9 93B4EA98 8D8FDDC1 86FFB7DC 90A6C08F 4DF435C9 34063199
1085 The generator is: 5.
1090 This prime is: 2^6144 - 2^6080 - 1 + 2^64 * { [2^6014 pi] +
1093 Its hexadecimal value is:
1095 FFFFFFFF FFFFFFFF C90FDAA2 2168C234 C4C6628B 80DC1CD1 29024E08
1096 8A67CC74 020BBEA6 3B139B22 514A0879 8E3404DD EF9519B3 CD3A431B
1097 302B0A6D F25F1437 4FE1356D 6D51C245 E485B576 625E7EC6 F44C42E9
1098 A637ED6B 0BFF5CB6 F406B7ED EE386BFB 5A899FA5 AE9F2411 7C4B1FE6
1099 49286651 ECE45B3D C2007CB8 A163BF05 98DA4836 1C55D39A 69163FA8
1100 FD24CF5F 83655D23 DCA3AD96 1C62F356 208552BB 9ED52907 7096966D
1101 670C354E 4ABC9804 F1746C08 CA18217C 32905E46 2E36CE3B E39E772C
1102 180E8603 9B2783A2 EC07A28F B5C55DF0 6F4C52C9 DE2BCBF6 95581718
1103 3995497C EA956AE5 15D22618 98FA0510 15728E5A 8AAAC42D AD33170D
1104 04507A33 A85521AB DF1CBA64 ECFB8504 58DBEF0A 8AEA7157 5D060C7D
1105 B3970F85 A6E1E4C7 ABF5AE8C DB0933D7 1E8C94E0 4A25619D CEE3D226
1106 1AD2EE6B F12FFA06 D98A0864 D8760273 3EC86A64 521F2B18 177B200C
1107 BBE11757 7A615D6C 770988C0 BAD946E2 08E24FA0 74E5AB31 43DB5BFC
1108 E0FD108E 4B82D120 A9210801 1A723C12 A787E6D7 88719A10 BDBA5B26
1109 99C32718 6AF4E23C 1A946834 B6150BDA 2583E9CA 2AD44CE8 DBBBC2DB
1110 04DE8EF9 2E8EFC14 1FBECAA6 287C5947 4E6BC05D 99B2964F A090C3A2
1111 233BA186 515BE7ED 1F612970 CEE2D7AF B81BDD76 2170481C D0069127
1112 D5B05AA9 93B4EA98 8D8FDDC1 86FFB7DC 90A6C08F 4DF435C9 34028492
1113 36C3FAB4 D27C7026 C1D4DCB2 602646DE C9751E76 3DBA37BD F8FF9406
1114 AD9E530E E5DB382F 413001AE B06A53ED 9027D831 179727B0 865A8918
1115 DA3EDBEB CF9B14ED 44CE6CBA CED4BB1B DB7F1447 E6CC254B 33205151
1119 Taylor, et al. Expires December 28, 2006 [Page 20]
1121 Internet-Draft Using SRP for TLS Authentication June 2006
1124 2BD7AF42 6FB8F401 378CD2BF 5983CA01 C64B92EC F032EA15 D1721D03
1125 F482D7CE 6E74FEF6 D55E702F 46980C82 B5A84031 900B1C9E 59E7C97F
1126 BEC7E8F3 23A97A7E 36CC88BE 0F1D45B7 FF585AC5 4BD407B2 2B4154AA
1127 CC8F6D7E BF48E1D8 14CC5ED2 0F8037E0 A79715EE F29BE328 06A1D58B
1128 B7C5DA76 F550AA3D 8A1FBFF0 EB19CCB1 A313D55C DA56C9EC 2EF29632
1129 387FE8D7 6E3C0468 043E8F66 3F4860EE 12BF2D5B 0B7474D6 E694F91E
1130 6DCC4024 FFFFFFFF FFFFFFFF
1133 The generator is: 5.
1138 This prime is: 2^8192 - 2^8128 - 1 + 2^64 * { [2^8062 pi] +
1141 Its hexadecimal value is:
1143 FFFFFFFF FFFFFFFF C90FDAA2 2168C234 C4C6628B 80DC1CD1 29024E08
1144 8A67CC74 020BBEA6 3B139B22 514A0879 8E3404DD EF9519B3 CD3A431B
1145 302B0A6D F25F1437 4FE1356D 6D51C245 E485B576 625E7EC6 F44C42E9
1146 A637ED6B 0BFF5CB6 F406B7ED EE386BFB 5A899FA5 AE9F2411 7C4B1FE6
1147 49286651 ECE45B3D C2007CB8 A163BF05 98DA4836 1C55D39A 69163FA8
1148 FD24CF5F 83655D23 DCA3AD96 1C62F356 208552BB 9ED52907 7096966D
1149 670C354E 4ABC9804 F1746C08 CA18217C 32905E46 2E36CE3B E39E772C
1150 180E8603 9B2783A2 EC07A28F B5C55DF0 6F4C52C9 DE2BCBF6 95581718
1151 3995497C EA956AE5 15D22618 98FA0510 15728E5A 8AAAC42D AD33170D
1152 04507A33 A85521AB DF1CBA64 ECFB8504 58DBEF0A 8AEA7157 5D060C7D
1153 B3970F85 A6E1E4C7 ABF5AE8C DB0933D7 1E8C94E0 4A25619D CEE3D226
1154 1AD2EE6B F12FFA06 D98A0864 D8760273 3EC86A64 521F2B18 177B200C
1155 BBE11757 7A615D6C 770988C0 BAD946E2 08E24FA0 74E5AB31 43DB5BFC
1156 E0FD108E 4B82D120 A9210801 1A723C12 A787E6D7 88719A10 BDBA5B26
1157 99C32718 6AF4E23C 1A946834 B6150BDA 2583E9CA 2AD44CE8 DBBBC2DB
1158 04DE8EF9 2E8EFC14 1FBECAA6 287C5947 4E6BC05D 99B2964F A090C3A2
1159 233BA186 515BE7ED 1F612970 CEE2D7AF B81BDD76 2170481C D0069127
1160 D5B05AA9 93B4EA98 8D8FDDC1 86FFB7DC 90A6C08F 4DF435C9 34028492
1161 36C3FAB4 D27C7026 C1D4DCB2 602646DE C9751E76 3DBA37BD F8FF9406
1162 AD9E530E E5DB382F 413001AE B06A53ED 9027D831 179727B0 865A8918
1163 DA3EDBEB CF9B14ED 44CE6CBA CED4BB1B DB7F1447 E6CC254B 33205151
1164 2BD7AF42 6FB8F401 378CD2BF 5983CA01 C64B92EC F032EA15 D1721D03
1165 F482D7CE 6E74FEF6 D55E702F 46980C82 B5A84031 900B1C9E 59E7C97F
1166 BEC7E8F3 23A97A7E 36CC88BE 0F1D45B7 FF585AC5 4BD407B2 2B4154AA
1167 CC8F6D7E BF48E1D8 14CC5ED2 0F8037E0 A79715EE F29BE328 06A1D58B
1168 B7C5DA76 F550AA3D 8A1FBFF0 EB19CCB1 A313D55C DA56C9EC 2EF29632
1169 387FE8D7 6E3C0468 043E8F66 3F4860EE 12BF2D5B 0B7474D6 E694F91E
1170 6DBE1159 74A3926F 12FEE5E4 38777CB6 A932DF8C D8BEC4D0 73B931BA
1171 3BC832B6 8D9DD300 741FA7BF 8AFC47ED 2576F693 6BA42466 3AAB639C
1175 Taylor, et al. Expires December 28, 2006 [Page 21]
1177 Internet-Draft Using SRP for TLS Authentication June 2006
1180 5AE4F568 3423B474 2BF1C978 238F16CB E39D652D E3FDB8BE FC848AD9
1181 22222E04 A4037C07 13EB57A8 1A23F0C7 3473FC64 6CEA306B 4BCBC886
1182 2F8385DD FA9D4B7F A2C087E8 79683303 ED5BDD3A 062B3CF5 B3A278A6
1183 6D2A13F8 3F44F82D DF310EE0 74AB6A36 4597E899 A0255DC1 64F31CC5
1184 0846851D F9AB4819 5DED7EA1 B1D510BD 7EE74D73 FAF36BC3 1ECFA268
1185 359046F4 EB879F92 4009438B 481C6CD7 889A002E D5EE382B C9190DA6
1186 FC026E47 9558E447 5677E9AA 9E3050E2 765694DF C81F56E8 80B96E71
1187 60C980DD 98EDD3DF FFFFFFFF FFFFFFFF
1190 The generator is: 19 (decimal).
1231 Taylor, et al. Expires December 28, 2006 [Page 22]
1233 Internet-Draft Using SRP for TLS Authentication June 2006
1236 Appendix B. SRP Test Vectors
1238 The following test vectors demonstrate calculation of the verifier
1239 and premaster secret.
1245 s = BEB25379 D1A8581E B5A72767 3A2441EE
1247 N, g = <1024-bit parameters from Appendix A>
1249 k = 7556AA04 5AEF2CDD 07ABAF0F 665C3E81 8913186F
1251 x = 94B7555A ABE9127C C58CCF49 93DB6CF8 4D16C124
1255 7E273DE8 696FFC4F 4E337D05 B4B375BE B0DDE156 9E8FA00A 9886D812
1256 9BADA1F1 822223CA 1A605B53 0E379BA4 729FDC59 F105B478 7E5186F5
1257 C671085A 1447B52A 48CF1970 B4FB6F84 00BBF4CE BFBB1681 52E08AB5
1258 EA53D15C 1AFF87B2 B9DA6E04 E058AD51 CC72BFC9 033B564E 26480D78
1259 E955A5E2 9E7AB245 DB2BE315 E2099AFB
1263 60975527 035CF2AD 1989806F 0407210B C81EDC04 E2762A56 AFD529DD
1268 E487CB59 D31AC550 471E81F0 0F6928E0 1DDA08E9 74A004F4 9E61F5D1
1273 61D5E490 F6F1B795 47B0704C 436F523D D0E560F0 C64115BB 72557EC4
1274 4352E890 3211C046 92272D8B 2D1A5358 A2CF1B6E 0BFCF99F 921530EC
1275 8E393561 79EAE45E 42BA92AE ACED8251 71E1E8B9 AF6D9C03 E1327F44
1276 BE087EF0 6530E69F 66615261 EEF54073 CA11CF58 58F0EDFD FE15EFEA
1277 B349EF5D 76988A36 72FAC47B 0769447B
1281 BD0C6151 2C692C0C B6D041FA 01BB152D 4916A1E7 7AF46AE1 05393011
1282 BAF38964 DC46A067 0DD125B9 5A981652 236F99D9 B681CBF8 7837EC99
1283 6C6DA044 53728610 D0C6DDB5 8B318885 D7D82C7F 8DEB75CE 7BD4FBAA
1287 Taylor, et al. Expires December 28, 2006 [Page 23]
1289 Internet-Draft Using SRP for TLS Authentication June 2006
1292 37089E6F 9C6059F3 88838E7A 00030B33 1EB76840 910440B1 B27AAEAE
1293 EB4012B7 D7665238 A8E3FB00 4B117B58
1297 CE38B959 3487DA98 554ED47D 70A7AE5F 462EF019
1299 <premaster secret> =
1301 B0DC82BA BCF30674 AE450C02 87745E79 90A3381F 63B387AA F271A10D
1302 233861E3 59B48220 F7C4693C 9AE12B0A 6F67809F 0876E2D0 13800D6C
1303 41BB59B6 D5979B5C 00A172B4 A2A5903A 0BDCAF8A 709585EB 2AFAFA8F
1304 3499B200 210DCC1F 10EB3394 3CD67FC8 8A2F39A4 BE5BEC4E C0A3212D
1305 C346D7E4 74B29EDE 8A469FFE CA686E5A
1343 Taylor, et al. Expires December 28, 2006 [Page 24]
1345 Internet-Draft Using SRP for TLS Authentication June 2006
1348 Appendix C. Acknowledgements
1350 Thanks to all on the IETF TLS mailing list for ideas and analysis.
1399 Taylor, et al. Expires December 28, 2006 [Page 25]
1401 Internet-Draft Using SRP for TLS Authentication June 2006
1409 Email: dtaylor@gnutls.org
1415 Email: tjw@cs.stanford.edu
1418 Nikos Mavrogiannopoulos
1421 Email: nmav@gnutls.org
1422 URI: http://www.gnutls.org/
1428 Email: trevp@trevp.net
1429 URI: http://trevp.net/
1455 Taylor, et al. Expires December 28, 2006 [Page 26]
1457 Internet-Draft Using SRP for TLS Authentication June 2006
1460 Intellectual Property Statement
1462 The IETF takes no position regarding the validity or scope of any
1463 Intellectual Property Rights or other rights that might be claimed to
1464 pertain to the implementation or use of the technology described in
1465 this document or the extent to which any license under such rights
1466 might or might not be available; nor does it represent that it has
1467 made any independent effort to identify any such rights. Information
1468 on the procedures with respect to rights in RFC documents can be
1469 found in BCP 78 and BCP 79.
1471 Copies of IPR disclosures made to the IETF Secretariat and any
1472 assurances of licenses to be made available, or the result of an
1473 attempt made to obtain a general license or permission for the use of
1474 such proprietary rights by implementers or users of this
1475 specification can be obtained from the IETF on-line IPR repository at
1476 http://www.ietf.org/ipr.
1478 The IETF invites any interested party to bring to its attention any
1479 copyrights, patents or patent applications, or other proprietary
1480 rights that may cover technology that may be required to implement
1481 this standard. Please address the information to the IETF at
1485 Disclaimer of Validity
1487 This document and the information contained herein are provided on an
1488 "AS IS" basis and THE CONTRIBUTOR, THE ORGANIZATION HE/SHE REPRESENTS
1489 OR IS SPONSORED BY (IF ANY), THE INTERNET SOCIETY AND THE INTERNET
1490 ENGINEERING TASK FORCE DISCLAIM ALL WARRANTIES, EXPRESS OR IMPLIED,
1491 INCLUDING BUT NOT LIMITED TO ANY WARRANTY THAT THE USE OF THE
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1493 WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE.
1498 Copyright (C) The Internet Society (2006). This document is subject
1499 to the rights, licenses and restrictions contained in BCP 78, and
1500 except as set forth therein, the authors retain all their rights.
1505 Funding for the RFC Editor function is currently provided by the
1511 Taylor, et al. Expires December 28, 2006 [Page 27]