TLS Working Group D. Taylor Internet-Draft Forge Research Pty Ltd Expires: February 17, 2005 T. Wu Stanford University N. Mavroyanopoulos T. Perrin August 19, 2004 Using SRP for TLS Authentication draft-ietf-tls-srp-08 Status of this Memo This document is an Internet-Draft and is in full conformance with all provisions of Section 10 of RFC2026. Internet-Drafts are working documents of the Internet Engineering Task Force (IETF), its areas, and its working groups. Note that other groups may also distribute working documents as Internet-Drafts. Internet-Drafts are draft documents valid for a maximum of six months and may be updated, replaced, or obsoleted by other documents at any time. It is inappropriate to use Internet-Drafts as reference material or to cite them other than as "work in progress." The list of current Internet-Drafts can be accessed at http://www.ietf.org/ietf/1id-abstracts.txt. The list of Internet-Draft Shadow Directories can be accessed at http://www.ietf.org/shadow.html. This Internet-Draft will expire on February 17, 2005. Copyright Notice Copyright (C) The Internet Society (2004). All Rights Reserved. Abstract This memo presents a technique for using the Secure Remote Password protocol ([SRP], [SRP-6]) as an authentication method for the Transport Layer Security protocol [TLS]. Taylor, et al. Expires February 17, 2005 [Page 1] Internet-Draft Using SRP for TLS Authentication August 2004 Table of Contents 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 3 2. SRP Authentication in TLS . . . . . . . . . . . . . . . . . . 4 2.1 Notation and Terminology . . . . . . . . . . . . . . . . . 4 2.2 Handshake Protocol Overview . . . . . . . . . . . . . . . 4 2.3 Text Preparation . . . . . . . . . . . . . . . . . . . . . 5 2.4 SRP Verifier Creation . . . . . . . . . . . . . . . . . . 5 2.5 Changes to the Handshake Message Contents . . . . . . . . 5 2.5.1 Client Hello . . . . . . . . . . . . . . . . . . . . . 5 2.5.2 Server Certificate . . . . . . . . . . . . . . . . . . 7 2.5.3 Server Key Exchange . . . . . . . . . . . . . . . . . 7 2.5.4 Client Key Exchange . . . . . . . . . . . . . . . . . 8 2.6 Calculating the Pre-master Secret . . . . . . . . . . . . 8 2.7 Cipher Suite Definitions . . . . . . . . . . . . . . . . . 9 2.8 New Message Structures . . . . . . . . . . . . . . . . . . 9 2.8.1 Client Hello . . . . . . . . . . . . . . . . . . . . . 9 2.8.2 Server Key Exchange . . . . . . . . . . . . . . . . . 10 2.8.3 Client Key Exchange . . . . . . . . . . . . . . . . . 10 2.9 Error Alerts . . . . . . . . . . . . . . . . . . . . . . . 11 3. Security Considerations . . . . . . . . . . . . . . . . . . . 12 4. References . . . . . . . . . . . . . . . . . . . . . . . . . . 13 4.1 Normative References . . . . . . . . . . . . . . . . . . . . 13 4.2 Informative References . . . . . . . . . . . . . . . . . . . 13 Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . 14 A. SRP Group Parameters . . . . . . . . . . . . . . . . . . . . . 15 B. Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . 19 Intellectual Property and Copyright Statements . . . . . . . . 20 Taylor, et al. Expires February 17, 2005 [Page 2] Internet-Draft Using SRP for TLS Authentication August 2004 1. Introduction At the time of writing TLS [TLS] uses public key certificates, or Kerberos, for authentication. These authentication methods do not seem well suited to the applications now being adapted to use TLS ([IMAP] or [FTP], for example). Given that these protocols are designed to use the user name and password method of authentication, being able to safely use user names and passwords provides an easier route to additional security. SRP ([SRP], [SRP-6]) is an authentication method that allows the use of user names and passwords over unencrypted channels without revealing the password to an eavesdropper. SRP also supplies a shared secret at the end of the authentication sequence that can be used to generate encryption keys. This document describes the use of the SRP authentication method for TLS. The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this document are to be interpreted as described in RFC 2119. Taylor, et al. Expires February 17, 2005 [Page 3] Internet-Draft Using SRP for TLS Authentication August 2004 2. SRP Authentication in TLS 2.1 Notation and Terminology The version of SRP used here is sometimes referred to as "SRP-6" [SRP-6]. This version is a slight improvement over "SRP-3", which was described in [SRP] and [RFC2945]. This document uses the variable names defined in [SRP-6]: N, g: group parameters (prime and generator) s: salt B, b: server's public and private values A, a: client's public and private values I: user name (aka "identity") P: password v: verifier 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 [RFC2945]. 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. Taylor, et al. Expires February 17, 2005 [Page 4] Internet-Draft Using SRP for TLS Authentication August 2004 Client Server | | Client Hello (I) ------------------------> | | <---------------------------- Server Hello | <---------------------------- Certificate* | <---------------------------- Server Key Exchange (N, g, s, B) | <---------------------------- Server Hello Done Client Key Exchange (A) -----------------> | [Change cipher spec] | Finished --------------------------------> | | [Change cipher spec] | <---------------------------- Finished | | Application Data <--------------> Application Data * Indicates an optional message which is not always sent. Figure 1 2.3 Text Preparation The user name and password strings shall be UTF-8 encoded Unicode, prepared using the [SASLPrep] profile of [StringPrep]. 2.4 SRP Verifier Creation The verifier is calculated as described in section 3 of [RFC2945]. We give the algorithm here for convenience. The verifier (v) is computed based on the salt (s), user name (I), password (P), and group parameters (N, g). The computation uses the [SHA1] hash algorithm: x = SHA1(s | SHA1(I | ":" | P)) v = g^x % N 2.5 Changes to the Handshake Message Contents This section describes the changes to the TLS handshake message contents when SRP is being used for authentication. The definitions of the new message contents and the on-the-wire changes are given in Section 2.8. 2.5.1 Client Hello The user name is appended to the standard client hello message using the hello message extension mechanism defined in [TLSEXT] (see Taylor, et al. Expires February 17, 2005 [Page 5] Internet-Draft Using SRP for TLS Authentication August 2004 Section 2.8.1). 2.5.1.1 Session Resumption When a client attempts to resume a session that uses SRP authentication, the client MUST include the user name extension in the client hello message, in case the server cannot or will not allow session resumption, meaning a full handshake is required. If the server does agree to resume an existing session the server MUST ignore the information in the SRP extension of the client hello message, except for its inclusion in the finished message hashes. This is to ensure attackers cannot replace the authenticated identity without supplying the proper authentication information. 2.5.1.2 Missing SRP Username The client may offer SRP ciphersuites in the hello message but omit the SRP extension. If the server would like to select an SRP ciphersuite in this case, the server MAY return a missing_srp_username alert (see Section 2.9) immediately after processing the client hello message. This alert signals the client to resend the hello message, this time with the SRP extension. This allows the client to advertise that it supports SRP, but not have to prompt the user for his user name and password, nor expose the user name in the clear, unless necessary. After sending the missing_srp_username alert, the server MUST leave the TLS connection open, yet reset its handshake protocol state so it is prepared to receive a second client hello message. Upon receiving the missing_srp_username alert, the client MUST either send a second client hello message, or send a fatal user_cancelled alert. If the client sends a second hello message, the second hello message MUST offer SRP ciphersuites, and MUST contain the SRP extension, and the server MUST choose one of the SRP ciphersuites. Both client hello messages MUST be treated as handshake messages and included in the hash calculations for the TLS Finished message. The premaster and master secret calculations will use the random value from the second client hello message, not the first. 2.5.1.3 Unknown SRP Username If the server doesn't have a verifier for the given user name, the server MAY abort the handshake with an unknown_srp_username alert (see Section 2.9). Alternatively, if the server wishes to hide the fact that this user name doesn't have a verifier, the server MAY simulate the protocol as if a verifier existed, but then reject the Taylor, et al. Expires February 17, 2005 [Page 6] Internet-Draft Using SRP for TLS Authentication August 2004 client's finished message with a bad_record_mac alert, as if the password was incorrect. To simulate the existence of an entry for each user name, the server must consistently return the same salt (s) and group (N, g) values for the same user name. For example, the server could store a secret "seed key" and then use HMAC-SHA1(seed_key, "salt" | user_name) to generate the salts [HMAC]. For B, the server can return a random value between 1 and N-1 inclusive. However, the server should take care to simulate computation delays. One way to do this is to generate a fake verifier using the "seed key" approach, and then proceed with the protocol as usual. 2.5.2 Server Certificate The server MUST send a certificate if it agrees to an SRP cipher suite that requires the server to provide additional authentication in the form of a digital signature. See Section 2.7 for details of which ciphersuites defined in this document require a server certificate to be sent. 2.5.3 Server Key Exchange The server key exchange message contains the prime (N), the generator (g), and the salt value (s) read from the SRP password file based on the user name (I) received in the client hello extension. The server key exchange message also contains the server's public value (B). The server calculates this value as B = k*v + g^b % N, where b is a random number which SHOULD be at least 256 bits in length, and k = SHA1(N | PAD(g)). If the server has sent a certificate message, the server key exchange message MUST be signed. The group parameters (N, g) sent in this message MUST have N as a safe prime (a prime of the form N=2q+1, where q is also prime). The integers from 1 to N-1 will form a group under multiplication % N, and g MUST be a generator of this group. The SRP group parameters in Appendix A are proven to have these properties, so the client SHOULD accept any parameters from this Appendix which have large enough N values to meet his security requirements. The client MAY accept other group parameters from the server, either by prior arrangement, or by checking the parameters himself. To check that N is a safe prime, the client should use some method such as performing 64 iterations of the Miller-Rabin test with random bases (selected from 2 to N-2) on both N and q (by performing 64 Taylor, et al. Expires February 17, 2005 [Page 7] Internet-Draft Using SRP for TLS Authentication August 2004 iterations, the probability of a false positive is no more than 2^-128). To check that g is a generator of the group, the client can check that 1 < g < N-1, and g^q % N equals N-1. Performing these checks may be time-consuming; after checking new parameters, the client may want to add them to a known-good list. Group parameters that are not accepted via one of the above methods MUST be rejected with an untrusted_srp_parameters alert (see Section 2.9). The client MUST abort the handshake with an illegal_parameter alert if B % N = 0. 2.5.4 Client Key Exchange The client key exchange message carries the client's public value (A). The client calculates this value as A = g^a % N, where a is a random number which SHOULD be at least 256 bits in length. The server MUST abort the handshake with an illegal_parameter alert if A % N = 0. 2.6 Calculating the Pre-master Secret The pre-master secret is calculated by the client as follows: I, P = N, g, s, B = a = random() A = g^a % N u = SHA1(PAD(A) | PAD(B)) k = SHA1(N | PAD(g)) x = SHA1(s | SHA1(I | ":" | P)) = (B - (k * g^x)) ^ (a + (u * x)) % N The pre-master secret is calculated by the server as follows: N, g, s, v = b = random() k = SHA1(N | PAD(g)) B = k*v + g^b % N A = u = SHA1(PAD(A) | PAD(B)) = (A * v^u) ^ b % N The finished messages perform the same function as the client and server evidence messages (M1 and M2) specified in [RFC2945]. If either the client or the server calculate an incorrect premaster Taylor, et al. Expires February 17, 2005 [Page 8] Internet-Draft Using SRP for TLS Authentication August 2004 secret, the finished messages will fail to decrypt properly, and the other party will return a bad_record_mac alert. If a client application receives a bad_record_mac alert when performing an SRP handshake, it should inform the user that the entered user name and password are incorrect. 2.7 Cipher Suite Definitions The following cipher suites are added by this draft. The usage of AES ciphersuites is as defined in [RFC3268]. CipherSuite TLS_SRP_SHA_WITH_3DES_EDE_CBC_SHA = { 0x00,0x50 }; CipherSuite TLS_SRP_SHA_RSA_WITH_3DES_EDE_CBC_SHA = { 0x00,0x51 }; CipherSuite TLS_SRP_SHA_DSS_WITH_3DES_EDE_CBC_SHA = { 0x00,0x52 }; CipherSuite TLS_SRP_SHA_WITH_AES_128_CBC_SHA = { 0x00,0x53 }; CipherSuite TLS_SRP_SHA_RSA_WITH_AES_128_CBC_SHA = { 0x00,0x54 }; CipherSuite TLS_SRP_SHA_DSS_WITH_AES_128_CBC_SHA = { 0x00,0x55 }; CipherSuite TLS_SRP_SHA_WITH_AES_256_CBC_SHA = { 0x00,0x56 }; CipherSuite TLS_SRP_SHA_RSA_WITH_AES_256_CBC_SHA = { 0x00,0x57 }; CipherSuite TLS_SRP_SHA_DSS_WITH_AES_256_CBC_SHA = { 0x00,0x58 }; Cipher suites that begin with TLS_SRP_SHA_RSA or TLS_SRP_SHA_DSS require the server to send a certificate message containing a certificate with the specified type of public key, and to sign the server key exchange message using a matching private key. Cipher suites that do not include a digital signature algorithm identifier assume the server is authenticated by its possesion of the SRP verifier. Implementations conforming to this specification MUST implement the TLS_SRP_SHA_WITH_3DES_EDE_CBC_SHA ciphersuite, SHOULD implement the TLS_SRP_SHA_WITH_AES_128_CBC_SHA and TLS_SRP_SHA_WITH_AES_256_CBC_SHA ciphersuites, and MAY implement the remaining ciphersuites. 2.8 New Message Structures This section shows the structure of the messages passed during a handshake that uses SRP for authentication. The representation language used is the same as that used in [TLS]. 2.8.1 Client Hello A new value, "srp(6)", has been added to the enumerated ExtensionType defined in [TLSEXT]. This value MUST be used as the extension number for the SRP extension. Taylor, et al. Expires February 17, 2005 [Page 9] Internet-Draft Using SRP for TLS Authentication August 2004 The "extension_data" field of the SRP extension SHALL contain: opaque srp_I<1..2^8-1> where srp_I is the user name, encoded per Section 2.4. 2.8.2 Server Key Exchange A new value, "srp", has been added to the enumerated KeyExchangeAlgorithm originally defined in [TLS]. When the value of KeyExchangeAlgorithm is set to "srp", the server's SRP parameters are sent in the server key exchange message, encoded in a ServerSRPParams structure. If a certificate is sent to the client the server key exchange message must be signed. enum { rsa, diffie_hellman, srp } KeyExchangeAlgorithm; struct { select (KeyExchangeAlgorithm) { case diffie_hellman: ServerDHParams params; Signature signed_params; case rsa: ServerRSAParams params; Signature signed_params; case srp: /* new entry */ ServerSRPParams params; Signature signed_params; }; } ServerKeyExchange; struct { opaque srp_N<1..2^16-1>; opaque srp_g<1..2^16-1>; opaque srp_s<1..2^8-1> opaque srp_B<1..2^16-1>; } ServerSRPParams; /* SRP parameters */ 2.8.3 Client Key Exchange When the value of KeyExchangeAlgorithm is set to "srp", the client's public value (A) is sent in the client key exchange message, encoded in a ClientSRPPublic structure. Taylor, et al. Expires February 17, 2005 [Page 10] Internet-Draft Using SRP for TLS Authentication August 2004 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 Three new error alerts are defined: o "unknown_srp_username" (120) - this alert MAY be sent by a server that receives an unknown user name. This alert is always fatal. See Section 2.5.1.3 for details. o "missing_srp_username" (121) - this alert MAY be sent by a server that would like to select an offered SRP ciphersuite, if the SRP extension is absent from the client's hello message. This alert is always a warning. Upon receiving this alert, the client MAY send a new hello message on the same connection, this time including the SRP extension. See Section 2.5.1.2 for details. o "untrusted_srp_parameters" (122) - this alert MUST be sent by a client that receives unknown or untrusted (N, g) values. This alert is always fatal. See Section 2.5.3 for details. Taylor, et al. Expires February 17, 2005 [Page 11] Internet-Draft Using SRP for TLS Authentication August 2004 3. Security Considerations If an attacker is able to steal the SRP verifier file, the attacker can masquerade as the real server, and can also use dictionary attacks to recover client passwords. An attacker could repeatedly contact an SRP server and try to guess a legitimate user's password. Servers SHOULD take steps to prevent this, such as limiting the rate of authentication attempts from a particular IP address, or against a particular user account, or locking the user account once a threshold of failed attempts is reached. The client's user name is sent in the clear in the Client Hello message. To avoid sending the user name in the clear, the client could first open a conventional anonymous, or server-authenticated connection, then renegotiate an SRP-authenticated connection with the handshake protected by the first connection. The checks described in Section 2.5.3 and Section 2.5.4 on the received values for A and B are crucial for security and MUST be performed. The private values a and b SHOULD be at least 256 bit random numbers, to give approximately 128 bits of security against certain methods of calculating discrete logarithms. If the client receives a missing_srp_username alert, the client should be aware that unless the handshake protocol is run to completion, this alert may have been inserted by an attacker. If the handshake protocol is not run to completion, the client should not make any decisions, nor form any assumptions, based on receiving this alert. It is possible to choose a (user name, password) pair such that the resulting verifier will also match other, related, (user name, password) pairs. Thus, anyone using verifiers should be careful not to assume that only a single (user name, password) pair matches the verifier. Taylor, et al. Expires February 17, 2005 [Page 12] Internet-Draft Using SRP for TLS Authentication August 2004 4. References 4.1 Normative References [TLS] Dierks, T. and C. Allen, "The TLS Protocol", RFC 2246, January 1999. [SRP-6] Wu, T., "SRP-6: Improvements and Refinements to the Secure Remote Password Protocol", October 2002, . [TLSEXT] Blake-Wilson, S., Nystrom, M., Hopwood, D., Mikkelsen, J. and T. Wright, "TLS Extensions", RFC 3546, June 2003. [StringPrep] Hoffman, P. and M. Blanchet, "Preparation of Internationalized Strings ("stringprep")", RFC 3454, December 2002. [SASLPrep] Zeilenga, K., "SASLprep: Stringprep profile for user names and passwords", draft-ietf-sasl-saslprep-10 (work in progress), July 2004. [RFC2945] Wu, T., "The SRP Authentication and Key Exchange System", RFC 2945, September 2000. [SHA1] "Announcing the Secure Hash Standard", FIPS 180-1, September 2000. [HMAC] Krawczyk, H., Bellare, M. and R. Canetti, "HMAC: Keyed-Hashing for Message Authentication", RFC 2104, February 1997. [RFC3268] Chown, P., "Advanced Encryption Standard (AES) Ciphersuites for Transport Layer Security (TLS)", RFC 3268, June 2002. [MODP] Kivinen, T. and M. Kojo, "More Modular Exponentiation (MODP) Diffie-Hellman groups for Internet Key Exchange (IKE)", RFC 3526, May 2003. 4.2 Informative References [IMAP] Newman, C., "Using TLS with IMAP, POP3 and ACAP", RFC 2595, June 1999. [FTP] Ford-Hutchinson, P., "Securing FTP with TLS", Taylor, et al. Expires February 17, 2005 [Page 13] Internet-Draft Using SRP for TLS Authentication August 2004 draft-murray-auth-ftp-ssl-15 (work in progress), August 2004. [SRP] Wu, T., "The Secure Remote Password Protocol", Proceedings of the 1998 Internet Society Network and Distributed System Security Symposium pp. 97-111, March 1998. Authors' Addresses David Taylor Forge Research Pty Ltd EMail: DavidTaylor@forge.com.au URI: http://www.forge.com.au/ Tom Wu Stanford University EMail: tjw@cs.stanford.edu Nikos Mavroyanopoulos EMail: nmav@gnutls.org URI: http://www.gnutls.org/ Trevor Perrin EMail: trevp@trevp.net URI: http://trevp.net/ Taylor, et al. Expires February 17, 2005 [Page 14] Internet-Draft Using SRP for TLS Authentication August 2004 Appendix A. SRP Group Parameters The 1024, 1536, and 2048-bit groups are taken from software developed by Tom Wu and Eugene Jhong for the Stanford SRP distribution, and subsequently proven to be prime. The larger primes are taken from [MODP], but generators have been calculated that are primitive roots of N, unlike the generators in [MODP]. The 1024-bit and 1536-bit groups MUST be supported. 1. 1024-bit Group The hexadecimal value for the prime is: EEAF0AB9 ADB38DD6 9C33F80A FA8FC5E8 60726187 75FF3C0B 9EA2314C 9C256576 D674DF74 96EA81D3 383B4813 D692C6E0 E0D5D8E2 50B98BE4 8E495C1D 6089DAD1 5DC7D7B4 6154D6B6 CE8EF4AD 69B15D49 82559B29 7BCF1885 C529F566 660E57EC 68EDBC3C 05726CC0 2FD4CBF4 976EAA9A FD5138FE 8376435B 9FC61D2F C0EB06E3 The generator is: 2. 2. 1536-bit Group The hexadecimal value for the prime is: 9DEF3CAF B939277A B1F12A86 17A47BBB DBA51DF4 99AC4C80 BEEEA961 4B19CC4D 5F4F5F55 6E27CBDE 51C6A94B E4607A29 1558903B A0D0F843 80B655BB 9A22E8DC DF028A7C EC67F0D0 8134B1C8 B9798914 9B609E0B E3BAB63D 47548381 DBC5B1FC 764E3F4B 53DD9DA1 158BFD3E 2B9C8CF5 6EDF0195 39349627 DB2FD53D 24B7C486 65772E43 7D6C7F8C E442734A F7CCB7AE 837C264A E3A9BEB8 7F8A2FE9 B8B5292E 5A021FFF 5E91479E 8CE7A28C 2442C6F3 15180F93 499A234D CF76E3FE D135F9BB The generator is: 2. 3. 2048-bit Group The hexadecimal value for the prime is: AC6BDB41 324A9A9B F166DE5E 1389582F AF72B665 1987EE07 FC319294 3DB56050 A37329CB B4A099ED 8193E075 7767A13D D52312AB 4B03310D CD7F48A9 DA04FD50 E8083969 EDB767B0 CF609517 9A163AB3 661A05FB D5FAAAE8 2918A996 2F0B93B8 55F97993 EC975EEA A80D740A DBF4FF74 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 Taylor, et al. Expires February 17, 2005 [Page 15] Internet-Draft Using SRP for TLS Authentication August 2004 The generator is: 2. 4. 3072-bit Group This prime is: 2^3072 - 2^3008 - 1 + 2^64 * { [2^2942 pi] + 1690314 } Its hexadecimal value is: FFFFFFFF FFFFFFFF C90FDAA2 2168C234 C4C6628B 80DC1CD1 29024E08 8A67CC74 020BBEA6 3B139B22 514A0879 8E3404DD EF9519B3 CD3A431B 302B0A6D F25F1437 4FE1356D 6D51C245 E485B576 625E7EC6 F44C42E9 A637ED6B 0BFF5CB6 F406B7ED EE386BFB 5A899FA5 AE9F2411 7C4B1FE6 49286651 ECE45B3D C2007CB8 A163BF05 98DA4836 1C55D39A 69163FA8 FD24CF5F 83655D23 DCA3AD96 1C62F356 208552BB 9ED52907 7096966D 670C354E 4ABC9804 F1746C08 CA18217C 32905E46 2E36CE3B E39E772C 180E8603 9B2783A2 EC07A28F B5C55DF0 6F4C52C9 DE2BCBF6 95581718 3995497C EA956AE5 15D22618 98FA0510 15728E5A 8AAAC42D AD33170D 04507A33 A85521AB DF1CBA64 ECFB8504 58DBEF0A 8AEA7157 5D060C7D B3970F85 A6E1E4C7 ABF5AE8C DB0933D7 1E8C94E0 4A25619D CEE3D226 1AD2EE6B F12FFA06 D98A0864 D8760273 3EC86A64 521F2B18 177B200C BBE11757 7A615D6C 770988C0 BAD946E2 08E24FA0 74E5AB31 43DB5BFC E0FD108E 4B82D120 A93AD2CA FFFFFFFF FFFFFFFF The generator is: 5. 5. 4096-bit Group This prime is: 2^4096 - 2^4032 - 1 + 2^64 * { [2^3966 pi] + 240904 } Its hexadecimal value is: FFFFFFFF FFFFFFFF C90FDAA2 2168C234 C4C6628B 80DC1CD1 29024E08 8A67CC74 020BBEA6 3B139B22 514A0879 8E3404DD EF9519B3 CD3A431B 302B0A6D F25F1437 4FE1356D 6D51C245 E485B576 625E7EC6 F44C42E9 A637ED6B 0BFF5CB6 F406B7ED EE386BFB 5A899FA5 AE9F2411 7C4B1FE6 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 Taylor, et al. Expires February 17, 2005 [Page 16] Internet-Draft Using SRP for TLS Authentication August 2004 D5B05AA9 93B4EA98 8D8FDDC1 86FFB7DC 90A6C08F 4DF435C9 34063199 FFFFFFFF FFFFFFFF The generator is: 5. 6. 6144-bit Group This prime is: 2^6144 - 2^6080 - 1 + 2^64 * { [2^6014 pi] + 929484 } Its hexadecimal value is: FFFFFFFF FFFFFFFF C90FDAA2 2168C234 C4C6628B 80DC1CD1 29024E08 8A67CC74 020BBEA6 3B139B22 514A0879 8E3404DD EF9519B3 CD3A431B 302B0A6D F25F1437 4FE1356D 6D51C245 E485B576 625E7EC6 F44C42E9 A637ED6B 0BFF5CB6 F406B7ED EE386BFB 5A899FA5 AE9F2411 7C4B1FE6 49286651 ECE45B3D C2007CB8 A163BF05 98DA4836 1C55D39A 69163FA8 FD24CF5F 83655D23 DCA3AD96 1C62F356 208552BB 9ED52907 7096966D 670C354E 4ABC9804 F1746C08 CA18217C 32905E46 2E36CE3B E39E772C 180E8603 9B2783A2 EC07A28F B5C55DF0 6F4C52C9 DE2BCBF6 95581718 3995497C EA956AE5 15D22618 98FA0510 15728E5A 8AAAC42D AD33170D 04507A33 A85521AB DF1CBA64 ECFB8504 58DBEF0A 8AEA7157 5D060C7D B3970F85 A6E1E4C7 ABF5AE8C DB0933D7 1E8C94E0 4A25619D CEE3D226 1AD2EE6B F12FFA06 D98A0864 D8760273 3EC86A64 521F2B18 177B200C BBE11757 7A615D6C 770988C0 BAD946E2 08E24FA0 74E5AB31 43DB5BFC E0FD108E 4B82D120 A9210801 1A723C12 A787E6D7 88719A10 BDBA5B26 99C32718 6AF4E23C 1A946834 B6150BDA 2583E9CA 2AD44CE8 DBBBC2DB 04DE8EF9 2E8EFC14 1FBECAA6 287C5947 4E6BC05D 99B2964F A090C3A2 233BA186 515BE7ED 1F612970 CEE2D7AF B81BDD76 2170481C D0069127 D5B05AA9 93B4EA98 8D8FDDC1 86FFB7DC 90A6C08F 4DF435C9 34028492 36C3FAB4 D27C7026 C1D4DCB2 602646DE C9751E76 3DBA37BD F8FF9406 AD9E530E E5DB382F 413001AE B06A53ED 9027D831 179727B0 865A8918 DA3EDBEB CF9B14ED 44CE6CBA CED4BB1B DB7F1447 E6CC254B 33205151 2BD7AF42 6FB8F401 378CD2BF 5983CA01 C64B92EC F032EA15 D1721D03 F482D7CE 6E74FEF6 D55E702F 46980C82 B5A84031 900B1C9E 59E7C97F BEC7E8F3 23A97A7E 36CC88BE 0F1D45B7 FF585AC5 4BD407B2 2B4154AA CC8F6D7E BF48E1D8 14CC5ED2 0F8037E0 A79715EE F29BE328 06A1D58B B7C5DA76 F550AA3D 8A1FBFF0 EB19CCB1 A313D55C DA56C9EC 2EF29632 387FE8D7 6E3C0468 043E8F66 3F4860EE 12BF2D5B 0B7474D6 E694F91E 6DCC4024 FFFFFFFF FFFFFFFF The generator is: 5. 7. 8192-bit Group This prime is: 2^8192 - 2^8128 - 1 + 2^64 * { [2^8062 pi] + 4743158 } Its hexadecimal value is: Taylor, et al. Expires February 17, 2005 [Page 17] Internet-Draft Using SRP for TLS Authentication August 2004 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. Expires February 17, 2005 [Page 18] Internet-Draft Using SRP for TLS Authentication August 2004 Appendix B. Acknowledgements Thanks to all on the IETF tls mailing list for ideas and analysis. Taylor, et al. Expires February 17, 2005 [Page 19] Internet-Draft Using SRP for TLS Authentication August 2004 Intellectual Property Statement The IETF takes no position regarding the validity or scope of any intellectual property or other rights that might be claimed to pertain to the implementation or use of the technology described in this document or the extent to which any license under such rights might or might not be available; neither does it represent that it has made any effort to identify any such rights. Information on the IETF's procedures with respect to rights in standards-track and standards-related documentation can be found in BCP-11. Copies of claims of rights made available for publication and any assurances of licenses to be made available, or the result of an attempt made to obtain a general license or permission for the use of such proprietary rights by implementors or users of this specification can be obtained from the IETF Secretariat. The IETF invites any interested party to bring to its attention any copyrights, patents or patent applications, or other proprietary rights which may cover technology that may be required to practice this standard. Please address the information to the IETF Executive Director. Full Copyright Statement Copyright (C) The Internet Society (2004). All Rights Reserved. This document and translations of it may be copied and furnished to others, and derivative works that comment on or otherwise explain it or assist in its implementation may be prepared, copied, published and distributed, in whole or in part, without restriction of any kind, provided that the above copyright notice and this paragraph are included on all such copies and derivative works. However, this document itself may not be modified in any way, such as by removing the copyright notice or references to the Internet Society or other Internet organizations, except as needed for the purpose of developing Internet standards in which case the procedures for copyrights defined in the Internet Standards process must be followed, or as required to translate it into languages other than English. The limited permissions granted above are perpetual and will not be revoked by the Internet Society or its successors or assignees. This document and the information contained herein is provided on an "AS IS" basis and THE INTERNET SOCIETY AND THE INTERNET ENGINEERING TASK FORCE DISCLAIMS ALL WARRANTIES, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO ANY WARRANTY THAT THE USE OF THE INFORMATION Taylor, et al. Expires February 17, 2005 [Page 20] Internet-Draft Using SRP for TLS Authentication August 2004 HEREIN WILL NOT INFRINGE ANY RIGHTS OR ANY IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE. Acknowledgment Funding for the RFC Editor function is currently provided by the Internet Society. Taylor, et al. Expires February 17, 2005 [Page 21]