2 TLS Working Group D. Taylor
3 Internet-Draft Forge Research Pty Ltd
4 Expires: September 15, 2005 T. Wu
10 Using SRP for TLS Authentication
15 This document is an Internet-Draft and is subject to all provisions
16 of section 3 of RFC 3667. By submitting this Internet-Draft, each
17 author represents that any applicable patent or other IPR claims of
18 which he or she is aware have been or will be disclosed, and any of
19 which he or she become aware will be disclosed, in accordance with
22 Internet-Drafts are working documents of the Internet Engineering
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35 The list of Internet-Draft Shadow Directories can be accessed at
36 http://www.ietf.org/shadow.html.
38 This Internet-Draft will expire on September 15, 2005.
42 Copyright (C) The Internet Society (2005).
46 This memo presents a technique for using the Secure Remote Password
47 protocol ([SRP], [SRP-6]) as an authentication method for the
48 Transport Layer Security protocol [TLS].
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56 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 3
57 2. SRP Authentication in TLS . . . . . . . . . . . . . . . . . . 4
58 2.1 Notation and Terminology . . . . . . . . . . . . . . . . . 4
59 2.2 Handshake Protocol Overview . . . . . . . . . . . . . . . 4
60 2.3 Text Preparation . . . . . . . . . . . . . . . . . . . . . 5
61 2.4 SRP Verifier Creation . . . . . . . . . . . . . . . . . . 5
62 2.5 Changes to the Handshake Message Contents . . . . . . . . 5
63 2.5.1 Client Hello . . . . . . . . . . . . . . . . . . . . . 5
64 2.5.2 Server Certificate . . . . . . . . . . . . . . . . . . 7
65 2.5.3 Server Key Exchange . . . . . . . . . . . . . . . . . 7
66 2.5.4 Client Key Exchange . . . . . . . . . . . . . . . . . 8
67 2.6 Calculating the Pre-master Secret . . . . . . . . . . . . 8
68 2.7 Cipher Suite Definitions . . . . . . . . . . . . . . . . . 9
69 2.8 New Message Structures . . . . . . . . . . . . . . . . . . 9
70 2.8.1 Client Hello . . . . . . . . . . . . . . . . . . . . . 9
71 2.8.2 Server Key Exchange . . . . . . . . . . . . . . . . . 10
72 2.8.3 Client Key Exchange . . . . . . . . . . . . . . . . . 10
73 2.9 Error Alerts . . . . . . . . . . . . . . . . . . . . . . . 11
74 3. Security Considerations . . . . . . . . . . . . . . . . . . . 12
75 4. References . . . . . . . . . . . . . . . . . . . . . . . . . . 14
76 4.1 Normative References . . . . . . . . . . . . . . . . . . . . 14
77 4.2 Informative References . . . . . . . . . . . . . . . . . . . 14
78 Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . 15
79 A. SRP Group Parameters . . . . . . . . . . . . . . . . . . . . . 16
80 B. SRP Test Vectors . . . . . . . . . . . . . . . . . . . . . . . 20
81 C. Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . 21
82 Intellectual Property and Copyright Statements . . . . . . . . 22
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99 At the time of writing TLS [TLS] uses public key certificates, or
100 Kerberos, for authentication.
102 These authentication methods do not seem well suited to the
103 applications now being adapted to use TLS ([IMAP] or [FTP], for
104 example). Given that these protocols are designed to use the user
105 name and password method of authentication, being able to safely use
106 user names and passwords provides an easier route to additional
109 SRP ([SRP], [SRP-6]) is an authentication method that allows the use
110 of user names and passwords over unencrypted channels without
111 revealing the password to an eavesdropper. SRP also supplies a
112 shared secret at the end of the authentication sequence that can be
113 used to generate encryption keys.
115 This document describes the use of the SRP authentication method for
118 The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
119 "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this
120 document are to be interpreted as described in RFC 2119.
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138 2. SRP Authentication in TLS
140 2.1 Notation and Terminology
142 The version of SRP used here is sometimes referred to as "SRP-6"
143 [SRP-6]. This version is a slight improvement over "SRP-3", which
144 was described in [SRP] and [RFC2945].
146 This document uses the variable names defined in [SRP-6]:
148 N, g: group parameters (prime and generator)
150 B, b: server's public and private values
151 A, a: client's public and private values
152 I: user name (aka "identity")
157 The | symbol indicates string concatenation, the ^ operator is the
158 exponentiation operation, and the % operator is the integer remainder
161 Conversion between integers and byte-strings assumes the
162 most-significant bytes are stored first, as per [TLS] and [RFC2945].
163 In the following text, if a conversion from integer to byte-string is
164 implicit, the most-significant byte in the resultant byte-string MUST
165 be non-zero. If a conversion is explicitly specified with the
166 operator PAD(), the integer will first be implicitly converted, then
167 the resultant byte-string will be left-padded with zeros (if
168 necessary) until its length equals the implicitly-converted length of
171 2.2 Handshake Protocol Overview
173 The advent of [SRP-6] allows the SRP protocol to be implemented using
174 the standard sequence of handshake messages defined in [TLS].
176 The parameters to various messages are given in the following
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189 Client Hello (I) ------------------------> |
190 | <---------------------------- Server Hello
191 | <---------------------------- Certificate*
192 | <---------------------------- Server Key Exchange (N, g, s, B)
193 | <---------------------------- Server Hello Done
194 Client Key Exchange (A) -----------------> |
195 [Change cipher spec] |
196 Finished --------------------------------> |
197 | [Change cipher spec]
198 | <---------------------------- Finished
200 Application Data <--------------> Application Data
202 * Indicates an optional message which is not always sent.
208 The user name and password strings shall be UTF-8 encoded Unicode,
209 prepared using the [SASLPrep] profile of [StringPrep].
211 2.4 SRP Verifier Creation
213 The verifier is calculated as described in section 3 of [RFC2945].
214 We give the algorithm here for convenience.
216 The verifier (v) is computed based on the salt (s), user name (I),
217 password (P), and group parameters (N, g). The computation uses the
218 [SHA1] hash algorithm:
220 x = SHA1(s | SHA1(I | ":" | P))
223 2.5 Changes to the Handshake Message Contents
225 This section describes the changes to the TLS handshake message
226 contents when SRP is being used for authentication. The definitions
227 of the new message contents and the on-the-wire changes are given in
232 The user name is appended to the standard client hello message using
233 the hello message extension mechanism defined in [TLSEXT] (see
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241 2.5.1.1 Session Resumption
243 When a client attempts to resume a session that uses SRP
244 authentication, the client MUST include the user name extension in
245 the client hello message, in case the server cannot or will not allow
246 session resumption, meaning a full handshake is required.
248 If the server does agree to resume an existing session the server
249 MUST ignore the information in the SRP extension of the client hello
250 message, except for its inclusion in the finished message hashes.
251 This is to ensure attackers cannot replace the authenticated identity
252 without supplying the proper authentication information.
254 2.5.1.2 Missing SRP Username
256 The client may offer SRP ciphersuites in the hello message but omit
257 the SRP extension. If the server would like to select an SRP
258 ciphersuite in this case, the server MAY return a
259 missing_srp_username alert (see Section 2.9) immediately after
260 processing the client hello message. This alert signals the client
261 to resend the hello message, this time with the SRP extension. This
262 allows the client to advertise that it supports SRP, but not have to
263 prompt the user for his user name and password, nor expose the user
264 name in the clear, unless necessary.
266 After sending the missing_srp_username alert, the server MUST leave
267 the TLS connection open, yet reset its handshake protocol state so it
268 is prepared to receive a second client hello message. Upon receiving
269 the missing_srp_username alert, the client MUST either send a second
270 client hello message, or send a fatal user_cancelled alert.
272 If the client sends a second hello message, the second hello message
273 MUST offer SRP ciphersuites, and MUST contain the SRP extension, and
274 the server MUST choose one of the SRP ciphersuites. Both client
275 hello messages MUST be treated as handshake messages and included in
276 the hash calculations for the TLS Finished message. The premaster
277 and master secret calculations will use the random value from the
278 second client hello message, not the first.
280 2.5.1.3 Unknown SRP Username
282 If the server doesn't have a verifier for the given user name, the
283 server MAY abort the handshake with an unknown_srp_username alert
284 (see Section 2.9). Alternatively, if the server wishes to hide the
285 fact that this user name doesn't have a verifier, the server MAY
286 simulate the protocol as if a verifier existed, but then reject the
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292 client's finished message with a bad_record_mac alert, as if the
293 password was incorrect.
295 To simulate the existence of an entry for each user name, the server
296 must consistently return the same salt (s) and group (N, g) values
297 for the same user name. For example, the server could store a secret
298 "seed key" and then use HMAC-SHA1(seed_key, "salt" | user_name) to
299 generate the salts [HMAC]. For B, the server can return a random
300 value between 1 and N-1 inclusive. However, the server should take
301 care to simulate computation delays. One way to do this is to
302 generate a fake verifier using the "seed key" approach, and then
303 proceed with the protocol as usual.
305 2.5.2 Server Certificate
307 The server MUST send a certificate if it agrees to an SRP cipher
308 suite that requires the server to provide additional authentication
309 in the form of a digital signature. See Section 2.7 for details of
310 which ciphersuites defined in this document require a server
311 certificate to be sent.
313 2.5.3 Server Key Exchange
315 The server key exchange message contains the prime (N), the generator
316 (g), and the salt value (s) read from the SRP password file based on
317 the user name (I) received in the client hello extension.
319 The server key exchange message also contains the server's public
320 value (B). The server calculates this value as B = k*v + g^b % N,
321 where b is a random number which SHOULD be at least 256 bits in
322 length, and k = SHA1(N | PAD(g)).
324 If the server has sent a certificate message, the server key exchange
325 message MUST be signed.
327 The group parameters (N, g) sent in this message MUST have N as a
328 safe prime (a prime of the form N=2q+1, where q is also prime). The
329 integers from 1 to N-1 will form a group under multiplication % N,
330 and g MUST be a generator of this group. The SRP group parameters in
331 Appendix A are proven to have these properties, so the client SHOULD
332 accept any parameters from this Appendix which have large enough N
333 values to meet his security requirements. The client MAY accept
334 other group parameters from the server, either by prior arrangement,
335 or by checking the parameters himself. See Section 3 for additional
336 security considerations relevant to the acceptance of the group
339 Group parameters that are not accepted via one of the above methods
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345 MUST be rejected with an untrusted_srp_parameters alert (see Section
348 The client MUST abort the handshake with an illegal_parameter alert
351 2.5.4 Client Key Exchange
353 The client key exchange message carries the client's public value
354 (A). The client calculates this value as A = g^a % N, where a is a
355 random number which SHOULD be at least 256 bits in length.
357 The server MUST abort the handshake with an illegal_parameter alert
360 2.6 Calculating the Pre-master Secret
362 The pre-master secret is calculated by the client as follows:
364 I, P = <read from user>
365 N, g, s, B = <read from server>
368 u = SHA1(PAD(A) | PAD(B))
370 x = SHA1(s | SHA1(I | ":" | P))
371 <premaster secret> = (B - (k * g^x)) ^ (a + (u * x)) % N
373 The pre-master secret is calculated by the server as follows:
375 N, g, s, v = <read from password file>
379 A = <read from client>
380 u = SHA1(PAD(A) | PAD(B))
381 <premaster secret> = (A * v^u) ^ b % N
383 The finished messages perform the same function as the client and
384 server evidence messages (M1 and M2) specified in [RFC2945]. If
385 either the client or the server calculate an incorrect premaster
386 secret, the finished messages will fail to decrypt properly, and the
387 other party will return a bad_record_mac alert.
389 If a client application receives a bad_record_mac alert when
390 performing an SRP handshake, it should inform the user that the
391 entered user name and password are incorrect.
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397 2.7 Cipher Suite Definitions
399 The following cipher suites are added by this draft. The usage of
400 AES ciphersuites is as defined in [RFC3268].
402 CipherSuite TLS_SRP_SHA_WITH_3DES_EDE_CBC_SHA = { 0x00,0x50 };
403 CipherSuite TLS_SRP_SHA_RSA_WITH_3DES_EDE_CBC_SHA = { 0x00,0x51 };
404 CipherSuite TLS_SRP_SHA_DSS_WITH_3DES_EDE_CBC_SHA = { 0x00,0x52 };
405 CipherSuite TLS_SRP_SHA_WITH_AES_128_CBC_SHA = { 0x00,0x53 };
406 CipherSuite TLS_SRP_SHA_RSA_WITH_AES_128_CBC_SHA = { 0x00,0x54 };
407 CipherSuite TLS_SRP_SHA_DSS_WITH_AES_128_CBC_SHA = { 0x00,0x55 };
408 CipherSuite TLS_SRP_SHA_WITH_AES_256_CBC_SHA = { 0x00,0x56 };
409 CipherSuite TLS_SRP_SHA_RSA_WITH_AES_256_CBC_SHA = { 0x00,0x57 };
410 CipherSuite TLS_SRP_SHA_DSS_WITH_AES_256_CBC_SHA = { 0x00,0x58 };
412 Cipher suites that begin with TLS_SRP_SHA_RSA or TLS_SRP_SHA_DSS
413 require the server to send a certificate message containing a
414 certificate with the specified type of public key, and to sign the
415 server key exchange message using a matching private key.
417 Cipher suites that do not include a digital signature algorithm
418 identifier assume the server is authenticated by its possesion of the
421 Implementations conforming to this specification MUST implement the
422 TLS_SRP_SHA_WITH_3DES_EDE_CBC_SHA ciphersuite, SHOULD implement the
423 TLS_SRP_SHA_WITH_AES_128_CBC_SHA and TLS_SRP_SHA_WITH_AES_256_CBC_SHA
424 ciphersuites, and MAY implement the remaining ciphersuites.
426 2.8 New Message Structures
428 This section shows the structure of the messages passed during a
429 handshake that uses SRP for authentication. The representation
430 language used is the same as that used in [TLS].
434 A new value, "srp(6)", has been added to the enumerated ExtensionType
435 defined in [TLSEXT]. This value MUST be used as the extension number
436 for the SRP extension.
438 The "extension_data" field of the SRP extension SHALL contain:
440 opaque srp_I<1..2^8-1>
442 where srp_I is the user name, encoded per Section 2.4.
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449 2.8.2 Server Key Exchange
451 A new value, "srp", has been added to the enumerated
452 KeyExchangeAlgorithm originally defined in [TLS].
454 When the value of KeyExchangeAlgorithm is set to "srp", the server's
455 SRP parameters are sent in the server key exchange message, encoded
456 in a ServerSRPParams structure.
458 If a certificate is sent to the client the server key exchange
459 message must be signed.
461 enum { rsa, diffie_hellman, srp } KeyExchangeAlgorithm;
464 select (KeyExchangeAlgorithm) {
466 ServerDHParams params;
467 Signature signed_params;
469 ServerRSAParams params;
470 Signature signed_params;
471 case srp: /* new entry */
472 ServerSRPParams params;
473 Signature signed_params;
478 opaque srp_N<1..2^16-1>;
479 opaque srp_g<1..2^16-1>;
480 opaque srp_s<1..2^8-1>
481 opaque srp_B<1..2^16-1>;
482 } ServerSRPParams; /* SRP parameters */
484 2.8.3 Client Key Exchange
486 When the value of KeyExchangeAlgorithm is set to "srp", the client's
487 public value (A) is sent in the client key exchange message, encoded
488 in a ClientSRPPublic structure.
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499 select (KeyExchangeAlgorithm) {
500 case rsa: EncryptedPreMasterSecret;
501 case diffie_hellman: ClientDiffieHellmanPublic;
502 case srp: ClientSRPPublic; /* new entry */
507 opaque srp_A<1..2^16-1>;
512 Three new error alerts are defined:
514 o "unknown_srp_username" (120) - this alert MAY be sent by a server
515 that receives an unknown user name. This alert is always fatal.
516 See Section 2.5.1.3 for details.
517 o "missing_srp_username" (121) - this alert MAY be sent by a server
518 that would like to select an offered SRP ciphersuite, if the SRP
519 extension is absent from the client's hello message. This alert
520 is always a warning. Upon receiving this alert, the client MAY
521 send a new hello message on the same connection, this time
522 including the SRP extension. See Section 2.5.1.2 for details.
523 o "untrusted_srp_parameters" (122) - this alert MUST be sent by a
524 client that receives unknown or untrusted (N, g) values. This
525 alert is always fatal. See Section 2.5.3 for details.
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541 3. Security Considerations
543 If an attacker is able to steal the SRP verifier file, the attacker
544 can masquerade as the real server, and can also use dictionary
545 attacks to recover client passwords.
547 An attacker could repeatedly contact an SRP server and try to guess a
548 legitimate user's password. Servers SHOULD take steps to prevent
549 this, such as limiting the rate of authentication attempts from a
550 particular IP address, or against a particular user account, or
551 locking the user account once a threshold of failed attempts is
554 The client's user name is sent in the clear in the Client Hello
555 message. To avoid sending the user name in the clear, the client
556 could first open a conventional anonymous, or server-authenticated
557 connection, then renegotiate an SRP-authenticated connection with the
558 handshake protected by the first connection.
560 The received parameters N and g in the Server Key Exchange message
561 are crucial for the security of the user's password. In particular,
562 an attacker may attempt to substitute values for which he can more
563 easily compute discrete logarithms [TrapDoor]. Algorithmic advances
564 and/or increases in computing power may necessitate increases in the
565 size of N. As a consequence, clients should ensure that the received
566 parameter N, in addition to passing the checks mentioned in 2.5.3, is
567 also large enough to make discrete logarithms computationally
568 infeasible. In addition, if a client accepts untrusted values N and
569 g from the Server Key Exchange message, it should ensure that it is
570 not of any special form that would make discrete logarithms easier to
571 compute. Because of the difficulty of performing this check in the
572 general case, implementors may opt to accept only those parameters
573 that come from a trusted source, such as those listed in Appendix A
574 and parameters locally configured through prior arrangement.
576 The checks described in Section 2.5.3 and Section 2.5.4 on the
577 received values for A and B are crucial for security and MUST be
580 The private values a and b SHOULD be at least 256 bit random numbers,
581 to give approximately 128 bits of security against certain methods of
582 calculating discrete logarithms.
584 If the client receives a missing_srp_username alert, the client
585 should be aware that unless the handshake protocol is run to
586 completion, this alert may have been inserted by an attacker. If the
587 handshake protocol is not run to completion, the client should not
588 make any decisions, nor form any assumptions, based on receiving this
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596 It is possible to choose a (user name, password) pair such that the
597 resulting verifier will also match other, related, (user name,
598 password) pairs. Thus, anyone using verifiers should be careful not
599 to assume that only a single (user name, password) pair matches the
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628 4.1 Normative References
630 [TLS] Dierks, T. and C. Allen, "The TLS Protocol", RFC 2246,
633 [SRP-6] Wu, T., "SRP-6: Improvements and Refinements to the Secure
634 Remote Password Protocol", October 2002,
635 <http://srp.stanford.edu/srp6.ps>.
637 [TLSEXT] Blake-Wilson, S., Nystrom, M., Hopwood, D., Mikkelsen, J.
638 and T. Wright, "TLS Extensions", RFC 3546, June 2003.
641 Hoffman, P. and M. Blanchet, "Preparation of
642 Internationalized Strings ("stringprep")", RFC 3454,
646 Zeilenga, K., "SASLprep: Stringprep profile for user names
647 and passwords", draft-ietf-sasl-saslprep-10 (work in
648 progress), July 2004.
650 [RFC2945] Wu, T., "The SRP Authentication and Key Exchange System",
651 RFC 2945, September 2000.
653 [SHA1] "Announcing the Secure Hash Standard", FIPS 180-1,
656 [HMAC] Krawczyk, H., Bellare, M. and R. Canetti, "HMAC:
657 Keyed-Hashing for Message Authentication", RFC 2104,
660 [RFC3268] Chown, P., "Advanced Encryption Standard (AES)
661 Ciphersuites for Transport Layer Security (TLS)", RFC
664 [MODP] Kivinen, T. and M. Kojo, "More Modular Exponentiation
665 (MODP) Diffie-Hellman groups for Internet Key Exchange
666 (IKE)", RFC 3526, May 2003.
668 4.2 Informative References
670 [IMAP] Newman, C., "Using TLS with IMAP, POP3 and ACAP", RFC
673 [FTP] Ford-Hutchinson, P., "Securing FTP with TLS",
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679 draft-murray-auth-ftp-ssl-16 (work in progress), February
682 [SRP] Wu, T., "The Secure Remote Password Protocol", Proceedings
683 of the 1998 Internet Society Network and Distributed
684 System Security Symposium pp. 97-111, March 1998.
687 Gordon, D., "Designing and Detecting Trapdoors for
688 Discrete Log Cryptosystems", Springer-Verlag Advances in
689 Cryptology - Crypto '92, pp. 66-75, 1993.
694 Forge Research Pty Ltd
696 EMail: DavidTaylor@forge.com.au
697 URI: http://www.forge.com.au/
702 EMail: tjw@cs.stanford.edu
704 Nikos Mavrogiannopoulos
706 EMail: nmav@gnutls.org
707 URI: http://www.gnutls.org/
711 EMail: trevp@trevp.net
712 URI: http://trevp.net/
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723 Appendix A. SRP Group Parameters
725 The 1024, 1536, and 2048-bit groups are taken from software developed
726 by Tom Wu and Eugene Jhong for the Stanford SRP distribution, and
727 subsequently proven to be prime. The larger primes are taken from
728 [MODP], but generators have been calculated that are primitive roots
729 of N, unlike the generators in [MODP].
731 The 1024-bit and 1536-bit groups MUST be supported.
735 The hexadecimal value for the prime is:
736 EEAF0AB9 ADB38DD6 9C33F80A FA8FC5E8 60726187 75FF3C0B 9EA2314C
737 9C256576 D674DF74 96EA81D3 383B4813 D692C6E0 E0D5D8E2 50B98BE4
738 8E495C1D 6089DAD1 5DC7D7B4 6154D6B6 CE8EF4AD 69B15D49 82559B29
739 7BCF1885 C529F566 660E57EC 68EDBC3C 05726CC0 2FD4CBF4 976EAA9A
740 FD5138FE 8376435B 9FC61D2F C0EB06E3
746 The hexadecimal value for the prime is:
747 9DEF3CAF B939277A B1F12A86 17A47BBB DBA51DF4 99AC4C80 BEEEA961
748 4B19CC4D 5F4F5F55 6E27CBDE 51C6A94B E4607A29 1558903B A0D0F843
749 80B655BB 9A22E8DC DF028A7C EC67F0D0 8134B1C8 B9798914 9B609E0B
750 E3BAB63D 47548381 DBC5B1FC 764E3F4B 53DD9DA1 158BFD3E 2B9C8CF5
751 6EDF0195 39349627 DB2FD53D 24B7C486 65772E43 7D6C7F8C E442734A
752 F7CCB7AE 837C264A E3A9BEB8 7F8A2FE9 B8B5292E 5A021FFF 5E91479E
753 8CE7A28C 2442C6F3 15180F93 499A234D CF76E3FE D135F9BB
759 The hexadecimal value for the prime is:
760 AC6BDB41 324A9A9B F166DE5E 1389582F AF72B665 1987EE07 FC319294
761 3DB56050 A37329CB B4A099ED 8193E075 7767A13D D52312AB 4B03310D
762 CD7F48A9 DA04FD50 E8083969 EDB767B0 CF609517 9A163AB3 661A05FB
763 D5FAAAE8 2918A996 2F0B93B8 55F97993 EC975EEA A80D740A DBF4FF74
764 7359D041 D5C33EA7 1D281E44 6B14773B CA97B43A 23FB8016 76BD207A
765 436C6481 F1D2B907 8717461A 5B9D32E6 88F87748 544523B5 24B0D57D
766 5EA77A27 75D2ECFA 032CFBDB F52FB378 61602790 04E57AE6 AF874E73
767 03CE5329 9CCC041C 7BC308D8 2A5698F3 A8D0C382 71AE35F8 E9DBFBB6
768 94B5C803 D89F7AE4 35DE236D 525F5475 9B65E372 FCD68EF2 0FA7111F
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773 Internet-Draft Using SRP for TLS Authentication March 2005
779 This prime is: 2^3072 - 2^3008 - 1 + 2^64 * { [2^2942 pi] +
782 Its hexadecimal value is:
783 FFFFFFFF FFFFFFFF C90FDAA2 2168C234 C4C6628B 80DC1CD1 29024E08
784 8A67CC74 020BBEA6 3B139B22 514A0879 8E3404DD EF9519B3 CD3A431B
785 302B0A6D F25F1437 4FE1356D 6D51C245 E485B576 625E7EC6 F44C42E9
786 A637ED6B 0BFF5CB6 F406B7ED EE386BFB 5A899FA5 AE9F2411 7C4B1FE6
787 49286651 ECE45B3D C2007CB8 A163BF05 98DA4836 1C55D39A 69163FA8
788 FD24CF5F 83655D23 DCA3AD96 1C62F356 208552BB 9ED52907 7096966D
789 670C354E 4ABC9804 F1746C08 CA18217C 32905E46 2E36CE3B E39E772C
790 180E8603 9B2783A2 EC07A28F B5C55DF0 6F4C52C9 DE2BCBF6 95581718
791 3995497C EA956AE5 15D22618 98FA0510 15728E5A 8AAAC42D AD33170D
792 04507A33 A85521AB DF1CBA64 ECFB8504 58DBEF0A 8AEA7157 5D060C7D
793 B3970F85 A6E1E4C7 ABF5AE8C DB0933D7 1E8C94E0 4A25619D CEE3D226
794 1AD2EE6B F12FFA06 D98A0864 D8760273 3EC86A64 521F2B18 177B200C
795 BBE11757 7A615D6C 770988C0 BAD946E2 08E24FA0 74E5AB31 43DB5BFC
796 E0FD108E 4B82D120 A93AD2CA FFFFFFFF FFFFFFFF
802 This prime is: 2^4096 - 2^4032 - 1 + 2^64 * { [2^3966 pi] +
805 Its hexadecimal value is:
806 FFFFFFFF FFFFFFFF C90FDAA2 2168C234 C4C6628B 80DC1CD1 29024E08
807 8A67CC74 020BBEA6 3B139B22 514A0879 8E3404DD EF9519B3 CD3A431B
808 302B0A6D F25F1437 4FE1356D 6D51C245 E485B576 625E7EC6 F44C42E9
809 A637ED6B 0BFF5CB6 F406B7ED EE386BFB 5A899FA5 AE9F2411 7C4B1FE6
810 49286651 ECE45B3D C2007CB8 A163BF05 98DA4836 1C55D39A 69163FA8
811 FD24CF5F 83655D23 DCA3AD96 1C62F356 208552BB 9ED52907 7096966D
812 670C354E 4ABC9804 F1746C08 CA18217C 32905E46 2E36CE3B E39E772C
813 180E8603 9B2783A2 EC07A28F B5C55DF0 6F4C52C9 DE2BCBF6 95581718
814 3995497C EA956AE5 15D22618 98FA0510 15728E5A 8AAAC42D AD33170D
815 04507A33 A85521AB DF1CBA64 ECFB8504 58DBEF0A 8AEA7157 5D060C7D
816 B3970F85 A6E1E4C7 ABF5AE8C DB0933D7 1E8C94E0 4A25619D CEE3D226
817 1AD2EE6B F12FFA06 D98A0864 D8760273 3EC86A64 521F2B18 177B200C
818 BBE11757 7A615D6C 770988C0 BAD946E2 08E24FA0 74E5AB31 43DB5BFC
819 E0FD108E 4B82D120 A9210801 1A723C12 A787E6D7 88719A10 BDBA5B26
820 99C32718 6AF4E23C 1A946834 B6150BDA 2583E9CA 2AD44CE8 DBBBC2DB
821 04DE8EF9 2E8EFC14 1FBECAA6 287C5947 4E6BC05D 99B2964F A090C3A2
822 233BA186 515BE7ED 1F612970 CEE2D7AF B81BDD76 2170481C D0069127
825 Taylor, et al. Expires September 15, 2005 [Page 17]
826 Internet-Draft Using SRP for TLS Authentication March 2005
828 D5B05AA9 93B4EA98 8D8FDDC1 86FFB7DC 90A6C08F 4DF435C9 34063199
835 This prime is: 2^6144 - 2^6080 - 1 + 2^64 * { [2^6014 pi] +
838 Its hexadecimal value is:
839 FFFFFFFF FFFFFFFF C90FDAA2 2168C234 C4C6628B 80DC1CD1 29024E08
840 8A67CC74 020BBEA6 3B139B22 514A0879 8E3404DD EF9519B3 CD3A431B
841 302B0A6D F25F1437 4FE1356D 6D51C245 E485B576 625E7EC6 F44C42E9
842 A637ED6B 0BFF5CB6 F406B7ED EE386BFB 5A899FA5 AE9F2411 7C4B1FE6
843 49286651 ECE45B3D C2007CB8 A163BF05 98DA4836 1C55D39A 69163FA8
844 FD24CF5F 83655D23 DCA3AD96 1C62F356 208552BB 9ED52907 7096966D
845 670C354E 4ABC9804 F1746C08 CA18217C 32905E46 2E36CE3B E39E772C
846 180E8603 9B2783A2 EC07A28F B5C55DF0 6F4C52C9 DE2BCBF6 95581718
847 3995497C EA956AE5 15D22618 98FA0510 15728E5A 8AAAC42D AD33170D
848 04507A33 A85521AB DF1CBA64 ECFB8504 58DBEF0A 8AEA7157 5D060C7D
849 B3970F85 A6E1E4C7 ABF5AE8C DB0933D7 1E8C94E0 4A25619D CEE3D226
850 1AD2EE6B F12FFA06 D98A0864 D8760273 3EC86A64 521F2B18 177B200C
851 BBE11757 7A615D6C 770988C0 BAD946E2 08E24FA0 74E5AB31 43DB5BFC
852 E0FD108E 4B82D120 A9210801 1A723C12 A787E6D7 88719A10 BDBA5B26
853 99C32718 6AF4E23C 1A946834 B6150BDA 2583E9CA 2AD44CE8 DBBBC2DB
854 04DE8EF9 2E8EFC14 1FBECAA6 287C5947 4E6BC05D 99B2964F A090C3A2
855 233BA186 515BE7ED 1F612970 CEE2D7AF B81BDD76 2170481C D0069127
856 D5B05AA9 93B4EA98 8D8FDDC1 86FFB7DC 90A6C08F 4DF435C9 34028492
857 36C3FAB4 D27C7026 C1D4DCB2 602646DE C9751E76 3DBA37BD F8FF9406
858 AD9E530E E5DB382F 413001AE B06A53ED 9027D831 179727B0 865A8918
859 DA3EDBEB CF9B14ED 44CE6CBA CED4BB1B DB7F1447 E6CC254B 33205151
860 2BD7AF42 6FB8F401 378CD2BF 5983CA01 C64B92EC F032EA15 D1721D03
861 F482D7CE 6E74FEF6 D55E702F 46980C82 B5A84031 900B1C9E 59E7C97F
862 BEC7E8F3 23A97A7E 36CC88BE 0F1D45B7 FF585AC5 4BD407B2 2B4154AA
863 CC8F6D7E BF48E1D8 14CC5ED2 0F8037E0 A79715EE F29BE328 06A1D58B
864 B7C5DA76 F550AA3D 8A1FBFF0 EB19CCB1 A313D55C DA56C9EC 2EF29632
865 387FE8D7 6E3C0468 043E8F66 3F4860EE 12BF2D5B 0B7474D6 E694F91E
866 6DCC4024 FFFFFFFF FFFFFFFF
872 This prime is: 2^8192 - 2^8128 - 1 + 2^64 * { [2^8062 pi] +
875 Its hexadecimal value is:
878 Taylor, et al. Expires September 15, 2005 [Page 18]
879 Internet-Draft Using SRP for TLS Authentication March 2005
881 FFFFFFFF FFFFFFFF C90FDAA2 2168C234 C4C6628B 80DC1CD1 29024E08
882 8A67CC74 020BBEA6 3B139B22 514A0879 8E3404DD EF9519B3 CD3A431B
883 302B0A6D F25F1437 4FE1356D 6D51C245 E485B576 625E7EC6 F44C42E9
884 A637ED6B 0BFF5CB6 F406B7ED EE386BFB 5A899FA5 AE9F2411 7C4B1FE6
885 49286651 ECE45B3D C2007CB8 A163BF05 98DA4836 1C55D39A 69163FA8
886 FD24CF5F 83655D23 DCA3AD96 1C62F356 208552BB 9ED52907 7096966D
887 670C354E 4ABC9804 F1746C08 CA18217C 32905E46 2E36CE3B E39E772C
888 180E8603 9B2783A2 EC07A28F B5C55DF0 6F4C52C9 DE2BCBF6 95581718
889 3995497C EA956AE5 15D22618 98FA0510 15728E5A 8AAAC42D AD33170D
890 04507A33 A85521AB DF1CBA64 ECFB8504 58DBEF0A 8AEA7157 5D060C7D
891 B3970F85 A6E1E4C7 ABF5AE8C DB0933D7 1E8C94E0 4A25619D CEE3D226
892 1AD2EE6B F12FFA06 D98A0864 D8760273 3EC86A64 521F2B18 177B200C
893 BBE11757 7A615D6C 770988C0 BAD946E2 08E24FA0 74E5AB31 43DB5BFC
894 E0FD108E 4B82D120 A9210801 1A723C12 A787E6D7 88719A10 BDBA5B26
895 99C32718 6AF4E23C 1A946834 B6150BDA 2583E9CA 2AD44CE8 DBBBC2DB
896 04DE8EF9 2E8EFC14 1FBECAA6 287C5947 4E6BC05D 99B2964F A090C3A2
897 233BA186 515BE7ED 1F612970 CEE2D7AF B81BDD76 2170481C D0069127
898 D5B05AA9 93B4EA98 8D8FDDC1 86FFB7DC 90A6C08F 4DF435C9 34028492
899 36C3FAB4 D27C7026 C1D4DCB2 602646DE C9751E76 3DBA37BD F8FF9406
900 AD9E530E E5DB382F 413001AE B06A53ED 9027D831 179727B0 865A8918
901 DA3EDBEB CF9B14ED 44CE6CBA CED4BB1B DB7F1447 E6CC254B 33205151
902 2BD7AF42 6FB8F401 378CD2BF 5983CA01 C64B92EC F032EA15 D1721D03
903 F482D7CE 6E74FEF6 D55E702F 46980C82 B5A84031 900B1C9E 59E7C97F
904 BEC7E8F3 23A97A7E 36CC88BE 0F1D45B7 FF585AC5 4BD407B2 2B4154AA
905 CC8F6D7E BF48E1D8 14CC5ED2 0F8037E0 A79715EE F29BE328 06A1D58B
906 B7C5DA76 F550AA3D 8A1FBFF0 EB19CCB1 A313D55C DA56C9EC 2EF29632
907 387FE8D7 6E3C0468 043E8F66 3F4860EE 12BF2D5B 0B7474D6 E694F91E
908 6DBE1159 74A3926F 12FEE5E4 38777CB6 A932DF8C D8BEC4D0 73B931BA
909 3BC832B6 8D9DD300 741FA7BF 8AFC47ED 2576F693 6BA42466 3AAB639C
910 5AE4F568 3423B474 2BF1C978 238F16CB E39D652D E3FDB8BE FC848AD9
911 22222E04 A4037C07 13EB57A8 1A23F0C7 3473FC64 6CEA306B 4BCBC886
912 2F8385DD FA9D4B7F A2C087E8 79683303 ED5BDD3A 062B3CF5 B3A278A6
913 6D2A13F8 3F44F82D DF310EE0 74AB6A36 4597E899 A0255DC1 64F31CC5
914 0846851D F9AB4819 5DED7EA1 B1D510BD 7EE74D73 FAF36BC3 1ECFA268
915 359046F4 EB879F92 4009438B 481C6CD7 889A002E D5EE382B C9190DA6
916 FC026E47 9558E447 5677E9AA 9E3050E2 765694DF C81F56E8 80B96E71
917 60C980DD 98EDD3DF FFFFFFFF FFFFFFFF
919 The generator is: 19 (decimal).
926 Taylor, et al. Expires September 15, 2005 [Page 19]
927 Internet-Draft Using SRP for TLS Authentication March 2005
929 Appendix B. SRP Test Vectors
931 The following test vectors demonstrate calculation of the verifier
932 and premaster secret.
936 s = BEB25379 D1A8581E B5A72767 3A2441EE
937 N, g = <1024-bit parameters from Appendix A>
938 k = 7556AA04 5AEF2CDD 07ABAF0F 665C3E81 8913186F
939 x = 94B7555A ABE9127C C58CCF49 93DB6CF8 4D16C124
941 7E273DE8 696FFC4F 4E337D05 B4B375BE B0DDE156 9E8FA00A 9886D812
942 9BADA1F1 822223CA 1A605B53 0E379BA4 729FDC59 F105B478 7E5186F5
943 C671085A 1447B52A 48CF1970 B4FB6F84 00BBF4CE BFBB1681 52E08AB5
944 EA53D15C 1AFF87B2 B9DA6E04 E058AD51 CC72BFC9 033B564E 26480D78
945 E955A5E2 9E7AB245 DB2BE315 E2099AFB
948 60975527 035CF2AD 1989806F 0407210B C81EDC04 E2762A56 AFD529DD
951 E487CB59 D31AC550 471E81F0 0F6928E0 1DDA08E9 74A004F4 9E61F5D1
954 61D5E490 F6F1B795 47B0704C 436F523D D0E560F0 C64115BB 72557EC4
955 4352E890 3211C046 92272D8B 2D1A5358 A2CF1B6E 0BFCF99F 921530EC
956 8E393561 79EAE45E 42BA92AE ACED8251 71E1E8B9 AF6D9C03 E1327F44
957 BE087EF0 6530E69F 66615261 EEF54073 CA11CF58 58F0EDFD FE15EFEA
958 B349EF5D 76988A36 72FAC47B 0769447B
960 BD0C6151 2C692C0C B6D041FA 01BB152D 4916A1E7 7AF46AE1 05393011
961 BAF38964 DC46A067 0DD125B9 5A981652 236F99D9 B681CBF8 7837EC99
962 6C6DA044 53728610 D0C6DDB5 8B318885 D7D82C7F 8DEB75CE 7BD4FBAA
963 37089E6F 9C6059F3 88838E7A 00030B33 1EB76840 910440B1 B27AAEAE
964 EB4012B7 D7665238 A8E3FB00 4B117B58
966 CE38B959 3487DA98 554ED47D 70A7AE5F 462EF019
968 B0DC82BA BCF30674 AE450C02 87745E79 90A3381F 63B387AA F271A10D
969 233861E3 59B48220 F7C4693C 9AE12B0A 6F67809F 0876E2D0 13800D6C
970 41BB59B6 D5979B5C 00A172B4 A2A5903A 0BDCAF8A 709585EB 2AFAFA8F
971 3499B200 210DCC1F 10EB3394 3CD67FC8 8A2F39A4 BE5BEC4E C0A3212D
972 C346D7E4 74B29EDE 8A469FFE CA686E5A
977 Taylor, et al. Expires September 15, 2005 [Page 20]
978 Internet-Draft Using SRP for TLS Authentication March 2005
980 Appendix C. Acknowledgements
982 Thanks to all on the IETF tls mailing list for ideas and analysis.
1007 Taylor, et al. Expires September 15, 2005 [Page 21]
1008 Internet-Draft Using SRP for TLS Authentication March 2005
1010 Intellectual Property Statement
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1056 Taylor, et al. Expires September 15, 2005 [Page 22]